[datatype=bibtex] [overwrite] [fieldsource=doi, final] [fieldset=eprint, null]
[fieldset=url, null] [datatype=bibtex,overwrite=true] inproceeding
[fieldsource=Collaboration, final=true] [fieldset=usera, origfieldval,
final=true]

BELLE2-CONF-2023-004

# Search for lepton-flavor-violating $\tau^{-}\to\ell^{-}\phi$ decays in
2019-2021 Belle II data

F. Abudinén  (The Belle II Collaboration)  0000-0002-6737-3528 I. Adachi  (The
Belle II Collaboration)  0000-0003-2287-0173 K. Adamczyk  (The Belle II
Collaboration)  0000-0001-6208-0876 L. Aggarwal  (The Belle II Collaboration)
0000-0002-0909-7537 P. Ahlburg  (The Belle II Collaboration)
0000-0002-9832-7604 H. Ahmed  (The Belle II Collaboration)
0000-0003-3976-7498 J. K. Ahn  (The Belle II Collaboration)
0000-0002-5795-2243 H. Aihara  (The Belle II Collaboration)
0000-0002-1907-5964 N. Akopov  (The Belle II Collaboration)
0000-0002-4425-2096 A. Aloisio  (The Belle II Collaboration)
0000-0002-3883-6693 L. Andricek  (The Belle II Collaboration)
0000-0003-1755-4475 N. Anh Ky  (The Belle II Collaboration)
0000-0003-0471-197X D. M. Asner  (The Belle II Collaboration)
0000-0002-1586-5790 H. Atmacan  (The Belle II Collaboration)
0000-0003-2435-501X V. Aulchenko  (The Belle II Collaboration)
0000-0002-5394-4406 T. Aushev  (The Belle II Collaboration)
0000-0002-6347-7055 V. Aushev  (The Belle II Collaboration)
0000-0002-8588-5308 M. Aversano  (The Belle II Collaboration)
0000-0001-9980-0953 V. Babu  (The Belle II Collaboration)  0000-0003-0419-6912
S. Bacher  (The Belle II Collaboration)  0000-0002-2656-2330 H. Bae  (The
Belle II Collaboration)  0000-0003-1393-8631 S. Bahinipati  (The Belle II
Collaboration)  0000-0002-3744-5332 A. M. Bakich  (The Belle II Collaboration)
0000-0001-8315-4854 P. Bambade  (The Belle II Collaboration)
0000-0001-7378-4852 Sw. Banerjee  (The Belle II Collaboration)
0000-0001-8852-2409 S. Bansal  (The Belle II Collaboration)
0000-0003-1992-0336 M. Barrett  (The Belle II Collaboration)
0000-0002-2095-603X G. Batignani  (The Belle II Collaboration)
0000-0003-3917-3104 J. Baudot  (The Belle II Collaboration)
0000-0001-5585-0991 M. Bauer  (The Belle II Collaboration)
0000-0002-0953-7387 A. Baur  (The Belle II Collaboration)  0000-0003-1360-3292
A. Beaubien  (The Belle II Collaboration)  0000-0001-9438-089X J. Becker  (The
Belle II Collaboration)  0000-0002-5082-5487 P. K. Behera  (The Belle II
Collaboration)  0000-0002-1527-2266 J. V. Bennett  (The Belle II
Collaboration)  0000-0002-5440-2668 E. Bernieri  (The Belle II Collaboration)
0000-0002-4787-2047 F. U. Bernlochner  (The Belle II Collaboration)
0000-0001-8153-2719 V. Bertacchi  (The Belle II Collaboration)
0000-0001-9971-1176 M. Bertemes  (The Belle II Collaboration)
0000-0001-5038-360X E. Bertholet  (The Belle II Collaboration)
0000-0002-3792-2450 M. Bessner  (The Belle II Collaboration)
0000-0003-1776-0439 S. Bettarini  (The Belle II Collaboration)
0000-0001-7742-2998 V. Bhardwaj  (The Belle II Collaboration)
0000-0001-8857-8621 B. Bhuyan  (The Belle II Collaboration)
0000-0001-6254-3594 F. Bianchi  (The Belle II Collaboration)
0000-0002-1524-6236 T. Bilka  (The Belle II Collaboration)
0000-0003-1449-6986 S. Bilokin  (The Belle II Collaboration)
0000-0003-0017-6260 D. Biswas  (The Belle II Collaboration)
0000-0002-7543-3471 A. Bobrov  (The Belle II Collaboration)
0000-0001-5735-8386 D. Bodrov  (The Belle II Collaboration)
0000-0001-5279-4787 A. Bolz  (The Belle II Collaboration)  0000-0002-4033-9223
A. Bondar  (The Belle II Collaboration)  0000-0002-5089-5338 G. Bonvicini
(The Belle II Collaboration)  0000-0003-4861-7918 J. Borah  (The Belle II
Collaboration)  0000-0003-2990-1913 A. Bozek  (The Belle II Collaboration)
0000-0002-5915-1319 M. Bračko  (The Belle II Collaboration)
0000-0002-2495-0524 P. Branchini  (The Belle II Collaboration)
0000-0002-2270-9673 R. A. Briere  (The Belle II Collaboration)
0000-0001-5229-1039 T. E. Browder  (The Belle II Collaboration)
0000-0001-7357-9007 D. N. Brown  (The Belle II Collaboration)
0000-0002-9635-4174 A. Budano  (The Belle II Collaboration)
0000-0002-0856-1131 S. Bussino  (The Belle II Collaboration)
0000-0002-3829-9592 M. Campajola  (The Belle II Collaboration)
0000-0003-2518-7134 L. Cao  (The Belle II Collaboration)  0000-0001-8332-5668
G. Casarosa  (The Belle II Collaboration)  0000-0003-4137-938X C. Cecchi  (The
Belle II Collaboration)  0000-0002-2192-8233 J. Cerasoli  (The Belle II
Collaboration)  0000-0001-9777-881X D. Červenkov  (The Belle II Collaboration)
0000-0002-1865-741X M.-C. Chang  (The Belle II Collaboration)
0000-0002-8650-6058 P. Chang  (The Belle II Collaboration)
0000-0003-4064-388X R. Cheaib  (The Belle II Collaboration)
0000-0001-5729-8926 P. Cheema  (The Belle II Collaboration)
0000-0001-8472-5727 V. Chekelian  (The Belle II Collaboration)
0000-0001-8860-8288 C. Chen  (The Belle II Collaboration)  0000-0003-1589-9955
Y. Q. Chen  (The Belle II Collaboration)  0000-0002-2057-1076 Y. Q. Chen  (The
Belle II Collaboration)  0000-0002-7285-3251 Y.-T. Chen  (The Belle II
Collaboration)  0000-0003-2639-2850 B. G. Cheon  (The Belle II Collaboration)
0000-0002-8803-4429 K. Chilikin  (The Belle II Collaboration)
0000-0001-7620-2053 K. Chirapatpimol  (The Belle II Collaboration)
0000-0003-2099-7760 H.-E. Cho  (The Belle II Collaboration)
0000-0002-7008-3759 K. Cho  (The Belle II Collaboration)  0000-0003-1705-7399
S.-J. Cho  (The Belle II Collaboration)  0000-0002-1673-5664 S.-K. Choi  (The
Belle II Collaboration)  0000-0003-2747-8277 S. Choudhury  (The Belle II
Collaboration)  0000-0001-9841-0216 D. Cinabro  (The Belle II Collaboration)
0000-0001-7347-6585 J. Cochran  (The Belle II Collaboration)
0000-0002-1492-914X L. Corona  (The Belle II Collaboration)
0000-0002-2577-9909 L. M. Cremaldi  (The Belle II Collaboration)
0000-0001-5550-7827 S. Cunliffe  (The Belle II Collaboration)
0000-0003-0167-8641 T. Czank  (The Belle II Collaboration)
0000-0001-6621-3373 S. Das  (The Belle II Collaboration)  0000-0001-6857-966X
F. Dattola  (The Belle II Collaboration)  0000-0003-3316-8574 E. De La Cruz-
Burelo  (The Belle II Collaboration)  0000-0002-7469-6974 S. A. De La Motte
(The Belle II Collaboration)  0000-0003-3905-6805 G. de Marino  (The Belle II
Collaboration)  0000-0002-6509-7793 G. De Nardo  (The Belle II Collaboration)
0000-0002-2047-9675 M. De Nuccio  (The Belle II Collaboration)
0000-0002-0972-9047 G. De Pietro  (The Belle II Collaboration)
0000-0001-8442-107X R. de Sangro  (The Belle II Collaboration)
0000-0002-3808-5455 B. Deschamps  (The Belle II Collaboration)
0000-0003-2497-5008 M. Destefanis  (The Belle II Collaboration)
0000-0003-1997-6751 S. Dey  (The Belle II Collaboration)  0000-0003-2997-3829
A. De Yta-Hernandez  (The Belle II Collaboration)  0000-0002-2162-7334 R.
Dhamija  (The Belle II Collaboration)  0000-0001-7052-3163 A. Di Canto  (The
Belle II Collaboration)  0000-0003-1233-3876 F. Di Capua  (The Belle II
Collaboration)  0000-0001-9076-5936 J. Dingfelder  (The Belle II
Collaboration)  0000-0001-5767-2121 Z. Doležal  (The Belle II Collaboration)
0000-0002-5662-3675 I. Domínguez Jiménez  (The Belle II Collaboration)
0000-0001-6831-3159 T. V. Dong  (The Belle II Collaboration)
0000-0003-3043-1939 M. Dorigo  (The Belle II Collaboration)
0000-0002-0681-6946 K. Dort  (The Belle II Collaboration)  0000-0003-0849-8774
D. Dossett  (The Belle II Collaboration)  0000-0002-5670-5582 S. Dreyer  (The
Belle II Collaboration)  0000-0002-6295-100X S. Dubey  (The Belle II
Collaboration)  0000-0002-1345-0970 S. Duell  (The Belle II Collaboration)
0000-0001-9918-9808 G. Dujany  (The Belle II Collaboration)
0000-0002-1345-8163 P. Ecker  (The Belle II Collaboration)
0000-0002-6817-6868 M. Eliachevitch  (The Belle II Collaboration)
0000-0003-2033-537X D. Epifanov  (The Belle II Collaboration)
0000-0001-8656-2693 P. Feichtinger  (The Belle II Collaboration)
0000-0003-3966-7497 T. Ferber  (The Belle II Collaboration)
0000-0002-6849-0427 D. Ferlewicz  (The Belle II Collaboration)
0000-0002-4374-1234 T. Fillinger  (The Belle II Collaboration)
0000-0001-9795-7412 C. Finck  (The Belle II Collaboration)
0000-0002-5068-5453 G. Finocchiaro  (The Belle II Collaboration)
0000-0002-3936-2151 P. Fischer  (The Belle II Collaboration)
0000-0002-9808-3574 K. Flood  (The Belle II Collaboration)
0000-0002-3463-6571 A. Fodor  (The Belle II Collaboration)
0000-0002-2821-759X F. Forti  (The Belle II Collaboration)
0000-0001-6535-7965 A. Frey  (The Belle II Collaboration)  0000-0001-7470-3874
M. Friedl  (The Belle II Collaboration)  0000-0002-7420-2559 B. G. Fulsom
(The Belle II Collaboration)  0000-0002-5862-9739 A. Gabrielli  (The Belle II
Collaboration)  0000-0001-7695-0537 N. Gabyshev  (The Belle II Collaboration)
0000-0002-8593-6857 E. Ganiev  (The Belle II Collaboration)
0000-0001-8346-8597 M. Garcia-Hernandez  (The Belle II Collaboration)
0000-0003-2393-3367 R. Garg  (The Belle II Collaboration)  0000-0002-7406-4707
A. Garmash  (The Belle II Collaboration)  0000-0003-2599-1405 G. Gaudino  (The
