General one-loop formulas for loop-induced processes $gg/\gamma \gamma \rightarrow \phi_i\phi_j$ with $\phi_i\phi_j = hh,~hH,~HH$ are presented in this paper. The analytic expressions evaluated in this study are valid for a class of Higgs Extensions of the Standard Model, $\textit{e.g.,}$ Inert Doublet Higgs, Two Higgs Doublet, Zee-Babu, and Triplet Higgs Models$\textit{.}$ Analytic expressions for one-loop form factors are expressesd in terms of the basic scalar one-loop two-, three-, and four-point functions following the output format of the packages $ {\tt LoopTools}$ and $ {\tt Collier}$ . Hence, physical results can be evaluated numerically using one of these packages. The analytic results are tested using several checks such as the ultraviolet finiteness and infrared finiteness of the one-loop amplitudes. Furthermore, the amplitudes obey the ward identity due to massless gauge bosons in the initial states. This identity is also verified numerically. Regarding applications, we present the phenomenological results for the investigated processes in the Zee-Babu model as a typical example. In particular, production cross-sections for the processes $\gamma \gamma\rightarrow hh$ are scanned over the parameter space of the Zee-Babu Model.

Vietnam

Khiem Hong Phan

Dzung Tri Tran

Thanh Huy Nguyen

One-loop analytical expressions for $\textit{gg}$/$\textit{γγ}$ → ϕ$_{i}$ϕ$_{j}$ in Higgs extensions of the standard model and their applications * This research is supported by Vietnam National Foundation for Science and Technology Development (103.01-2023.16). Khiem Hong Phan and Dzung Tri Tran express their gratitude to all the valuable support from Duy Tan University, for the 30th anniversary of establishment (Nov. 11, 1994 - Nov. 11, 2024) towards ''Integral, Sustainable and Stable Development''

In 2020, a di-<math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> resonance centered at around 6.9 GeV was discovered by the LHCb Collaboration and was later confirmed by the ATLAS and CMS Collaborations. In addition to the 6.9-GeV resonance, its low-energy counterpart centered at around 6552 MeV was also observed by the CMS Collaboration. They are generally considered as fully charm tetraquarks. In this paper, we calculate the inclusive decay width of molecules composed of two <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math>’s and genuine fully charm tetraquarks into light hadrons and into open charms, respectively. Assuming them as <math><mi>S</mi></math>-wave states, we consider all possible spin configurations, namely, spin-0 and spin-2, that decay exclusively into double <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math>, and find that the ratio (<math><mi>R</mi></math>) of the decay width for the light-hadron final states to that for the charmed final states differs significantly among different spin configurations, which can help to explore the nature of the observed di-<math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> resonances.

China

Hong-Fei Zhang

Xue-Mei Mo

Thailand

Yu-Peng Yan

Hadronic decay of exotic mesons consisting of four charm quarks

Within the framework of nonrelativistic QCD (NRQCD), we calculate the fragmentation function for a charm quark into an S-wave fully-charmed tetraquark, denoted as T 4c . The charm-to-T 4c  fragmentation function is expressed as a sum of products of the perturbatively calculable short-distance coefficients and the nonperturbative long-distance matrix elements (LDMEs). The short-distance coefficients are ascertained through the perturbative matching procedure at lowest order in α  s  expansion. The LDMEs are approximated using the T 4c  four-body wave functions at the origin, which have been evaluated by various phenomenological potential models in literature. Incorporating the celebrated QCD factorization and the charm-to-T 4c  fragmentation function, we predict the T 4c  production rate at high transverse momentum p  T  regime in colliders. Both the differential distribution over p  T  and the integrated cross sections are predicted at the LHC. The cross sections for T 4c  states production can reach several femtobarns to several hundreds femtobarns, suggesting a substantial potential for T 4c  event production at the LHC. Additionally, we estimate for the photoproduction of T 4c  in electron-proton (ep) collisions. It is observed that the cross sections for these processes are moderate at the HERA and EIC, and relatively small at the EicC. Given the luminosities of these colliders, the prospect of detecting these fully-charmed tetraquarks at ep colliders is somewhat challenging.

