[a]Sezen Sekmen, for the CMS Collaboration

# Digging deeper into SUSY parameter space with the CMS experiment

###### Abstract

The classic searches for supersymmetry have not given any strong indication
for new physics. Therefore CMS is designing dedicated searches to target the
more difficult and specific supersymmetry scenarios. This contribution present
three such recent searches based on 13 TeV proton-proton collisions recorded
with the CMS detector in 2016, 2017 and 2018: a search for heavy gluinos
cascading via heavy next-to-lightest neutralino in final states with boosted Z
bosons and missing transverse momentum; a search for compressed supersymmetry
in final states with soft taus; and a search for compressed, long-lived
charginos in hadronic final states with disappearing tracks.

The Compact Muon Solenoid (CMS) Experiment [1] at the Large Hadron Collider
(LHC) has collected an unprecedented 137 fb-1of data with proton-proton
collisions at a center-of-mass energy of 13 TeV, which is continuously
explored for traces of supersymmetry in a wide variety of searches. As of
2020, classical searches, such as those looking for gluinos and squarks in
inclusive SUSY final states with a large number of search bins, looking for
top squarks in hadronic, single lepton or dilepton final states, or looking
for charginos or neutralinos in single lepton, dilepton or trilepton final
states have not yet observed a deviation from the standard model (SM), and
excluded parts of the SUSY parameter space. However, SUSY can still be
realized in many alternative well-motivated ways in hidden, remote corners of
the vast, multi-dimensional SUSY parameter space, to which the more standard
and inclusive searches may not be sensitive. Nowadays, CMS is enriching its
physics program by an increasing diversity of dedicated searches to probe such
corners and enhance the chances of discovery.

One example of a special scenario with a final state difficult to observe is
that of a compressed mass spectrum where masses of two accessible SUSY
partners are very close to each other. Here, decays of the heavier particle
lead to final states with low momentum (soft) objects and low missing
transverse momentum. Such final states are explored by searches that use soft
objects and a high momentum initial state radiation jet. Another consequence
of compressed spectra can be long-lived particles, for which an increasing
number of searches are being developed. On the opposite end, there are
scenarios with high mass SUSY partners and high mass differences, for which
several searches featuring objects with high Lorentz boost, leading to merged
decay products, and thus substructure, are being designed. Moreoever, there
are dedicated searches for direct production of sleptons or staus, which are
hard to access due to low cross sections and challenges in triggering. Cascade
decays with Higgs boson are also explored by explicitly reconstructing the
Higgs boson and incorporating it into multi-object SUSY final states.
Additionally, signatures with special combinations of objects predicted by
certain SUSY scenarios, such as $\gamma+b$ jets or $\gamma+$ lepton are
investigated. Besides all these searches, which are mainly targeting
$R$-parity conserving models, a whole suite of analyses targeting variations
of $R$-parity violating SUSY scenarios exist or are in progress. This
contribution presents 3 examples of recent non-classical SUSY searches based
on CMS data collected in 2016, 2017 and 2018, aiming to dig deeper into the
SUSY parameter space.

Boosted $ZZ+p_{T}^{miss}$ search:  The first search is targeting a scenario
motivated by naturalness, where pair-produced gluinos with $\sim$2-3 TeV mass
decay cascading via a massive $\tilde{\chi}^{0}_{2}$ to a light
$\tilde{\chi}^{0}_{1}$ and a $Z$ boson [2]. The large mass difference between
$\tilde{\chi}^{0}_{2}$ and $\tilde{\chi}^{0}_{1}$ give the $Z$ bosons a large
Lorentz boost. The signature for a boosted $Z$ boson candidate is a wide-cone
jet having a measured mass compatible with the $Z$ boson mass. The analysis,
performed on 137 fb-1 of 13 TeV data, selects events with 0 leptons, $\geq 2$
$Z$ bosons, $\geq 2$ jets, missing transverse momentum $p_{T}^{miss}>300$ GeV
and hadronic transverse momentum $H_{T}>400$ GeV. The $Z$ boson candidates are
selected among anti-$k_{T}$ jets with a size parameter of 0.8 (AK8 jets), and
are required to have $p_{T}>200$ GeV and a mass of $40$ GeV$<m_{AK8jet}<140$
GeV. The 2nd highest $p_{T}$ $Z$ boson should be separated from any $b$-jet by
an angular distance of $\Delta R(Z_{2},b)>0.8$ to eliminate backgrounds.

The dominant SM background in this final state is the
$Z(\rightarrow\nu\nu)+$jets process. SM backgrounds are estimated directly
from data, in control regions defined using the masses of the $Z$ candidate
jets as seen in Figure 1, top left. The mass sideband control regions are used
to fit the leading AK8 jet mass distribution for estimating the background
normalization integrated over $p_{T}^{miss}$, as seen in Figure 1, top right.
The $p_{T}^{miss}$ control region is used to derive the $p_{T}^{miss}$ shape,
based on the assumption that jet mass and $p_{T}^{miss}$ have minimal
correlation.

The estimated background yields are shown as a function of $p_{T}^{miss}$ and
compared to data, as shown in Figure 1, bottom left. No excess over the SM
expectation is observed. The results are interpreted using a simplified SUSY
model of gluino pair production in which the gluino decays to a low momentum
quark pair and $\tilde{\chi}^{0}_{2}$, and $\tilde{\chi}^{0}_{2}$ decays to a
boosted $Z+\tilde{\chi}^{0}_{1}$, where
$m_{\tilde{g}}-m_{\tilde{\chi}^{0}_{2}}=50$ GeV and
$m_{\tilde{\chi}^{0}_{1}}=1$ GeV, as shown in Figure 1, bottom right. For this
scenario, data exclude gluino masses below 1920 GeV at 95% confidence level.

Figure 1: Definition of the search and control regions in the plane of
subleading vs. leading jet mass (top left), leading AK8 jet mass shape fit in
the mass sidebands (top right), observed data and background prediction as
functions of $p_{T}^{miss}$ (bottom left), and the 95% CL upper limit on the
production cross section for the gluino signal model as a function of the
gluino mass (bottom right) in the boosted $ZZ+p_{T}^{miss}$ search [2].