Belle II Collaboration)  0000-0001-5983-1552 V. Gaur  (The Belle II
Collaboration)  0000-0002-8880-6134 A. Gaz  (The Belle II Collaboration)
0000-0001-6754-3315 U. Gebauer  (The Belle II Collaboration)
0000-0002-5679-2209 A. Gellrich  (The Belle II Collaboration)
0000-0003-0974-6231 G. Ghevondyan  (The Belle II Collaboration)
0000-0003-0096-3555 D. Ghosh  (The Belle II Collaboration)
0000-0002-3458-9824 G. Giakoustidis  (The Belle II Collaboration)
0000-0001-5982-1784 R. Giordano  (The Belle II Collaboration)
0000-0002-5496-7247 A. Giri  (The Belle II Collaboration)  0000-0002-8895-0128
A. Glazov  (The Belle II Collaboration)  0000-0002-8553-7338 B. Gobbo  (The
Belle II Collaboration)  0000-0002-3147-4562 R. Godang  (The Belle II
Collaboration)  0000-0002-8317-0579 P. Goldenzweig  (The Belle II
Collaboration)  0000-0001-8785-847X B. Golob  (The Belle II Collaboration)
0000-0001-9632-5616 G. Gong  (The Belle II Collaboration)  0000-0001-7192-1833
P. Grace  (The Belle II Collaboration)  0000-0001-9005-7403 W. Gradl  (The
Belle II Collaboration)  0000-0002-9974-8320 M. Graf-Schreiber  (The Belle II
Collaboration)  0000-0003-4613-1041 T. Grammatico  (The Belle II
Collaboration)  0000-0002-2818-9744 S. Granderath  (The Belle II
Collaboration)  0000-0002-9945-463X E. Graziani  (The Belle II Collaboration)
0000-0001-8602-5652 D. Greenwald  (The Belle II Collaboration)
0000-0001-6964-8399 Z. Gruberová  (The Belle II Collaboration)
0000-0002-5691-1044 T. Gu  (The Belle II Collaboration)  0000-0002-1470-6536
Y. Guan  (The Belle II Collaboration)  0000-0002-5541-2278 K. Gudkova  (The
Belle II Collaboration)  0000-0002-5858-3187 C. Hadjivasiliou  (The Belle II
Collaboration)  0000-0002-2234-0001 S. Halder  (The Belle II Collaboration)
0000-0002-6280-494X Y. Han  (The Belle II Collaboration)  0000-0001-6775-5932
K. Hara  (The Belle II Collaboration)  0000-0002-5361-1871 T. Hara  (The Belle
II Collaboration)  0000-0002-4321-0417 O. Hartbrich  (The Belle II
Collaboration)  0000-0001-7741-4381 K. Hayasaka  (The Belle II Collaboration)
0000-0002-6347-433X H. Hayashii  (The Belle II Collaboration)
0000-0002-5138-5903 S. Hazra  (The Belle II Collaboration)
0000-0001-6954-9593 C. Hearty  (The Belle II Collaboration)
0000-0001-6568-0252 M. T. Hedges  (The Belle II Collaboration)
0000-0001-6504-1872 I. Heredia de la Cruz  (The Belle II Collaboration)
0000-0002-8133-6467 M. Hernández Villanueva  (The Belle II Collaboration)
0000-0002-6322-5587 A. Hershenhorn  (The Belle II Collaboration)
0000-0001-8753-5451 T. Higuchi  (The Belle II Collaboration)
0000-0002-7761-3505 E. C. Hill  (The Belle II Collaboration)
0000-0002-1725-7414 H. Hirata  (The Belle II Collaboration)
0000-0001-9005-4616 M. Hoek  (The Belle II Collaboration)  0000-0002-1893-8764
M. Hohmann  (The Belle II Collaboration)  0000-0001-5147-4781 T. Hotta  (The
Belle II Collaboration)  0000-0002-1079-5826 C.-L. Hsu  (The Belle II
Collaboration)  0000-0002-1641-430X K. Huang  (The Belle II Collaboration)
0000-0001-9342-7406 T. Humair  (The Belle II Collaboration)
0000-0002-2922-9779 T. Iijima  (The Belle II Collaboration)
0000-0002-4271-711X K. Inami  (The Belle II Collaboration)
0000-0003-2765-7072 G. Inguglia  (The Belle II Collaboration)
0000-0003-0331-8279 N. Ipsita  (The Belle II Collaboration)
0000-0002-2927-3366 J. Irakkathil Jabbar  (The Belle II Collaboration)
0000-0001-7948-1633 A. Ishikawa  (The Belle II Collaboration)
0000-0002-3561-5633 S. Ito  (The Belle II Collaboration)  0000-0003-2737-8145
R. Itoh  (The Belle II Collaboration)  0000-0003-1590-0266 M. Iwasaki  (The
Belle II Collaboration)  0000-0002-9402-7559 Y. Iwasaki  (The Belle II
Collaboration)  0000-0001-7261-2557 S. Iwata  (The Belle II Collaboration)
0009-0005-5017-8098 P. Jackson  (The Belle II Collaboration)
0000-0002-0847-402X W. W. Jacobs  (The Belle II Collaboration)
0000-0002-9996-6336 D. E. Jaffe  (The Belle II Collaboration)
0000-0003-3122-4384 E.-J. Jang  (The Belle II Collaboration)
0000-0002-1935-9887 H. B. Jeon  (The Belle II Collaboration)
0000-0002-0857-0353 Q. P. Ji  (The Belle II Collaboration)
0000-0003-2963-2565 S. Jia  (The Belle II Collaboration)  0000-0001-8176-8545
Y. Jin  (The Belle II Collaboration)  0000-0002-7323-0830 K. K. Joo  (The
Belle II Collaboration)  0000-0002-5515-0087 H. Junkerkalefeld  (The Belle II
Collaboration)  0000-0003-3987-9895 I. Kadenko  (The Belle II Collaboration)
0000-0001-8766-4229 H. Kakuno  (The Belle II Collaboration)
0000-0002-9957-6055 M. Kaleta  (The Belle II Collaboration)
0000-0002-2863-5476 D. Kalita  (The Belle II Collaboration)
0000-0003-3054-1222 A. B. Kaliyar  (The Belle II Collaboration)
0000-0002-2211-619X J. Kandra  (The Belle II Collaboration)
0000-0001-5635-1000 K. H. Kang  (The Belle II Collaboration)
0000-0002-6816-0751 S. Kang  (The Belle II Collaboration)  0000-0002-5320-7043
P. Kapusta  (The Belle II Collaboration)  0000-0003-1235-1935 R. Karl  (The
Belle II Collaboration)  0000-0002-3619-0876 G. Karyan  (The Belle II
Collaboration)  0000-0001-5365-3716 Y. Kato  (The Belle II Collaboration)
0000-0001-6314-4288 T. Kawasaki  (The Belle II Collaboration)
0000-0002-4089-5238 C. Ketter  (The Belle II Collaboration)
0000-0002-5161-9722 C. Kiesling  (The Belle II Collaboration)
0000-0002-2209-535X C.-H. Kim  (The Belle II Collaboration)
0000-0002-5743-7698 D. Y. Kim  (The Belle II Collaboration)
0000-0001-8125-9070 H. J. Kim  (The Belle II Collaboration)
0000-0001-9787-4684 K.-H. Kim  (The Belle II Collaboration)
0000-0002-4659-1112 Y.-K. Kim  (The Belle II Collaboration)
0000-0002-9695-8103 Y. J. Kim  (The Belle II Collaboration)
0000-0001-9511-9634 T. D. Kimmel  (The Belle II Collaboration)
0000-0002-9743-8249 H. Kindo  (The Belle II Collaboration)
0000-0002-6756-3591 K. Kinoshita  (The Belle II Collaboration)
0000-0001-7175-4182 C. Kleinwort  (The Belle II Collaboration)
0000-0002-9017-9504 P. Kodyš  (The Belle II Collaboration)
0000-0002-8644-2349 T. Koga  (The Belle II Collaboration)  0000-0002-1644-2001
S. Kohani  (The Belle II Collaboration)  0000-0003-3869-6552 K. Kojima  (The
Belle II Collaboration)  0000-0002-3638-0266 T. Konno  (The Belle II
Collaboration)  0000-0003-2487-8080 A. Korobov  (The Belle II Collaboration)
0000-0001-5959-8172 S. Korpar  (The Belle II Collaboration)
0000-0003-0971-0968 E. Kovalenko  (The Belle II Collaboration)
0000-0001-8084-1931 R. Kowalewski  (The Belle II Collaboration)
0000-0002-7314-0990 T. M. G. Kraetzschmar  (The Belle II Collaboration)
0000-0001-8395-2928 P. Križan  (The Belle II Collaboration)
0000-0002-4967-7675 J. F. Krohn  (The Belle II Collaboration)
0000-0002-5001-0675 P. Krokovny  (The Belle II Collaboration)
0000-0002-1236-4667 W. Kuehn  (The Belle II Collaboration)
0000-0001-6018-9878 T. Kuhr  (The Belle II Collaboration)  0000-0001-6251-8049
J. Kumar  (The Belle II Collaboration)  0000-0002-8465-433X M. Kumar  (The
Belle II Collaboration)  0000-0002-6627-9708 R. Kumar  (The Belle II
Collaboration)  0000-0002-6277-2626 K. Kumara  (The Belle II Collaboration)
0000-0003-1572-5365 T. Kumita  (The Belle II Collaboration)
0000-0001-7572-4538 T. Kunigo  (The Belle II Collaboration)
0000-0001-9613-2849 S. Kurz  (The Belle II Collaboration)  0000-0002-1797-5774
A. Kuzmin  (The Belle II Collaboration)  0000-0002-7011-5044 P. Kvasnička
(The Belle II Collaboration)  0000-0001-6281-0648 Y.-J. Kwon  (The Belle II
Collaboration)  0000-0001-9448-5691 S. Lacaprara  (The Belle II Collaboration)
0000-0002-0551-7696 Y.-T. Lai  (The Belle II Collaboration)
0000-0001-9553-3421 C. La Licata  (The Belle II Collaboration)
0000-0002-8946-8202 K. Lalwani  (The Belle II Collaboration)
0000-0002-7294-396X T. Lam  (The Belle II Collaboration)  0000-0001-9128-6806
L. Lanceri  (The Belle II Collaboration)  0000-0001-8220-3095 J. S. Lange
(The Belle II Collaboration)  0000-0003-0234-0474 M. Laurenza  (The Belle II
Collaboration)  0000-0002-7400-6013 K. Lautenbach  (The Belle II
Collaboration)  0000-0003-3762-694X P. J. Laycock  (The Belle II
Collaboration)  0000-0002-8572-5339 R. Leboucher  (The Belle II Collaboration)
0000-0003-3097-6613 F. R. Le Diberder  (The Belle II Collaboration)
0000-0002-9073-5689 S. C. Lee  (The Belle II Collaboration)
0000-0002-9835-1006 P. Leitl  (The Belle II Collaboration)
0000-0002-1336-9558 D. Levit  (The Belle II Collaboration)
0000-0001-5789-6205 P. M. Lewis  (The Belle II Collaboration)
0000-0002-5991-622X C. Li  (The Belle II Collaboration)  0000-0002-3240-4523
L. K. Li  (The Belle II Collaboration)  0000-0002-7366-1307 S. X. Li  (The
Belle II Collaboration)  0000-0003-4669-1495 Y. B. Li  (The Belle II
Collaboration)  0000-0002-9909-2851 J. Libby  (The Belle II Collaboration)
0000-0002-1219-3247 K. Lieret  (The Belle II Collaboration)
0000-0003-2792-7511 J. Lin  (The Belle II Collaboration)  0000-0002-3653-2899
Z. Liptak  (The Belle II Collaboration)  0000-0002-6491-8131 Q. Y. Liu  (The
Belle II Collaboration)  0000-0002-7684-0415 Z. A. Liu  (The Belle II
