In this paper we study a complete set of scalar and pseudoscalar four-quark operators, with a particular emphasis on their renormalization within a gauge-invariant renormalization scheme (GIRS). We focus on operators that do not mix with lower-dimensional operators by virtue of their transformation properties under the flavor-symmetry group. This class includes all <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>F</mi><mo>=</mo><mn>2</mn></math> operators, as well as their partners that transform under the same irreducible representations of the flavor group. These encompass a substantial subset of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>F</mi><mo>=</mo><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>F</mi><mo>=</mo><mn>0</mn></math> operators. The present analysis provides a detailed classification of all four-quark operators, exploring their Fierz identities, symmetry properties, and mixing patterns. Different variants of GIRS are explored, including a “democratic” version that treats all mixing operators uniformly. For selected variants, which exhibit smaller mixing effects, we present the conversion matrices from GIRS to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>MS</mi><mo stretchy="true">¯</mo></mover></math> scheme at next-to-leading order.

Cyprus

G. Spanoudes

M. Costa

K. Mitsidi

H. Panagopoulos

Classification of four-quark operators with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>F</mi><mo>≤</mo><mn>2</mn></math> under flavor symmetry and their renormalization in a gauge-invariant scheme

We investigate late-time cosmic acceleration within the framework of $\textit{f}$($\textit{Q}$) gravity supplemented by a phenomenological nonlinear equation of state of the form $$p = A\rho - B\sqrt{\rho }.$$ Adopting a power-law ansatz $$f(Q)=\gamma ,(Q/Q_0)^{n},$$ we derive analytic expressions for the energy density and Hubble function and confront the model with a combined dataset consisting of CC, SNIa, BAO, quasar, and GRB observations covering $$0.106<z<2.33.$$ A Bayesian MCMC analysis constrains the parameter set $${H_0, A, B, c, n}$$ and yields $$H_0 \simeq 71.6^{+1.0}_{-1.9}~\text {km}~\text {s}^{-1}~\text {Mpc}^{-1}$$ for the joint sample, together with a transition redshift $$z_{\textrm{tr}}\approx 0.68.$$ Cosmographic diagnostics indicate a present-day deceleration parameter $$q_0\approx -0.59,$$ with mild deviations of the jerk and snap parameters from their $$\Lambda $$ CDM values at low redshift. Thermodynamic and causal consistency is ensured by the condition $$0\le c_s^2(z)\le 1,$$ while the matter-sector energy conditions remain satisfied up to $$z\sim {\mathcal {O}}(1).$$ A statistical comparison with the concordance model shows that the proposed $$f(Q)+$$ nEoS scenario achieves a goodness of fit comparable to $$\Lambda $$ CDM over the same dataset, with $$\chi ^{2_{\min }^{\textrm{model}}}=255.93$$ versus $$\chi ^{2_{\min }^{\Lambda \textrm{CDM}}}=260.5$$ and $$\chi ^2_\textrm{red}\approx 0.96$$ for both cases. The Akaike Information Criterion yields $$\Delta {\textrm{AIC}}\approx 1.4,$$ indicating statistical equivalence with a mild preference for $$\Lambda $$ CDM due to its smaller parameter space. Therefore, the model provides a viable description of the late-time expansion history, allowing controlled deviations from $$\Lambda $$ CDM that modestly alleviate, though do not resolve, the $$H_0$$ tension. Several other interesting properties of a nEoS are also elucidated upon.

Türkiye

Mehmet Özansoy

India

Bhupendra Shukla

Değer Sofuoğlu

South Africa

Aroonkumar Beesham

Rajnee Tripathi

Cosmic acceleration in $\textit{f}$($\textit{Q}$) gravity: a nonlinear equation of state approach

The decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> is studied using a sample of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>2712.4</mn><mo>±</mo><mn>14.3</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mtext> </mtext><mtext> </mtext><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></math> events collected with the BESIII detector. The decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> is observed for the first time in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></math> decays via the intermediate state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> and the product branching fraction <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><mi>η</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>×</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>η</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">)</mo><mo>×</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">)</mo></mrow></math> is determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>3.77</mn><mo>±</mo><mn>0.43</mn><mo>±</mo><mn>0.30</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup></math>, where the first uncertainty is statistical and the second is systematic. The branching fraction of isospin-violating decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1285</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo><msup><mi>π</mi><mn>0</mn></msup><mo stretchy="false">→</mo><mi>γ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> is determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>7.36</mn><mo>±</mo><mn>2.25</mn><mo>±</mo><mn>2.36</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>8</mn></mrow></msup></math> with statistical significance of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2.9</mn><mi>σ</mi></math>. Since no <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub></math> signal is evident in either the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo><msup><mi>π</mi><mn>0</mn></msup></math> mass spectrum, upper limits are set to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">)</mo><mo>×</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup><mo stretchy="false">)</mo><mo>&lt;</mo><mn>3.09</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">→</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">)</mo><mo>×</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">)</mo><mo>&lt;</mo><mn>7.97</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>8</mn></mrow></msup></mrow></math> at 90% confidence level, respectively.

China

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

Germany

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

JINR

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

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

South Korea

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

Observation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><mi>η</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo></math> via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo><msup><mi>π</mi><mn>0</mn></msup></math>

Fission fragment spectroscopic measurement has been carried out for the system, 232Th( 9Be, <italic>f</italic>) at E <inf><italic>lab</italic></inf> = 46 MeV. The prompt gamma rays decaying from the excited states of the fission fragments were detected using the INGA (Indian National Gamma Array) spectrometer. The dynamical aspects of the fissioning reaction has been investigated by measuring the contributions from the complete as well as incomplete fusion-fission channels. The relative cumulative isotopic yield distribution profiles of the even-even fission fragments have been measured by using the prompt <italic>&#947;</italic>-ray coincidence analysis technique. From the pair wise measured yields of the fission fragments, the contributions of the competing complete ( 9Be + 232Th &#8239;&#8594;&#8239; 241Pu*) and incomplete (n + 232Th &#8239;&#8594;&#8239; 233Th* and 4,5He + 232Th &#8239;&#8594;&#8239; 236,237U*) fusion-fission channels have been extracted, and the respective values are found to be (66 &#8239;&#177;&#8239; 6)% and (34 &#8239;&#177;&#8239; 4)%. The individual contributions from the two accompanying incomplete fusion-fission channels are also independently measured, and both the channels seem to contribute almost in equal proportions. The measured yields are found to be in good agreement with the GEF (GEneral description of Fission) model predicted results obtained by incorporating the measured contributing factors from the competing fissioning channels. The observed findings are also validated by performing the analysis based on the Bayesian inference method.

Krishna Debnath

Aniruddha Dey

P.K. Nayak

A.K. Mondal

R. Shil

A. Kundu

Biswajit Das

K. Mandal

S. Biswas

P. Dey

A. Bairagya

Vishal Malik

A. Sindhu

B. Mukherjee

D.C. Biswas

R. Palit

K. Banerjee

S. Mukhopadhyay

A. Chakraborty

Exploring fission dynamics of 232th( 9be, <italic>f</italic>) following prompt <italic>&#947;</italic>-ray spectroscopy

In this study, we investigate the attributes of compact stars within the configuration of <math altimg='si12.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>G</mi><mo>,</mo><mi>&#966;</mi><mo>)</mo></mrow></math> gravity, by incorporating the Gauss-Bonnet term <italic>G</italic> and a scalar field &#966;. By adopting different functional forms of <math altimg='si12.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>G</mi><mo>,</mo><mi>&#966;</mi><mo>)</mo></mrow></math>, we analyze their impact on the equilibrium structure of dense stellar objects. Further, we adopt the Krori-Barua metric potential, defined as <math altimg='si13.svg'><mrow><mi>&#957;</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>B</mi><msup><mi>r</mi><mn>2</mn></msup><mo linebreak='goodbreak'>+</mo><mi>C</mi></mrow></math> and <math altimg='si14.svg'><mrow><mi>&#955;</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>A</mi><msup><mi>r</mi><mn>2</mn></msup><mo>,</mo></mrow></math> here, <italic>A, B</italic> and <italic>C</italic> are constants. To ensure a physically viable compact configuration, we impose matching conditions between the interior spherically symmetric space-time and the Schwarzschild geometry. Moreover, we investigate the attributes of the celestial star models by assuming the <math altimg='si12.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>G</mi><mo>,</mo><mi>&#966;</mi><mo>)</mo></mrow></math> gravity model. We attain the modified field equations and examine key physical characteristics, namely energy density and pressure components, stability conditions, equation of state, and energy constraints. These findings provide new insights into the viability of alternative gravity models in explaining extreme astrophysical environments and offer potential observational signatures to constrain <math altimg='si12.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>G</mi><mo>,</mo><mi>&#966;</mi><mo>)</mo></mrow></math> gravity through future gravitational wave and electromagnetic observations.

