We present the results of a multimethodological study aimed at investigating the interaction between graphene and tritium during its <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi></math>-decay to helium, under different levels of loading and geometrical configurations. We combine density-functional theory (DFT) to evaluate the interaction potentials, with calculations of the decay rate, in order to study the consequences that the presence of the substrate has on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi></math>-decay spectrum of tritium. We determine the shape of the event rate, accounting for the effects of (part of) the corresponding condensed-matter degrees of freedom. In the context of future neutrino experiments, our results provide important information aimed at the optimization of hosting material. Furthermore, our work outlines a novel theoretical and computational scheme to account for the different timescales involved in the process and to address a question at the boundary between high- and low-energy physics. This requires nonconventional declinations of DFT combined with full quantum treatments of the nuclear configuration involved in the decay process. Our results pave the way for future studies aimed at determining the physics reach of upcoming neutrino mass experiments.

United States

Andrea Casale

Italy

Angelo Esposito

Guido Menichetti

Valentina Tozzini

<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi></math>-decay spectrum of tritiated graphene: Combining nuclear quantum mechanics with density functional theory

We use the light front quark model to investigate the form factors in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><mi>B</mi><mover accent="true"><mi>B</mi><mo>¯</mo></mover></mrow></math> collision proceses with <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>B</mi><mo>=</mo><mi mathvariant="normal">Λ</mi><mo>,</mo><mspace width="4pt"></mspace><mi mathvariant="normal">Σ</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Ξ</mi></math>. These form factor behaviors are calculated based on the Bethe-Salpeter formalism with <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>q</mi><mo>+</mo></msup><mo>&gt;</mo><mn>0</mn></mrow></math> to effectively account for nonvalence contributions. We show that our results of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>q</mi><mn>2</mn></msup></math>-dependent form factors closely match the BESIII data. In particular, we obtain that <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>|</mo></mrow><msub><mi>G</mi><mi>eff</mi></msub><mrow><mo>|</mo><mo>=</mo><mo>(</mo></mrow><mn>0.921</mn><mo>,</mo><mspace width="0.16em"></mspace><mn>0.098</mn><mo>,</mo><mspace width="0.16em"></mspace><mn>0.189</mn></mrow></math>) and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi>R</mi><mo>=</mo><mo>|</mo></mrow><mfrac><msub><mi>G</mi><mi>E</mi></msub><msub><mi>G</mi><mi>M</mi></msub></mfrac><mrow><mo>|</mo><mo>=</mo><mrow><mo>(</mo><mn>0.97</mn><mo>,</mo><mspace width="0.16em"></mspace><mn>0.89</mn><mo>,</mo><mspace width="0.16em"></mspace><mn>0.936</mn><mo>)</mo></mrow></mrow></mrow></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mi mathvariant="normal">Λ</mi><mo>¯</mo></mover></mrow><mo>,</mo><mo> </mo><mrow><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup><msup><mi mathvariant="normal">Σ</mi><mo>−</mo></msup><mo>,</mo><mspace width="0.16em"></mspace><msup><mi mathvariant="normal">Ξ</mi><mo>+</mo></msup><msup><mi mathvariant="normal">Ξ</mi><mo>+</mo></msup><mrow><mo>)</mo></mrow></mrow></math> with <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>q</mi><mn>2</mn></msup><mo>=</mo><mrow><mo>(</mo><mn>5.74</mn><mo>,</mo><mspace width="0.16em"></mspace><mn>6.0</mn><mo>,</mo><mspace width="0.16em"></mspace><mn>7.0</mn><mo>)</mo></mrow><mspace width="0.16em"></mspace><msup><mrow><mi>GeV</mi></mrow><mn>2</mn></msup></mrow></math>.

China

Chong-Chung Lih

Chao-Qiang Geng

Time-like electromagnetic form factors of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Λ</mi><mo>,</mo><mo> </mo><mi mathvariant="normal">Σ</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">Ξ</mi><mo>+</mo></msup></math> in a light-front quark model

We study finite-volume (FV) corrections to determinations of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mi>A</mi></msub></math> via lattice quantum chromodynamics (QCD) using analytic results and numerical analysis. We observe that <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow></math> heavy Baryon chiral perturbation theory does not provide an unambiguous prediction for the sign of the FV correction, which is not surprising when one also considers large-<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>N</mi><mi>c</mi></msub></math> constraints on the axial couplings. We further show that nonmonotonic FV corrections are naturally allowed when one considers either including explicit <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Δ</mi></math>-resonance degrees of freedom or one works to higher orders in the chiral expansion. We investigate the potential impact of these FV corrections with a precision study of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mi>A</mi></msub></math> using models of FV corrections that are monotonic and nonmonotonic. Using lattice QCD data that is approximately at the 1% level of precision, we do not see significant evidence of nonmonotonic corrections. Looking forward to the next phase of lattice QCD calculations, we estimate that calculations that are between the 0.1% and 1% level of precision may be sensitive to these FV artifacts. Finally, we present an update of the CalLat prediction of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mi>A</mi></msub></math> in the isospin limit with subpercent precision, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>g</mi><mi>A</mi><mi>QCD</mi></msubsup><mo>=</mo><mn>1.2674</mn><mrow><mo>(</mo><mn>96</mn><mo>)</mo></mrow></mrow></math>.