Compressed SUSY search with soft taus:  The second search targets directly or
indirectly produced staus with low $m_{\tilde{\tau}}-m_{\tilde{\chi}^{0}_{1}}$
($<50$ GeV), a compressed case favored by dark matter coannihilation
scenarios, where the coannihilation between the stau and the lightest
neutralino can generate the observed relic density. It is the first LHC search
for a signature of one soft, hadronically decaying $\tau$ lepton ($\tau_{h}$),
one energetic jet from initial-state radiation (ISR), and large transverse
momentum imbalance [3]. The search, using 77 fb-1 of 13 TeV data, selects
events having exactly one $\tau_{h}$ with $20<p_{T}(\tau_{h})<40$ GeV, an ISR
jet with $p_{T}>100$ GeV, $p_{T}^{miss}>230$ GeV, angular separation between
the ISR jet and $p_{T}^{miss}$ $\Delta R(j_{ISR},p_{T}^{miss})>0.7$ and zero
$b$-jets. The analysis looks for an excess in the distribution of $\tau$
transverse mass
$m_{T}(\tau_{h},p_{T}^{miss})=\sqrt{2p_{T}^{miss}p_{T}(\tau_{h})(1-\cos\Delta\phi(\vec{p}_{T}^{miss},\tau_{h}))}$.

The dominant SM backgrounds are $tt+$jets and $W/Z+$jets. Their $m_{T}$ shapes
are estimated from control regions and yields are extrapolated from
simulation. Data-simulation agreement in control regions is used to validate
the modeling of the $\tau_{h}$ selections and to measure data-tosimulation
scale factors to correct ISR jet and the $p_{T}^{miss}$ modeling. For QCD
multijet backgrounds, both $m_{T}$ shape and yields are estimated from data
control regions. The resulting $m_{T}$ distribution is shown in Figure 2, top,
where data are seen to be consistent with the SM. Figure 2 (bottom left) shows
the interpretation of this result in a simplified SUSY model of
$\tilde{\chi}^{0}_{2}\tilde{\chi}^{\pm}_{1}/\tilde{\chi}_{1}^{+}\tilde{\chi}_{1}^{-}$
production. For 100% wino $\tilde{\chi}^{0}_{2}/\chi_{1}$,
$m_{\tilde{\chi}^{\pm}_{1}}-m_{\tilde{\chi}^{0}_{1}}=50$ GeV,
$m_{\tilde{\tau}}=\frac{1}{2}(m_{\tilde{\chi}^{\pm}_{1}}+m_{\tilde{\chi}^{0}_{1}})$
and
BR($\tilde{\chi}^{\pm}_{1}\rightarrow\tilde{\tau}\nu_{\tau}\rightarrow\tau\tilde{\chi}^{0}_{1}\nu_{\tau})=100\%$,
$\tilde{\chi}^{0}_{2}/\tilde{\chi}^{\pm}_{1}$ masses up to 290 GeV are
excluded at 95% confidence level. This sensitivity exceeds that of all other
searches to date, including the LEP exclusion of $m_{\chi_{1}}>103.5$ GeV in
compressed scenarios [4]. Figure 2, bottom right shows the ratio of the 95% CL
upper limit on the direct $\tilde{\tau}$ production signal cross section to
the theoretical cross section as a function of $m_{\tilde{\tau}}$ and $\Delta
m(\tilde{\tau},\tilde{\chi}^{0}_{1})$. No sensitivity is achieved to direct
stau pair production yet.

Figure 2: The $m_{T}$ distribution of data, background prediction and signal
benchmarks in the signal region (top); the 95% CL upper limits on the
$\tilde{\chi}^{0}_{2}\tilde{\chi}^{\pm}_{1}/\tilde{\chi}_{1}^{+}\tilde{\chi}_{1}^{-}$
production cross sections as a function of $m(\tilde{\chi}_{1}^{\pm})$ (bottom
left); and ratio of the 95% CL upper limit on the direct $\tilde{\tau}$ pair
production cross section to the theory prediction as function of
$m(\tilde{\tau})$ and $\Delta m(\tilde{\tau},\tilde{\chi}_{0}^{1})$ (bottom
right) in the compressed SUSY search with soft taus [3].

Disappearing track search using $M_{T2}$:  For compressed SUSY with
$m_{\tilde{\chi}^{\pm}_{1}}-m_{\tilde{\chi}^{0}_{1}}\sim O(100~{}MeV)$,
$\tilde{\chi}^{\pm}_{1}$ is long lived. It would decay in the CMS tracker to a
soft, undetectable pion and a $\tilde{\chi}^{0}_{1}$. This would lead to a
disappearing track $+E_{T}^{miss}$ signature. The final search presented here
looks in 137 fb-1 of 13 TeV data for such compressed charginos in gluino or
squark decays by extending the classical inclusive hadronic search based on
the stransverse mass variable $M_{T2}$ with final states consisting of
disappearing tracks (DTs) and at least 2 jets and $M_{T2}>200$ GeV [5]. The
search explores categories of short and medium/long DT selections, which
consist of hits in the pixel or pixel $+$ strip tracking detectors of CMS,
respectively, in order to search for a wide range of lifetimes. Including DTs
in the search gives a possibility to loosen kinematic requirements without
accumulating large amounts of backgrounds. For instance, the $M_{T2}$
requirement is reduced from 400 to 200 GeV. The analysis categorizes events in
68 search bins defined in jet multiplicity, hadronic transverse momentum
$H_{T}$, DT length and DT $p_{T}$. Main sources of backgrounds are hadrons and
leptons poorly reconstructed in the tracker and tracks built out of incorrect
combinations of hits. They are estimated by calculating fake rates in data
control regions and applying these fake rates to DT candidates.

Figure 3: Exclusion limits at 95% CL for direct gluino pair production where
the gluinos decay to light-flavor quarks (top left), light squark pair
production (top center), and top squark pair production (top right) with
$c\tau_{0}(\tilde{\chi}^{\pm}_{1})=50$ cm. Exclusion limits on
$m_{\tilde{\chi}^{0}_{1}}$ with
$m_{\tilde{\chi}^{\pm}_{1}}=m_{\tilde{\chi}^{0}_{1}}+O(100MeV)$ as a function
of $\tilde{\chi}^{\pm}_{1}$ proper decay length for gluino pair production
with $m_{\tilde{g}}=1900$ GeV (bottom left), squark pair production with
$m_{\tilde{q}}=1500$ GeV (bottom center), and top squark pair production with
$m_{\tilde{t}}=1000$ GeV (bottom right) in the disappearing track search using
$M_{T2}$ [5].

