We propose a novel method for extracting non-singlet (NS) fragmentation functions (FFs) of light charged hadrons from charge asymmetries measured in hadron fragmentation using data from both single-inclusive electron-positron annihilation and semi-inclusive deep-inelastic scattering processes. We determine the NS FFs for pions and kaons at next-to-next-to-leading order in Quantum Chromodynamics through a comprehensive uncertainty analysis. The extracted FFs reveal a scaling index of approximately 0.7 at large momentum fractions and low energy scales, a strangeness suppression factor of approximately 0.5, and universality in fragmentation of light mesons. Our findings establish a valuable benchmark for testing non-perturbative QCD models and Monte Carlo event generators, and serve as crucial inputs for future electron-ion colliders.

China

Jun Gao

Chong-Yang Liu

Bin Zhou

Determination of fragmentation functions from charge asymmetries in hadron production * The work of Jun Gao is supported by the National Natural Science Foundation of China (NSFC) (12275173), the Shanghai Municipal Education Commission (2024AIZD007) and open fund of Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education)

The 2HDM+S is the singlet extension of the two-Higgs-doublet model (2HDM). The singlet field and its mixing with the 2HDM Higgs sector lead to new contributions to the electroweak precision observables, in particular, the oblique parameters. In this study, we performed a systematic investigation of the impacts of each mixing angle on the oblique parameters. We adopted the mixing angles and physical Higgs masses as our parameters, which allow a mapping when a specific symmetry structure of the Higgs potential and various theoretical considerations are taken into account. We identified five benchmark cases, where at most one mixing angle was nonzero, and analyzed the 95% C.L. allowed parameter space using the oblique parameters. In the alignment limit of the 2HDM, we find that, other than the usual mass relations of $m_H\sim m_{H^\pm}$ or $m_A\sim m_{H^\pm}$ , electroweak precision measurements also impose an upper limit on the neutral Higgs masses. In the cases with nonzero singlet mixing with the 2HDM Higgses $\textit{H}$ or $\textit{A}$, we find approximate mass relations of $c^2_{\alpha_{HS}} m_{H} + s^2_{\alpha_{HS}}m_{h_S} = m_{H^\pm}$ or $c^2_{\alpha_{AS}} m_{A} + s^2_{\alpha_{AS}}m_{A_S} = m_{H^\pm}$ . These relations are universal to the 2HDM+S models, with or without further symmetry assumption. We also studied the non-alignment limit of the 2HDM+S, which typically has tighter constraints on the masses and mixing angles. Finally, we examined the complementarity between the electroweak precision analyses and the Higgs coupling precision measurements.

Cheng Li

Juxiang Li

Shufang Su

Wei Su

Electroweak precision constraints of the 2HDM+S * Cheng Li, Juxiang Li, and Wei Su are supported by the Natural Science Foundation of China (NSFC) (12305115), Shenzhen Science and Technology Program (202206193000001, 20220816094256002), Guangdong Provincial Key Laboratory of Gamma-Gamma Collider and Its Comprehensive Applications (2024KSYS001), and Guangdong Provincial Key Laboratory of Advanced Particle Detection Technology (2024B1212010005). Juxiang Li is also supported by the Fundamental Research Funds for the Central Universities, and the Sun Yat-sen University Science Foundation. Shufang Su is supported by the Department of Energy (DEFG02-13ER41976/DE-SC0009913)