Pakistan

Zoya Asghar

Jordan

Azerbaijan

M. Farasat Shamir

Saudi Arabia

Fatemah Mofarreh

Uzbekistan

Javlon Rayimbaev

Otaboyev Sirajiddin

Fayzullo Shayimov

Exploring compact stars in modified <math altimg='si12.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>G</mi><mo>,</mo><mi>&#966;</mi><mo>)</mo></mrow></math> gravity

We investigate the gravitational baryogenesis scenario within the context of $\textit{F}$($\textit{R}$) gravity’s rainbow which incorporates both modified gravity and energy-dependent spacetime. This study explores a mechanism for generating baryon asymmetry based on the interaction between the derivative of the Ricci scalar $\textit{R}$ and the baryon current within the framework of $\textit{F}$($\textit{R}$) gravity’s rainbow. The rainbow functions, arising from quantum gravity effects, modify the gravitational interaction and the Friedmann equations, leading to a distinct evolution of the baryon asymmetry compared to standard $\textit{F}$($\textit{R}$) gravity. We analyze the conditions under which a viable baryon asymmetry can be produced, taking into account the constraints from cosmological observations and the specific form of the $\textit{F}$($\textit{R}$) function. By examining the cosmological equations in the context of $\textit{F}$($\textit{R}$) gravity’s rainbow, we obtain power-law solutions for these equations. We also identify the decoupling temperature and the ratio of baryonic number to entropy density in this model, depending on the model’s parameters. First, we discuss the acceptable intervals of the model’s parameters which are defined by constraints on the background quantity. We note that the decoupling temperature and the ratio of baryon-to-entropy in these models depend on the value of the rainbow function. We compare the predictions of this model with the existing observational data. Our results suggest that $\textit{F}$($\textit{R}$) gravity’s rainbow provides a novel mechanism for gravitational baryogenesis, potentially explaining the observed baryon asymmetry in the universe while incorporating quantum gravity corrections.