The search found no deviation in data from the SM expectation. Figure 3 shows
the interpretation of the search results in various simplified SUSY models.
The top row shows exclusion limits at 95% CL for direct gluino pair production
where the gluinos decay to light-flavor (u, d, s, c) quarks (top left), light
squark pair production (top center), and top squark pair production (top
right) for $c\tau_{0}(\tilde{\chi}^{\pm}_{1})=50$ cm. Extending the inclusive
$M_{T2}$ search with disappearing tracks increased $m_{\tilde{g}}$ reach from
$\sim$2 to $2.46$ TeV and $m_{\tilde{\chi}^{0}_{1}}$ reach from $\sim$1.2 to
$\sim$2 TeV for gluino pair production; $m_{\tilde{q}}$ reach from $\sim$1.8
to $\sim$2.1 TeV and $m_{\tilde{\chi}^{0}_{1}}$ reach from $\sim$0.8 to
$\sim$1.6 TeV for squark pair production, and $m_{\tilde{t}}$ reach from
$\sim$1.2 to 1.65 TeV and $m_{\tilde{\chi}^{0}_{1}}$ reach from $\sim$0.55 to
$\sim$1.25 TeV for stop pair production. In all cases, sensitivity in the
compressed region was significantly improved. The bottom row in Figure 3 shows
exclusion limits versus chargino decay length for selected gluino, squark and
stop masses.

In summary, 3 recent examples of dedicated CMS SUSY searches targeting
specific scenarios and exclusive signatures were presented, namely, a boosted
$ZZ+p_{T}^{miss}$ search, which extended the gluino mass reach to 1.9 TeV for
$m_{\tilde{g}}-m_{\tilde{\chi}^{0}_{2}}=50$ GeV; a soft hadronic
$\tau+p_{T}^{miss}+$ISR jet search for compressed staus motivated by dark
matter coannihilation models, which obtained a sensitivity for charginos
extending the LEP limits; and a search that added regions with disappearing
tracks to the inclusive hadronic $M_{T2}$ search, which increased gluino and
squark mass limits by 400-600 GeV and significantly improved sensitivity in
the compressed region. Other searches dedicated to specific final states have
been performed earlier, such as the search for $H\rightarrow gg$ using razor
and $M_{T2}$ variables [6]; searches for hadronic and semileptonic staus [7,
8]; $E_{T}^{miss}$ and boosted Higgs to $bb$ [9]; SUSY in vector boson fusion
channels [10]; RPV smuons [11]; selectrons and smuons [12]; the searches in
diphoton and $E_{T}^{miss}$ final states [13], $b$ jets and photons final
states [14], and photon, lepton and $E_{T}^{miss}$ final states [15]. More
searches are ongoing for soft opposite-sign 2 lepton signatures and steath and
RPV stops.

Acknowledgements:  I would like to thank my colleagues in the CMS
Collaboration for their hard work in producing the results in this
contribution, and to the organizers of ICHEP 2020 for their efforts in
realizing this important conference virtually during the difficult Covid-19
period.

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# Observation of the helicity-selection-rule suppressed decay of the
$\chi_{c2}$ charmonium state

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Zhu39, Y. C. Zhu46,a, Y. S. Zhu1, Z. A. Zhu1, J. Zhuang1,a, L. Zotti49A,49C,
B. S. Zou1, J. H. Zou1 (BESIII Collaboration) 1 Institute of High Energy
Physics, Beijing 100049, People’s Republic of China
2 Beihang University, Beijing 100191, People’s Republic of China
3 Beijing Institute of Petrochemical Technology, Beijing 102617, People’s
Republic of China
4 Bochum Ruhr-University, D-44780 Bochum, Germany
5 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
6 Central China Normal University, Wuhan 430079, People’s Republic of China
7 China Center of Advanced Science and Technology, Beijing 100190, People’s
Republic of China
8 COMSATS Institute of Information Technology, Lahore, Defence Road, Off
Raiwind Road, 54000 Lahore, Pakistan
9 G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090,
Russia
10 GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
11 Guangxi Normal University, Guilin 541004, People’s Republic of China
12 Guangxi University, Nanning 530004, People’s Republic of China
13 Hangzhou Normal University, Hangzhou 310036, People’s Republic of China
14 Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz,
Germany
15 Henan Normal University, Xinxiang 453007, People’s Republic of China
16 Henan University of Science and Technology, Luoyang 471003, People’s
Republic of China
17 Huangshan College, Huangshan 245000, People’s Republic of China
18 Hunan University, Changsha 410082, People’s Republic of China
19 Indiana University, Bloomington, Indiana 47405, USA
20 (A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy; (B)INFN
and University of Perugia, I-06100, Perugia, Italy
21 (A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of
Ferrara, I-44122, Ferrara, Italy
22 Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45,
D-55099 Mainz, Germany
23 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
24 Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-
Buff-Ring 16, D-35392 Giessen, Germany
25 KVI-CART, University of Groningen, NL-9747 AA Groningen, The Netherlands
26 Lanzhou University, Lanzhou 730000, People’s Republic of China
27 Liaoning University, Shenyang 110036, People’s Republic of China
28 Nanjing Normal University, Nanjing 210023, People’s Republic of China
29 Nanjing University, Nanjing 210093, People’s Republic of China
30 Nankai University, Tianjin 300071, People’s Republic of China
31 Peking University, Beijing 100871, People’s Republic of China
32 Seoul National University, Seoul, 151-747 Korea
33 Shandong University, Jinan 250100, People’s Republic of China
34 Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
35 Shanxi University, Taiyuan 030006, People’s Republic of China
36 Sichuan University, Chengdu 610064, People’s Republic of China
37 Soochow University, Suzhou 215006, People’s Republic of China
38 Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
39 Tsinghua University, Beijing 100084, People’s Republic of China
40 (A)Ankara University, 06100 Tandogan, Ankara, Turkey; (B)Istanbul Bilgi
University, 34060 Eyup, Istanbul, Turkey; (C)Uludag University, 16059 Bursa,
Turkey; (D)Near East University, Nicosia, North Cyprus, Mersin 10, Turkey
41 University of Chinese Academy of Sciences, Beijing 100049, People’s
Republic of China
42 University of Hawaii, Honolulu, Hawaii 96822, USA
43 University of Minnesota, Minneapolis, Minnesota 55455, USA
44 University of Rochester, Rochester, New York 14627, USA
45 University of Science and Technology Liaoning, Anshan 114051, People’s
Republic of China
46 University of Science and Technology of China, Hefei 230026, People’s
Republic of China
47 University of South China, Hengyang 421001, People’s Republic of China
48 University of the Punjab, Lahore-54590, Pakistan
49 (A)University of Turin, I-10125, Turin, Italy; (B)University of Eastern
Piedmont, I-15121, Alessandria, Italy; (C)INFN, I-10125, Turin, Italy
50 Uppsala University, Box 516, SE-75120 Uppsala, Sweden
51 Wuhan University, Wuhan 430072, People’s Republic of China
52 Zhejiang University, Hangzhou 310027, People’s Republic of China
53 Zhengzhou University, Zhengzhou 450001, People’s Republic of China
a Also at State Key Laboratory of Particle Detection and Electronics, Beijing
100049, Hefei 230026, People’s Republic of China
b Also at Bogazici University, 34342 Istanbul, Turkey
c Also at the Moscow Institute of Physics and Technology, Moscow 141700,
Russia
d Also at the Functional Electronics Laboratory, Tomsk State University,
Tomsk, 634050, Russia
e Also at the Novosibirsk State University, Novosibirsk, 630090, Russia
f Also at the NRC ”Kurchatov Institute”, PNPI, 188300, Gatchina, Russia
g Also at University of Texas at Dallas, Richardson, Texas 75083, USA
h Also at Istanbul Arel University, 34295 Istanbul, Turkey
i Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany
j Also at Key Laboratory for Particle Physics, Astrophysics and Cosmology,
Ministry of Education; Shanghai Key Laboratory for Particle Physics and
Cosmology; Institute of Nuclear and Particle Physics, Shanghai 200240,
People’s Republic of China