Zack Hall

Dimitra A. Pefkou

Aaron S. Meyer

Thomas R. Richardson

Raúl A. Briceño

M.A. Clark

Switzerland

Martin Hoferichter

Emanuele Mereghetti

Henry Monge-Camacho

Colin Morningstar

Amy Nicholson

Pavlos Vranas

André Walker-Loud

Signs of nonmonotonic finite-volume corrections to <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mi>A</mi></msub></math>

The higher-twist formalism is used at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>O</mi><mo>(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo>)</mo></mrow></math> to compute all possible medium-induced single-scattering emission kernels for an incoming highly energetic and virtual quark traversing the nuclear environment. The effects of the heavy-quark mass scale are taken into account [<a href="http://dx.doi.org/10.1103/PhysRevC.94.054902">Phys. Rev. C 94, 054902 (2016)</a>] both in the initial state as well as in the final state, along with interactions involving both in-medium Glauber gluons and quarks [<a href="http://dx.doi.org/10.1016/j.nuclphysa.2007.06.009">Nucl. Phys. A 793, 128 (2007)</a>], as well as coherence effects [<a href="http://dx.doi.org/10.1103/PhysRevC.105.024908">Phys. Rev. C 105, 024908 (2022)</a>]. As this study is a continuation of our work on medium-induced photon production [<a href="http://dx.doi.org/10.1103/bmmf-9zv5">Phys. Rev. C 112, 025204 (2025)</a>], the general factorization procedure for <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mtext>−</mtext><mi>A</mi></mrow></math> deep-inelastic scattering is still used. An incoming quark energy loss in the nuclear medium yields four possible scattering kernels <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="script">K</mi><mi>i</mi></msub></math> with the following final states: (i) <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>q</mi><mo>+</mo><mi>g</mi></mrow></math>; (ii) <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>g</mi><mo>+</mo><mi>g</mi></mrow></math>; and (iii) <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>q</mi><mo>+</mo><msup><mover accent="true"><mi>q</mi><mo>¯</mo></mover><mo>′</mo></msup></mrow></math>, where the quark <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math> may have a flavor different from the antiquark <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mover accent="true"><mi>q</mi><mo>¯</mo></mover><mo>′</mo></msup></math>; and (iv) <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>q</mi><mo>+</mo><msup><mi>q</mi><mo>′</mo></msup></mrow></math>, where, again, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math> may have a flavor different from <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>q</mi><mo>′</mo></msup></math>. The collisional kernels include full phase factors from all nonvanishing diagrams and complete first-order derivative in the longitudinal direction (<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>k</mi><mo>−</mo></msup></math>) as well as second-order derivative in the transverse momentum (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>k</mi><mo>⊥</mo></msub></math>) gradient expansion. Furthermore, in-medium parton distribution functions and the related jet transport coefficients have a hard transverse-momentum dependence (of the emitted quark or gluon) present within the phase factor.

Canada

Amit Kumar

Gojko Vujanovic

Glauber quark and gluon contributions to quark energy loss at next-to-leading order and next-to-leading twist

Building on the newly available solution of the Balitsky-Kovchegov (BK) equation with the full impact-parameter dependence, we extend the study of parton evolution from proton to nuclear targets. Since a key part of the scientific program for future experimental facilities such as the EIC is to study gluon dynamics and shed new light on the phenomenon of parton saturation, we present predictions for key processes, such as deep-inelastic scattering or the diffractive production of vector mesons, on a variety of nuclear targets. Besides the standard BK equation, we employ its linearized version to identify a promising channel to search for gluon saturation in the nuclear collisions. Furthermore, we implement a tetrahedral model of oxygen to search for deviations from the standard, isotropic, Woods-Saxon approach. In addition to the future colliders, the presented results are also of interest for the current studies of nuclear vector-meson production at the LHC.

