Neutrino oscillation experiments have confirmed that neutrinos are massive particles and that lepton flavors are mixed. To explain the observed lepton mass spectra and flavor mixing patterns, flavor symmetry plays a crucial and unique role. In this paper, we propose a useful symmetry-breaking scheme by applying $S_{3L} \times S_{3R} \rightarrow $ $ S_{2L} \times S_{2R} \rightarrow \emptyset$ within both charged-lepton and neutrino sectors at the mass-matrix level. For the three distinct residual subgroups $S_{2L}^{(23)} \times S_{2R}^{(23)}$ , $S_{2L}^{(13)} \times S_{2R}^{(13)}$ , and $S_{2L}^{(12)} \times S_{2R}^{(12)}$ that are under consideration, we systematically analyze the various parameterizations of the lepton mass matrices. It is shown that all three scenarios are in good agreement with current neutrino oscillation data. Notably, within the latest best-fit values of neutrino oscillation parameters, the predicted values of the Dirac CP-violating phase $\textit{δ}$ are $294.6^\circ$ , $302.3^\circ$ , and $287.0^\circ$ , respectively. To further assess the viability of the model, a comprehensive numerical analysis is performed by utilizing neutrino oscillation parameters at the $3\sigma$ level. It is found that the allowed ranges of $\textit{δ}$ are $281.2^\circ \rightarrow 338.7^\circ$ , $287.0^\circ \rightarrow 342.2^\circ$ , and $282.7^\circ \rightarrow 297.0^\circ$ , which all fall within its $3\sigma$ range. These results indicate that the proposed symmetry-breaking scheme $S_{3L} \times S_{3R} \rightarrow S_{2L} \times S_{2R} \rightarrow \emptyset$ can naturally explain the realistic lepton mass hierarchy and mixing pattern, thereby providing valuable theoretical perspectives for future research.

China

Chang-Qi Hu

Chun-Yuan Li

Xiao Liang

Xing-Hua Yang

Dai-Xing Zhang

Further study on lepton mass spectra and flavor mixing with $\textit{S}$ 3$\textit{L}$ × $\textit{S}$ 3$\textit{R}$ flavor symmetry * Supported in part by the National Natural Science Foundation of China (12105162, 12305106), the Natural Science Foundation of Shandong Province (ZR2021QA058, ZR2021QA040) and the Youth Innovation Technology Project of Higher School in Shandong Province (2023KJ146)

In this work, we investigate possible bound states in the $ D_s\bar{D}_s $ system using the Bethe-Salpeter (BS) formalism within both the ladder and instantaneous approximations. By numerically solving the Bethe-Salpeter equation with a kernel that incorporates contributions from $\textit{ϕ}$ and $ J/\psi $ meson exchanges, we confirm the existence of a loosely bound state. Furthermore, we explore the partial decay widths of the $ D_s\bar{D}_s $ bound state into the $ D\bar{D} $ , $ \eta_c\eta $ , and $ J/\psi\omega $ channels, and observe that these widths are sensitive to the model parameter $\textit{α}$. Notably, we find the dominant decay channel for the $ D_s\bar{D}_s $ bound state to be $ D\bar{D} $ .

Jing-Juan Qi

Zhen-Yang Wang

Zhu-Feng Zhang

Xin-Heng Guo

The properties of the $\textit{S}$-wave D$_{s}$ D $_{s}$ bound state * Supported by the National Natural Science Foundation of China (12405115, 12275024, 12105149)

<p>We compute the coefficients <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mi>T</mi><mo>,</mo><mi>B</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>c</mi><mn>4</mn></msub><mo stretchy="false">(</mo><mi>T</mi><mo>,</mo><mi>B</mi><mo stretchy="false">)</mo></math> of the Taylor expansion for the pressure in powers of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>B</mi></msub><mo>/</mo><mi>T</mi></math> in the presence of a large magnetic field within perturbative quantum chromodynamics (QCD) at finite temperature and baryon density up to two-loops for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>3</mn></math> flavors with physical quark masses. We also present results for the excess of pressure, baryon density, and baryon number susceptibility as functions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>B</mi></msub></math>, as well as susceptibilities as functions of the temperature in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">{</mo><msub><mi>μ</mi><mi>B</mi></msub><mo>,</mo><msub><mi>μ</mi><mi>Q</mi></msub><mo>,</mo><msub><mi>μ</mi><mi>S</mi></msub><mo stretchy="false">}</mo></math> basis. Our results can be directly compared to recent lattice QCD data. Even though current lattice results do not overlap with its region of validity, perturbative results seem to be compatible with those obtained on the lattice for large temperatures.</p>