Iran

Parviz Goodarzi

Gravitational baryogenesis in $\textit{F}$($\textit{R}$) gravity’s rainbow

We construct an exact analytic solution of the revised small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> helicity evolution equations from Borden, Kovchegov, and Li [Helicity evolution at small x: Quark to gluon and gluon to quark transition operators, <a href="http://dx.doi.org/10.1007/JHEP09(2024)037">J. High Energy Phys. 09 (2024) 037</a>], where the contributions of the quark-to-gluon and gluon-to-quark transition operators were newly included. These evolution equations are written in the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> and -<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub></math> limit and are double-logarithmic, resumming powers of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub><msup><mi>ln</mi><mn>2</mn></msup><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><mi>x</mi><mo stretchy="false">)</mo></math>. Here <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub></math> are the numbers of quark colors and flavors, respectively, while <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math> is the strong coupling constant and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> is the Bjorken-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> variable. Using our solution, we obtain analytic, small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>, large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> and -<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub></math> expressions for the flavor singlet quark and gluon helicity parton distribution functions (PDFs) and for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mn>1</mn></msub></math> structure function as double-inverse Laplace transforms. We also extract analytic expressions for the eigenvalues of the matrix of polarized Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) anomalous dimensions and, subsequently, analytic expressions for each of the four individual polarized anomalous dimensions themselves (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>γ</mi><mrow><mi>q</mi><mi>q</mi></mrow></msub><mo>,</mo><mi mathvariant="normal">Δ</mi><msub><mi>γ</mi><mrow><mi>q</mi><mi>G</mi></mrow></msub><mo>,</mo><mi mathvariant="normal">Δ</mi><msub><mi>γ</mi><mrow><mi>G</mi><mi>q</mi></mrow></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>γ</mi><mrow><mi>G</mi><mi>G</mi></mrow></msub></math>): these expressions resum powers of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub><mo>/</mo><msup><mi>ω</mi><mn>2</mn></msup></math> to all orders at large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub></math> (with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi></math> the Mellin moment variable). We extract the leading small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> asymptotic power-law growth of the helicity distributions, given by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi mathvariant="normal">Σ</mi><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo><mo>∼</mo><mi mathvariant="normal">Δ</mi><mi>G</mi><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo><mo>∼</mo><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo><mo>∼</mo><msup><mrow><mo stretchy="false">(</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><mo stretchy="false">)</mo></mrow><msub><mi>α</mi><mi>h</mi></msub></msup></math>, where the intercept <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>h</mi></msub></math> satisfies an algebraic equation. Although the algebraic complexity of the equation prevented us from obtaining a general analytic expression for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>h</mi></msub></math>, we determine <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>h</mi></msub></math> numerically for various values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub></math> (and, for the special case of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><msub><mi>N</mi><mi>c</mi></msub></math>, we determine <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>h</mi></msub></math> analytically). We further obtain the explicit asymptotic expressions for the helicity distributions, which yield numerical values for the ratio of the gluon helicity PDF to the flavor singlet quark helicity PDF in the small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> asymptotic limit (for different <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>/</mo><msub><mi>N</mi><mi>c</mi></msub></math>). Just as for the analytic solution to small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> helicity evolution equations in the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> limit constructed in Borden and Kovchegov [Analytic solution for the revised helicity evolution at small x and large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">N</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math>: New resummed gluon-gluon polarized anomalous dimension and intercept, <a href="http://dx.doi.org/10.1103/PhysRevD.108.014001">Phys. Rev. D 108, 014001 (2023)</a>] and for the iterative solution to the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> and -<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub></math> helicity evolution equations constructed in Borden, Kovchegov, and Li [Helicity evolution at small x: Quark to gluon and gluon to quark transition operators, <a href="http://dx.doi.org/10.1007/JHEP09(2024)037">J. High Energy Phys. 09 (2024) 037</a>], we again find that all our predictions for polarized DGLAP anomalous dimensions are fully consistent with the existing finite-order calculations. Similar to the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> case [Borden and Kovchegov, Analytic solution for the revised helicity evolution at small x and large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">N</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math>: New resummed gluon-gluon polarized anomalous dimension and intercept, <a href="http://dx.doi.org/10.1103/PhysRevD.108.014001">Phys. Rev. D 108, 014001 (2023)</a>], our intercept <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>h</mi></msub></math> (evaluated at various <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub></math> values) exhibits a very slight disagreement with the predictions made within the infrared evolution equations framework in Bartels et al. [Flavor singlet contribution to the structure function G(1) at small x, <a href="http://dx.doi.org/10.1007/s002880050285">Z. Phys. C 72, 627 (1996)</a>], Blümlein and Vogt [The singlet contribution to the structure function <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>, <a href="http://dx.doi.org/10.1016/0370-2693(96)00958-6">Phys. Lett. B 386, 350 (1996)</a>], Boussarie et al. [Proton spin structure at small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>, <a href="http://dx.doi.org/10.1016/j.physletb.2019.134817">Phys. Lett. B 797, 134817 (2019)</a>].

Jeremy Borden

Yuri V. Kovchegov

Analytic solution for the helicity evolution equations at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> and large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub></math>

We present a cosmological analysis of an exponential $\textit{f}$($\textit{Q}$) gravity model, within the dynamical systems formalism. Following the method introduced by Böhmer et al. (Universe 9:166, 2023), the modified Friedmann modified equations are successfully reduced to an autonomous system. Given the exponential form of $\textit{f}$($\textit{Q}$), the equilibrium conditions result in transcendental equations, which we approximate to identify the critical points. We therefore perform a general stability analysis of these points in terms of the model parameters. Finally, we extend the model by including a linear dark energy-dark matter interaction, where the equilibrium points are found with their stability properties. The model exhibits the three main domination epochs in the Universe, as well as a non-trivial impact on the late-time de Sitter attractor.