Czechia

J. Cepila

M. Matas

M. Vaculciak

Probing nuclear structure with the Balitsky-Kovchegov equation in full impact-parameter dependence

In the present work, I explore the production of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo>¯</mo></mover><mn>0</mn></msup></mrow></math> using <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></mrow></math> collision data at ten center-of-mass energies between 3.51 and 4.95 GeV collected with the BESIII detector at the BEPCII collider and corresponding to an integrated luminosity of 30 <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi>fb</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> to study the structure of baryons. The data collected by the BESIII detector are useful for the study of XYZ states, and this collaboration continues the exploration of these exotic charmoniumlike states. At higher center-of-mass energies the baryon-antibaryon pair production in electron-positron annihilation provides a powerful tool. In this paper, I investigate a hyperon pair produced in the electron-positron annihilation reactions, and I present the phenomenological results for the process using the BESIII detector at the BEPCII collider. In the reaction <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo>¯</mo></mover><mn>0</mn></msup></mrow></math>, I consider two different contributions: one from the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math>-meson loop and the other from the three-gluon charmonium annihilation. In this process I calculate the total cross section including the contributions of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math>-meson loop and three-gluon loops as well as the interference of all diagrams. In the case of a purely electromagnetic mechanism for these contributions, large relative phases are generated. For a large momentum transferred region I get as a byproduct a fit of the electromagnetic form factor of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup></math> hyperon. In the present work, in addition to the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ψ</mi><mo>(</mo><mn>3770</mn><mo>)</mo></mrow></math> charmonium, I also take into account the contributions of other charmonium (-like) states, such as <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ψ</mi><mo>(</mo><mn>4040</mn><mo>)</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ψ</mi><mo>(</mo><mn>4160</mn><mo>)</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Y</mi><mo>(</mo><mn>4230</mn><mo>)</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Y</mi><mo>(</mo><mn>4360</mn><mo>)</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ψ</mi><mo>(</mo><mn>4415</mn><mo>)</mo></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Y</mi><mo>(</mo><mn>4660</mn><mo>)</mo></mrow></math>. On the whole my results are in good agreement with the available experimental data.

JINR

Azad I. Ahmadov

Cross section of the process <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>e</mi><mo>+</mo></msup><mo>+</mo><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><mo>+</mo><msup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo>¯</mo></mover><mn>0</mn></msup></mrow></math> in the vicinity of charmonium <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ψ</mi><mo>(</mo><mn>3770</mn><mo>)</mo></mrow></math> and in the charmonium (-like) state including the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math>-meson loop and three-gluon contributions

Based on the kinetic theory with relaxation time approximation, we investigate the bulk viscosity <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>ζ</mi><mo>)</mo></math> and its ratio to shear viscosity <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>(</mo><mi>ζ</mi><mo>/</mo><mi>η</mi><mo>)</mo></mrow></math> of quark matter at finite temperature and chemical potential with the in-medium particle masses derived in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> flavor Polyakov-loop improved Nambu–Jona-Lasinio model. We explore the behaviors of specific bulk viscosity <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>(</mo><mi>ζ</mi><mo>/</mo><mi>s</mi><mo>)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>η</mi></mrow></math> across different QCD phase transitions, including the Mott phase transition, the chiral crossover, and the first-order transition with the associated metastable phase. The calculation shows that both <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>s</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>η</mi></mrow></math> are extremely small at high temperatures, approaching the nature of a conformal theory. Larger <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>s</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>η</mi></mrow></math> are derived near the chiral phase transition at finite temperature. Along the chiral crossover line, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>s</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>η</mi></mrow></math> generally increase with decreasing temperature, though <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>η</mi></mrow></math> exhibits a slight decline near the critical end point. On the boundary of the first-order transition, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>s</mi></mrow></math> shows a nonmonotonic variation with temperature. Furthermore, an additional peak structure emerges beyond the chiral phase boundary for both <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>s</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ζ</mi><mo>/</mo><mi>η</mi></mrow></math>, with magnitudes even exceeding those near the chiral crossover of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>u</mi><mo>,</mo><mi>d</mi></mrow></math> quarks. Our analysis indicates this peak originates from the chiral crossover transformation of strange quark.