Collaboration)  0000-0002-2896-1386 Z. Q. Liu  (The Belle II Collaboration)
0000-0002-0290-3022 D. Liventsev  (The Belle II Collaboration)
0000-0003-3416-0056 S. Longo  (The Belle II Collaboration)
0000-0002-8124-8969 A. Lozar  (The Belle II Collaboration)
0000-0002-0569-6882 T. Lueck  (The Belle II Collaboration)
0000-0003-3915-2506 T. Luo  (The Belle II Collaboration)  0000-0001-5139-5784
C. Lyu  (The Belle II Collaboration)  0000-0002-2275-0473 Y. Ma  (The Belle II
Collaboration)  0000-0001-8412-8308 M. Maggiora  (The Belle II Collaboration)
0000-0003-4143-9127 S. P. Maharana  (The Belle II Collaboration)
0000-0002-1746-4683 R. Maiti  (The Belle II Collaboration)
0000-0001-5534-7149 S. Maity  (The Belle II Collaboration)
0000-0003-3076-9243 R. Manfredi  (The Belle II Collaboration)
0000-0002-8552-6276 E. Manoni  (The Belle II Collaboration)
0000-0002-9826-7947 A. C. Manthei  (The Belle II Collaboration)
0000-0002-6900-5729 M. Mantovano  (The Belle II Collaboration)
0000-0002-5979-5050 D. Marcantonio  (The Belle II Collaboration)
0000-0002-1315-8646 S. Marcello  (The Belle II Collaboration)
0000-0003-4144-863X C. Marinas  (The Belle II Collaboration)
0000-0003-1903-3251 L. Martel  (The Belle II Collaboration)
0000-0001-8562-0038 C. Martellini  (The Belle II Collaboration)
0000-0002-7189-8343 A. Martini  (The Belle II Collaboration)
0000-0003-1161-4983 T. Martinov  (The Belle II Collaboration)
0000-0001-7846-1913 L. Massaccesi  (The Belle II Collaboration)
0000-0003-1762-4699 M. Masuda  (The Belle II Collaboration)
0000-0002-7109-5583 T. Matsuda  (The Belle II Collaboration)
0000-0003-4673-570X K. Matsuoka  (The Belle II Collaboration)
0000-0003-1706-9365 D. Matvienko  (The Belle II Collaboration)
0000-0002-2698-5448 S. K. Maurya  (The Belle II Collaboration)
0000-0002-7764-5777 J. A. McKenna  (The Belle II Collaboration)
0000-0001-9871-9002 J. McNeil  (The Belle II Collaboration)
0000-0002-2481-1014 F. Meggendorfer  (The Belle II Collaboration)
0000-0002-1466-7207 F. Meier  (The Belle II Collaboration)
0000-0002-6088-0412 M. Merola  (The Belle II Collaboration)
0000-0002-7082-8108 F. Metzner  (The Belle II Collaboration)
0000-0002-0128-264X M. Milesi  (The Belle II Collaboration)
0000-0002-8805-1886 C. Miller  (The Belle II Collaboration)
0000-0003-2631-1790 K. Miyabayashi  (The Belle II Collaboration)
0000-0003-4352-734X H. Miyake  (The Belle II Collaboration)
0000-0002-7079-8236 H. Miyata  (The Belle II Collaboration)
0000-0002-1026-2894 R. Mizuk  (The Belle II Collaboration)
0000-0002-2209-6969 G. B. Mohanty  (The Belle II Collaboration)
0000-0001-6850-7666 N. Molina-Gonzalez  (The Belle II Collaboration)
0000-0002-0903-1722 S. Mondal  (The Belle II Collaboration)
0000-0002-3054-8400 S. Moneta  (The Belle II Collaboration)
0000-0003-2184-7510 H. Moon  (The Belle II Collaboration)  0000-0001-5213-6477
H.-G. Moser  (The Belle II Collaboration)  0000-0003-3579-9951 M. Mrvar  (The
Belle II Collaboration)  0000-0001-6388-3005 Th. Muller  (The Belle II
Collaboration)  0000-0003-4337-0098 R. Mussa  (The Belle II Collaboration)
0000-0002-0294-9071 I. Nakamura  (The Belle II Collaboration)
0000-0002-7640-5456 K. R. Nakamura  (The Belle II Collaboration)
0000-0001-7012-7355 E. Nakano  (The Belle II Collaboration)
0000-0003-2282-5217 M. Nakao  (The Belle II Collaboration)
0000-0001-8424-7075 H. Nakayama  (The Belle II Collaboration)
0000-0002-2030-9967 H. Nakazawa  (The Belle II Collaboration)
0000-0003-1684-6628 Y. Nakazawa  (The Belle II Collaboration)
0000-0002-6271-5808 A. Narimani Charan  (The Belle II Collaboration)
0000-0002-5975-550X M. Naruki  (The Belle II Collaboration)
0000-0003-1773-2999 D. Narwal  (The Belle II Collaboration)
0000-0001-6585-7767 Z. Natkaniec  (The Belle II Collaboration)
0000-0003-0486-9291 A. Natochii  (The Belle II Collaboration)
0000-0002-1076-814X L. Nayak  (The Belle II Collaboration)
0000-0002-7739-914X M. Nayak  (The Belle II Collaboration)
0000-0002-2572-4692 G. Nazaryan  (The Belle II Collaboration)
0000-0002-9434-6197 C. Niebuhr  (The Belle II Collaboration)
0000-0002-4375-9741 M. Niiyama  (The Belle II Collaboration)
0000-0003-1746-586X J. Ninkovic  (The Belle II Collaboration)
0000-0003-1523-3635 N. K. Nisar  (The Belle II Collaboration)
0000-0001-9562-1253 S. Nishida  (The Belle II Collaboration)
0000-0001-6373-2346 K. Nishimura  (The Belle II Collaboration)
0000-0001-8818-8922 M. H. A. Nouxman  (The Belle II Collaboration)
0000-0003-1243-161X K. Ogawa  (The Belle II Collaboration)
0000-0003-2220-7224 S. Ogawa  (The Belle II Collaboration)
0000-0002-7310-5079 S. L. Olsen  (The Belle II Collaboration)
0000-0002-6388-9885 Y. Onishchuk  (The Belle II Collaboration)
0000-0002-8261-7543 H. Ono  (The Belle II Collaboration)  0000-0003-4486-0064
Y. Onuki  (The Belle II Collaboration)  0000-0002-1646-6847 P. Oskin  (The
Belle II Collaboration)  0000-0002-7524-0936 E. R. Oxford  (The Belle II
Collaboration)  0000-0002-0813-4578 H. Ozaki  (The Belle II Collaboration)
0000-0001-6901-1881 P. Pakhlov  (The Belle II Collaboration)
0000-0001-7426-4824 G. Pakhlova  (The Belle II Collaboration)
0000-0001-7518-3022 A. Paladino  (The Belle II Collaboration)
0000-0002-3370-259X T. Pang  (The Belle II Collaboration)  0000-0003-1204-0846
A. Panta  (The Belle II Collaboration)  0000-0001-6385-7712 E. Paoloni  (The
Belle II Collaboration)  0000-0001-5969-8712 S. Pardi  (The Belle II
Collaboration)  0000-0001-7994-0537 K. Parham  (The Belle II Collaboration)
0000-0001-9556-2433 H. Park  (The Belle II Collaboration)  0000-0001-6087-2052
S.-H. Park  (The Belle II Collaboration)  0000-0001-6019-6218 B. Paschen  (The
Belle II Collaboration)  0000-0003-1546-4548 A. Passeri  (The Belle II
Collaboration)  0000-0003-4864-3411 A. Pathak  (The Belle II Collaboration)
0000-0001-9861-2942 S. Patra  (The Belle II Collaboration)
0000-0002-4114-1091 S. Paul  (The Belle II Collaboration)  0000-0002-8813-0437
T. K. Pedlar  (The Belle II Collaboration)  0000-0001-9839-7373 I. Peruzzi
(The Belle II Collaboration)  0000-0001-6729-8436 R. Peschke  (The Belle II
Collaboration)  0000-0002-2529-8515 R. Pestotnik  (The Belle II Collaboration)
0000-0003-1804-9470 F. Pham  (The Belle II Collaboration)  0000-0003-0608-2302
M. Piccolo  (The Belle II Collaboration)  0000-0001-9750-0551 L. E. Piilonen
(The Belle II Collaboration)  0000-0001-6836-0748 G. Pinna Angioni  (The Belle
II Collaboration)  0000-0003-0808-8281 P. L. M. Podesta-Lerma  (The Belle II
Collaboration)  0000-0002-8152-9605 T. Podobnik  (The Belle II Collaboration)
0000-0002-6131-819X S. Pokharel  (The Belle II Collaboration)
0000-0002-3367-738X L. Polat  (The Belle II Collaboration)
0000-0002-2260-8012 V. Popov  (The Belle II Collaboration)
0000-0003-0208-2583 C. Praz  (The Belle II Collaboration)  0000-0002-6154-885X
S. Prell  (The Belle II Collaboration)  0000-0002-0195-8005 E. Prencipe  (The
Belle II Collaboration)  0000-0002-9465-2493 M. T. Prim  (The Belle II
Collaboration)  0000-0002-1407-7450 M. V. Purohit  (The Belle II
Collaboration)  0000-0002-8381-8689 H. Purwar  (The Belle II Collaboration)
0000-0002-3876-7069 N. Rad  (The Belle II Collaboration)  0000-0002-5204-0851
P. Rados  (The Belle II Collaboration)  0000-0003-0690-8100 G. Raeuber  (The
Belle II Collaboration)  0000-0003-2948-5155 S. Raiz  (The Belle II
Collaboration)  0000-0001-7010-8066 A. Ramirez Morales  (The Belle II
Collaboration)  0000-0001-8821-5708 N. Rauls  (The Belle II Collaboration)
0000-0002-6583-4888 M. Reif  (The Belle II Collaboration)  0000-0002-0706-0247
S. Reiter  (The Belle II Collaboration)  0000-0002-6542-9954 M. Remnev  (The
Belle II Collaboration)  0000-0001-6975-1724 I. Ripp-Baudot  (The Belle II
Collaboration)  0000-0002-1897-8272 M. Ritter  (The Belle II Collaboration)
0000-0001-6507-4631 M. Ritzert  (The Belle II Collaboration)
0000-0003-2928-7044 G. Rizzo  (The Belle II Collaboration)
0000-0003-1788-2866 L. B. Rizzuto  (The Belle II Collaboration)
0000-0001-6621-6646 S. H. Robertson  (The Belle II Collaboration)
0000-0003-4096-8393 P. Rocchetti  (The Belle II Collaboration)
0000-0002-2839-3489 D. Rodríguez Pérez  (The Belle II Collaboration)
0000-0001-8505-649X M. Roehrken  (The Belle II Collaboration)
0000-0003-0654-2866 J. M. Roney  (The Belle II Collaboration)
0000-0001-7802-4617 C. Rosenfeld  (The Belle II Collaboration)
0000-0003-3857-1223 A. Rostomyan  (The Belle II Collaboration)
0000-0003-1839-8152 N. Rout  (The Belle II Collaboration)  0000-0002-4310-3638
M. Rozanska  (The Belle II Collaboration)  0000-0003-2651-5021 G. Russo  (The
Belle II Collaboration)  0000-0001-5823-4393 D. Sahoo  (The Belle II
Collaboration)  0000-0002-5600-9413 Y. Sakai  (The Belle II Collaboration)
0000-0001-9163-3409 D. A. Sanders  (The Belle II Collaboration)
0000-0002-4902-966X S. Sandilya  (The Belle II Collaboration)
0000-0002-4199-4369 A. Sangal  (The Belle II Collaboration)
0000-0001-5853-349X L. Santelj  (The Belle II Collaboration)
0000-0003-3904-2956 P. Sartori  (The Belle II Collaboration)