###### Abstract

The decays of $\chi_{c2}\to K^{+}K^{-}\pi^{0}$, $K_{S}K^{\pm}\pi^{\mp}$ and
$\pi^{+}\pi^{-}\pi^{0}$ are studied with the $\psi(3686)$ data samples
collected with the Beijing Spectrometer (BESIII). For the first time, the
branching fractions of $\chi_{c2}\to K^{\ast}\overline{K}$, $\chi_{c2}\to
a_{2}^{\pm}(1320)\pi^{\mp}/a_{2}^{0}(1320)\pi^{0}$ and
$\chi_{c2}\to\rho(770)^{\pm}\pi^{\mp}$ are measured. Here
$K^{\ast}\overline{K}$ denotes both $K^{\ast\pm}K^{\mp}$ and its isospin-
conjugated process $K^{\ast 0}\overline{K}{}^{0}+\rm{c.c.}$, and $K^{\ast}$
denotes the resonances $K^{\ast}(892)$, $K^{\ast}_{2}(1430)$ and
$K^{\ast}_{3}(1780)$. The observations indicate a strong violation of the
helicity selection rule in $\chi_{c2}$ decays into vector and pseudoscalar
meson pairs. The measured branching fractions of $\chi_{c2}\to
K^{\ast}(892)\overline{K}$ are more than 10 times larger than the upper limit
of $\chi_{c2}\to\rho(770)^{\pm}\pi^{\mp}$, which is so far the first direct
observation of a significant $U$-spin symmetry breaking effect in charmonium
decays.

###### pacs:

13.25.Gv, 12.38.Qk

The helicity selection rule (HSR) Brodsky:1981kj ; Chernyak:1981zz ;
Chernyak:1983ej  is one of the most important consequences of perturbative
quantum chromodynamics (pQCD) at leading twist accuracy. In the charmonium
energy region, although there are observations that pQCD plays a dominant
role, there are also many hints that non-perturbative mechanisms can become
important Chernyak:1983ej ; nonpqcd1 ; nonpqcd2 ; nonpqcd3 . Exclusive decays
of the $P$-wave charmonium state $\chi_{c2}\to VP$, where $V$ and $P$ denote
light vector and pseudoscalar mesons, respectively, are ideal for testing the
HSR and pinning down the mechanisms that may violate the leading pQCD
approximation.

Another reason the decays of $\chi_{c2}\to VP$ are of great interest is that
this process is ideal for probing the long-range interactions arising from
intermediate $D$-meson loop transitions. As pointed out in Ref. zhaoq , if the
intermediate $D$-meson loops provide the non-perturbative mechanism to violate
the HSR, this can be identified by the measurements of $\chi_{c2}\to
K^{\ast}(892)\overline{K}$ and $\chi_{c2}\to\rho(770)^{\pm}\pi^{\mp}$.

In this Letter, we present a partial wave analysis (PWA) of the process
$\chi_{c2}\to K\overline{K}\pi$ (denotes $K^{+}K^{-}\pi^{0}$ and
$K_{S}K^{\pm}\pi^{\mp}$) and a measurement of
$\chi_{c2}\to\pi^{+}\pi^{-}\pi^{0}$. We have two $\psi(3686)$ samples of
$(106.8\pm 0.8)\times 10^{6}$ (160 pb-1) wang  and $(341.1\pm 2.1)\times
10^{6}$ (510 pb-1) wang1  events collected in 2009 and 2012 by BESIII bes3 ,
respectively. Only the 2009 data sample is used in the analysis of
$\chi_{c2}\to K\overline{K}\pi$, and the full data sample is used in
$\chi_{c2}\to\pi^{+}\pi^{-}\pi^{0}$ since it has a smaller branching fraction.
An independent sample of about 44 pb-1 taken at $\sqrt{s}=3.65$ GeV is
utilized to investigate the potential background from the continuum process. A
sample of Monte Carlo (MC) simulated events of generic $\psi(3686)$ decays
(inclusive MC sample) is used to study backgrounds. The optimization of the
event selection and the estimation of physics backgrounds are performed with
Monte Carlo simulations of $\psi(3686)$ inclusive/exclusive decays.