Colombia

Ivan Vasquez

A. Oliveros

Phase space analysis of an exponential model in $\textit{f}$($\textit{Q}$) gravity including linear dark-sector interactions

The aim of this paper is to develop the non-interacting Barrow holographic dark energy model in the <italic>f</italic>( <italic>Q</italic>) gravity (where <italic>Q</italic> is the non-metricity) using a correspondence approach. To proceed it further, we utilize the hubble horizon as the infrared cutoff and assume a power-law form for the scale factor. The cosmological effects of the model are analyzed using the equation of state parameter and phase plane analysis. Additionally, the stability of the model is examined through the squared speed of sound. The results indicate that <italic>&#969;<inf>BHDE</inf></italic> corresponds to the phantom era (i.e., <math altimg='si7.svg'><mrow><msub><mi>&#969;</mi><mrow><mi>B</mi><mi>H</mi><mi>D</mi><mi>E</mi></mrow></msub><mo linebreak='goodbreak'>&lt;</mo><mo>&#8722;</mo><mn>1</mn></mrow></math>, which indicates an expansion faster than the standard accelerated expansion). The <math altimg='si8.svg'><mrow><mo>(</mo><msub><mi>&#969;</mi><mrow><mi>B</mi><mi>H</mi><mi>D</mi><mi>E</mi></mrow></msub><mo linebreak='goodbreak'>&#8722;</mo><msubsup><mi>&#969;</mi><mrow><mi>B</mi><mi>H</mi><mi>D</mi><mi>E</mi></mrow><mo>&#8242;</mo></msubsup><mo>)</mo></mrow></math> plane lies in the freezing region, while the statefinder analysis reveals Chaplygin gas like characteristics. Furthermore, the stability analysis confirms that the model remains stable throughout the cosmic evolution. We can conclude that the results are in good agreement with current observations.

Madiha Ajmal

Eman M. Moneer

M. Sharif

Euaggelos E. Zotos

Cosmological analysis of non-interacting barrow holographic dark energy model in <italic>f</italic>( <italic>Q</italic>) gravity

The dependence of $$\textrm{f}_{0}$$ (980) production on the final-state charged-particle multiplicity is reported for proton–proton (pp) collisions at the centre-of-mass energy, $$\sqrt{s}=$$ 13 TeV. The production of $$\textrm{f}_{0}$$ (980) is measured with the ALICE detector via the $$\textrm{f}_0 (980) \rightarrow \pi ^{+}\pi ^{-}$$ decay channel in a midrapidity region of $$|y|<$$ 0.5. The evolution of the integrated yields and mean transverse momentum of f $$_{0}$$ (980) as a function of charged-particle multiplicity measured in pp at $$\sqrt{s}=$$ 13 TeV follows the trends observed in pp at $$\sqrt{s}=$$ 5.02 TeV and in proton–lead (p–Pb) collisions at $$\sqrt{s_{\textrm{NN}}}=$$ 5.02 TeV. Particle yield ratios of $$\textrm{f}_{0}$$ (980) to $$\pi ^{\pm }$$ and $$\textrm{K}^{*}$$ (892) $$^{0}$$ are found to decrease with increasing charged-particle multiplicity. These particle ratios are compared with calculations from the canonical statistical thermal model as a function of charged-particle multiplicity. The thermal model calculations provide a better description of the decreasing trend of particle ratios when no strange or antistrange quark composition for f $$_{0}$$ (980) is assumed, which suggests that the data do not support significant hidden strangeness in the $$\textrm{f}_{0} (980)$$ .

I. Abualrob

S. Acharya

Switzerland

G. Aglieri Rinella

L. Aglietta

M. Agnello

N. Agrawal

Z. Ahammed

S. Ahmad

Slovakia

I. Ahuja

Indonesia

ZUL. Akbar

A. Akindinov

V. Akishina

M. Al-Turany

D. Aleksandrov

B. Alessandro

H. Alfanda

Mexico

R. Alfaro Molina

Multiplicity dependence of f $$_{\textbf{0}}$$ (980) production in pp collisions at $$\mathbf {\sqrt{s}}=$$ 13 TeV