<p>Within the framework of an equivparticle model employing mean-field approximation, we investigate systematically the mass spectra of color-singlet <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>-quark configurations with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>3</mn></math>, 6, 9, 12, 15, and 18, which are assumed to be spherically symmetric with quarks occupying the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><msub><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></math> state, i.e., compact multibaryon states. At a given quark number <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>, these states collectively form a single irreducible representation under SU(6) symmetry. Our analysis yields comprehensive mass formulas that characterize these SU(6) multiplets, providing a unified description of their mass spectra. In order to effectively constrain the parameter space of the model and improve the prediction accuracy, we carry out a Bayesian parameter inference based on the experimental masses of eight baryons and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mn>03</mn></msub></math>. The posterior probability density functions and their correlations of the model parameters are examined, based on which we further predict the masses of various multibaryon states and provide their 68% and 90% credible intervals. In our prediction, H-dibaryon, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mn>03</mn></msub></math>, and the dibaryon with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mo>=</mo><mo>−</mo><mn>6</mn></math> are all bound states relative to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mi mathvariant="normal">Λ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi mathvariant="normal">Δ</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ω</mi><mi mathvariant="normal">Ω</mi></math> thresholds, while slight probabilities of other stable dibaryons (23.64% more stable than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Ω</mi><mo>−</mo></msup><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup></math> for the state with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mo>=</mo><mo>−</mo><mn>5</mn></math> and 92.49% more stable than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mi mathvariant="normal">Ξ</mi><mo>−</mo></msup></math> for the state wtih <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mo>=</mo><mo>−</mo><mn>4</mn></math>) and tribaryons (0.25% more stable than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Ξ</mi><mo>−</mo></msup><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup></math> for the state wtih <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mo>=</mo><mo>−</mo><mn>6</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math>; 2.19% more stable than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mi mathvariant="normal">Ξ</mi><mo>−</mo></msup></math> for the state with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mo>=</mo><mo>−</mo><mn>5</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math>; and 2.21% more stable than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mi mathvariant="normal">Λ</mi><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup></math> for the state with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mo>=</mo><mo>−</mo><mn>4</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math>) are observed as well. For heavier compact multibaryon states, it is unlikely for them to be stable. The stable and unstable multibaryon states examined in this work may persist in compact stars, which could be helpful for us to understand the essence of pulsarlike objects.</p>

Hao-Song You

Xinmei Zhu

Cheng-Jun Xia

Jialun Ping

Ren-Xin Xu

Multibaryon states in the framework of an equivparticle model

Utilizing an equiparticle model with both linear confinement and leading-order perturbative interactions, we obtain systematically the properties of strangelets and nonstrange quark matter (<math><mi>u</mi><mi>d</mi><mi>QM</mi></math>) nuggets at various baryon (<math><mi>A</mi></math>) and charge (<math><mi>Z</mi></math>) numbers, where the detailed single-quark-energy levels are fixed by solving Dirac equations in mean-field approximation. We then examine the structures of compact dwarfs made of light strangelets or <math><mi>u</mi><mi>d</mi><mi>QM</mi></math> nuggets forming body-centered cubic lattices in a uniform electron background. Despite that the strangelets and <math><mi>u</mi><mi>d</mi><mi>QM</mi></math> nuggets generally become more stable at larger <math><mi>A</mi></math>, the compact dwarfs are still stable since the fusion reactions between those objects do not take place in the presence of a Coulomb barrier, which is similar to the cases of light nuclei in normal white dwarfs. If <math><mi>u</mi><mi>d</mi><mi>QM</mi></math> dwarfs or strangelet dwarfs are covered with normal matter, their masses and radii become larger but do not exceed those of ordinary white dwarfs. Finally, we investigate the radial oscillation frequencies of <math><mi>u</mi><mi>d</mi><mi>QM</mi></math> dwarfs and strangelet dwarfs and find that their frequencies are typically higher than traditional white dwarfs. The stability of compact dwarfs are then analyzed by examining radial oscillation frequencies of the fundamental mode, where compact dwarfs covered by normal matter are still stable.

Hao Sun

Hong-Bo Li

Compact dwarfs made of light-quark nuggets

We study the magnetized strangelets in the baryon density-dependent quark mass model, including the effects of both confinement and lead-order perturbation interactions. The properties of magnetized strangelets are investigated under the field strength <math><mrow><mn>2</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>17</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>G</mi></mrow></math>, where the anisotropy caused by the strong magnetic field is insignificant and can be treated approximately as an isotropic system. The consideration of anomalous magnetic moments in the energy spectrum naturally solves the difficulty of infrared divergence encountered in integrating the density of states. The Coulomb interaction is accounted for using a self-consistent treatment. The energy per baryon, mechanically stable radius, strangeness, and electric charge of magnetized strangelets are presented, where their dependence on the field strength and parameter of confinement and perturbation are investigated.