Xiao-Wei Bai

Feng Feng

Chang-Man Gan

United States

Yingsheng Huang

Wen-Long Sang

Producing fully-charmed tetraquarks via charm quark fragmentation in colliders

The identification of jets originating from quarks and gluons, often referred to as quark/gluon tagging, plays an important role in various analyses performed at the Large Hadron Collider, as Standard Model measurements and searches for new particles decaying to quarks often rely on suppressing a large gluon-induced background. This paper describes the measurement of the efficiencies of quark/gluon taggers developed within the ATLAS Collaboration, using $\sqrt{s} = 13$ TeV proton–proton collision data with an integrated luminosity of 140 fb $^{-1}$ collected by the ATLAS experiment. Two taggers with high performances in rejecting jets from gluon over jets from quarks are studied: one tagger is based on requirements on the number of inner-detector tracks associated with the jet, and the other combines several jet substructure observables using a boosted decision tree. A method is established to determine the quark/gluon fraction in data, by using quark/gluon-enriched subsamples defined by the jet pseudorapidity. Differences in tagging efficiency between data and simulation are provided for jets with transverse momentum between 500 GeV and 2 TeV and for multiple tagger working points.

France

G. Aad

B. Abbott

Germany

K. Abeling

N.J. Abicht

S.H. Abidi

Morocco

A. Aboulhorma

Israel

H. Abramowicz

H. Abreu

Y. Abulaiti

Italy

United Kingdom

B.S. Acharya

C. Adam Bourdarios

Poland

L. Adamczyk

S.V. Addepalli

M.J. Addison

J. Adelman

A. Adiguzel

T. Adye

A.A. Affolder

Switzerland

Y. Afik

Spain

M.N. Agaras

J. Agarwala

A. Aggarwal

Romania

C. Agheorghiesei

A. Ahmad

Azerbaijan

F. Ahmadov

Canada

W.S. Ahmed

S. Ahuja

X. Ai

G. Aielli

A. Aikot

M. Ait Tamlihat

B. Aitbenchikh

I. Aizenberg

M. Akbiyik

Sweden

T.P.A. Åkesson

A.V. Akimov

Japan

D. Akiyama

N.N. Akolkar

K. Al Khoury

G.L. Alberghi

J. Albert

P. Albicocco

G.L. Albouy

S. Alderweireldt

M. Aleksa

I.N. Aleksandrov

C. Alexa

Greece

T. Alexopoulos

F. Alfonsi

M. Algren

M. Alhroob

Czechia

B. Ali

H.M.J. Ali

S. Ali

S.W. Alibocus

M. Aliev

G. Alimonti

W. Alkakhi

C. Allaire

B.M.M. Allbrooke

J.F. Allen

Chile

C.A. Allendes Flores

P.P. Allport

A. Aloisio

Argentina

F. Alonso

C. Alpigiani

M. Alvarez Estevez

A. Alvarez Fernandez

M. Alves Cardoso

M.G. Alviggi

M. Aly

Brazil

Y. Amaral Coutinho

A. Ambler

C. Amelung

M. Amerl

C.G. Ames

D. Amidei

Portugal

S.P. Amor Dos Santos

K.R. Amos

Norway

V. Ananiev

C. Anastopoulos

T. Andeen

J.K. Anders

S.Y. Andrean

A. Andreazza

S. Angelidakis

A. Angerami

A.V. Anisenkov

A. Annovi

C. Antel

M.T. Anthony

E. Antipov

M. Antonelli

F. Anulli

M. Aoki

T. Aoki

J.A. Aparisi Pozo

M.A. Aparo

L. Aperio Bella

C. Appelt

Performance and calibration of quark/gluon-jet taggers using 140 fb$^{−1}$ of $\textit{pp}$ collisions at ${{\sqrt{\boldsymbol s}\bf = 13}}$ TeV with the ATLAS detector * We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; ANID, Chile; CAS, MOST and NSFC, China; Minciencias, Colombia; MEYS CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS and CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF and MPG, Germany; GSRI, Greece; RGC and Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MEiN, Poland; FCT, Portugal; MNE/IFA, Romania; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DSI/NRF, South Africa; MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taipei; TENMAK, Türkiye; STFC, United Kingdom; DOE and NSF, United States of America. In addition, individual groups and members have received support from BCKDF, CANARIE, CRC and DRAC, Canada; PRIMUS 21/SCI/017 and UNCE SCI/013, Czech Republic; COST, ERC, ERDF, Horizon 2020, ICSC-Next Generation EU and Marie Skłodowska-Curie Actions, European Union; Investissements d'Avenir Labex, Investissements d'Avenir Idex and ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and MINERVA, Israel; Norwegian Financial Mechanism 2014-2021, Norway; NCN and NAWA, Poland; La Caixa Banking Foundation, CERCA Programme Generalitat de Catalunya and PROMETEO and GenT Programmes Generalitat Valenciana, Spain; Göran Gustafssons Stiftelse, Sweden; The Royal Society and Leverhulme Trust, United Kingdom.