0000-0002-9528-4338 Y. Sato  (The Belle II Collaboration)  0000-0003-3751-2803
V. Savinov  (The Belle II Collaboration)  0000-0002-9184-2830 B. Scavino  (The
Belle II Collaboration)  0000-0003-1771-9161 C. Schmitt  (The Belle II
Collaboration)  0000-0002-3787-687X J. Schmitz  (The Belle II Collaboration)
0000-0001-8274-8124 M. Schnepf  (The Belle II Collaboration)
0000-0003-0623-0184 H. Schreeck  (The Belle II Collaboration)
0000-0002-2287-8047 J. Schueler  (The Belle II Collaboration)
0000-0002-2722-6953 C. Schwanda  (The Belle II Collaboration)
0000-0003-4844-5028 A. J. Schwartz  (The Belle II Collaboration)
0000-0002-7310-1983 B. Schwenker  (The Belle II Collaboration)
0000-0002-7120-3732 M. Schwickardi  (The Belle II Collaboration)
0000-0003-2033-6700 Y. Seino  (The Belle II Collaboration)
0000-0002-8378-4255 A. Selce  (The Belle II Collaboration)
0000-0001-8228-9781 K. Senyo  (The Belle II Collaboration)
0000-0002-1615-9118 J. Serrano  (The Belle II Collaboration)
0000-0003-2489-7812 M. E. Sevior  (The Belle II Collaboration)
0000-0002-4824-101X C. Sfienti  (The Belle II Collaboration)
0000-0002-5921-8819 W. Shan  (The Belle II Collaboration)  0000-0003-2811-2218
C. Sharma  (The Belle II Collaboration)  0000-0002-1312-0429 V. Shebalin  (The
Belle II Collaboration)  0000-0003-1012-0957 C. P. Shen  (The Belle II
Collaboration)  0000-0002-9012-4618 X. D. Shi  (The Belle II Collaboration)
0000-0002-7006-6107 H. Shibuya  (The Belle II Collaboration)
0000-0002-0197-6270 T. Shillington  (The Belle II Collaboration)
0000-0003-3862-4380 J.-G. Shiu  (The Belle II Collaboration)
0000-0002-8478-5639 D. Shtol  (The Belle II Collaboration)
0000-0002-0622-6065 B. Shwartz  (The Belle II Collaboration)
0000-0002-1456-1496 A. Sibidanov  (The Belle II Collaboration)
0000-0001-8805-4895 F. Simon  (The Belle II Collaboration)
0000-0002-5978-0289 J. B. Singh  (The Belle II Collaboration)
0000-0001-9029-2462 J. Skorupa  (The Belle II Collaboration)
0000-0002-8566-621X K. Smith  (The Belle II Collaboration)
0000-0003-0446-9474 R. J. Sobie  (The Belle II Collaboration)
0000-0001-7430-7599 A. Soffer  (The Belle II Collaboration)
0000-0002-0749-2146 A. Sokolov  (The Belle II Collaboration)
0000-0002-9420-0091 Y. Soloviev  (The Belle II Collaboration)
0000-0003-1136-2827 E. Solovieva  (The Belle II Collaboration)
0000-0002-5735-4059 S. Spataro  (The Belle II Collaboration)
0000-0001-9601-405X B. Spruck  (The Belle II Collaboration)
0000-0002-3060-2729 M. Starič  (The Belle II Collaboration)
0000-0001-8751-5944 P. Stavroulakis  (The Belle II Collaboration)
0000-0001-9914-7261 S. Stefkova  (The Belle II Collaboration)
0000-0003-2628-530X Z. S. Stottler  (The Belle II Collaboration)
0000-0002-1898-5333 R. Stroili  (The Belle II Collaboration)
0000-0002-3453-142X J. Strube  (The Belle II Collaboration)
0000-0001-7470-9301 J. Stypula  (The Belle II Collaboration)
0000-0002-5844-7476 Y. Sue  (The Belle II Collaboration)  0000-0003-2430-8707
R. Sugiura  (The Belle II Collaboration)  0000-0002-6044-5445 M. Sumihama
(The Belle II Collaboration)  0000-0002-8954-0585 K. Sumisawa  (The Belle II
Collaboration)  0000-0001-7003-7210 W. Sutcliffe  (The Belle II Collaboration)
0000-0002-9795-3582 S. Y. Suzuki  (The Belle II Collaboration)
0000-0002-7135-4901 H. Svidras  (The Belle II Collaboration)
0000-0003-4198-2517 M. Tabata  (The Belle II Collaboration)
0000-0001-6138-1028 M. Takahashi  (The Belle II Collaboration)
0000-0003-1171-5960 M. Takizawa  (The Belle II Collaboration)
0000-0001-8225-3973 U. Tamponi  (The Belle II Collaboration)
0000-0001-6651-0706 S. Tanaka  (The Belle II Collaboration)
0000-0002-6029-6216 K. Tanida  (The Belle II Collaboration)
0000-0002-8255-3746 H. Tanigawa  (The Belle II Collaboration)
0000-0003-3681-9985 N. Taniguchi  (The Belle II Collaboration)
0000-0002-1462-0564 Y. Tao  (The Belle II Collaboration)  0000-0002-9186-2591
F. Tenchini  (The Belle II Collaboration)  0000-0003-3469-9377 A. Thaller
(The Belle II Collaboration)  0000-0003-4171-6219 O. Tittel  (The Belle II
Collaboration)  0000-0001-9128-6240 R. Tiwary  (The Belle II Collaboration)
0000-0002-5887-1883 D. Tonelli  (The Belle II Collaboration)
0000-0002-1494-7882 E. Torassa  (The Belle II Collaboration)
0000-0003-2321-0599 N. Toutounji  (The Belle II Collaboration)
0000-0002-1937-6732 K. Trabelsi  (The Belle II Collaboration)
0000-0001-6567-3036 I. Tsaklidis  (The Belle II Collaboration)
0000-0003-3584-4484 T. Tsuboyama  (The Belle II Collaboration)
0000-0002-4575-1997 N. Tsuzuki  (The Belle II Collaboration)
0000-0003-1141-1908 M. Uchida  (The Belle II Collaboration)
0000-0003-4904-6168 I. Ueda  (The Belle II Collaboration)  0000-0002-6833-4344
S. Uehara  (The Belle II Collaboration)  0000-0001-7377-5016 Y. Uematsu  (The
Belle II Collaboration)  0000-0002-0296-4028 T. Ueno  (The Belle II
Collaboration)  0000-0002-9130-2850 T. Uglov  (The Belle II Collaboration)
0000-0002-4944-1830 K. Unger  (The Belle II Collaboration)
0000-0001-7378-6671 Y. Unno  (The Belle II Collaboration)  0000-0003-3355-765X
K. Uno  (The Belle II Collaboration)  0000-0002-2209-8198 S. Uno  (The Belle
II Collaboration)  0000-0002-3401-0480 P. Urquijo  (The Belle II
Collaboration)  0000-0002-0887-7953 Y. Ushiroda  (The Belle II Collaboration)
0000-0003-3174-403X Y. V. Usov  (The Belle II Collaboration)
0000-0003-3144-2920 S. E. Vahsen  (The Belle II Collaboration)
0000-0003-1685-9824 R. van Tonder  (The Belle II Collaboration)
0000-0002-7448-4816 G. S. Varner  (The Belle II Collaboration)
0000-0002-0302-8151 K. E. Varvell  (The Belle II Collaboration)
0000-0003-1017-1295 A. Vinokurova  (The Belle II Collaboration)
0000-0003-4220-8056 V. S. Vismaya  (The Belle II Collaboration)
0000-0002-1606-5349 L. Vitale  (The Belle II Collaboration)
0000-0003-3354-2300 V. Vobbilisetti  (The Belle II Collaboration)
0000-0002-4399-5082 V. Vorobyev  (The Belle II Collaboration)
0000-0002-6660-868X A. Vossen  (The Belle II Collaboration)
0000-0003-0983-4936 B. Wach  (The Belle II Collaboration)  0000-0003-3533-7669
E. Waheed  (The Belle II Collaboration)  0000-0001-7774-0363 M. Wakai  (The
Belle II Collaboration)  0000-0003-2818-3155 H. M. Wakeling  (The Belle II
Collaboration)  0000-0003-4606-7895 S. Wallner  (The Belle II Collaboration)
0000-0002-9105-1625 W. Wan Abdullah  (The Belle II Collaboration)
0000-0001-5798-9145 B. Wang  (The Belle II Collaboration)  0000-0001-6136-6952
C. H. Wang  (The Belle II Collaboration)  0000-0001-6760-9839 E. Wang  (The
Belle II Collaboration)  0000-0001-6391-5118 M.-Z. Wang  (The Belle II
Collaboration)  0000-0002-0979-8341 X. L. Wang  (The Belle II Collaboration)
0000-0001-5805-1255 Z. Wang  (The Belle II Collaboration)  0000-0002-3536-4950
A. Warburton  (The Belle II Collaboration)  0000-0002-2298-7315 M. Watanabe
(The Belle II Collaboration)  0000-0001-6917-6694 S. Watanuki  (The Belle II
Collaboration)  0000-0002-5241-6628 J. Webb  (The Belle II Collaboration)
0000-0002-5294-6856 S. Wehle  (The Belle II Collaboration)
0000-0002-6168-1829 M. Welsch  (The Belle II Collaboration)
0000-0002-3026-1872 O. Werbycka  (The Belle II Collaboration)
0000-0002-0614-8773 C. Wessel  (The Belle II Collaboration)
0000-0003-0959-4784 J. Wiechczynski  (The Belle II Collaboration)
0000-0002-3151-6072 P. Wieduwilt  (The Belle II Collaboration)
0000-0002-1706-5359 H. Windel  (The Belle II Collaboration)
0000-0001-9472-0786 E. Won  (The Belle II Collaboration)  0000-0002-4245-7442
L. J. Wu  (The Belle II Collaboration)  0000-0002-3171-2436 Y. Xie  (The Belle
II Collaboration)  0000-0002-0170-2798 X. P. Xu  (The Belle II Collaboration)
0000-0001-5096-1182 B. D. Yabsley  (The Belle II Collaboration)
0000-0002-2680-0474 S. Yamada  (The Belle II Collaboration)
0000-0002-8858-9336 W. Yan  (The Belle II Collaboration)  0000-0003-0713-0871
S. B. Yang  (The Belle II Collaboration)  0000-0002-9543-7971 J. Yelton  (The
Belle II Collaboration)  0000-0001-8840-3346 J. H. Yin  (The Belle II
Collaboration)  0000-0002-1479-9349 Y. M. Yook  (The Belle II Collaboration)
0000-0002-4912-048X K. Yoshihara  (The Belle II Collaboration)
0000-0002-3656-2326 C. Z. Yuan  (The Belle II Collaboration)
0000-0002-1652-6686 Y. Yusa  (The Belle II Collaboration)  0000-0002-4001-9748
L. Zani  (The Belle II Collaboration)  0000-0003-4957-805X J. Z. Zhang  (The
Belle II Collaboration)  0000-0001-6535-0659 Y. Zhang  (The Belle II
Collaboration)  0000-0003-3780-6676 Y. Zhang  (The Belle II Collaboration)
0000-0003-2961-2820 Z. Zhang  (The Belle II Collaboration)
0000-0001-6140-2044 V. Zhilich  (The Belle II Collaboration)
0000-0002-0907-5565 J. S. Zhou  (The Belle II Collaboration)
0000-0002-6413-4687 Q. D. Zhou  (The Belle II Collaboration)
0000-0001-5968-6359 X. Y. Zhou  (The Belle II Collaboration)
0000-0002-0299-4657 V. I. Zhukova  (The Belle II Collaboration)
0000-0002-8253-641X V. Zhulanov  (The Belle II Collaboration)
0000-0002-0306-9199 R. Žlebčík  (The Belle II Collaboration)
0000-0003-1644-8523