Huai-Min Chen

Xiao-Wei Li

Jing-Tao Wang

Guang-Xiong Peng

Magnetized strangelets with anomalous magnetic moment and Coulomb interactions

We investigate the properties of strangelets at finite temperature <math><mrow><mi>T</mi></mrow></math>, where an equivparticle model is adopted with both the linear confinement and leading-order perturbative interactions accounted for using density-dependent quark masses. The shell effects are examined by solving the Dirac equations for quarks in the mean-field approximation, which diminish with temperature as the occupation probability of each single-particle levels fixed by the Fermi-Dirac statistics, i.e., shell dampening. Consequently, instead of decreasing with temperature, the surface tension extracted from a liquid-drop formula increases with <math><mi>T</mi></math> until reaching its peak at <math><mrow><mi>T</mi><mo>≈</mo><mn>20</mn><mi>–</mi><mn>40</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math> with vanishing shell corrections, where the formula roughly reproduces the free energy per baryon of all strangelets. The curvature term, nevertheless, decreases with <math><mi>T</mi></math> despite the presence of shell effects. The neutron and proton emission rates are fixed microscopically according to the external nucleon gas densities that are in equilibrium with strangelets, which generally increase with <math><mi>T</mi></math> (<math><mo>≲</mo><mn>50</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>) for stable strangelets but decrease for those that are unstable against nucleon emission at <math><mi>T</mi><mo>=</mo><mn>0</mn></math>. The energy, free energy, entropy, charge-to-mass ratio, strangeness per baryon, and root-mean-square radius of <math><mi>β</mi></math>-stable strangelets obtained with various parameter sets are presented as well. The results indicated in this work are useful for understanding the products of binary compact star mergers and heavy-ion collisions.

Jian-Feng Xu

Strangelets at finite temperature: Nucleon emission rates, interface, and shell effects

By combining relativistic mean field models and equivparticle models with density-dependent quark masses, we construct explicitly “a quark Fermi sea” and “a baryonic Fermi surface” to model the quarkyonic phase, where baryons with momentums ranging from zero to Fermi momentums are included. The properties of nuclear matter, quark matter, and quarkyonic matter are then investigated in a unified manner, where quarkyonic matter is more stable and energy minimization is still applicable to obtain the microscopic properties of dense matter. Three different covariant density functionals TW99, PKDD, and DD-ME2 are adopted in our work, where TW99 gives satisfactory predictions for the properties of nuclear matter in both neutron stars and heavy-ion collisions and quarkyonic transition is unfavorable. Nevertheless, if PKDD with larger slope of symmetry energy <math><mrow><mi>L</mi></mrow></math> or DD-ME2 with larger skewness coefficient <math><mi>J</mi></math> are adopted, the corresponding equations of state (EOSs) are too stiff according to both experimental and astrophysical constraints. The situation is improved if quarkyonic transition takes place, where the EOSs become softer and can accommodate various experimental and astrophysical constraints.

Hao-Miao Jin

Ting-Ting Sun

Quarkyonic matter and quarkyonic stars in an extended relativistic mean field model

Based on an equivparticle model, we investigate the in-medium quark condensate in neutron stars. Carrying out a Taylor expansion of the nuclear binding energy to the order of <math><msup><mrow><mi>ρ</mi></mrow><mrow><mn>3</mn></mrow></msup></math>, we obtain a series of EOSs for neutron star matter, which are confronted with the latest nuclear and astrophysical constraints. The in-medium quark condensate is then extracted from the constrained properties of neutron star matter, which decreases non-linearly with density. However, the chiral symmetry is only partially restored with non-vanishing quark condensates, which may vanish at a density that is out of reach for neutron stars.