Brazil

Eduardo S. Fraga

Letícia F. Palhares

United States

Tulio E. Restrepo

Susceptibilities and Taylor coefficients of magnetic QCD from perturbation theory

<p>Using the Monte Carlo <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>HYDJET</mi><mo>+</mo><mo>+</mo></mrow></math> model, we investigate the transverse momentum (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>) spectra of heavy-flavor hadrons, namely <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup><mo>,</mo><mo> </mo><msup><mover><mi>D</mi><mo>¯</mo></mover><mn>0</mn></msup><mo>,</mo><mo> </mo><msup><mi>D</mi><mo>+</mo></msup><mo>,</mo><mo> </mo><msup><mi>D</mi><mo>−</mo></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math>, along with the nuclear modification factors of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mo>±</mo></msup></math> in Au <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo></math> Au collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>200</mn></mrow></math> GeV RHIC energy across various centrality bins. This work extends the earlier study by relaxing the assumption of identical chemical and thermal freezeout and by exploring the effect of a higher chemical freezeout temperature relative to thermal freezeout. The study also explores the centrality and mass dependence of the charm enhancement factor (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>γ</mi><mi>c</mi></msub></math>). Furthermore, we investigate medium-induced energy loss, particle-antiparticle asymmetry, and the role of fragmentation in the hadronization process. The <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>HYDJET</mi><mo>+</mo><mo>+</mo></mrow></math> model, with its default parameters, is unable to reproduce heavy hadron yields due to their early thermal freezeout and initial state production of heavy quarks. Therefore, a systematic tuning of model parameters is performed to improve the overall agreement with experimental data. Additionally, to assess the performance of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>HYDJET</mi><mo>+</mo><mo>+</mo></mrow></math> model relative to other theoretical approaches, its results are compared with the TAMU, SUBATECH, Torino, and Duke models, for which corresponding simulation data are available. This study shows a decreasing trend in <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>γ</mi><mi>c</mi></msub></math> from central to peripheral collisions. Moreover, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>γ</mi><mi>c</mi></msub></math> increases with increasing charm-hadron mass. The model approximately reproduces the experimental data of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math> spectra at low and intermediate <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>. However, it overestimates the data at high <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>, indicating a need for improvements in modeling the energy loss of heavy quarks. The nuclear modification factors (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub></math>) for <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup></math> mesons exhibit significant suppression at high <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>. At low <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub><mo>,</mo><mo> </mo><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub></math> results show deviations from the data, reflecting limitations in the model where coalescence becomes important. The antiparticle-to-particle ratios are consistent with experimental data, whereas mixed-particle ratios are underestimated, revealing the model's limitation in estimating the baryon-to-meson enhancement.</p>

India

Sunidhi Saxena

Rajiv Gupta

Gauri Devi

Ajay Kumar

Heavy hadron production in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Au</mi><mo>+</mo><mi>Au</mi></math> collisions at a center-of-mass energy of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>200</mn></mrow></math> GeV