###### Abstract

We report a search for lepton-flavor-violating decays
$\tau^{-}\to\ell^{-}\phi$ ($\ell^{-}=e^{-},\mu^{-}$) at the Belle II
experiment, using a sample of electron-positron data produced at the SuperKEKB
collider in 2019-2021 and corresponding to an integrated luminosity of 190
fb-1. We use a new untagged selection for $e^{+}e^{-}\to\tau^{+}\tau^{-}$
events, where the signal $\tau$ is searched for as a neutrinoless final state
of a single charged lepton and a $\phi$ meson and the other $\tau$ is not
reconstructed in any specific decay mode, in contrast to previous measurements
by the BaBar and Belle experiments. We find no evidence for
$\tau^{-}\to\ell^{-}\phi$ decays and obtain upper limits on the branching
fractions at 90% confidence level of 23 $\times 10^{-8}$ and 9.7$\times
10^{-8}$ for $\tau^{-}\rightarrow e^{-}\phi$ and
$\tau^{-}\rightarrow\mu^{-}\phi$, respectively.

##  1 Introduction

In the Standard Model (SM), lepton flavor is only accidentally conserved. The
observation of neutrino oscillations not only introduces direct violation of
neutrino flavor, but also charged-lepton flavor violation (LFV) through weak
interaction charged currents. Decays that involve LFV are predicted to occur
at rates close to $10^{-50}$[1, 2], far beyond the reach of current and future
experiments. The observation of LFV decays would therefore provide
indisputable evidence of non-SM physics.

Over the past four decades, CLEO II, experiments at the $B$ factories, and at
the LHC have searched for LFV decays of the tau lepton, $\tau$. The most
stringent upper limits on the branching fractions of several hypothetical tau
decays are of the order of 10-8 [3]. Among these are limits on the decays to
final states with a lepton, either electron or muon, and a vector meson. In
particular, in recent years there has been great interest in
$\tau^{-}\to\ell^{-}\phi$ (charge-conjugated decays are implied throughout the
paper) due to the $B$ meson anomalies reported by LHCb [4, 5] and $B$-factory
experiments [3, 6, 7]. These measurements hint at potential lepton-flavor-
universality violation in $b\to s\ell^{+}\ell^{-}$ and $b\to
c\ell\mathrm{bar}{\nu}$ transitions, which might indicate a special role of
the third lepton generation, with large enhancements of tau LFV decays.
Specifically, leptoquark models that could accommodate both anomalies predict
branching fractions for $\tau^{-}\to\mu^{-}\phi$ in the range from 10-11 to a
few times 10-8 [8, 9], potentially accessible by the Belle II experiment with
a data set of several inverse attobarns. The limits previously obtained by the
BaBar and Belle experiments, using respectively 451 fb-1 and 854 fb-1 of data,
are given in Table 1 [10, 11]. Both experiments relied on the reconstruction
of $e^{+}e^{-}\to\tau^{+}\tau^{-}$ events where one tau decays as
$\tau^{-}\rightarrow\ell^{-}\phi$ and the other tau decays into a final state
with a single charged particle (1-prong tagging).

Here, we report on a search for the $\tau^{-}\rightarrow\ell^{-}\phi$ decays
based on an untagged selection, in which, in contrast to the previous
searches, only the signal tau decay mode is explicitly reconstructed.
Background events are suppressed by a set of requirements on topological and
kinematic variables followed by a selection based on a boosted decision tree
(BDT) algorithm that also includes kinematic variables and quantities related
to the tracks and clusters not associated with the signal tau decays (rest-of-
event variables). The signal is searched for in a two-dimensional plane
$(M_{\tau},\Delta E_{\tau})$, with $\Delta E_{\tau}=E^{*}_{\tau}-\sqrt{s}/2$
where $E^{*}_{\tau}$ and $M_{\tau}$ are respectively the reconstructed energy
in the center-of-mass (c.m.) frame and the invariant mass of the signal $\tau$
candidate, and $\sqrt{s}$ is the collision energy. In cases where no
significant signal is observed, upper limits are derived using the CLs method
[12, 13].

Table 1: Expected and observed upper limits at 90% C.L. on $\tau^{-}\rightarrow\ell^{-}\phi$ branching fractions obtained by BaBar [10] (451 fb-1) and Belle [11] (854 fb-1).  Experiment |  $\mathcal{B}^{90}_{\mathrm{UL}}(e\phi)\ (\times 10^{-8})$ |  $\mathcal{B}^{90}_{\mathrm{UL}}(\mu\phi)\ (\times 10^{-8})$
---|---|---
exp. / obs. |  exp. / obs.
BaBar |  $5.0$ / $3.1$ |  $8.2$ / $19$
Belle |  $4.3$ / $3.1$ |  $4.9$ / $8.4$

##  2 The Belle II detector and Data Set

Belle II [14] is a particle physics experiment operating at the SuperKEKB
asymmetric-energy electron-positron collider, located at KEK in Tsukuba,
Japan. The energies of the electron and positron beams are respectively 7 GeV
and 4 GeV with a boost of the c.m. frame $\beta\gamma$ = 0.28 relative to the
laboratory frame. The detector is composed of multiple layers of subdetectors
arranged in a cylindrical structure with a central barrel and forward and
backward endcaps. The $z$ axis of the laboratory frame is defined as the
symmetry axis of the solenoid, pointing approximately along the incoming
electron beam. The innermost component is the vertex detector, consisting of
two inner layers of silicon pixels and four outer layers of silicon strips.
The second pixel layer is partially installed, covering one sixth of the
azimuthal angle. The main tracking subdetector is a large helium-based small-
cell drift chamber (CDC) that also provides measurements of ionization-energy
losses used for charged-particle identification. Outside the drift chamber, a
Cherenkov-light imaging and time-of-propagation detector provides charged-
particle identification in the barrel region, complemented in the forward
endcap by a proximity-focusing, ring-imaging Cherenkov detector with an
aerogel radiator. An electromagnetic calorimeter (ECL) consists of a barrel
and two endcap sections made of CsI(Tl) crystals. A uniform 1.5 T magnetic
field aligned with the beams is provided by a superconducting solenoid
situated outside the calorimeter. Multiple layers of scintillators and
resistive-plate chambers, located between the magnetic flux-return iron
plates, constitute the $K^{0}_{L}$ and muon identification system (KLM).