The $\chi_{c2}$ candidates, produced in $\psi(3686)$ radiative decays, are
reconstructed from the final states $K^{+}K^{-}\pi^{0}$,
$K_{S}K^{\pm}\pi^{\mp}$, and $\pi^{+}\pi^{-}\pi^{0}$. Each charged track is
required to have a polar angle $\theta$ in the main drift chamber (MDC) that
satisfies $|\cos\theta|<0.93$, and have the point of closest approach to the
$e^{+}e^{-}$ interaction point within 10 cm in the beam direction ($|V_{z}|$),
and 1 cm in the plane perpendicular to the beam direction ($V_{r}$). The
energy loss $dE/dx$ in the MDC and the information from the time-of-flight
(TOF) system are combined to form particle identification (PID) confidence
levels (C.L.) for the $\pi,~{}K$, and $p$ hypotheses, and each track is
assigned with the hypothesis corresponding to the highest C.L. The $K_{S}$
candidates are reconstructed from two oppositely charged tracks with loose
vertex requirements ($|V_{z}|<30$ cm and $V_{r}<10$ cm) and without PID
(assumed to be pions). Then the candidate with invariant mass closest to the
$K_{S}$ nominal mass and the decay length provided by a secondary vertex fit
algorithm greater than 0.25 cm, is selected for further study in the decay
$\psi(3686)\to\gamma K_{S}K^{\pm}\pi^{\mp}$. The candidate events are required
to have two charged tracks with zero net charge, where the tracks from the
$K_{S}$ candidate are not taken into account. Two pions and one kaon are
required for the decays $\psi(3686)\to\gamma\pi^{+}\pi^{-}\pi^{0}$ and
$\psi(3686)\to\gamma K_{S}K^{\pm}\pi^{\mp}$, respectively, and no PID
requirement is applied for the decay $\psi(3686)\to\gamma K^{+}K^{-}\pi^{0}$.
The photon candidates are required to have energy larger than 25 (50) MeV in
the Electromagnetic Calorimeter (EMC) barrel (end cap) region
$|\cos\theta|<0.8$ ($0.86<|\cos\theta|<0.93$), and have an angle relative to
the nearest charged tracks larger than $10^{\circ}$. To suppress electronic
noise and energy deposits unrelated to the event, the EMC cluster time must be
within 700 ns from the event start time. At least three and one photons are
required for the decay
$\psi(3686)\to\gamma\pi^{+}\pi^{-}\pi^{0}$/$K^{+}K^{-}\pi^{0}$ and
$\psi(3686)\to\gamma K_{S}K^{\pm}\pi^{\mp}$, respectively.

A fit with four kinematic constraints (4C) enforcing four-momentum
conservation between the initial $\psi(3686)$ and the final state is performed
for each process. If there are more photons than required in one event, all
possible combinations of photons are considered and only the one with the
least $\chi_{4C}^{2}$ of the kinematic fit is retained for further analysis.
The $\chi_{4C}^{2}$ is required to be less than 80 and 60 for the decay
$\psi(3686)\to\gamma K^{+}K^{-}\pi^{0}$ and $\psi(3686)\to\gamma
K_{S}K^{\pm}\pi^{\mp}$, respectively. The $\pi^{0}$ candidate is reconstructed
from the two selected photons whose invariant mass is closest to the $\pi^{0}$
nominal mass, and satisfies
$|M_{\gamma\gamma}-M_{\pi^{0}}|<10~{}\,\mathrm{MeV}/c^{2}$. For the decay mode
$\psi(3686)\to\gamma\pi^{+}\pi^{-}\pi^{0}$, a 5C kinematic fit is performed
with an additional $\pi^{0}$ mass constraint, and $\chi^{2}_{5C}<60$ is
required. To remove the backgrounds $\psi(3686)\to\pi^{0}\pi^{0}J/\psi$
($J/\psi\to l^{+}l^{-}$, $l=e,\mu$), the invariant mass of
$K^{+}K^{-}$/$\pi^{+}\pi^{-}$ is required to be less than 3.0
$\,\mathrm{GeV}/c^{2}$ for the decay $\psi(3686)\to\gamma
K^{+}K^{-}\pi^{0}/\gamma\pi^{+}\pi^{-}\pi^{0}$. In the decay mode
$\psi(3686)\to\gamma\pi^{+}\pi^{-}\pi^{0}$, the $\pi^{0}$ recoil mass is
required to be less than 3.0 $\,\mathrm{GeV}/c^{2}$ to suppress the background
$\psi(3686)\to\pi^{0}J/\psi$, and
$M_{\gamma\pi^{0}}\not\in(0.7,0.85)~{}\,\mathrm{GeV}/c^{2}$ is required to
veto the background $\psi(3686)\to\omega\pi^{+}\pi^{-}$
($\omega\to\gamma\pi^{0}$).

The $K\overline{K}\pi$ invariant mass for the decay $\psi(3686)\to\gamma
K^{+}K^{-}\pi^{0}$ and $\psi(3686)\to\gamma K_{S}K^{\pm}\pi^{\mp}$ are shown
in Fig. 1(a) and (b), respectively. The $\chi_{c1,2}$ signals appear
prominently with a small background. From the analysis of the $\psi(3686)$
inclusive MC sample and the continuum data at $\sqrt{s}=3.65$ GeV, the main
backgrounds are from the decays $\psi(3686)\to\pi^{0}\pi^{0}J/\psi$
($J/\psi\to\pi^{+}\pi^{-}\pi^{0}/\mu\mu$), and $\psi(3686)\to
K_{1}(1270)^{\pm}K^{\mp}$ ($K_{1}(1270)^{\pm}\to
K^{\pm}\pi^{0}\pi^{0}/\rho(770)^{\pm}K_{S}$). All of these backgrounds show a
smooth distribution, and do not produce a peak around the $\chi_{cJ}$ mass
region. Unbinned maximum likelihood fits are performed to the selected
candidates, where the $\chi_{c1,2}$ signals are described with the MC
simulated shapes convoluted with a Gaussian function accounting for the
resolution difference between data and MC simulation, and the backgrounds are
described with a $2^{nd}$ order polynomial function. There are 1215 and 1176
candidate events for $\chi_{c2}\to K^{+}K^{-}\pi^{0}$ and $\chi_{c2}\to
K_{S}K^{\pm}\pi^{\mp}$ within the $\chi_{c2}$ signal region
$|M_{K\overline{K}\pi}-M_{\chi_{c2}}|\leq 15~{}\,\mathrm{MeV}/c^{2}$.
Non-$\pi^{0}$ ($K^{+}K^{-}\pi^{0}$ mode only) and non-$\chi_{c2}$ backgrounds
are estimated with the events in the sideband regions, which are also used in
the PWA as described in the following. The numbers of background events are
estimated to be 240 and 80 for $\chi_{c2}\to K^{+}K^{-}\pi^{0}$ and
$\chi_{c2}\to K_{S}K^{\pm}\pi^{\mp}$, respectively.

Figure 1: (color online) Invariant mass distribution of (a)
$K^{+}K^{-}\pi^{0}$ and (b) $K_{S}K^{\pm}\pi^{\mp}$ for the decay
$\psi(3686)\to\gamma K\overline{K}\pi$, and the corresponding Dalitz
distributions (c) and (d) for the candidates within
$|M_{KK\pi}-M_{\chi_{c2}}|<15$ $\,\mathrm{MeV}/c^{2}$. The dots with error
bars are for data, the blue solid curves are the overall fit results, the red
dotted curves are the signals, and the green shaded areas are the background.

