arXiv subjects

Shu-Sheng Xu

Publications and source records attributed to Shu-Sheng Xu.

At least 19 recordsLinked to original sources

arXiv2025

Quantum States in Twisted Tubes with Linear Cross-Section Variation

We study the quantum dynamics of a particle confined in a twisted tube with a linearly varying cross section. By relating a general linear transformation matrix to the system's Hamiltonian, we use an extended thin-layer method to derive an effective Hamiltonian for tangential motion under mild and general linear transformations. Explicit forms are provided for three fundamental transformations: rotation, scaling, and shearing. Rotation introduces a gauge field coupled to angular momentum, while scaling and shearing produce geometric potentials that lift degeneracies in non-circular cross sections. In square cross sections, these transformations cause energy splittings among formerly degenerate states, whereas circular cross sections retain degeneracy. Through an example combining rotation and squeezing, we analyze state evolution and compute the quantum geometric tensor to quantify geometric response. Our results demonstrate how geometric transformations can tailor quantum states and suggest that circular waveguides are more robust against mode mixing.

quant-ph↗

arXiv2021

Pion superfluid phase transition at finite isospin chemical potential

The pion superfluidity phase transition at $T-μ_I$ and $μ_q-μ_I$ planes are studied in the framework of Dyson-Schwinger equations. The rainbow truncation and Gaussian effective gluon propagator are employed to calculate pion condensate, $\langleπ\rangle$, as a function of $μ_I$ at finite $T$ and $μ_q$. At $T=(0, 80, 113, 120)$~MeV, the $\langleπ\rangle$ keeps zero when $μ_I$ is less than a critical value $μ_{Ic}(T)$. The $\langleπ\rangle$ at $T=113$~MeV agrees with the lattice QCD result. At the $T-μ_I$ plane, the pion superfluid phase appears at low temperature and high isospin chemical potential region. At finite $μ_q$, $\langleπ\rangle$ varying with $μ_I$ almost coincide for $μ_q<400$~MeV. At $μ_q-μ_I$ plane, the pion superfluid phase appears at $μ_I\gtrsim m_π$ when $μ_q<400$~MeV.

hep-ph↗

arXiv2021

Phase structures of neutral dense quark matter and application to strange stars

In the contact interaction model, the quark propagator has only one solution, chiral symmetry breaking solution, at vanish temperature and density. Inspire by Y. Jiang and Z.-F. Cui, we introduce 2+1 flavors quark condensates feedback on coupling strength, the Wigner solution appears in some region of parameters. It enables us to tackle chiral phase transition as two-phase coexistences. At finite chemical potential, we analyze the chiral phase transition to the conditions of electric charge neutrality and $β$ equilibrium. The four chemical potentials, $μ_u$, $μ_d$, $μ_s$ and $μ_e$, are constrained by three conditions, there is one independent variable that remained, we choose the average quark chemical potential as the free variable. All quark masses and number densities suffer discontinuities at the phase transition point. The strange quarks appear after the phase transition due to the system needs more energy to produce a d-quark than an s-quark. Take the EOS as an input, the TOV equations are solved numerically, we show that the mass-radius relation is sensitive to the EOSs. The maximum mass of strange quark stars is not susceptible to our introduced parameter $Λ_q$.

hep-ph↗

arXiv2021

QCD equation of state and the structure of neutron stars in NJL model

The chiral and pion superfluidity phase transitions are studied within NJL model. The model parameters are fitted by pion mass and decay constant together with recent isospin density from lattice QCD. The dense and cold QCD matter suffered the first order chiral phase transition during the quark chemical potential increase. Based on the studies of phase structures, the equation of states~(EoS) of dense QCD matter are calculated with the conditions of $β$ equilibrium and electric charge neutrality. Take the EoS as input, the mass-radius relation of neutron stars are predicted, which is consistent with recent observations of heaviest mass and radius of $1.4M_\odot$.

nucl-th↗

arXiv2020

Perturbative method to estimate meson masses in the framework of Bethe-Salpeter equation beyond its dominant interaction

We propose a novel method to calculate the meson mass in the framework of Dyson-Schwinger equation and Bethe-Salpeter equation, once their dominant interactions are identified. The method is based on the perturbation theory of matrix, which is widely used in quantum mechanics. Taking interactions other than the dominant ones as perturbations, we derive the first order correction of quark propagator. Implementing the perturbation on BSE, the mass correction at first order is then given. We exemplify this method with the well known Rainbow-Ladder (RL) truncation, and go beyond the RL using a simple model, i.e., the Munczek-Nemirovsky~(MN) model, by studying the pion and $ρ$ mesons mass shift. The results are all in good agreement with those obtained by fully solving the BSE beyond RL. Our perturbative method therefore can be used to give a semi-quantitative estimate of meson mass correction in cases when the BSEs are complicated by interactions that go beyond the dominant one.

