Inspired by the observation of the ${\eta}_{t}$ meson at the LHC and the promising prospect of the ${\eta}_{t}$ meson available at the approaching HL-LHC, branching ratios for the ${\eta}_{t}$ ${\to}$ $f\bar{f}$ , $gg$ , ${\gamma}{\gamma}$ , $W^{+}W^{-}$ , $Z^{0}Z^{0}$ , $Z^{0}{\gamma}$ , and $Z^{0}H$ decays are roughly estimated. It is found that tens of opposite-charge dilepton events from the ${\eta}_{t}$ ${\to}$ $W^{+}W^{-}$ decay and hundreds of events from the ${\eta}_{t}$ ${\to}$ $Z^{0}H$ ${\to}$ ${\ell}^{+}{\ell}^{-}H$ decay using the single $Z^{0}$ boson tagging method are expected to be accessible. This estimation provides a reference for future experimental study on the ${\eta}_{t}$ meson.

China

Yueling Yang

Bingbing Yang

Jiazhi Li

Zhaojie Lü

Junfeng Sun

Searching for the toponium ${{\boldsymbol\eta}_{\boldsymbol t}}$ with the ${{\boldsymbol\eta}_{\boldsymbol t}}$ ${\boldsymbol\to}$ ${{\boldsymbol W}^{\bf +}{\boldsymbol W}^{\bf -}}$ decay * Supported by the National Natural Science Foundation of China (12275068, 12275067), the National Key R&D Program of China (2023YFA1606000), the Natural Science Foundation of Henan Province (252300421491, 242300420250), and the Science and Technology R&D Program Joint Fund Project of Henan Province (225200810030), as well as the Science and Technology Innovation Leading Talent Support Program of Henan Province (254200510039)

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.

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)

We construct the Hamiltonian formulation of the isotropic Universe in a generic metric $\textit{f}$($\textit{R}$)-theory in the Jordan frame. We canonically quantize the Universe volume via a polymer formulation, and we adopt the scalar field naturally arising from this scenario as a physical clock. Being within the limit of cut-off values of the space volume, we are legitimized to neglect, at first approximation level, the self-interacting potential term associated with the scalar field. We first study the semi-classical polymer dynamics, outlining the emergence of a bouncing cosmology, both in the internal as well as in the synchronous time. In this latter time variable, we are also able to compare the obtained picture with that of a standard polymer Big-Bounce. We see that in the studied case, the collapsing and expanding branches are no longer symmetric with respect to the minimum volume configuration. Then, we fully quantize the system dynamics in the momentum representation, constructing a suitable dynamical Hilbert space and setting up the dynamics of localized wave packets. The mean value dynamics, both for the momentum and volume spaces, is characterized by a bouncing dynamics as described via the internal time, which closely resembles that one obtained in Loop Quantum Cosmology and Polymerization, respectively.

Italy

Maria Limongi

Simone Lo Franco

Giovanni Montani

Sebastiano Segreto

Big-bounce in quantum f(R)-cosmology: polymer dynamics with internal time

<p>We demonstrate that the scalaron, a scalar degree of freedom, emerging from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>f</mi><mo stretchy="false">(</mo><mi>R</mi><mo stretchy="false">)</mo></math> theory of gravity, can account for the observed dark matter (DM) abundance if its mass is around the MeV scale, to ensure its cosmological stability. Focusing on two well-known <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>f</mi><mo stretchy="false">(</mo><mi>R</mi><mo stretchy="false">)</mo></math> gravity models, we systematically show that if scalaron production proceeds via the freeze-in mechanism, the right relic abundance is satisfied over a very narrow window of reheating temperature <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mn>14</mn></msup><mo>≲</mo><msub><mi>T</mi><mrow><mi>rh</mi></mrow></msub><mo>≲</mo><msup><mn>10</mn><mn>16</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. We delineate the viable parameter space of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>f</mi><mo stretchy="false">(</mo><mi>R</mi><mo stretchy="false">)</mo></math> models consistent with the observed DM abundance, and highlight relevant experimental constraints from searches targeting DM decay signatures.</p>

