Based on a sample of $2.7\times10^{9}$ $\psi(3686)$ events collected by the BESIII detector operating at the BEPCII collider, the decay $\psi(3686)\to\gamma\chi_{cJ}, \chi_{cJ}\to\eta\eta\eta^{\prime}$ is analyzed. The decay modes $\chi_{c1}$ and $\chi_{c2}\to\eta\eta\eta^{\prime}$ are observed for the first time, and their corresponding branching fractions are determined to be ${\cal{B}}(\chi_{c1}\to\eta\eta\eta^{\prime}) = $ $ (1.40\, \pm 0.13\, (\text{stat.}) \pm 0.09\, (\text{sys.})) \times 10^{-4}$ and ${\cal{B}}(\chi_{c2}\to\eta\eta\eta^{\prime}) = (4.18\, \pm 0.84\, (\text{stat.}) \pm 0.48\, (\text{sys.})) \times 10^{-5}$ . An upper limit on the branching fraction of $\chi_{c0}\to\eta\eta\eta^{\prime}$ is set as $2.59 \times 10^{-5}$ at a 90% confidence level (CL). A partial wave analysis (PWA) of the decay $\chi_{c1}\to\eta\eta\eta^{\prime}$ is performed to search for the $1^{-+}$ exotic state $\eta_1(1855)$ . The PWA result indicates that the structure in the $\eta\eta^{\prime}$ mass spectrum is attributed to $f_0(1500)$ , while in the $\eta\eta$ mass spectrum, it is attributed to the $0^{++}$ phase space. The upper limit of ${\cal{B}}(\chi_{c1}\to\eta_{1}(1855)\eta) \cdot {\cal{B}}(\eta_{1}(1855)\to\eta\eta^{\prime}) \lt $ $ 9.79 \times 10^{-5}$ is set based on the PWA at 90% CL.

China

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. 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

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.J. Chen

Z.K. Chen

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

J. Cottee-Meldrum

J.J. Cui

H.L. Dai

J.P. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denysenko

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

Y.Y. 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

L. Feng

Q.X. Feng

Search for $\textit{η}$ $_{1}$(1855) in $\textit{χ}$ $\textit{cJ}$ → $\textit{ηηη}$′ decays * Supported in part by National Key R&D Program of China (2023YFA1606000, 2023YFA1606704); National Natural Science Foundation of China (NSFC) (11635010, 11935015, 11935016, 11935018, 12025502, 12035009, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017, 12361141819); the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; CAS (YSBR-101); 100 Talents Program of CAS; The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; Agencia Nacional de Investigación y Desarrollo de Chile (ANID), Chile (ANID PIA/APOYO AFB230003); German Research Foundation DFG (FOR5327); Istituto Nazionale di Fisica Nucleare, Italy; Knut and Alice Wallenberg Foundation (2021.0174, 2021.0299); Ministry of Development of Turkey (DPT2006K-120470); National Research Foundation of Korea ( 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 ( B50G670107); Polish National Science Centre (2024/53/B/ST2/00975); Swedish Research Council (2019.04595); U. S. Department of Energy (DE-FG02-05ER41374)

We introduce a novel level crossing phenomenon in the mass mixing between QCD axions: one canonical QCD axion and one $ Z_{{\cal{N}}} $ axion. The level crossing can occur at or slightly before the QCD phase transition critical temperature, depending on the ratio of the axion decay constants, $ \sim 1.69 $ . The cosmological evolution of the mass eigenvalues in these two scenarios is similar; however, the transition of axion energy density differs significantly. Finally, we estimate the relic density of the QCD axion dark matter in this context. Additionally, this level crossing may have some interesting cosmological implications.

Hai-Jun Li

Yu-Feng Zhou

Mass mixing between QCD axions * Supported by the CAS Project for Young Scientists in Basic Research YSBR-006, the National Key R&D Program of China (2017YFA0402204), and the National Natural Science Foundation of China (11821505, 11825506, 12047503)

We use a modified relativistic quark model to study the properties of excited charmed and charmed strange mesons. We calculate the masses and wave functions of conventional charmed and charmed strange mesons incorporating both spin and $\textit{S}$-$\textit{D}$ mixing effects and fit parameters of the potential model with known experimental states using differential evolution techniques. Using leading Born-Oppenheimer expansion, we compute the spectrum and wave functions of the first gluonic excited state of charmed and charmed strange mesons. We examine the effects of gluonic excitation on the spectrum of the resulting hybrid mesons. Using our calculated spectrum and wave functions, we determine the radiative transitions of the conventional and hybrid open charm mesons. We compare our calculations with experimental data and other works. We expect our results will be beneficial in the detection of charmed and charmed strange conventional and hybrid mesons.