We systematically investigate the <italic>S</italic>-wave interactions between Nambu-Goldstone bosons (NGBs) and charmed mesons in the <math altimg='si65.svg'><mrow><mo>(</mo><mi>S</mi><mo>,</mo><mi>I</mi><mo>)</mo><mo>=</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></math> sector using the chiral unitary approach. The scattering amplitudes incorporate both the Weinberg-Tomozawa term and additional contributions from <italic>s</italic>- and <italic>u</italic>-channel exchanges of <math altimg='si1.svg'><mrow><mi>c</mi><mover accent='true'><mi>s</mi><mo>&#175;</mo></mover></mrow></math> states predicted by the constituent quark model (CQM). Through analytic continuation of the unitarized amplitudes to the complex energy plane, we identify multiple poles corresponding to bound states and resonances. Our analysis reveals a rich spectrum of <italic>D<inf>sJ</inf></italic> states across <math altimg='si66.svg'><mrow><msup><mi>J</mi><mi>P</mi></msup><mo linebreak='goodbreak'>=</mo><msup><mn>0</mn><mo>+</mo></msup><mo>,</mo><msup><mn>1</mn><mo>+</mo></msup><mo>,</mo><msup><mn>1</mn><mo>&#8722;</mo></msup></mrow></math>, and <math altimg='si67.svg'><msup><mn>2</mn><mo>&#8722;</mo></msup></math> sectors, providing new insights into the nature of established resonances like <math altimg='si68.svg'><mrow><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>*</mo></msubsup><mrow><mo>(</mo><mn>2317</mn><mo>)</mo></mrow></mrow></math> and <italic>D</italic> <inf><italic>s</italic>1</inf>(2460), while predicting several new states that could be observed in future experiments.

Liu-Lin Wang

Xing-Meng Zhao

Xiao-Hai Liu

Mao-Jun Yan

New spectrum of charm-strange meson with constituent quark model <math altimg='si1.svg'><mrow><mi>c</mi><mover accent='true'><mi>s</mi><mo>&#175;</mo></mover></mrow></math> contributions

Measurements are presented of the W and Z boson production cross sections in proton-proton collisions at a center-of-mass energy of 13.6 TeV. Data collected in 2022 and corresponding to an integrated luminosity of 5.01 fb with one or two identified muons in the final state are analyzed. The results for the products of total inclusive cross sections and branching fractions for muonic decays of W and Z bosons are $${11}.{93}\pm 0.0{8}\left({\text{syst}}\right)\pm 0.{17}{\left({\text{lumi}}\right)}_{-0.07}^{+0.07}$$ (acceptance) nb for W boson production, $$8.86\pm 0.06\left({\text{syst}}\right)\pm 0.12{\left({\text{lu}}{\text{mi}}\right)}_{-0.06}^{+0.05}$$ (acceptance) nb for W boson production, and $$2.021\pm 0.009\left({\text{syst}}\right)\pm 0.028{\left({\text{lumi}}\right)}_{-0.013}^{+0.011}$$ (acceptance) nb for the Z boson production in the dimuon mass range of 60–120 GeV, all with negligible statistical uncertainties. Furthermore, the corresponding fiducial cross sections, as well as cross section ratios for both fiducial and total phase space, are provided. The ratios include charge-separated results for W boson production (W and W ) and the sum of the two contributions (W ), each relative to the measured Z boson production cross section. Additionally, the ratio of the measured cross sections for W and W boson production is reported. All measurements are in agreement with theoretical predictions, calculated at next-to-next-to-leading order accuracy in quantum chromodynamics.