In this paper, we evaluate, up to QCD next-to-next-to-next-to-leading order, the <math><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup></math> decay constant, which, within the nonrelativistic QCD (NRQCD) framework, is factorized as the product of the short-distance coefficient (SDC) and the long-distance matrix element. For the first time, the renormalization constant and the anomalous dimension for the NRQCD vector current composed of <math><mi>c</mi><mover><mrow><mi>b</mi></mrow><mrow><mo>¯</mo></mrow></mover></math>, which are functions of the charm quark mass <math><msub><mrow><mi>m</mi></mrow><mrow><mi>c</mi></mrow></msub></math>, the bottom quark mass <math><msub><mrow><mi>m</mi></mrow><mrow><mi>b</mi></mrow></msub></math> and the factorization scale <math><msub><mrow><mi>μ</mi></mrow><mrow><mi>Λ</mi></mrow></msub></math>, are obtained analytically at <math><mi>O</mi><mo>(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></math> and <math><mi>O</mi><mo>(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mo>)</mo></math>. The SDC is calculated up to <math><mi>O</mi><mo>(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mo>)</mo></math> in perturbative expansion. Explicitly, the <math><mi>O</mi><mo>(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></math> correction to the SDC is analytically calculated in terms of logarithmic and polylogarithmic functions of <math><mi>r</mi><mo>≡</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>/</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>c</mi></mrow></msub></math>, and the <math><mi>O</mi><mo>(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mo>)</mo></math> correction to the SDC is numerically calculated at a series of values of r, ranging from 2.1 to 4.0. Surprisingly, we find that the nontrivial part of the SDC at <math><mi>O</mi><mo>(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mo>)</mo></math> can be well estimated by a linear function of r. In addition, we find that the <math><mi>O</mi><mo>(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></math> and <math><mi>O</mi><mo>(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mo>)</mo></math> corrections to the decay constant and decay width are considerable and very significant, which indicates a very poor convergence for the perturbative expansion.

Ming-Zhen Zhou

Decay constant of Accurate up to

In this Letter, we study the exclusive decay of <math><mrow><mi>ϒ</mi></mrow></math> into <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> in association with <math><msub><mi>η</mi><mi>c</mi></msub></math> (<math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mrow></math>). The decay widths for different helicity configurations are evaluated up to QCD next-to-leading order within the nonrelativistic QCD framework. We find that the QCD corrections notably mitigate the renormalization scale dependence of the decay widths for all the processes. The branching fraction of <math><mrow><mi>ϒ</mi><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>+</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow></msub></mrow></math> is obtained as <math><mrow><msubsup><mrow><mn>3.73</mn></mrow><mrow><mo>−</mo><mn>2.06</mn><mo>−</mo><mn>1.19</mn></mrow><mrow><mo>+</mo><mn>5.10</mn><mo>+</mo><mn>0.10</mn></mrow></msubsup><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math>, which agrees well with the Belle measurement, i.e., <math><mrow><mi>Br</mi><mo>(</mo><mi>ϒ</mi><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>+</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>)</mo><mo>=</mo><mspace></mspace><mo>(</mo><mn>3.90</mn><mo>±</mo><mn>1.21</mn><mo>±</mo><mn>0.23</mn><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math>. For the other processes, our results of the branching fractions are compatible with the upper limits given by the Belle experiments, except for <math><mrow><mi>ϒ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>+</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow></msub></mrow></math>, where some tension exists between theory and experiment. Having the polarized decay widths, we study the <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> polarization, which turns out to be independent of any nonperturbative parameters. Further, according to our calculation, it is promising to measure all the processes at Super <math><mi>B</mi></math> factory thanks to the high luminosity.

