We compute the contributions of heavy quarks to the deep-inelastic scattering structure functions $\textit{F}$ and $\textit{F}$ at next-to-leading order of perturbative QCD in the ACOT scheme. Both analytic results including the details of the calculation as well as numerical results for the neutral and charged current cases are presented. Our study thus lays the groundwork for future measurements of these two structure functions in experiments such as the SHiP experiment.

Germany

Edoardo Spezzano

Tomas Ježo

Australia

Michael Klasen

United States

Peter Risse

France

Ingo Schienbein

Heavy-quark contributions to the DIS structure functions $\textit{F}$ 4 and $\textit{F}$ 5 at NLO in the ACOT scheme

Gauss–Bonnet inflation typically affects the dynamics over an extended portion of the trajectory, making it difficult to isolate a controlled imprint at CMB scales. We consider a trajectory-selective coupling $$\mu (\phi ,X)$$ that gates the Gauss–Bonnet sector in phase space, enabling the higher-curvature contribution to be localized within a finite e-fold window while remaining negligible elsewhere. We identify stable inflationary solutions consistent with this localization and enforce standard ghost and gradient stability conditions for both scalar and tensor perturbations. For these viable backgrounds we compute pivot-scale observables and examine their dependence on the overall Gauss–Bonnet strength and on the kinetic gating. The framework offers a controlled route for realizing localized higher-curvature effects with predictable consequences for CMB-scale measurements.

Iran

Ali Seidabadi

Sara Saghafi

Kourosh Nozari

Beyond $$f(\phi ){\mathcal {G}}$$ : Gauss–Bonnet inflation with $$\mu (\phi ,X)$$

We extend an earlier lattice QCD analysis of heavy-quark current-current correlators to obtain new values for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>MS</mi><mo stretchy="true">¯</mo></mover></math> masses of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math> quarks. The analysis uses gluon configurations from the MILC Collaboration with vacuum polarization contributions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi></math> quarks (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>f</mi></msub><mo>=</mo><mn>4</mn></math>), and lattice spacings down to 0.032 fm. We find that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>m</mi><mo stretchy="false">¯</mo></mover><mi>b</mi></msub><mo stretchy="false">(</mo><msub><mover accent="true"><mi>m</mi><mo stretchy="false">¯</mo></mover><mi>b</mi></msub><mo>,</mo><msub><mi>n</mi><mi>f</mi></msub><mo>=</mo><mn>5</mn><mo stretchy="false">)</mo><mo>=</mo><mrow><mn>4.1923</mn><mo stretchy="false">(</mo><mn>63</mn><mo stretchy="false">)</mo></mrow><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>m</mi><mo stretchy="false">¯</mo></mover><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>,</mo><msub><mi>n</mi><mi>f</mi></msub><mo>=</mo><mn>4</mn><mo stretchy="false">)</mo><mo>=</mo><mspace linebreak="goodbreak"></mspace><mrow><mn>0.9813</mn><mo stretchy="false">(</mo><mn>34</mn><mo stretchy="false">)</mo></mrow><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>m</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></msub><mo stretchy="false">(</mo><mn>3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>,</mo><msub><mi>n</mi><mi>f</mi></msub><mo>=</mo><mn>4</mn><mo stretchy="false">)</mo><mo>=</mo><mrow><mn>83.39</mn><mo stretchy="false">(</mo><mn>26</mn><mo stretchy="false">)</mo></mrow><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. These results are corrected for QED by including (quenched) QED in the simulations. They are among the most accurate values by any method to date. We give a detailed analysis of finite-lattice-spacing errors that shows why the highly improved staggered quark discretization of the quark action is particularly useful for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-quark simulations even for lattices where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><msub><mi>m</mi><mi>b</mi></msub><mo>≈</mo><mn>1</mn></math>. We also calculate QED and isospin corrections to the (fictitious) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>s</mi></msub></math>-meson mass, which is used to tune <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math>-quark masses in lattice simulations.