In the PWA, the process $\chi_{c2}\to K\overline{K}\pi$ is assumed to proceed
via the quasi two-body decays, i.e. $\chi_{c2}\to a_{2}\pi$ and
$K^{*}\overline{K}$ followed by $a_{2}\to K\overline{K}$ and $K^{*}\to K\pi$.
The amplitudes of the two-body decays are constructed with the helicity-
covariant method chung . For a particle decaying into two-body final states,
i.e. $A(J,m)\to B(s,\lambda)C(\sigma,\nu)$, where spin and helicity are
indicated in the parentheses, its helicity covariant amplitude
$F_{\lambda,\nu}$ chung  is:

$F_{\lambda,\nu}=\sum\limits_{LS}Ag_{LS}\langle
L0S\delta|J\delta\rangle\langle s\lambda\sigma-\nu|S\delta\rangle
r^{L}B_{L}(r),$ (1)

where $A\equiv\sqrt{\frac{2L+1}{2J+1}}$, $g_{LS}$ is the coupling constant for
the partial wave with orbital angular momentum $L$ and spin $S$ (with
$z$-projection $\delta$), $r$ is the relative momentum between the two
daughter particles in the initial particle rest frame, and $B_{L}$ is the
barrier factor zoubs:2003pj . The conservation of parity is applied in the
equation. Recent measurements show that the contributions of higher order
magnetic and electric multipoles in the $\psi(3686)$ radiative transition to
$\chi_{c2}$ are negligible, and the $E1$ transition is the dominant process
e1transition . Hence, the helicity amplitudes are constructed to satisfy the
$E1$ transition relation E1relation  and parity conservation, namely,
$F_{1,2}=\sqrt{2}F_{1,1}=\sqrt{6}F_{1,0}$ and $F_{0,0}=0$. The corresponding
$g_{LS}$ are taken as complex values. The relative magnitudes and phases are
determined by an un-binned maximum likelihood fit to data with the package
MINUIT minuit . The background contribution to the likelihood value is
estimated with the events in the sideband regions and is subtracted zhuc . For
the PWA method check, a input data is generated with inclusion of all states
in the baseline solution, and coupling constants are fixed to the PWA
solution. After the detector simulation and selection criteria, the same PWA
fit procedure is performed, the fit results are consistent with that of the
input data within the statistical errors.

As shown in the Dalitz plots of Fig. 1(c) and (d), clear signals for
$K^{\ast}(892)$ and $K^{\ast}_{2}(1430)$ are observed in the $K\pi$ system.
The resonances $K^{\ast}(892)$ and $K^{\ast}_{2}(1430)$ in the $K\pi$ system
as well as the $a_{2}(1320)$ in the $K\overline{K}$ system, which has a
significance larger than $8\sigma$ in both decay modes, are included in the
baseline solution. For consistency, the $K_{3}^{\ast}(1780)$ signal, which is
of a significance larger than $5\sigma$ in the decay $\chi_{c2}\to
K_{S}K^{\pm}\pi^{\mp}$, but only $2\sigma$ in $\chi_{c2}\to
K^{+}K^{-}\pi^{0}$, is also included. A contribution from the direct
$\chi_{c2}\to K\overline{K}\pi$ three-body decay, which is parameterized with
a non-resonant component with spin-parity $J^{p}=2^{+}$ in the $K\overline{K}$
system, is also considered. Other possible excited $K^{\ast}$ states in $K\pi$
system and the states in the $K\overline{K}$ system listed in PDG PDG , which
have a significance less than $5\sigma$, are not included, but they are
considered as a source of systematic uncertainty. The coupling constants for
the charge-conjugate modes are treated to be the same.

Figures 2 and 3(a)-(c) show the invariant mass distribution and the projection
of the PWA for the decays $\chi_{c2}\to K^{+}K^{-}\pi^{0}$ and $\chi_{c2}\to
K_{S}K^{\pm}\pi^{\mp}$, respectively. The signal yields for the individual
processes with a given intermediate state and the corresponding statistical
uncertainties are calculated according to the fit results. The resultant
branching fractions for the decays $\chi_{c2}\to K^{\ast}\overline{K}$ and
$\chi_{c2}\to a_{2}(1320)\pi$ are summarized in Table 1. The branching
fractions for the processes including charged $K^{\ast}$ intermediate states
are consistent between the two decay modes, and are combined by considering
the correlation of uncertainties between the two modes sunzt . The $K^{\ast}$
isospin-conjugate modes are consistent with each other within $2\sigma$, as
expected by isospin symmetry.

Figure 2: (color online) Projections of the fit results onto the invariant mass of (a) $K^{\pm}\pi^{0}$ and (b) $K^{+}K^{-}$ in the decay $\chi_{c2}\to K^{+}K^{-}\pi^{0}$, where dots with error bars are for data, the blue solid histograms are the overall fit results, the yellow shaded histograms are for the background estimated using $\chi_{c2}$ sideband events, and the contributions from different components are indicated in the inset.  Figure 3: (color online) Projections of the fit results onto the invariant mass of (a) $K^{\pm}\pi^{\mp}$, (b) $K_{S}\pi^{\pm}$ and (c) $K_{S}K^{\pm}$ in the decay $\chi_{c2}\to K_{S}K^{\pm}\pi^{\mp}$ as well as (d) $\pi^{\pm}\pi^{0}$ in the decay $\chi_{c2}\to\pi^{+}\pi^{-}\pi^{0}$, where dots with error bars are for data, the blue solid histograms are the overall fit results, and the contributions from other components are indicated in the inset. Table 1: The measured branching fractions $(\times 10^{-4})$ for the decays $\chi_{c2}\to(K\pi)\overline{K}$ and $\chi_{c2}\to(K\overline{K})\pi$. The first uncertainties are statistical, and the second are systematic (Here, $K^{\ast}$, $K^{\ast}_{2}$, $K^{\ast}_{3}$, and $a_{2}$ refer to $K^{\ast}(892)$, $K^{\ast}_{2}(1430)$, $K^{\ast}_{3}(1780)$, and $a_{2}(1320)$, respectively).  Mode | $K^{+}K^{-}\pi^{0}$ | $K_{S}K^{\pm}\pi^{\mp}$ | Combined
---|---|---|---
$K^{\ast\pm}K^{\mp}$ | $1.8\pm 0.2\pm 0.2$ | $1.4\pm 0.2\pm 0.2$ | $1.5\pm 0.1\pm 0.2$
$K^{\ast 0}\overline{K}{}^{0}$ | $-$ | $1.3\pm 0.2\pm 0.2$ | $-$
$K_{2}^{\ast\pm}K^{\mp}$ | $18.2\pm 0.8\pm 1.6$ | $13.6\pm 0.8\pm 1.4$ | $15.5\pm 0.6\pm 1.2$
$K_{2}^{\ast 0}\overline{K}{}^{0}$ | $-$ | $13.0\pm 1.0\pm 1.5$ | $-$
$K_{3}^{\ast\pm}K^{\mp}$ | $5.3\pm 0.5\pm 0.9$ | $5.9\pm 1.1\pm 1.5$ | $5.4\pm 0.5\pm 0.7$
$K_{3}^{\ast 0}\overline{K}{}^{0}$ | $-$ | $5.9\pm 1.6\pm 1.5$ | $-$
$a_{2}^{0}\pi^{0}$ | $13.5\pm 1.6\pm 3.2$ | $-$ | $-$
$a_{2}^{\pm}\pi^{\mp}$ | $-$ | $18.4\pm 3.3\pm 5.5$ | $-$