The data used in this analysis are collected from electron-positron collisions
at a c.m. energy $\sqrt{s}=10.58$ GeV between March 2019 and July 2021 and
correspond to an integrated luminosity of 190 fb-1.

In order to define a selection to suppress backgrounds and estimate the signal
efficiencies, we use simulated samples. For the study of the signal processes,
we use 2 million $e^{+}e^{-}\to\tau^{+}\tau^{-}$ events for each
$\tau^{-}\rightarrow\ell^{-}\phi$ mode, where one tau decays into the LFV
channel and the other into a known final state. In addition, we use simulated
background samples consisting of $e^{+}e^{-}\to\tau^{+}\tau^{-}$ events
generated with KKMC [15] in which tau decays are handled by TAUOLA [16] and
their radiative corrections by PHOTOS [17]; $\Upsilon(4S)\to B\mathrm{bar}{B}$
generated with EvtGen [18]; $e^{+}e^{-}\to q\mathrm{bar}{q}$ $(q=u,d,s,c)$
continuum events generated with KKMC and quarks hadronization simulated with
PYTHIA [19]; $e^{+}e^{-}\to\mu^{+}\mu^{-}(\gamma)$ generated with KKMC and
$e^{+}e^{-}\to e^{+}e^{-}(\gamma)$ Bhabha-scattering background generated with
BABAYAGA.NLO [20, 21]. The total generated luminosity corresponds to 6 ab-1
for tau pairs and continuum samples, 1 ab-1 for the $B\mathrm{bar}{B}$ and
dimuon final states and 100 fb-1 for Bhabha events.

The detector response is simulated with Geant4 [22]. Data sets are analyzed
using the Belle II analysis software basf2 [23, 24], which also provides a
simulation of the trigger system.

##  3 Candidate reconstruction and event selection

This search exploits an online event selection (trigger) mainly relying on
information provided by the ECL. Events are required to satisfy a minimal set
of requirements on the energy depositions in the ECL (clusters) and their
minimum energies. The most relevant is the requirement to have at least three
ECL clusters, of which at least one is above 300 MeV. Moreover, events
consistent with Bhabha scattering are rejected by a dedicated trigger veto
based on the energies and angles of two clusters in the ECL.

The $\tau$ lepton pairs produced in $e^{+}e^{-}$ annihilations are back-to-
back in the c.m. frame. Their decay products are well separated into two
opposite hemispheres, defined by the plane perpendicular to the thrust axis
$\mathbf{\hat{n}}_{T}$, which is the vector maximizing the quantity

$T=\max_{\mathbf{\hat{n}}_{T}}\left(\dfrac{\sum_{i}\left|\mathbf{p}_{i}\cdot\mathbf{\hat{n}}_{T}\right|}{\sum_{i}\left|\mathbf{p}_{i}\right|}\right),$
(1)

where $\mathbf{p}_{i}$ is the momentum of final state particle $i$, including
both charged and neutral particles.

In the offline reconstruction, charged-particle trajectories (tracks) are
required to come from the interaction point (IP), with transverse ($dr$) and
longitudinal ($dz$) projections of the distance of the closest approach
respectively less than 1 and 3 cm in absolute value.

Identification of muons relies mostly on charged-particle penetration depth in
the KLM for momenta larger than 0.7 GeV/$c$ and on information from the CDC
and ECL otherwise. Particle-identification likelihoods are obtained by
combining information from the relevant subdetectors. The ratio between the
muon likelihood and the sum of the likelihoods of all particle hypotheses is
required to exceed 0.99, resulting in 86.9% efficiency for selecting muon
candidates with momenta in the range $1.0<p<1.5$ GeV/$c$and within the KLM
barrel acceptance. The rate for a pion to be misidentified as a muon is 2.8%.

Electrons are primarily identified by comparing momenta measured by tracking
with energies of associated ECL depositions. This information and additional
measurements characterizing the calorimeter clusters are used as input to a
boosted decision tree (BDT) classifier that combines ECL-based measurements
with the other subdetectors’ normalized likelihoods. For charged-particle
momenta in the range $1.0<p<1.5$ GeV/$c$, the rate for pions to be
misidentified as electrons is 0.1% at 90% selection efficiency for electron
candidates. Additionally, electrons are corrected for bremsstrahlung losses by
summing the four-momenta of any photon found within a 0.15 radian wide cone
around the direction of the electron momentum and with a minimum energy of 20
MeV. Kaons are selected as tracks coming from the IP consistent with the kaon
mass hypothesis. For the kaon with the highest transverse momentum, we require
that the ratio between the kaon likelihood and the sum of the likelihoods of
all particle hypotheses is greater than 0.5. A $\phi$ candidate is then
reconstructed as a pair of oppositely charged kaons with an invariant mass
$1.014<M_{K^{+}K^{-}}<1.024$ GeV/$c^{2}$. The selected mass region, indicated
by the vertical dashed red lines in Figure 1, is optimized by maximizing the
Punzi figure of merit [25], configured for a search sensitivity at 3$\sigma$
level (in units of one-sided Gaussian).

Figure 1: Reconstructed $\phi$ candidate invariant mass $M_{K^{+}K^{-}}$ for
the electron (left) and muon (right) modes after the candidate reconstruction
and selections up to the $\phi$ candidate mass window definition. The solid
stacked histograms are the simulated background samples for an equivalent
generated luminosity of 2 ab-1, while the blue dotted histogram represents the
signal simulation for $\tau\to\ell\phi$ decays, scaled to arbitrary branching
fractions ($\mathcal{B}$). The vertical dashed lines show the edges of the
region where events are retained for further analysis.

The signal $\tau$ candidate is reconstructed as one lepton candidate, either
electron or muon, which defines the search channel mode, and one $\phi$
candidate belonging to the same hemisphere. The total number of reconstructed
tracks in the event is required to be smaller or equal to six. No attempt is
made to explicitly reconstruct the other $\tau$ lepton. Instead we use the
inclusive properties of all other particles in the event to suppress
backgrounds.

Photons are reconstructed from ECL clusters within the CDC acceptance and not
associated with any track. Photons used for $\pi^{0}$ reconstruction are
required to have an energy deposit of at least 0.1 GeV. Neutral pions are then
identified as photon pairs with masses within $0.115<M_{\gamma\gamma}<0.152$
GeV/$c^{2}$. Photons used to reconstruct $\pi^{0}$ candidates are not
considered for electron bremsstrahlung correction. Photons that satisfy the
above conditions, but are not used for bremsstrahlung correction, nor in the
$\pi^{0}$ reconstruction, and with energies greater than 0.2 GeV are used to
define the thrust and the CLEO cones [26]. The latter are variables computed
from the momentum flow of the reconstructed particles binned in 10∘ cones
around a given axis (e.g. the collision or thrust axis) [27].

All the tracks and clusters that are not used in the signal reconstruction
form the rest of the event (ROE), whose kinematic properties are exploited for
further background suppression. The following criteria must be satisfied to be
retained as part of the ROE: photons are required to have energies of at least
50 MeV and tracks must have a transverse momentum higher than 50 MeV$/c$ with
$|dz|<10\ \mathrm{cm}$ and $|dr|<5\ \mathrm{cm}$.

We define rectangular regions in the two-dimensional plane ($M_{\tau},\Delta
E_{\tau}$). The distribution of $\Delta E_{\tau}$ is expected to peak at zero
for correctly reconstructed signal candidates and $M_{\tau}$ peaks at the
known $\tau$ mass [28]. The rectangular boxes are centered at the signal peak
in the ($M_{\tau},\Delta E_{\tau}$) plane, with side lengths equal to
multiples of their resolutions $\delta$. For each variable, $\delta$ is
estimated by fitting the sum of a Crystal Ball and two Gaussian functions to
the signal distribution, and then taking the weighted average of the three
respective widths. Their values are reported in Table 2.

Table 2: Resolutions $\delta$ obtained from the fits to $M_{\tau}$ and $\Delta E_{\tau}$ distributions on the simulated electron (muon) signal sample. Mode |  Variable |  $\delta$
---|---|---
$e\phi$ |  $M_{\tau}$ |  $11.3\pm 0.2\ \mathrm{MeV}/c^{2}$
$\Delta E_{\tau}$ |  $41.0\pm 0.8\ \mathrm{MeV}$
$\mu\phi$ |  $M_{\tau}$ |  $5.6\pm 0.2\ \mathrm{MeV}/c^{2}$
$\Delta E_{\tau}$ |  $27.1\pm 0.6\ \mathrm{MeV}$

A $\pm 20\delta$ wide rectangular region is used for the selection
optimization on simulation, while all reconstructed events outside this box in
the ($M_{\tau}$, $\Delta E_{\tau}$) plane are rejected. The $\pm 3\delta$ and
$\pm 2\delta$ boxes are used as signal regions (SR) for the final signal-yield
extraction in the electron and muon modes, respectively. Events inside the
above-defined signal regions in data are hidden during the optimization of the
selection to avoid introducing experimental bias. These regions are
illustrated in Figure 2. Structures due to the initial and final state
radiation, seen respectively as longer tails in the negative $\Delta E_{\tau}$
and $M_{\tau}$ directions, are visible in the plots. Final state radiation
affects mainly the electron mode and it is corrected for in the event
reconstruction by taking into account the bremsstrahlung losses.

Figure 2: Reconstructed events for the simulated signal samples in the
$M_{\tau}$-$\Delta E_{\tau}$ plane. The edges of the $\pm 3\delta$ for
$\tau\to e\phi$, $\pm 2\delta$ for $\tau\to\mu\phi$, and $\pm 20\delta$
regions are marked as red and blue rectangles, respectively, for the electron
(muon) mode in the left (right) plot. The sidebands (SB) are the areas inside
the blue boxes and outside the red ones.

##  4 Background suppression

The background originates from radiative dilepton and four-lepton final states
(low-multiplicity), incorrectly reconstructed SM
$e^{+}e^{-}$$\rightarrow\tau^{+}\tau^{-}$ and continuum hadronization
processes from $e^{+}e^{-}$$\rightarrow q\mathrm{bar}{q}$ events. To remove
the low-multiplicity background, we exploit the zeroth order CLEO cone; the
angle between the momentum of the reconstructed signal $\tau$ and the closest
track ($\theta_{\tau-\mathrm{closest}}$); and the opening angle between the
two reconstructed kaons ($\theta_{K1-K2}$) for the electron mode. We require
the zeroth CLEO cone to be less than $8.5$ GeV/$c$;
$\theta_{\tau-\mathrm{closest}}$ larger than 0.02 rad, and $\theta_{K1-K2}$
less than 0.01 rad, respectively. We select events with thrust axis magnitude
$T<0.99$ for the muon mode. The reconstruction and selection described above
reject 97.9% of the total simulated background for the electron channel and
86.3% for the muon channel, and retain 11% and 9% of signal candidates inside
the $\pm 3\delta$ and the $\pm 2\delta$ signal regions for the electron and
muon modes, respectively.