Yu-Dong Zhang

Higher-Order QCD Corrections to <math><mrow><mi>ϒ</mi></mrow></math> Decay into Double Charmonia

Within the framework of nonrelativistic QCD (NRQCD) factorization, we calculate the next-to-leading-order (NLO) perturbative corrections to the radiative decay Υ → η  c (χ  cJ ) + γ. Both the helicity amplitudes and the helicity decay widths are obtained. It is the first computation for the processes involving both bottomonium and charmonium at two-loop accuracy. By employing the Cheng-Wu theorem, we are able to convert most of complex-valued master integrals (MIs) into real-valued MIs, which makes the numerical integration much efficient. Our results indicate the   <math> <mi>O</mi> <mfenced> <msub> <mi>α</mi> <mi>s</mi> </msub> </mfenced> </math>  $$ \mathcal{O}\left({\alpha}_s\right) $$  corrections are moderate for η  c  and χ  c2 production, and are quite marginal for χ  c0 and χ  c1 production. It is impressive to note the NLO corrections considerably reduce the renormalization scale dependence in both the decay widths and the branching fractions for χ  cJ , and slightly improve that for η  c . With the NRQCD matrix elements evaluated via the Buchmüller-Tye potential model, we find the decay width for η  c  production is one-order-of-magnitude larger than χ  cJ  production, which may provide a good opportunity to search for Υ → η  c  + γ in experiment. In addition, the decay width for χ  c1 production is several times larger than those for χ  c0,2. Finally, we find the NLO NRQCD prediction for the branching fraction of Υ → χ  c1 + γ is only half of the lower bound of the experimental data measured recently by Belle. Moreover, there exists serious contradiction between theory and experiment for Υ → η  c  + γ. The discrepancies between theory and experiment deserve further research efforts.

Next-to-leading-order QCD corrections to a vector bottomonium radiative decay into a charmonium

The η  c  meson leptoproduction is calculated within the nonrelativistic QCD framework for the first time. It is found that the colour-singlet channel, although suppressed by a factor of α  s  relative to the colour-octet ones, provides important contribution for almost all the experimental conditions, which disagrees with some of the expectations before computation. We present the differential cross sections with respect to   <math> <msubsup> <mi>p</mi> <mi>t</mi> <mn>2</mn> </msubsup> </math>  $$ {p}_t^2 $$ ,   <math> <msubsup> <mi>p</mi> <mi>t</mi> <mrow> <mo>★</mo> <mn>2</mn> </mrow> </msubsup> </math>  $$ {p}_t^{\bigstar 2} $$ , Q 2, W, and z, for both HERA and EIC experimental conditions as a reference for future studies. The scale dependence and long-distance-matrix-element dependence are also investigated in this paper.

Kinematic distributions of the η  c  leptoproduction in association with light hadrons

α-particle preformation factors, one of the most significant quantities in α decay, are systematically investigated, which are extracted from the ratios between theoretical α-decay half-lives calculated by the generalized liquid drop model and experimental data. The results indicate that both α-particle preformation factors <math><msub><mrow><mi>P</mi></mrow><mrow><mi>α</mi></mrow></msub></math> and α decay energy <math><msub><mrow><mi>Q</mi></mrow><mrow><mi>α</mi></mrow></msub></math> are important observed quantities for revealing the nuclear shell structure information. And a nice linear relationship exists between <math><msub><mrow><mi>log</mi></mrow><mrow><mn>10</mn></mrow></msub><mo>⁡</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>α</mi></mrow></msub></math> and <math><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>α</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msubsup></math>, which means the famous Geiger-Nuttall law can not only describe α decay half-lives but deal with α-particle preformation factors, as well as the nuclear shell effects play key roles in α-particle preformation. Furthermore, the results indicate that <math><mi>Z</mi><mo>=</mo><mn>82</mn></math> and <math><mi>N</mi><mo>=</mo><mn>126</mn></math> closed shells play more important roles than <math><mi>Z</mi><mo>=</mo><mn>50</mn></math> and <math><mi>N</mi><mo>=</mo><mn>82</mn></math> shell closures in which the shell effect of <math><mi>N</mi><mo>=</mo><mn>126</mn></math> is stronger than that of <math><mi>Z</mi><mo>=</mo><mn>82</mn></math> in the α decay process. Besides, the unpaired nucleons will inhibit the preformation of α-particle. After considering the above significant physical effects, a global analytic formula with only twelve parameters for α-particle preformation factors is proposed based on the direct observation quantity of the nuclear shell effect i.e., α decay energy. The outstanding precision of this formula in describing the α-particle preformation factors indicates that it can be used to perform accurate calculations for α decay half-lives as well as provide some general guidance for microscopic study on α-particle preformation factors and nuclear structure.