The large branching fraction of $\chi_{c2}\to K^{\ast}_{2}\overline{K}$ is a
direct indication of the significant HSR violation effects. Note that the
helicity amplitude ratios $|F_{2,0}|^{2}/|F_{1,0}|^{2}$, estimated with the
fitted $g_{LS}$ (see Table 2), suggest the dominance of $F_{1,0}$ in the
transition amplitudes. The amplitude $F_{1,0}$ contributes to the leading HSR
violation effects and scales as $(\Lambda_{\rm QCD})/m_{c})^{6}$ due to its
asymptotic behavior Chernyak:1981zz ; zhaoq . In comparison with the HSR
conserved channel $\chi_{c2}\to VV$, which scales as $(\Lambda_{\rm
QCD}/m_{c})^{4}$, the ratio of $\chi_{c2}\to K^{\ast}_{2}\overline{K}$ to $VV$
is expected to be suppressed by a factor of $(\Lambda_{\rm QCD}/m_{c})^{2}\sim
0.02$ with $\Lambda_{\rm QCD}\sim 0.2$ $\,\mathrm{GeV}/c^{2}$ and the charm
quark mass $m_{c}\sim 1.5$ $\,\mathrm{GeV}/c^{2}$. However, the measured
branching fraction of $\chi_{c2}\to K^{\ast}_{2}\overline{K}$ appears to be
the same order of magnitude as that for $\chi_{c2}\to VV$ pingrg , which
indicates a significant violation of HSR in $\chi_{c2}\to
K^{\ast}_{2}\overline{K}$.

Table 2: The measured ratios of helicity amplitude squared $|F_{2,0}|^{2}/|F_{1,0}|^{2}$, where the uncertainties are statistical only. |  $K^{+}K^{-}\pi^{0}$ | $K_{S}K^{\pm}\pi^{\mp}$
---|---|---
|  Charged $K^{\ast}$ |  Charged $K^{\ast}$ |  Neutral $K^{\ast}$
$K^{\ast}_{2}(1430)$ | $0.046\pm 0.001$ | $0.042\pm 0.019$ | $0.031\pm 0.018$

In the analysis of the decay $\psi(3686)\to\gamma\pi^{+}\pi^{-}\pi^{0}$, the
$\chi_{c2}$ signal is extracted by the requirement
$|M_{\pi^{+}\pi^{-}\pi^{0}}-M_{\chi_{c2}}|\leq 15$ $\,\mathrm{MeV}/c^{2}$. The
potential background from direct $e^{+}e^{-}$ annihilation is found to be
negligible by studying the continuum data taken at $\sqrt{s}=3.65$ GeV. The
backgrounds from $\psi(3686)$ decay are investigated with the $\psi(3686)$
inclusive MC sample; the only surviving $\chi_{c2}$ events are those that
directly decay to $\pi^{+}\pi^{-}\pi^{0}$ without any intermediate state.
There are also non-$\chi_{c2}$ backgrounds, which can be estimated by the
events in the $\chi_{c2}$ sideband regions. Figure 3(d) shows the invariant
mass of $\pi^{\pm}\pi^{0}$ for the selected candidates, together with the
binned likelihood fit results. Here the fit components include the
$\rho(770)^{\pm}$ signal, the direct decay $\chi_{c2}\to\pi^{+}\pi^{-}\pi^{0}$
and the non-$\chi_{c2}$ background. The $\rho(770)^{\pm}$ signal and the
direct $\chi_{c2}$ three-body decay are modeled with the MC simulated shapes
convoluted with a Gaussian function with free parameters. The resonant
parameters of the $\rho(770)^{\pm}$ are set to the values in the PDG PDG . The
fitted signal yields are $14.7\pm 8.9$ and $63.6\pm 13.0$, and the
corresponding resultant branching fractions are $(0.64\pm 0.39\pm 0.07)\times
10^{-5}$ and $(2.1\pm 0.4\pm 0.2)\times 10^{-5}$ for
$\chi_{c2}\to\rho(770)^{\pm}\pi^{\mp}$ and the direct decay
$\chi_{c2}\to\pi^{+}\pi^{-}\pi^{0}$, respectively, where the first
uncertainties are statistical, and the second are systematic. Since the
statistical significance for the $\chi_{c2}\to\rho(770)^{\pm}\pi^{\mp}$ is
only $2.8\sigma$, the upper limit at the 90% C.L. for the branching fraction
is set to $1.1\times 10^{-5}$ by the method of Feldman-Cousins approach with
the systematic uncertainties consideration up .

The uncertainties from the branching fractions of
$\psi(3686)\to\gamma\chi_{c2}$, $K_{S}\to\pi^{+}\pi^{-}$,
$\pi^{0}\to\gamma\gamma$, $a_{2}(1320)\to K\overline{K}$, and $K^{\ast}\to
K\pi$ are quoted from the PDG PDG . The uncertainty on the number of
$\psi(3686)$ events is about $0.8\%$ wang ; wang1 . The uncertainties
associated with the tracking and PID are 1% for every charged track xugf . The
uncertainty related with EMC shower reconstruction efficiency is 1% per shower
xugf . The uncertainties associated with the kinematic fit are estimated to be
0.5% and 0.6% for the 4C and 5C fit, respectively, by using a method to
correct the charged-track helix parameters guoyp . The uncertainty associated
with the $K_{S}$ reconstruction is estimated to be 2.5% guoyp . The
uncertainties related with the $\pi^{0}$ selection, the requirements on the
$\pi^{0}$ recoil mass and the $\omega$ background veto (in
$\chi_{c2}\to\rho(770)^{\pm}\pi^{\mp}$ mode only) are negligible.