Armenia

V. Chekhovsky

A. Hayrapetyan

V. Makarenko

A. Tumasyan

Austria

W. Adam

J. Andrejkovic

L. Benato

T. Bergauer

S. Chatterjee

K. Damanakis

M. Dragicevic

P. Hussain

M. Jeitler

N. Krammer

A. Li

D. Liko

I. Mikulec

J. Schieck

R. Schöfbeck

D. Schwarz

M. Sonawane

W. Waltenberger

C.E. Wulz

Belgium

T. Janssen

H. Kwon

T. Laer

P. Mechelen

N. Breugelmans

J. D’Hondt

S. Dansana

A. Moor

M. Delcourt

F. Heyen

Y. Hong

S. Lowette

I. Makarenko

D. Müller

S. Tavernier

M. Tytgat

G. Onsem

S. Putte

D. Vannerom

B. Bilin

B. Clerbaux

A. Das

I. Bruyn

G. Lentdecker

H. Evard

L. Favart

P. Gianneios

A. Khalilzadeh

F. Khan

A. Malara

M. Shahzad

L. Thomas

M. Vanden Bemden

C. Velde

P. Vanlaer

M. Coen

D. Dobur

G. Gokbulut

J. Knolle

L. Lambrecht

D. Marckx

K. Skovpen

N. Den Bossche

J. Linden

J. Vandenbroeck

L. Wezenbeek

S. Bein

A. Benecke

A. Bethani

G. Bruno

C. Caputo

J. De Favereau De Jeneret

C. Delaere

I. Donertas

A. Giammanco

A. Guzel

Sa. Jain

V. Lemaitre

J. Lidrych

P. Mastrapasqua

T. Tran

S. Turkcapar

G. Alves

E. Coelho

G. Correia Silva

C. Hensel

T. Menezes De Oliveira

C. Mora Herrera

P. Rebello Teles

M. Soeiro

E. Tonelli Manganote

A. Vilela Pereira

W. Aldá Júnior

M. Barroso Ferreira Filho

H. Brandao Malbouisson

W. Carvalho

J. Chinellato

Measurements of the inclusive W and Z boson production cross sections and their ratios in proton-proton collisions at $$\sqrt{s}=13.6$$ TeV

We propose a new method for constructing the consistent space of scattering amplitudes by parameterizing the imaginary parts of partial waves and utilizing dispersion relations, crossing symmetry, and full unitarity. Using this framework, we explicitly compute bounds on the leading couplings and examine the Regge behaviors of the constructed amplitudes. The method also readily accommodates spinning bound states, which we use to constrain glueball couplings. By incorporating dispersion relations, our approach inherently satisfies the Froissart-Martin/Jin-Martin bounds or softer high-energy behaviors by construction. This, in turn, allows us to formulate a new class of fractionally subtracted dispersion relations, through which we investigate the sensitivity of coupling bounds to the asymptotic growth rate.

United Kingdom

Claudia Rham

Andrew Tolley

Zhuo-Hui Wang

Shuang-Yong Zhou

Primal S-matrix bootstrap with dispersion relations

Based on $ (10087\pm 44)\times10^{6} $ $ J/\psi $ events collected with the BESIII detector, we search for the lepton number violating decay $ J/\psi \to K^+K^+e^-e^- + c.c. $ for the first time. The upper limit on the branching fraction of this decay is set to $ 2.1 \times 10^{-9} $ at the 90% confidence level with a frequentist method. This is the first search for $ J/\psi $ decays with a lepton number change by two, offering valuable insights into the underlying physical processes.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

Germany

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

O. Bakina

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M.B. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

R.A. Briere

A. Brueggemann

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

T.T. Chang

G.R. Che

Y.Z. Che

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.L. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

Search for the lepton number violating process ${{\boldsymbol J}/{\boldsymbol\psi }{\bf\to}{\boldsymbol K}^{\bf +}{\boldsymbol K}^{\bf +}{\boldsymbol e}^{\bf -}{\boldsymbol e}^{\bf -}{\bf +}{\boldsymbol {c.c.}}}$ * This work is supported in part by National Key R&D Program of China under Contracts Nos. 2023YFA1606000, 2023YFA1606704; National Natural Science Foundation of China (NSFC) under Contracts Nos. 12035009, 11635010, 11935015, 11935016, 11935018, 12025502, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017, 12361141819; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; CAS under Contract No. YSBR-101; 100 Talents Program of CAS; The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; German Research Foundation DFG under Contract No. FOR5327; Istituto Nazionale di Fisica Nucleare, Italy; Knut and Alice Wallenberg Foundation under Contracts Nos. 2021.0174, 2021.0299; Ministry of Development of Turkey under Contract No. DPT2006K-120470; National Research Foundation of Korea under Contract No. NRF-2022R1A2C1092335; National Science and Technology fund of Mongolia; National Science Research and Innovation Fund (NSRF) via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation of Thailand under Contract No. B50G670107; Polish National Science Centre under Contract No. 2024/53/B/ST2/00975; Swedish Research Council under Contract No. 2019.04595; U. S. Department of Energy under Contract No. DE-FG02-05ER41374