Quark condensate and chiral symmetry restoration in neutron stars

Realistic estimations on the elastic properties of neutron star matter are carried out with a large strain (<math><mi>ε</mi><mo>≲</mo><mn>0.5</mn></math>) in the framework of relativistic-mean-field model with Thomas-Fermi approximation, where various crystalline configurations are considered in a fully three-dimensional geometry with reflection symmetry. Our calculation confirms the validity of assuming Coulomb crystals for the droplet phase above neutron drip density, which nonetheless does not work at large densities since the elastic constants are found to be decreasing after reaching their peaks. Similarly, the analytic formulae derived in the incompressible liquid-drop model give excellent description for the rod phase at small densities, which overestimates the elastic constants at larger densities. For slabs, due to the negligence on the variations of their thicknesses, the analytic formulae from liquid-drop model agree qualitatively but not quantitatively with our numerical estimations. By fitting to the numerical results, these analytic formulae are improved by introducing dampening factors. The impacts of nuclear symmetry energy are examined adopting two parameter sets, corresponding to the slope of symmetry energy <math><mi>L</mi><mo>=</mo><mn>41.34</mn></math> and 89.39 MeV. Even with the uncertainties caused by the anisotropy in polycrystallines, the elastic properties of neutron star matter obtained with <math><mi>L</mi><mo>=</mo><mn>41.34</mn></math> and 89.39 MeV are distinctively different, results in detectable differences in various neutron star activities.

Japan

Toshiki Maruyama

Nobutoshi Yasutake

Toshitaka Tatsumi

Ying-Xun Zhang

Elastic properties of nuclear pasta in a fully three-dimensional geometry

The interface effects of quark matter play important roles in the properties of compact stars and small nuggets, such as strangelets and nonstrange quark matter (<math><mi>u</mi><mi>d</mi><mi>QM</mi></math>) nuggets. By introducing a density derivative term to the Lagrangian density and adopting Thomas-Fermi approximation, we find it is possible to reproduce the results obtained by solving Dirac equations. Adopting certain parameter sets, the energy per baryon of <math><mi>u</mi><mi>d</mi><mi>QM</mi></math> nuggets decreases with baryon number <math><mi>A</mi></math> and become more stable than nuclei at <math><mi>A</mi><mo>≳</mo><mn>300</mn></math>. The effects of quark matter symmetry energy are examined, where <math><mi>u</mi><mi>d</mi><mi>QM</mi></math> nuggets at <math><mi>A</mi><mo>≈</mo><mn>1000</mn></math> can be more stable than others if large symmetry energy is adopted. In such cases, larger <math><mi>u</mi><mi>d</mi><mi>QM</mi></math> nuggets will decay via fission and the surface of a <math><mi>u</mi><mi>d</mi><mi>QM</mi></math> star will fragment into a crust made of <math><mi>u</mi><mi>d</mi><mi>QM</mi></math> nuggets and electrons, which resembles the cases of a strange star’s crust. The corresponding microscopic structures are then investigated adopting spherical and cylindrical approximations for the Wigner-Seitz cells, where the droplet phase is found to be the most stable configuration with <math><mi>u</mi><mi>d</mi><mi>QM</mi></math> stars’ crusts and <math><mi>u</mi><mi>d</mi><mi>QM</mi></math> dwarfs made of <math><mi>u</mi><mi>d</mi><mi>QM</mi></math> nuggets (<math><mi>A</mi><mo>≈</mo><mn>1000</mn></math>) and electrons. For the cases considered here, the crust thickness of <math><mi>u</mi><mi>d</mi><mi>QM</mi></math> stars is typically <math><mo>∼</mo><mn>200</mn><mtext> </mtext><mtext> </mtext><mi>m</mi></math>, which reaches a few kilometers if we neglect the interface effects and adopt Gibbs construction. The masses and radii of <math><mi>u</mi><mi>d</mi><mi>QM</mi></math> dwarfs are smaller than typical white dwarfs, which would increase if the interface effects are neglected.