The remaining background events are mainly from continuum processes and are
further suppressed by combining event-shape variables, kinematic properties of
the signal $\tau$ candidate, of the reconstructed $\phi$ resonance, of the
final-state particles, and variables related to the ROE, into a binary BDT
classifier implemented with the XGBoost library [29]. The BDT is trained over
a portion of the simulated signal and background events. The optimal selection
on the BDT output is determined by minimizing the upper limit computed from
the expected number of background events in the simulation in the $\pm
5\delta$ wide boxes in the ($M_{\tau}$, $\Delta E_{\tau}$) plane.

After the application of the BDT selection, there is a significant
contribution to the remaining background observed in data control regions for
the electron mode from the $V^{0}$-photoproduction process
$e^{+}e^{-}$$\rightarrow e^{+}e^{-}\phi$. No simulation of this process is
available. Therefore we devise a data driven veto to reject this contribution:
events reconstructed in the electron mode are rejected if they have more than
one electron candidate in the final state or the second-order CLEO cone with
respect to the collision axis is larger than 0.4 or the cosine of the angle
between the reconstructed signal $\tau$ momentum and its direction of flight
is smaller than zero.

The signal efficiency, extracted from the remaining independent sample as the
ratio between events passing the selections inside the signal region and the
total generated events, is corrected for the measured discrepancies in the
particle-identification efficiency between data and simulation. The final
efficiencies for the electron and muon modes are respectively $(6.1\pm 0.9)\%$
and $(6.5\pm 0.6)\%$, where the quoted uncertainty is the total systematic
uncertainty computed from the list in Table 4.

The agreement between data and simulation after the final selections is
validated by using the region outside the signal boxes in the ($M_{\tau}$,
$\Delta E_{\tau}$) plane, from $\pm 3\delta$ for the electron and from $\pm
2\delta$ for the muon mode up to $\pm 20\delta$, corresponding to the area
outside the red box and inside the blue one in the plots in Figure 2. The
$M_{\tau}$ and $\Delta E_{\tau}$ distributions in the sideband regions after
the final selections on data and simulation are shown in Figure 3. The
simulated samples are scaled to data luminosity and corrected for the
differences observed between data and simulation in particle identification
efficiencies. The numbers of expected background events from the simulation
are 7.4${}^{+1.1}_{-1.0}$ and 7.3${}^{+0.8}_{-0.7}$ for the electron and muon
modes, where the associated asymmetric errors are statistical; in data, we
observe 12.0${}^{+4.5}_{-3.4}$ and 9.0${}^{+4.1}_{-2.9}$ events, respectively.
This results in ratios between data and simulation of, respectively,
1.6${}^{+0.6}_{-0.5}$ and 1.2${}^{+0.5}_{-0.4}$, which shows a data and
simulation agreement compatible with unity.

Figure 3:  Comparison of the $M_{\tau}$ (left) and $\Delta E_{\tau}$ (right)
distributions in the sideband regions of data (the points with error bars) and
simulation (colored stacked histograms), for the $\tau^{-}\rightarrow
e^{-}\phi$ (top) and $\tau^{-}\rightarrow\mu^{-}\phi$ (bottom) channels, after
all selection requirements. Subpanel plots show the data to MC ratios,
consistent with unity within the uncertainties.

##  5 Yield extraction

We estimate the final yields in a Poisson-experiment approach by counting the
number of observed events in data inside the SR. To estimate the number of
expected background events $N_{\mathrm{exp}}$ inside the SR, we use the
$M_{\tau}$ sidebands within the $\pm 3(2)\delta$ $\Delta E_{\tau}$ band,
defined as reduced sidebands (RSB). Therefore, the expected background is

$N_{\mathrm{exp}}=N_{\mathrm{data}}\times r_{\mathrm{MC}}$ (2)

where $N_{\mathrm{data}}$ is the yield in the data inside the RSB regions and
$r_{MC}$ is the ratio measured on simulation between the events inside the
signal box and those retained in the RSB region.

The MC ratios are respectively $0.23^{+0.16}_{-0.10}$ and
$0.12^{+0.07}_{-0.04}$ for the electron and muon channels, where the
associated uncertainties are statistical only, since we assume that any
possible systematic contribution due to the simulation, reconstruction, or
selections cancel out in the computed ratio. Having observed one and three
events in the data RSB for the electron and muon modes, respectively, we
compute the expected background in the signal boxes to be 0.23 for the
electron mode and 0.36 for the muon mode. The results are summarized in Table
3. Figure 4 shows the remaining events in the ($M_{\tau}$, $\Delta E_{\tau}$)
plane for data and simulated samples after the final selections.

Table 3: Final selection efficiencies and yields on data and simulation for
specific regions of the ($M_{\tau}$, $\Delta E_{\tau}$) plane: the signal
regions (SR) and the reduced sidebands (RSB) for both channels. The expected
data yield in the SR $N_{\mathrm{exp}}$ is the product of the yield
$N_{\mathrm{data}}$ observed in the RSB and the MC background ratio
$r_{\mathrm{MC}}$. The final observed yields in the data SR are also reported
in the last row. Statistical (stat) and systematic (syst) uncertainties are
omitted wherever negligible.

Quantity Region Mode $e\phi$ $\mu\phi$ Signal efficiency
$\varepsilon_{\mathrm{\ell\phi}}$ SR (6.1 $\pm$ 0.9$\leavevmode\nobreak\
\mathrm{(syst)}$)% (6.5 $\pm$ 0.6$\leavevmode\nobreak\ \mathrm{(syst)}$)%
$r_{\mathrm{MC}}$ SR / RSB $0.23^{+0.16}_{-0.10}$ $\mathrm{(stat)}$
$0.12^{+0.07}_{-0.04}$ $\mathrm{(stat)}$ $N_{\mathrm{data}}$ RSB
1.0${}^{+2.3}_{-0.8}$ $\mathrm{(stat)}$ 3.0${}^{+2.9}_{-1.6}$
$\mathrm{(stat)}$ $N_{\mathrm{exp}}$ SR 0.23${}^{+0.55}_{-0.21}$
$\mathrm{(stat)}$ 0.36${}^{+0.39}_{-0.23}$ $\mathrm{(stat)}$
$N_{\mathrm{obs}}$ SR 2.0${}^{+2.6}_{-1.3}$ $\mathrm{(stat)}$
0.0${}^{+1.8}_{-0.0}$ $\mathrm{(stat)}$

Figure 4: Scatter plots of $\Delta E_{\tau}$ vs $M_{\tau}$ for simulated SM
background and data in the $\tau^{-}\rightarrow e^{-}\phi$ (left) and
$\tau^{-}\rightarrow\mu^{-}\phi$ (right) channels, after all selections. The
red squares represent the signal regions (SR), while the green lines delineate
the $\pm 3\delta$ ($e\phi$) or $\pm 2\delta$ ($\mu\phi$) $\Delta E_{\tau}$
band (RSB) used for estimating the expected number of events in the SR. The
RSB region is the area outside the red box and inside the green solid lines.

##  6 Upper limit computation

The 90% confidence level (C.L.) upper limits on the
$\tau^{-}\rightarrow\ell^{-}\phi$ branching fractions are computed as

$\mathcal{B}_{\mathrm{UL}}(\tau\to\ell\phi)=\frac{s}{L\times
2\sigma_{\tau\tau}\times\varepsilon_{\mathrm{\ell\phi}}},$ (3)

where $s$ is the corresponding 90% C.L. upper limit on
$N_{\mathrm{obs}}-N_{\mathrm{exp}}$, the difference between the observed and
expected data yields. The other inputs to Equation 3 are the integrated
luminosity $L=190\pm 1\leavevmode\nobreak\ \mathrm{fb^{-1}}$ of the analyzed
data sample; the $\tau$-pair production cross section
$\sigma_{\tau\tau}=0.919\pm 0.003\leavevmode\nobreak\ \mathrm{nb}$ and the
signal efficiency $\varepsilon_{\mathrm{\ell\phi}}$. The selection of a
specific final state for the $\phi$ candidate reconstructed as
$\phi\rightarrow K^{+}K^{-}$ is already included in the total signal
efficiency $\varepsilon_{\mathrm{\ell\phi}}$, as the simulated samples allow
for any possible known decays of the $\phi$. Therefore no normalization to
$\mathcal{B}(\phi\rightarrow K^{+}K^{-})$ is needed in Equation 3.

We estimate upper limits with the CLs [12, 13] method in a frequentist
approach implemented in the pyhf library [30, 31]. We generate $10000$ toys at
50 points distributed uniformly in the branching fraction range $(0-0.5\times
10^{-7})$. Results in Table 3 are taken as inputs to Equation 3 and used to
compute the branching fraction value at each scan point. The total statistical
and systematic uncertainties affecting each of the experimental inputs are
combined in quadrature. The total relative uncertainty on $L\times
2\sigma_{\tau\tau}\times\varepsilon_{\mathrm{\ell\phi}}$ is 15% for the
electron channel and 8.7% for the muon, as discussed in Section 7. The
dominant uncertainty on $N_{\mathrm{exp}}$ is statistical and is reported in
Table 3 for each analyzed channel. Figure 5 shows the $\mathrm{CL}_{s}$ curves
computed as a function of the upper limit on the branching fractions. The
dashed black line shows the expected $\mathrm{CL}_{s}$ and the green and
yellow bands give the $\pm 1\sigma$ and $\pm 2\sigma$ contours, respectively.
The expected limits for the $\tau^{-}\rightarrow e^{-}\phi$ and
$\tau^{-}\rightarrow\mu^{-}\phi$ modes are $15\times 10^{-8}$ and $9.9\times
10^{-8}$, respectively.

##  7 Systematic uncertainties

Systematic uncertainties arise from detector effects and differences between
data and simulation, due to possible mismodeling in the generation and
reconstruction of the simulated samples. A summary of considered systematic
uncertainties on each parameter entering the measurement is provided in Table
4.

Contributions to the systematic uncertainty on the total signal efficiency
arise from uncertainties is particle-identification performance, trigger
efficiency, track reconstruction efficiencies, and possible differences
between data and simulation in signal distributions of variables used in the
background-suppression selections.

Discrepancies in particle identification for leptons and charged hadrons
between data and simulation are measured in control samples and the derived
corrections are applied to the reconstructed events in simulation. The applied
corrections are then varied within their statistical and systematic
uncertainties, and the final selection efficiency for each configuration is
calculated. We assign the maximum relative difference with respect to the
nominal efficiency as the systematic contribution due to particle
identification. This corresponds to a relative uncertainty of 0.8% and 0.3%
for the electron and the muon modes, respectively.