Pakistan

Saba Noor

Faisal Akram

Bilal Masud

Study of excited $\textit{D}$ and D$_{s}$ mesons in a relativized quark model * F. A. acknowledges HEC grant 20-15728/NRPU/R&D/HEC/2021, Pakistan

This study investigates the intrinsic electric dipole moment (EDM) of the $\textit{τ}$ lepton, which is an important quantity in the search for physics beyond the Standard Model (BSM). In preparation for future measurements at the Super Tau-Charm Facility (STCF), we employ Monte Carlo simulations of the $ e^+e^- \rightarrow \tau^+\tau^- $ process and optimize the analysis methodology for EDM extraction. Machine learning techniques are implemented to efficiently identify signal events ( $ \tau^\pm\rightarrow \pi^\pm\pi^0\nu_\tau $ ), which result in a significant improvement in signal-to-noise ratio. Our optimized event selection algorithm achieves 80.0% signal purity with 6.3% efficiency. We develop an analytical approach for $\textit{τ}$ lepton momentum reconstruction and derive the squared spin density matrix along with optimal observables, which maximize the sensitivity to $ d_\tau $ . The relationship between these observables and the EDM is established with the estimated sensitivity of $ |d_\tau| \lt 3.89\times 10^{-18}\,e\cdot\mathrm{cm} $ at a 68% confidence level. These results provide a foundation for future experimental measurements of the $\textit{τ}$ lepton EDM in STCF experiments.

Xulei Sun

Yongcheng Wu

Xiaorong Zhou

Sensitivity study of the tau lepton electric dipole moment at the Super Tau-Charm Facility * Supported by the National Key R&D Program of China (2022YFA1602200, 2023YFA1607200); the National Natural Science Foundation of China (NSFC) (12341501, 12341503, 12341504); the international partnership program of the Chinese Academy of Sciences (211134KYSB20200057). Xulei Sun is supported by the Undergraduate Research Program of the University of Science and Technology of China and the Xinhe Scholar Program of the School of the Gifted Young

This paper investigates the spectral form factor (SFF) of the quadratic $\textit{R}$-para-particle Sachdev-Ye-Kitaev ($\textit{R}$-PSYK ) model with various random matrix ensemble couplings. We generalize previous work on Gaussian Unitary Ensemble (GUE) couplings to all three Gaussian ensembles (GUE, GOE, GSE) and three circular ensembles (CUE, COE, CSE). Through analytical and numerical methods, we establish precise correspondences between GUE and CUE results, demonstrating their SFFs satisfy $$ {\mathcal{K}}_{\textrm{GUE}}(2t) $$ ≈ $$ {\mathcal{K}}_{\textrm{CUE}}(t) $$ in the time regime 1 ≪ $\textit{t}$ ≪ $\textit{N}$. For the symplectic ensembles, we observe similar behavior with appropriate time rescaling, while we only provide the calculation method for the orthogonal ensembles.

Tingfei Li

Spectral form factor of quadratic $\textit{R}$-para-particle SYK model with random matrix coupling

In this work we introduce the rescaled <math altimg='si1.svg'><msup><mi mathvariant='script'>R</mi><mn>2</mn></msup></math>-corrected minimally coupled scalar field theory, a theory that contains minimal quantum corrections of the single scalar field Lagrangian. We develop the theoretical framework in the Jordan frame where the baryons geodesics are free fall geodesics and we do not treat the theory as a two scalar field theory in the Einstein frame. The theoretical framework can be reduced to a single scalar field theory framework by using a perturbative expansion at the level of the field equations, making the resulting theory easy to tackle analytically. The first two quantum corrections contain two terms, a linear <math altimg='si20.svg'><mrow><mo>&#8764;</mo><mi mathvariant='script'>R</mi></mrow></math> and a quadratic term <math altimg='si21.svg'><mrow><mo>&#8764;</mo><msup><mi mathvariant='script'>R</mi><mn>2</mn></msup></mrow></math>. The effect of the linear term alters the Einstein-Hilbert term, making the resulting theory a rescaled version of Einstein-Hilbert gravity. Due to the presence of the rescaled Einstein-Hilbert term <math altimg='si22.svg'><mrow><mo>&#8764;</mo><mi>&#955;</mi><mfrac><mi mathvariant='script'>R</mi><mrow><mn>16</mn><mi>&#960;</mi><mi>G</mi></mrow></mfrac></mrow></math>, the gravitational constant will no longer be that of Newton&#8217;s, but a rescaled one <math altimg='si23.svg'><mfrac><mi>G</mi><mi>&#955;</mi></mfrac></math> and hence gravity can be stronger primordially, or even weaker. The perspective of having stronger gravity primordially, is compatible with intuition, since one expects a stronger gravity primordially, but having a weaker gravity for some reason is not prohibited theoretically. The attribute of our theoretical framework is that it allows a stronger gravity primordially, which returns to ordinary gravity as the curvature of the Universe decreases. We examine the effects of the quantum terms on several mainstream scalar field inflationary potentials, such as hybrid inflation, monomial inflation and power-law inflation, and we demonstrate that the hybrid inflation and power-law inflation, which are 3-parameter models, are compatible with the Atacama Cosmology Telescope data in the strong gravity limit, while the monomial inflation, which is a 4-parameter model, can be compatible with the Atacama Cosmology Telescope data in the weak gravity limit, however the model suffers from perturbative expansion break down during inflation.