hep-ph↗

arXiv2020

Chiral transition and the chiral charge density of the hot and dense QCD matter

We study the chirally imbalanced hot and dense strongly interacting matter by means of the Dyson-Schwinger equations (DSEs). The chiral phase diagram is studied in the presence of chiral chemical potential $μ_5$. The chiral quark condensate $\langle \barψ ψ\rangle$ is obtained with the Cornwall-Jackiw-Tomboulis (CJT) effective action in concert with the Rainbow truncation. Catalysis effect of dynamical chiral symmetry breaking (DCSB) by $μ_5$ is observed. We examine with two popular gluon models and consistency is found within the DSE approach, as well as in comparison with lattice QCD. The CEP location $(μ_E,T_E)$ shifts toward larger $T_E$ but constant $μ_E$ as $μ_5$ increases. A technique is then introduced to compute the chiral charge density $n_5$ from the fully dressed quark propagator. We find the $n_5$ generally increases with temperature $T$, quark number chemical potential $μ$ and $μ_5$. Since the chiral magnetic effect (CME) is typically investigated with peripheral collisions, we also investigate the finite size effect on $n_5$ and find an increase in $n_5$ with smaller system size.

hep-ph↗

arXiv2020

Semileptonic decays of $D_{(s)}$ mesons

A symmetry-preserving continuum approach to meson bound-states in quantum field theory, employed elsewhere to describe numerous $π$- and $K$-meson electroweak processes, is used to analyse leptonic and semileptonic decays of $D_{(s)}$ mesons. Each semileptonic transition is conventionally characterised by the value of the dominant form factor at $t=0$ and the following results are obtained herein: $f_+^{D_s\to K}(0) = 0.673(40)$; $f_+^{D\to π}(0)=0.618(31)$; and $f_+^{D\to K}(0)=0.756(36)$. Working with the computed $t$-dependence of these form factors and standard averaged values for $|V_{cd}|$, $|V_{cs}|$, one arrives at the following predictions for the associated branching fractions: ${\cal B}_{D_s^+\to K^0 e^+ ν_e} = 3.31(33)\times 10^{-3}$; ${\cal B}_{D^0\to π^- e^+ ν_e} = 2.73(22)\times 10^{-3}$; and ${\cal B}_{D^0\to K^- e^+ ν_e} = 3.83(28)$%. Alternatively, using the calculated $t$-dependence, agreement with contemporary empirical results for these branching fractions requires $|V_{cd}|=0.221(9)$, $|V_{us}|=0.953(34)$. With all $D_{(s)}$ transition form factors in hand, the nature of SU$(3)$-flavour symmetry-breaking in this array of processes can be analysed; and just as in the $π$-$K$ sector, the magnitude of such effects is found to be determined by the scales associated with emergent mass generation in the Standard Model, not those originating with the Higgs mechanism.

hep-ph↗

arXiv2019

Elastic electromagnetic form factors of vector mesons

A symmetry-preserving approach to the two valence-body continuum bound-state problem is used to calculate the elastic electromagnetic form factors of the $ρ$-meson and subsequently to study the evolution of vector-meson form factors with current-quark mass. To facilitate a range of additional comparisons, $K^\ast$ form factors are also computed. The analysis reveals that: vector mesons are larger than pseudoscalar mesons; composite vector mesons are non-spherical, with magnetic and quadrupole moments that deviate $\sim 30$\% from point-particle values; in many ways, vector-meson properties are as much influenced by emergent mass as those of pseudoscalars; and vector meson electric form factors possess a zero at spacelike momentum transfer. Qualitative similarities between the electric form factors of the $ρ$ and the proton, $G_E^p$, are used to argue that the character of emergent mass in the Standard Model can force a zero in $G_E^p$. Morover, the existence of a zero in vector meson electric form factors entails that a single-pole vector meson dominance model can only be of limited use in estimating properties of off-shell vector mesons, providing poor guidance for systems in which the Higgs-mechanism of mass generation is dominant.

nucl-th↗

arXiv2019

Pion and Kaon Structure at the Electron-Ion Collider

Understanding the origin and dynamics of hadron structure and in turn that of atomic nuclei is a central goal of nuclear physics. This challenge entails the questions of how does the roughly 1 GeV mass-scale that characterizes atomic nuclei appear; why does it have the observed value; and, enigmatically, why are the composite Nambu-Goldstone (NG) bosons in quantum chromodynamics (QCD) abnormally light in comparison? In this perspective, we provide an analysis of the mass budget of the pion and proton in QCD; discuss the special role of the kaon, which lies near the boundary between dominance of strong and Higgs mass-generation mechanisms; and explain the need for a coherent effort in QCD phenomenology and continuum calculations, in exa-scale computing as provided by lattice QCD, and in experiments to make progress in understanding the origins of hadron masses and the distribution of that mass within them. We compare the unique capabilities foreseen at the electron-ion collider (EIC) with those at the hadron-electron ring accelerator (HERA), the only previous electron-proton collider; and describe five key experimental measurements, enabled by the EIC and aimed at delivering fundamental insights that will generate concrete answers to the questions of how mass and structure arise in the pion and kaon, the Standard Model's NG modes, whose surprisingly low mass is critical to the evolution of our Universe.