In the decay $\chi_{c2}\to\rho(770)^{\pm}\pi^{\mp}$, the uncertainties due to
the bin size and the fit range in the fit are estimated by repeating the fit
with alternative bin sizes and fit ranges. The uncertainty due to the shape of
$\chi_{c2}\to\pi^{+}\pi^{-}\pi^{0}$ is estimated by replacing the MC simulated
line shape with a $3^{rd}$ polynomial function. The uncertainty due to the
shape of the background is estimated by changing the $\chi_{c2}$ sideband
regions.

In the decay $\chi_{c2}\to K\overline{K}\pi$, the uncertainties due to the
contribution from $K^{*}(1410)$ and $K^{*}(1680)$ are estimated by including
these states in the fit. The uncertainties associated with the backgrounds are
determined by changing the $\chi_{c2}$ and $\pi^{0}$ sideband regions. The
spin density matrix corresponding to the $E1$ transition E1relation  is used
in the nominal fit. To estimate the uncertainty, contributions from the
quadrupole ($M2$) and other high order multipoles to the matrix e1transition
are included in the fit, and the changes in the final results are treated as a
systematic uncertainty. The uncertainties associated with the resonance
parameters of intermediate states are estimated by varying their values by
$1\sigma$ of their uncertainties quoted in the PDG PDG . The uncertainty due
to the barrier radius zoubs:2003pj  when calculating $B_{L}(r)$ in Eq. (1) is
estimated by alternative fits with $r=0.25$ or 0.75 fm, respectively, where
$r=0.6$ fm is the nominal value. The uncertainty associated with the direct
three-body decay $\chi_{c2}\to K\overline{K}\pi$ is estimated by alternative
fits with other spin-parity hypotheses, $e.g.$ a $0^{-}$ or $3^{-}$ non-
resonant component in the $K\overline{K}$ or $K\pi$ systems. The largest
changes in the signal yields are taken as systematic uncertainties. Assuming
all the systematic errors are independent, the overall systematic obtained by
taking the quadrature sum of the individual values.

In summary, the HSR suppressed processes of $\chi_{c2}\to
K^{\ast}(892)\overline{K}$ and $\chi_{c2}\to\rho(770)^{\pm}\pi^{\mp}$ are
studied with the $\psi(3686)$ data collected by BESIII for the first time. The
branching fractions of $\chi_{c2}\to K^{\ast}(892)^{\pm}K^{\mp}$ and
$\chi_{c2}\to K^{\ast}(892)^{0}\overline{K}{}^{0}+\rm{c.c.}$ are measured to
be $(1.5\pm 0.1\pm 0.2)\times 10^{-4}$ and $(1.3\pm 0.2\pm 0.2)\times
10^{-4}$, respectively, which are rather sizeable with respect to those of the
HSR conserving decay $\chi_{c2}\to VV$ PDG ; pingrg . These branching
fractions are at least one order of magnitude larger than the upper limit of
the branching fraction of $\chi_{c2}\to\rho(770)^{\pm}\pi^{\mp}$ $(1.1\times
10^{-5})$. It is worth noting that this phenomenon is anticipated by the HSR
violation mechanism proposed in Ref. zhaoq . Namely, the HSR violation in
$\chi_{c2}\to K^{\ast}(892)\overline{K}$ occurs via the intermediate meson
loops due to the large $U$-spin symmetry breaking, while that in
$\chi_{c2}\to\rho(770)^{\pm}\pi^{\mp}$ is due to isospin symmetry breaking.
Due to the large mass difference between $s$ and $u/d$ quarks, the $U$-spin
symmetry is broken more severely in comparison with isospin symmetry. This
results in the larger decay branching for $\chi_{c2}\to
K^{\ast}(892)\overline{K}$ than that for
$\chi_{c2}\to\rho(770)^{\pm}\pi^{\mp}$. The results are crucial for further
quantifying the HSR violation mechanisms zhaoq  and also provide deeper
insights into the underlying strong interaction dynamics in the charmonium
energy region.

The BESIII collaboration thanks the staff of BEPCII and the IHEP computing
center for their strong support. This work is supported in part by National
Key Basic Research Program of China under Contract No. 2015CB856700; National
Natural Science Foundation of China (NSFC) under Contracts Nos. 11175188,
11375205, 11425525, 11565006, 11521505, 11235011, 11322544, 11335008,
11425524, 11635010; the Chinese Academy of Sciences (CAS) Large-Scale
Scientific Facility Program; the CAS Center for Excellence in Particle Physics
(CCEPP); the Collaborative Innovation Center for Particles and Interactions
(CICPI); Joint Large-Scale Scientific Facility Funds of the NSFC and CAS under
Contracts Nos. U1232201, U1332201; CAS under Contracts Nos. KJCX2-YW-N29,
KJCX2-YW-N45; 100 Talents Program of CAS; National 1000 Talents Program of
China; INPAC and Shanghai Key Laboratory for Particle Physics and Cosmology;
German Research Foundation DFG under Contracts Nos. Collaborative Research
Center CRC 1044, FOR 2359; Istituto Nazionale di Fisica Nucleare, Italy; Joint
Large-Scale Scientific Facility Funds of the NSFC and CAS under Contract No.
U1532257; Joint Large-Scale Scientific Facility Funds of the NSFC and CAS
under Contract No. U1532258; Koninklijke Nederlandse Akademie van
Wetenschappen (KNAW) under Contract No. 530-4CDP03; Ministry of Development of
Turkey under Contract No. DPT2006K-120470; National Natural Science Foundation
of China (NSFC) under Contract No. 11575133; NSFC under Contract No. 11275266;
The Swedish Resarch Council; U. S. Department of Energy under Contracts Nos.
DE-FG02-05ER41374, DE-SC-0010504, DE-SC0012069; U.S. National Science
Foundation; University of Groningen (RuG) and the Helmholtzzentrum fuer
Schwerionenforschung GmbH (GSI), Darmstadt; WCU Program of National Research
Foundation of Korea under Contract No. R32-2008-000-10155-0.

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