Chong-long Xie

Guo-yun Shao

Ming-zheng-xuan Wu

Wei-bo He

Bulk viscosity of quark matter across the QCD phase transitions

Recent theoretical analyses show that spin current can be induced by the baryon chemical potential gradient <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>∇</mi><msub><mi>μ</mi><mi>B</mi></msub></mrow></math> which becomes sizable in the fireballs created in heavy-ion collisions (HIC) at a beam energy of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="script">O</mi><mo>(</mo><mn>10</mn><mo>)</mo></mrow></math> GeV. This spin transport phenomenon can be considered as the cousin effect of the spin-Hall effect (SHE) in condensed matter systems with <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>∇</mi><msub><mi>μ</mi><mi>B</mi></msub></mrow></math> playing the role of the analogous electric field. In this letter, we study this important mechanism, which we call “baryonic SHE” or <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>∇</mi><msub><mi>μ</mi><mi>B</mi></msub></mrow></math>-induced polarization (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>∇</mi><msub><mi>μ</mi><mi>B</mi></msub></mrow></math>-IP), for differential spin polarization generation that has not been systematically explored before. We predict the signature of the baryonic SHE in HIC using a <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>)</mo><mi mathvariant="normal">D</mi></mrow></math> viscous hydrodynamic model MUSIC with a multiphase transport initial condition. We propose to use the second Fourier coefficients of the net spin polarization of Λ hyperon as sensitive probes for the baryonic SHE. Those baryonic SHE observables show a qualitative difference in sign and beam energy dependence for the situations with and without the baryonic SHE. Future experimental observation of these distinct qualitative features would provide strong evidence for the existence of this “baryonic SHE” in the hot and dense quantum chromodynamics matter.

Baochi Fu

Long-Gang Pang

Huichao Song

Yi Yin

Signatures of a baryonic spin-Hall effect in dense QCD matter

The chiral magnetic effect (CME) in relativistic heavy-ion collisions originates from a chirality imbalance among quarks within metastable QCD vacuum domains and may be linked to charge-parity violation, which is believed to play a crucial role in the matter-antimatter asymmetry of the universe. Over the past two decades, extensive experimental efforts at the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider have been devoted to the search for evidence of the CME. Recent advances have greatly improved our understanding of background contributions that can mimic CME-like signals. In particular, analyses utilizing techniques designed to suppress flow-related backgrounds indicate that the CME signal at the RHIC, if present, is small. To further investigate potential background sources, particularly those associated with strong electromagnetic fields, we estimate the contribution from coherent photon-nuclear interactions. These interactions are driven by intense electromagnetic fields produced in ultrarelativistic heavy-ion collisions, with cross sections that scale with the field strength. Notably, the polarization of the incident photons is aligned with the electric field, which is oriented along the impact parameter direction and perpendicular to the magnetic field. Consequently, such processes can generate charge-dependent correlations that mimic key features of the CME signal, yet originate from different physics mechanisms and are distinct from flow-induced backgrounds. In this study, we quantitatively assess the influence of these coherent photon-nuclear interactions on the precision measurement of the CME, aiming to improve the separation of the genuine CME signal from these background contributions.

Jing Gu

Jinhui Chen

Jie Zhao

Isolation of photon-nuclear interaction backgrounds in the search for the chiral magnetic effect in relativistic heavy-ion collisions

We investigate the inclusive <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> production in proton-proton <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>(</mo><mi>p</mi><mi>p</mi><mo>)</mo></mrow></math> collisions at center-of-mass energies <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>5.02</mn></mrow></math>, 7, and 13 TeV using the parton and hadron cascade model PACIAE 4.0. This model extends PYTHIA 8.3 by incorporating partonic and hadronic rescatterings before and after hadronization, respectively. Compared to our earlier study [K.-F. Ye et al., <a href="http://dx.doi.org/10.1103/PhysRevC.109.035201">Phys. Rev. C 109, 035201 (2024)</a>], which considered only the color-singlet processes, the present work includes both the color-singlet and color-octet contributions within the nonrelativistic QCD (NRQCD) framework. In addition to the NRQCD, we also consider the contributions from the cluster collapse and weak decays of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> hadrons. We find that the simulated inclusive <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> transverse momentum differential cross sections agree well with the experimental data at both the middle and forward rapidities. We provide a quantitative analysis of the relative contributions for different production mechanisms and their energy and rapidity dependence in the inclusive <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> production. Furthermore, we offer a quantification of the relative contributions of the various components and their energy and rapidity dependence in the NRQCD channels, including the direct production via the hard scattering and the feed-down from the decays of heavier charmonium states such as <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ψ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></math>. Finally, we examine the effects of partonic and hadronic rescatterings and offer the quantitative estimate of their impact on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> production. These results are entirely new and represent a significant step forward in understanding the mechanisms of the inclusive <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> production in high-energy <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions.

Jin-Peng Zhang

Guan-Yu Wang

Wen-Chao Zhang

Bo Feng

An-Ke Lei

Zhi-Lei She

Hua Zheng

Dai-Mei Zhou

Yu-Liang Yan

Ben-Hao Sa

Inclusive <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> productions in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>5.02</mn><mo>,</mo><mo> </mo><mn>7</mn><mo>,</mo><mo> </mo><mtext>and</mtext><mo> </mo><mn>13</mn><mo> </mo><mi>TeV</mi></mrow></math> with the parton and hadron cascade model PACIAE