India

Basabendu Barman

Ashmita Das

Rakesh Kumar SivaKumar

Rudra Pratap Udgata

Freeze-in production of scalaron dark matter in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>R</mi><mo stretchy="false">)</mo></mrow></math> gravity

In this work, we derive a new class of analytic black hole solutions within the framework of <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity, where the black hole is surrounded by an anisotropic fluid acting as the matter source. We consider both linear and nonlinear forms of the function <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math>, enabling a detailed exploration of how anisotropic pressures and different <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> influence the spacetime structure. Furthermore, we derive the conditions on the coupling parameters ( <italic>&#946;</italic> <inf>1</inf>, <italic>&#946;</italic> <inf>2</inf>, <italic>&#946;</italic> <inf>3</inf>) under which the energy condition is satisfied. Utilising these constraints, we then investigate the thermodynamic behaviour of the resulting black hole solutions in the presence of various matter fields. An important outcome of this study is that the results obtained deviate from those predicted by standard General Relativity. It is also observed that these deviations depend explicitly on the interaction between the matter Lagrangian <math altimg='si9.svg'><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub></math> and the trace <italic>T</italic> of the energy-momentum tensor.

Aniruddha Ghosh

Ujjal Debnath

The new black hole solution with anisotropic fluid in <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity: Thermodynamics

This letter investigates the contribution of the <math altimg='si9.svg'><mrow><msqrt><mrow><mo>&#8722;</mo><mi>g</mi></mrow></msqrt><mi>&#958;</mi><mi>R</mi><msup><mi>&#981;</mi><mn>2</mn></msup></mrow></math> non-minimal interaction to the long range gravitational potential for massive scalar fields, found from the non-relativistic limit of the 2-2 scattering amplitude with graviton exchanges. Such coupling is most naturally motivated from the renormalisation of a scalar field theory with quartic self interaction in a curved spacetime. This is qualitatively different from the minimal ones like <math altimg='si10.svg'><mrow><msqrt><mi>G</mi></msqrt><msup><mi>h</mi><mrow><mi>&#956;</mi><mi>&#957;</mi></mrow></msup><msub><mi>T</mi><mrow><mi>&#956;</mi><mi>&#957;</mi></mrow></msub></mrow></math>, as the vertices corresponding to the former does not explicitly contain any scalar momenta, but instead explicitly contains the momentum carried by graviton line. For the minimal vertex, the long range gravitational potential up to one loop <math altimg='si11.svg'><mrow><mo>(</mo><mi mathvariant='script'>O</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>,</mo><mi mathvariant='script'>O</mi><mrow><mo>(</mo><msup><mi>G</mi><mn>2</mn></msup><mo>)</mo></mrow><mo>)</mo></mrow></math> was obtained earlier from the terms non-analytic in the transfer momentum, <math altimg='si12.svg'><mrow><msup><mi>q</mi><mrow><mo>&#8722;</mo><mn>2</mn></mrow></msup><mo>,</mo><mspace width='0.33em' /><msup><mi>q</mi><mrow><mo>&#8722;</mo><mn>1</mn></mrow></msup><mo>,</mo><mspace width='0.33em' /><mi>ln</mi><msup><mi>q</mi><mn>2</mn></msup></mrow></math>, yielding potentials respectively like <math altimg='si13.svg'><msup><mi>r</mi><mrow><mo>&#8722;</mo><mn>1</mn></mrow></msup></math>, <math altimg='si14.svg'><msup><mi>r</mi><mrow><mo>&#8722;</mo><mn>2</mn></mrow></msup></math>, <math altimg='si15.svg'><msup><mi>r</mi><mrow><mo>&#8722;</mo><mn>3</mn></mrow></msup></math>. However owing to the aforesaid explicit appearance of graviton&#8217;s transfer momentum for the non-minimal vertices, the leading contribution in this case comes at <math altimg='si6.svg'><mrow><mi mathvariant='script'>O</mi><mo>(</mo><mi>&#958;</mi><msup><mi>G</mi><mn>2</mn></msup><mo>)</mo></mrow></math>, and turns out to be subleading compared to even <math altimg='si15.svg'><msup><mi>r</mi><mrow><mo>&#8722;</mo><mn>3</mn></mrow></msup></math>. In order to complement this &#8216;screening&#8217; effect, we consider the three graviton vertex generated by the <math altimg='si16.svg'><mrow><mo>&#8764;</mo><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><msqrt><mrow><mo>&#8722;</mo><mi>g</mi></mrow></msqrt><mo linebreak='goodbreak'>/</mo><mi>G</mi></mrow></math> term in the action, where &#923; is the cosmological constant. This vertex does not contain any graviton momentum explicitly. With this vertex, and assuming short scale scattering much small compared to the Hubble horizon, we compute the seagull, the vacuum polarisation and the fish diagrams and obtain the 2-2 scattering amplitudes. The leading two body gravitational potential at <math altimg='si17.svg'><mrow><mi mathvariant='script'>O</mi><mo>(</mo><mi>&#958;</mi><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><msup><mi>G</mi><mn>2</mn></msup><mo>)</mo></mrow></math> behaves like <math altimg='si13.svg'><msup><mi>r</mi><mrow><mo>&#8722;</mo><mn>1</mn></mrow></msup></math>, even though it is much subleading compared to Newton&#8217;s potential due to the appearance of &#923;. We also discuss the scenario where this potential dominates the aforesaid <math altimg='si6.svg'><mrow><mi mathvariant='script'>O</mi><mo>(</mo><mi>&#958;</mi><msup><mi>G</mi><mn>2</mn></msup><mo>)</mo></mrow></math> one.