Jun-Gang Deng

Correlation between -particle Preformation Factor and Decay Energy

Within the framework of nonrelativistic QCD factorization formalism, we compute the helicity amplitude as well as the decay width of <math><msub><mi>η</mi><mrow><mi>Q</mi><mn>2</mn></mrow></msub></math> (<math><mrow><mi>Q</mi><mo>=</mo><mi>c</mi></mrow></math>, <math><mrow><mi>b</mi></mrow></math>) electromagnetic decay into two photons up to next-to-next-to-leading order in <math><msub><mi>α</mi><mi>s</mi></msub></math> expansion. For the first time, we verify the validity of nonrelativistic QCD factorization for the <math><mrow><mi>D</mi></mrow></math>-wave quarkonium decay at next-to-next-to-leading order. We find that the <math><mi>O</mi><mo>(</mo><msub><mi>α</mi><mi>s</mi></msub><mo>)</mo></math> and <math><mi>O</mi><mo>(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo>)</mo></math> corrections to the helicity amplitude are negative and moderate, nevertheless both corrections combine to suppress the leading-order prediction for the decay width significantly. By approximating the total decay width of <math><msub><mi>η</mi><mrow><mi>Q</mi><mn>2</mn></mrow></msub></math> as the sum of those for the hadronic decay and the electric <math><mi>E</mi><mn>1</mn></math> transition, we obtain the branching ratios <math><mtext>Br</mtext><mo>(</mo><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>→</mo><mn>2</mn><mi>γ</mi><mo>)</mo><mo>≈</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math> and <math><mtext>Br</mtext><mo>(</mo><msub><mi>η</mi><mrow><mi>b</mi><mn>2</mn></mrow></msub><mo>→</mo><mn>2</mn><mi>γ</mi><mo>)</mo><mo>≈</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup></math>. To explore the potential measurement on <math><msub><mi>η</mi><mrow><mi>Q</mi><mn>2</mn></mrow></msub></math>, we further evaluate the production cross section of <math><msub><mi>η</mi><mrow><mi>Q</mi><mn>2</mn></mrow></msub></math> at LHCb at the lowest order in <math><msub><mi>α</mi><mi>s</mi></msub></math> expansion. With the kinematic constraint on the longitudinal rapidity <math><mn>4.5</mn><mo>&gt;</mo><mi>y</mi><mo>&gt;</mo><mn>2</mn></math> and transverse momentum <math><msub><mi>P</mi><mi>T</mi></msub><mo>&gt;</mo><mo>(</mo><mn>2</mn><mi>–</mi><mn>4</mn><mo>)</mo><msub><mi>m</mi><mi>Q</mi></msub></math> for <math><msub><mi>η</mi><mrow><mi>Q</mi><mn>2</mn></mrow></msub></math>, we find the cross section can reach 2–50 nb for <math><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></math>, and 1–22 pb for <math><msub><mi>η</mi><mrow><mi>b</mi><mn>2</mn></mrow></msub></math>. Considering the integrated luminosity <math><mi>L</mi><mo>=</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>7</mn></math>, 13 TeV, we estimate that there are several hundreds events of <math><mi>p</mi><mi>p</mi><mo>→</mo><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>→</mo><mn>2</mn><mi>γ</mi></math>. Since the background is relatively clean, it is promising to reconstruct <math><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></math> through its electromagnetic decay. On the other hand, due to the small branching ratio and production cross section, it is quite challenging to detect <math><msub><mi>η</mi><mrow><mi>b</mi><mn>2</mn></mrow></msub><mo>→</mo><mn>2</mn><mi>γ</mi></math> at LHCb.

Li Yang

Study on <math><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>(</mo><msub><mi>η</mi><mrow><mi>b</mi><mn>2</mn></mrow></msub><mo>)</mo></math> electromagnetic decay into double photons