Greece

Kazakhstan

V.K. Oikonomou

Strong gravity effects on <math altimg='si1.svg'><msup><mi mathvariant='script'>R</mi><mn>2</mn></msup></math>-corrected single scalar field inflation and compatibility with the ACT data

<p>We construct a realistic supersymmetric model for superheavy metastable cosmic strings (CSs) that can be investigated in the current pulsar timing array (PTA) experiments. It is based on shifted <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math>-hybrid inflation in which the symmetry breaking <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>4</mn><msub><mo stretchy="false">)</mo><mi>c</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>L</mi></msub><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>R</mi></msub><mo stretchy="false">→</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mo stretchy="false">)</mo><mi>c</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>L</mi></msub><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>R</mi></msub></math> proceeds along an inflationary trajectory such that the topologically unstable primordial monopoles are inflated away. The breaking of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>R</mi></msub><mo stretchy="false">→</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>Y</mi></msub></math> after inflation ends yields the superheavy metastable CSs carrying the right handed neutrino zero modes that generate the stochastic gravitational wave background, which we show is consistent with the current PTA dataset and the LIGO O3 run. The scalar spectral index <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>s</mi></msub></math> and the tensor-to-scalar ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi></math> are compatible with the Planck 2018 and Atacama Cosmology Telescope measurements. Both reheating and leptogenesis are briefly discussed.</p>

Adeela Afzal

Maria Mehmood

Saudi Arabia

Mansoor Ur Rehman

Qaisar Shafi

Supersymmetric hybrid inflation and current-carrying metastable cosmic strings in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>4</mn><msub><mo stretchy="false">)</mo><mi>c</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>L</mi></msub><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>R</mi></msub></math>

The classical Isaacson’s procedure for describing back-reaction of the averaged energy–momentum for high frequency gravitational waves is generalized to the $\textit{f}$($\textit{R}$) gravity case. From the beginning it is assumed that an initial background could be arbitrary one. Then, we restrict the background to be de Sitter, which is a novelty regarding the study of a back-reaction in $\textit{f}$($\textit{R}$) gravity. Consideration of the de Sitter space as a background spacetime allows us to provide the averaging procedure completely. Using the results on the de Sitter space and generalizing the Isaacson procedure, we construct the averaged energy–momentum on an additionally curved (averaged) background. Consistency tests for de Sitter spacetime are performed both at the background and perturbative regimes. Our results generalize previous studies in which the authors consider the flat (Minkowski) spacetime as the initial background.

Petr Tretyakov

Alexander Petrov

On energy–momentum tensor for gravitational waves in $\textit{f}$($\textit{R}$) gravity

This study is concern to the homothetic symmetry approach to get exact solutions for locally rotationally symmetric (LRS) Bianchi type-I spacetimes within the framework of <math altimg='si108.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></math> gravity, revealing that such spacetimes posses homothetic symmetry of different dimensions. By employing the Rif tree algorithm implemented in Maple, we systematically transform the symmetry and field equations into a set of constraints on the metric functions, enabling the derivation of exact analytical forms for the homothetic vector fields. Furthermore, we compute the corresponding physical quantities, including the energy density <math altimg='si109.svg'><mi>&#961;</mi></math>, pressure <math altimg='si110.svg'><mi>p</mi></math>, Ricci scalar <math altimg='si111.svg'><mi>R</mi></math>, shear scalar <math altimg='si8.svg'><msup><mi>&#963;</mi><mn>2</mn></msup></math>, equation of state <math altimg='si112.svg'><mi>w</mi></math> and modified gravity function <math altimg='si113.svg'><mrow><mi>F</mi><mo>(</mo><mi>r</mi><mo>)</mo></mrow></math>, for each solution, providing crucial insights into the geometric and physical properties of these spacetimes within the <math altimg='si107.svg'><mrow><mi>F</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></math> gravity.

Jamshed Khan

Sumaira Saleem Akhtar

Ambreen Ayub

Exact LRS Bianchi type I solutions in quadratic <math altimg='si107.svg'><mrow><mi>F</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></math> gravity from homothetic symmetries: A Rif tree approach

We propose a holographic realization of symmetry operators for symmetries associated to isometries in terms of non-BPS Kaluza-Klein monopoles. Their existence is supported by dualities, and their action can be inferred by consistency with well-known String Theory constructions. We use our proposal to describe the U(1) superconformal R-symmetry of the Klebanov-Witten 4d $$ \mathcal{N} $$ = 1 theory dual to Type IIB String Theory on $\textit{AdS}$ × $\textit{T}$ . We precisely reproduce the expectations from field theory, including the ’t Hooft self-anomaly of the R-symmetry and the mixed ’t Hooft anomaly with the baryonic symmetry. For a choice of boundary conditions, the R-symmetry becomes non-invertible and the worldvolume action for the non-BPS Kaluza-Klein monopole precisely accounts for this.