Avijit Sen Majumder

Sourav Bhattacharya

<italic>&#958;R&#981;</italic> <sup>2</sup> coupling, cosmological constant and quantum gravitational corrections to Newton&#8217;s potential

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

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

United States

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

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z. Chen

Z.K. Chen

J.C. Cheng

L.N. Cheng

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

J. Cottee-Meldrum

H.L. Dai

J.P. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denisenko

M. Destefanis

F. De Mori

B. Ding

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

X.L. Du

Y.Y. Duan

Z.H. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

R. Farinelli

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

J.H. Feng

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

We investigate the valence quark distributions of pions at a low initial scale ( $Q^2_0$ ) using Tsallis entropy, a non-extensive measure that effectively captures long-range correlations among internal constituents. Utilizing the maximum entropy approach, we adopt two distinct functional forms and fit experimental data using the elegant GLR-MQ-ZRS evolution equation to derive the model parameters. Our findings indicate that the resulting valence quark distributions provide an optimal fit to the experimental data, with $\textit{q}$ values deviating from unity. This deviation indicates that correlations among valence quarks play a significant role in shaping understanding of the internal structures of pions. Additionally, our computations of the first three moments of the pion quark distributions at $ Q^2 = 4$ GeV$^{2}$ display consistency with other theoretical models, thereby reinforcing the importance of incorporating valence quark correlations within this analytical framework.

Jingxuan Chen

Xiaopeng Wang

Yanbing Cai

Xurong Chen

Qian Wang

Valence quark distributions of pions: insights from Tsallis entropy * Supported by National Key R&D Program of China (2024YFE0109800, 2024YFE0109802); National Natural Science Foundation of China (12375073) and Guizhou Provincial Basic Research Program (Natural Science) (QKHJC-ZK[2023]YB027)