United Kingdom

Brian Colquhoun

Christine T.H. Davies

Daniel Hatton

G. Peter Lepage

New high-precision <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math> masses from pseudoscalar-pseudoscalar correlators in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>f</mi></msub><mo>=</mo><mn>4</mn></math> lattice QCD

The non-conservation of the energy-momentum tensor in $\textit{f}$($\textit{R}$, $\textit{T}$) gravity can be interpreted as an effective manifestation of dissipation. Motivated by this, we propose a new formulation of $\textit{f}$($\textit{R}$, $\textit{T}$) gravity based on the Herglotz variational principle, which extends the usual Hamilton variational principle to dissipative systems by allowing the Lagrangian to depend explicitly on the action. The resulting gravitational field equations extend those of $\textit{f}$($\textit{R}$, $\textit{T}$) gravity by including Herglotz contributions. In the Newtonian limit, these contributions modify the gravitational potential, allowing us to constrain the Herglotz vector through Mercury’s perihelion precession and the relativistic light deflection. The Herglotz corrections lead to a scaling law consistent with observations from the Cassini spacecraft. Examining two representative cosmological models, the Herglotz vector effectively reduces to a single function that, under suitable conditions, can play the role of a cosmological constant, providing an alternative mechanism for the Universe’s accelerated expansion. Within the Herglotz variational approach, the linear $$f(R,T)=R+\alpha T$$ model, previously ruled out in the standard formulation due to its fixed deceleration parameter, becomes consistent with observations for a certain choice of the Herglotz vector.

Romania

Marek Wazny

Lehel Csillag

Portugal

Miguel Pinto

Tiberiu Harko

Herglotz-type $\textit{f}$($\textit{R}$, $\textit{T}$) gravity

This paper presents a gravastar model developed within the framework of <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>Q</mi><mo>)</mo></mrow></math> gravity using the Durgapal metric potential, allowing for a smooth and regular spacetime throughout the entire configuration. The model is structured with three distinct regions that include a central core filled with dark energy having negative pressure, a surrounding shell made of ultrarelativistic stiff matter, and an outer region that follows the Schwarzschild solution. By solving the modified field equations, we obtain exact expressions for physical quantities such as energy density, pressure, and metric components. The analysis focuses on the shell region, where proper length, total energy, entropy, and surface redshift are examined to understand the physical nature and stability of the configuration. Numerical values are determined using observational data from the compact star Vela X1, showing that the model remains free from singularities and does not form an event horizon. These results suggest that gravastars described in <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>Q</mi><mo>)</mo></mrow></math> gravity offer a meaningful and realistic alternative to black holes and provide valuable insight into the study of compact objects through modified theories of gravity.

India

Chaitra Chooda Chalavadi

V. Venkatesha

Phalaksha Murthy B

Geometric analysis of gravastars in <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>Q</mi><mo>)</mo></mrow></math> gravity with Durgapal metric potential

<list id='lst0001'><list-item id='lstitem0001'><label>&#8226;</label><para id='p0001'><italic>f</italic>(<italic>G</italic>) Gravity.</para></list-item><list-item id='lstitem0002'><label>&#8226;</label><para id='p0002'>Bulk viscous cosmological model.</para></list-item><list-item id='lstitem0003'><label>&#8226;</label><para id='p0003'>Bianchi type III cosmological model.</para></list-item></list>

Nihir Basumatary

Mukunda Dewri

Derphungshar Basumatary

Investigating accelerating bulk viscous cosmological model universe in <italic>f</italic>( <italic>G</italic>) gravity

The <italic>f</italic> <inf>0</inf>(980) is a light scalar meson whose internal structure remains under debate and investigation. Assuming that the <italic>f</italic> <inf>0</inf>(980) is a <math altimg='si4.svg'><mrow><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> molecule that can only survive at the kinetic freeze-out of the evolving bulk matter, we implement the coalescence model to study its transverse momentum ( <italic>p<inf>T</inf></italic>) spectra and elliptic flow ( <italic>v</italic> <inf>2</inf>) in high-multiplicity p-Pb collisions at <math altimg='si5.svg'><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo linebreak='goodbreak'>=</mo><mn>5.02</mn></mrow></math> TeV. Using the well-tuned kaon phase-space distributions from the Hydro-Coal-Frag model, our <math altimg='si4.svg'><mrow><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> coalescence calculations with reasonable values for the <italic>f</italic> <inf>0</inf>(980) radius successfully reproduce the elliptic flow measured by CMS over the range 0&#8239;&lt;&#8239; <italic>p<inf>T</inf></italic>&#8239;&lt;&#8239;12 GeV and also agree with the <italic>p<inf>T</inf></italic>-spectra from ALICE. These results in heavy ion collisions are compatible with the <math altimg='si4.svg'><mrow><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> molecular picture of the <italic>f</italic> <inf>0</inf>(980) with effective root-mean-square (RMS) radius. We also find that the number-of-constituent scaling of <italic>v</italic> <inf>2</inf> for the <italic>f</italic> <inf>0</inf>(980) is violated in p-Pb collisions at the LHC because most <italic>f</italic> <inf>0</inf>(980) are produced from the coalescence of kaons that have different momenta. Our study demonstrates the necessity of realistic coalescence model calculations and also explains why the CMS interpretation of the <italic>f</italic> <inf>0</inf>(980) as an ordinary <math altimg='si6.svg'><mrow><mi>q</mi><mover accent='true'><mi>q</mi><mo>&#175;</mo></mover></mrow></math> meson is no longer valid by interpreting the measured <italic>v</italic> <inf>2</inf> with a simple scaling formula based on the assumption of equal momentum coalescence. The investigation also provides a novel way to explore the internal structure of light exotic hadrons that can be abundantly produced in relativistic heavy and/or light ion collisions.