The difference between data and simulation in the track-reconstruction
efficiency is measured with tau-pair events and yields a 0.3% systematic
uncertainty per track. We assign a relative uncertainty of 0.9% on the signal
efficiency due to tracking.

The trigger efficiencies in data and simulation agree to better than the 1%
level. We assign an uncertainty estimated from the signal simulation due to a
possible bias in the method to compare trigger efficiencies between data and
simulation. The absolute trigger efficiency, defined as the number of events
in signal simulation that meet the ECL trigger selections required for this
analysis divided by the total generated, cannot be measured directly in the
data. Only the efficiency relative to orthogonal trigger lines with respect to
those used for the signal selection can be accessed. The latter is calculated
as the fraction of events passing the ECL trigger selections among all events
selected by independent trigger selections based on CDC information. The
differences of the ratios of these two efficiencies from unity are assigned as
0.4% and 0.9% systematic uncertainties for the electron and muon modes,
respectively.

Potential differences in distributions between data and simulation of
variables used in the selection may lead to a systematic uncertainty affecting
the total signal efficiency. This is estimated from two control samples,
$D^{+}_{\mathrm{s}}\rightarrow\phi\pi^{+}$ and
$\tau^{-}\to\pi^{-}\pi^{+}\pi^{-}\nu_{\tau}$ to ensure the maximum kinematic
overlap with signal samples for the variables entering the BDT. Variables
showing the largest discrepancies between data and simulation are corrected
bin-by-bin using the control samples. We then retrain a BDT on the corrected
samples and recompute the signal efficiency. We assess the systematic
uncertainty as the difference with respect to the nominal efficiency values
quoted in Table 3. This procedure gives the largest contribution to the
estimated systematic uncertainty, that is 15.2% and 8.5% for the electron and
muon modes, respectively. To compensate for the imperfections of the magnetic-
field map used in the event reconstruction, misalignment of the detector, and
mismodeling in the density and type of detector and beam-pipe material, we
scale the charged-particle momenta by a correction factor, measured from the
shift observed in data on the invariant mass of $D^{0}$ relative to its known
value [28]. The corresponding systematic uncertainty is obtained by varying
the correction factor according to its uncertainty, which leads to different
data yields in the sideband region, and thus different numbers of expected
events $N_{\mathrm{exp}}$. The resulting systematic uncertainty, taken as the
difference with the nominal value, is 0.6% (0.4%) for the electron (muon)
mode. The systematic uncertainty on the integrated luminosity $L$, measured on
two samples of Bhabha and diphoton events [32], is evaluated from the
difference observed between the results from the two methods and amounts to
0.6% relative uncertainty. We also assign an uncertainty of 0.003 nb on the
$\tau$-pair production cross section at the c.m. energy of 10.58 GeV,
according to Ref. [33].

Table 4: Relative systematic uncertainties entering the upper limit computation as a function of the decay mode. Affected quantity |  Source |  Mode
---|---|---
$e\phi$ |  $\mu\phi$
$\varepsilon_{\mathrm{\ell\phi}}$ |  Particle identification |  0.8% |  0.3%
Tracking efficiency |  0.9%
Trigger efficiency |  0.4% |  0.9%
Signal variable mismodeling |  15.2% |  8.5%
$N_{\mathrm{exp}}$ |  Momentum scale |  0.6% |  0.4%
$L$ |  Luminosity |  0.6%
$\sigma_{\tau\tau}$ |  Tau-pair cross section |  0.3%

##  8 Results and conclusions

In 190 fb-1 data, after the final selections, we observe two and zero events
for the electron and muon channels, respectively, inside the $\pm 3\delta$ and
$\pm 2\delta$ signal regions, as shown in the scatter plots in Figure 4. Data
yields are compatible with expectations in Table 3. Figure 5 shows the
observed $\mathrm{CL}_{s}$ curves in agreement with the expected within the
yellow $\pm 2\sigma$ band. In the absence of any significant signal excess, we
determine the 90% C.L. upper limits on the branching fractions to be
$\mathcal{B}(\tau^{-}\rightarrow e^{-}\phi)$ < $23\times 10^{-8}$ and
$\mathcal{B}(\tau^{-}\rightarrow\mu^{-}\phi)$ < $9.7\times 10^{-8}$. In
contrast to the one-prong tag technique used by previous searches at Babar and
Belle, this analysis demonstrates the successful first application of the new
untagged approach, combined with a background suppression via BDT classifiers,
in the reconstruction of tau pairs events at Belle II. With this method, we
obtain twice the final signal efficiency for the muon mode.

Figure 5: Observed (solid black curve) and expected (dashed black curve)
$\mathrm{CL}_{s}$ as a function of the assumed branching fractions of
$\tau^{-}\rightarrow e^{-}\phi$ (top) and $\tau^{-}\rightarrow\mu^{-}\phi$
(bottom). The red lines correspond to the 90% C.L.s

## Acknowledgements

This work, based on data collected using the Belle II detector, which was
built and commissioned prior to March 2019, was supported by Science Committee
of the Republic of Armenia Grant No. 20TTCG-1C010; Australian Research Council
and research Grants No. DE220100462, No. DP180102629, No. DP170102389, No.
DP170102204, No. DP150103061, No. FT130100303, No. FT130100018, and No.
FT120100745; Austrian Federal Ministry of Education, Science and Research,
Austrian Science Fund No. P 31361-N36 and No. J4625-N, and Horizon 2020 ERC
Starting Grant No. 947006 “InterLeptons”; Natural Sciences and Engineering
Research Council of Canada, Compute Canada and CANARIE; Chinese Academy of
Sciences and research Grant No. QYZDJ-SSW-SLH011, National Natural Science
Foundation of China and research Grants No. 11521505, No. 11575017, No.
11675166, No. 11761141009, No. 11705209, and No. 11975076, LiaoNing
Revitalization Talents Program under Contract No. XLYC1807135, Shanghai
Pujiang Program under Grant No. 18PJ1401000, Shandong Provincial Natural
Science Foundation Project ZR2022JQ02, and the CAS Center for Excellence in
Particle Physics (CCEPP); the Ministry of Education, Youth, and Sports of the
Czech Republic under Contract No. LTT17020 and Charles University Grant No.
SVV 260448 and the Czech Science Foundation Grant No. 22-18469S; European
Research Council, Seventh Framework PIEF-GA-2013-622527, Horizon 2020 ERC-
Advanced Grants No. 267104 and No. 884719, Horizon 2020 ERC-Consolidator Grant
No. 819127, Horizon 2020 Marie Sklodowska-Curie Grant Agreement No. 700525
"NIOBE" and No. 101026516, and Horizon 2020 Marie Sklodowska-Curie RISE
project JENNIFER2 Grant Agreement No. 822070 (European grants); L’Institut
National de Physique Nucléaire et de Physique des Particules (IN2P3) du CNRS
(France); BMBF, DFG, HGF, MPG, and AvH Foundation (Germany); Department of
Atomic Energy under Project Identification No. RTI 4002 and Department of
Science and Technology (India); Israel Science Foundation Grant No. 2476/17,
U.S.-Israel Binational Science Foundation Grant No. 2016113, and Israel
Ministry of Science Grant No. 3-16543; Istituto Nazionale di Fisica Nucleare
and the research grants BELLE2; Japan Society for the Promotion of Science,
Grant-in-Aid for Scientific Research Grants No. 16H03968, No. 16H03993, No.
16H06492, No. 16K05323, No. 17H01133, No. 17H05405, No. 18K03621, No.
18H03710, No. 18H05226, No. 19H00682, No. 22H00144, No. 26220706, and No.
26400255, the National Institute of Informatics, and Science Information
NETwork 5 (SINET5), and the Ministry of Education, Culture, Sports, Science,
and Technology (MEXT) of Japan; National Research Foundation (NRF) of Korea
Grants No. 2016R1D1A1B02012900, No. 2018R1A2B3003643, No. 2018R1A6A1A06024970,
No. 2018R1D1A1B07047294, No. 2019R1I1A3A01058933, No. 2022R1A2C1003993, and
No. RS-2022-00197659, Radiation Science Research Institute, Foreign Large-size
Research Facility Application Supporting project, the Global Science
Experimental Data Hub Center of the Korea Institute of Science and Technology
Information and KREONET/GLORIAD; Universiti Malaya RU grant, Akademi Sains
Malaysia, and Ministry of Education Malaysia; Frontiers of Science Program
Contracts No. FOINS-296, No. CB-221329, No. CB-236394, No. CB-254409, and No.
CB-180023, and No. SEP-CINVESTAV research Grant No. 237 (Mexico); the Polish
Ministry of Science and Higher Education and the National Science Center; the
Ministry of Science and Higher Education of the Russian Federation, Agreement
No. 14.W03.31.0026, and the HSE University Basic Research Program, Moscow;
University of Tabuk research Grants No. S-0256-1438 and No. S-0280-1439 (Saudi
Arabia); Slovenian Research Agency and research Grants No. J1-9124 and No.
P1-0135; Agencia Estatal de Investigacion, Spain Grant No. RYC2020-029875-I
and Generalitat Valenciana, Spain Grant No. CIDEGENT/2018/020 Ministry of
Science and Technology and research Grants No. MOST106-2112-M-002-005-MY3 and
No. MOST107-2119-M-002-035-MY3, and the Ministry of Education (Taiwan);
Thailand Center of Excellence in Physics; TUBITAK ULAKBIM (Turkey); National
Research Foundation of Ukraine, project No. 2020.02/0257, and Ministry of
Education and Science of Ukraine; the U.S. National Science Foundation and
research Grants No. PHY-1913789 and No. PHY-2111604, and the U.S. Department
of Energy and research Awards No. DE-AC06-76RLO1830, No. DE-SC0007983, No. DE-
SC0009824, No. DE-SC0009973, No. DE-SC0010007, No. DE-SC0010073, No. DE-
SC0010118, No. DE-SC0010504, No. DE-SC0011784, No. DE-SC0012704, No. DE-
SC0019230, No. DE-SC0021274, No. DE-SC0022350; and the Vietnam Academy of
Science and Technology (VAST) under Grant No. DL0000.05/21-23.

These acknowledgements are not to be interpreted as an endorsement of any
statement made by any of our institutes, funding agencies, governments, or
their representatives.

We thank the SuperKEKB team for delivering high-luminosity collisions; the KEK
cryogenics group for the efficient operation of the detector solenoid magnet;
the KEK computer group and the NII for on-site computing support and SINET6
network support; and the raw-data centers at BNL, DESY, GridKa, IN2P3, INFN,
and the University of Victoria for offsite computing support.

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