The correct choice for the matter Lagrangian <math altimg='si17.svg'><mrow><mo>(</mo><msub><mi mathvariant='script'>L</mi><mi mathvariant='script'>M</mi></msub><mo>)</mo></mrow></math> in the framework of <italic>f</italic>( <italic>R, T</italic>) theory of gravity, has been a fundamental yet often overlooked ambiguity. It has been a long-standing issue, whether to choose <math altimg='si1.svg'><mrow><msub><mi mathvariant='script'>L</mi><mi mathvariant='script'>M</mi></msub><mo linebreak='goodbreak'>=</mo><mi>p</mi></mrow></math> or <math altimg='si18.svg'><mrow><mo>&#8722;</mo><mi>&#961;</mi></mrow></math> as the proper definition of matter sector. In this work, we show that both choices lead to the same energy-momentum tensor, from thermodynamic point of view. However, for these two choices, the structure of the TOV equations are different. We construct and solve TOV equations using MIT bag model equation of state for <math altimg='si1.svg'><mrow><msub><mi mathvariant='script'>L</mi><mi mathvariant='script'>M</mi></msub><mo linebreak='goodbreak'>=</mo><mi>p</mi></mrow></math> and <math altimg='si18.svg'><mrow><mo>&#8722;</mo><mi>&#961;</mi></mrow></math>, and study the impact of the choices for matter Lagrangian on the maximum mass limit as well as M-R plot of compact stars. It is interesting to note that allowed range of gravity-matter coupling constant ( <italic>&#945;<inf>c</inf></italic>) is also different for <math altimg='si1.svg'><mrow><msub><mi mathvariant='script'>L</mi><mi mathvariant='script'>M</mi></msub><mo linebreak='goodbreak'>=</mo><mi>p</mi></mrow></math> and <math altimg='si5.svg'><mrow><msub><mi mathvariant='script'>L</mi><mi mathvariant='script'>M</mi></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mi>&#961;</mi></mrow></math>, i.e., <italic>&#945;<inf>c</inf></italic> can not be taken arbitrarily. Notably, through <math altimg='si1.svg'><mrow><msub><mi mathvariant='script'>L</mi><mi mathvariant='script'>M</mi></msub><mo linebreak='goodbreak'>=</mo><mi>p</mi></mrow></math>, we achieve a maximum mass of 2.78&#8201; <italic>M</italic> <inf>&#8857;</inf>, whereas for <math altimg='si5.svg'><mrow><msub><mi mathvariant='script'>L</mi><mi mathvariant='script'>M</mi></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mi>&#961;</mi></mrow></math>, we obtain a maximum mass of 2.41&#8201; <italic>M</italic> <inf>&#8857;</inf>. So, despite the same energy-momentum tensor for different choices of <math altimg='si19.svg'><msub><mi mathvariant='script'>L</mi><mi mathvariant='script'>M</mi></msub></math>, the upper limit of maximum mass is significantly modified.

Debadri Bhattacharjee

Pradip Kumar Chattopadhyay

Thermodynamic invariance of the energy-momentum tensor under matter-Lagrangian choices and its astrophysical implications in <italic>f</italic>( <italic>R, T</italic>) gravity

This study investigates the dynamics of dissipative gravitational collapse within the framework of <italic>f</italic>( <italic>R</italic>) gravity, focusing on the exponential correction model <math altimg='si7.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>R</mi><mo linebreak='goodbreak'>&#8722;</mo><msub><mi>&#946;</mi><mn>1</mn></msub><msub><mi>R</mi><mi>s</mi></msub><mrow><mo stretchy='true'>(</mo><mn>1</mn><mo linebreak='badbreak'>&#8722;</mo><msup><mi>e</mi><mrow><mo>&#8722;</mo><mi>R</mi><mo>/</mo><msub><mi>R</mi><mi>s</mi></msub></mrow></msup><mo stretchy='true'>)</mo></mrow></mrow></math> and incorporating the concept of a horizon function. The model considers a radiating anisotropic stellar object with string density, matched to an exterior Vaidya spacetime. We thoroughly derive the junction conditions at the stellar boundary and emphasize the role of non-zero radial pressure induced by heat flux. By employing the horizon function alongside the exponential correction model and Finch-Skea metric assumptions, we examine the conditions under which black holes can form as a final state of collapse. A graphical analysis supports the theoretical model, demonstrating how the presence of string density influences the collapse process and can prevent total mass vanishing, thereby allowing black hole formation in <italic>f</italic>( <italic>R</italic>) gravity.

Azerbaijan

Pakistan

M. Ilyas

Zaib Un Nisa Shinwari

Fawad Khan

Sidra Marwat

Role of density inhomogeneity in dissipative collapse through Finch-Skea spacetime in <italic>f</italic>( <italic>R</italic>) gravity