China

Yili Wang

Wenbin Zhao

Che Ming Ko

Feng-Kun Guo

Ju-Jun Xie

Huichao Song

Probing the structure of <italic>f</italic> <inf>0</inf>(980) from the elliptic flow in p-Pb collisions at the LHC

I present a calculation of the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><msub><mi>σ</mi><mi>r</mi></msub><msub><mi>F</mi><mn>2</mn></msub></mfrac><mrow><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math> in a momentum-space approach using the Block-Durand-Ha parametrization of the proton structure function <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>F</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math>. The results are compared with the H1 data and extended to high inelasticity. I also examine the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><msub><mi>σ</mi><mi>r</mi></msub><msub><mi>F</mi><mn>2</mn></msub></mfrac><mrow><mo>(</mo><mfrac><msup><mi>Q</mi><mn>2</mn></msup><mi>s</mi></mfrac><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math> obtained at a fixed <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>s</mi></msqrt></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>Q</mi><mn>2</mn></msup></math> to the minimum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>Q</mi><mn>2</mn></msup><mo>/</mo><mi>s</mi></mrow></math>, comparing them with both the HERA data and the color dipole model bounds. These results and comparisons with HERA data demonstrate that the suggested method for the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>σ</mi><mi>r</mi></msub><msub><mi>F</mi><mn>2</mn></msub></mfrac></math> can be applied in analyses of the CERN Large Hadron Collider and Future Circular Collider projects. The effect of adding a simple higher twist term of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>F</mi><mn>2</mn></msub><mo>*</mo><msub><mi>H</mi><mn>2</mn></msub><mo>/</mo><msup><mi>Q</mi><mn>2</mn></msup></mrow></math> to the description of the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><msub><mi>σ</mi><mi>r</mi></msub><msub><mi>F</mi><mn>2</mn></msub></mfrac><mrow><mo>(</mo><mfrac><msup><mi>Q</mi><mn>2</mn></msup><mi>s</mi></mfrac><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math> at low-<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> and low-<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>Q</mi><mn>2</mn></msup></math> values for comparison with the color dipole bounds and the HERA data is investigated.

G.R. Boroun

Investigation of the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><msub><mi>σ</mi><mi>r</mi></msub><msub><mi>F</mi><mn>2</mn></msub></mfrac><mrow><mo>(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>/</mo><mi>s</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math> in the momentum-space approach

We employed the chiral unitarity approach to investigate the decay process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>, by considering that the low lying nucleon resonance <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> and the low lying scalar meson <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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> that could be dynamically generated through the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave pseudoscalar meson-octet baryon and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave pseudoscalar-meson–pseudoscalar-meson interactions, respectively. In the invariant mass distributions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>, we observe a distinct peak structure associated with the resonant state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> and a bit enhancement near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> threshold that is corresponding to the mesons <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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math>, respectively. Consequently, we recommend more precise experimental measurements of this process in the future.

Ruitian Li

Xuan Luo

Hao Sun

Theoretical study of <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>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> in the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>

We explore black hole solutions in the context of Born-Infeld- <italic>f</italic>( <italic>R</italic>) gravity, a modified gravitational framework that extends both Born-Infeld and <italic>f</italic>( <italic>R</italic>) theories. By adopting a static, spherically symmetric spacetime ansatz, we derive an exact black hole solution and investigate its geometrical structure. We proceed to analyze the thermodynamic properties of the solution, including the Hawking temperature, entropy, and specific heat, with particular emphasis on their dependence on the model parameters. Our results reveal novel thermodynamic behavior that deviates significantly from the standard predictions of general relativity. A comparative study with the Schwarzschild-AdS black holes is also presented, showing how Born-Infeld- <italic>f</italic>( <italic>R</italic>) corrections alter black hole thermodynamics.

Türkiye

Salih Kibaroğlu

Born–Infeld- <italic>f</italic>( <italic>R</italic>) black holes