nucl-ex↗

arXiv2019

Masses of ground-state mesons and baryons, including those with heavy quarks

Using a confining, symmetry-preserving regularisation of a vector$\times$vector contact interaction, we compute the spectra of ground-state pseudoscalar and vector $(f\bar g)$ mesons, scalar and axial-vector $(fg)$ diquarks, and $J^P=1/2^+, 3/2^+$ $(fgh)$ baryons, where $f,g,h \in \{u,d,s,c,b\}$. The diquark correlations are essentially dynamical and play a key role in formulating and solving the three-valence-quark baryon problems. The baryon spectrum obtained from this largely-algebraic approach reproduces the 22 known experimental masses with an accuracy of $2.9(2.4)$%. It also possesses the richness of states typical of constituent-quark models, predicting many heavy-quark baryons not yet observed. This study indicates that diquark correlations are an important component of all baryons; and owing to the dynamical character of the diquarks, it is typically the lightest allowed diquark correlation which defines the most important component of a baryon's Faddeev amplitude.

nucl-th↗

arXiv2018

Wigner solution of the quark gap equation

Solutions and their evolutions of the quark gap equation are studied within the Nambu-Jona--Lasinio model, which is a basic issue for studying the QCD phase structure and locating the possible critical end point. It is shown that in the chiral limit case of the vacuum, chiral symmetry will hold if the coupling strength $G$ is small, then the system only has the Wigner solution at $M=0$. If increasing $G$, two symmetric minima will appear as the positive and `negative' Nambu solutions, however, the solution $M=0$ now corresponds to a maximum instead of a minimum of the thermodynamical potential, so is not a physically stable state anymore (we call it `pseudo-Wigner solution'). Besides, it is shown that as the current quark mass $m$ increases, the pseudo-Wigner solution will become negative, and disappear together with the negative Nambu solution if $m$ is large enough. Similar things happen if we increase the temperature or quark chemical potential $μ$. Some interesting phenomenon is, from some $μ$ a second local minimum will show up. As $μ$ increases gradually, it will be stabler than the Nambu solution, survives even the Nambu solution disappears, and approaches $m$, which are just the features of the Wigner solution we expect.

hep-ph↗

arXiv2018

New Perspective on Hybrid Mesons

It is thought that strong interactions within the Standard Model can generate bound-states in which non-Abelian gauge-bosons play a dual role, serving both as force and matter fields. In this context we introduce a novel approach to the hybrid-meson (valence-gluon+quark+antiquark) bound-state problem in relativistic quantum field theory. Exploiting the existence of strong two-body correlations in the gluon-quark, $q_g=[gq]$, and gluon-antiquark, $\bar q_g=[g\bar q]$ channels, we argue that a sound description of hybrid properties can be obtained by solving a coupled-pair of effectively two-body equations; and, consequently, that hybrids may be viewed as highly-correlated $q_g \bar q \leftrightarrow q \bar q_g$ bound-states. Analogies may be drawn between this picture of hybrid structure and that of baryons, in which quark+quark (diquark) correlations play a key role. The potential of this formulation is illustrated by calculating the spectrum of light-quark isovector hybrid mesons.

nucl-th↗

arXiv2018

A new algorithm towards quasi-Wigner solution of the gap equation beyond the chiral limit

We propose a new algorithm to solve the quasi-Wigner solution of the gap equation beyond chiral limit. Employing a Gaussian gluon model and rainbow truncation, we find that the quasi-Wigner solution exists in a limited region of current quark mass, $m<43.1$ MeV, at zero temperature $T$ and zero chemical potential $μ$. The difference between Cornwall-Jackiw-Tomboulis (CJT) effective actions of quasi-Wigner and Nambu-Goldstone solutions shows that the Nambu-Goldstone solution is chosen by physics. Moreover, the quasi-Wigner solution is studied at finite temperature and chemical potential, the far infrared mass function of quasi-Wigner solution is negative and decrease along with $T$ at $μ=0$. Its susceptibility is divergent at certain temperature with small $m$, and this temperature decreases along with $m$. Taking $T=80$ MeV as an example, the quasi-Wigner solution is shown at finite chemical potential upto $μ=350$ MeV as well as Nambu solution, the coexistence of these two solutions indicates that the QCD system suffers the first order phase transition. The first order chiral phase transition line is determined by the difference of CJT effective actions.

hep-ph↗

arXiv2018

Pion and kaon valence-quark quasiparton distributions

Algebraic Ansaetze for the Poincaré-covariant Bethe-Salpeter wave functions of the pion and kaon are used to calculate their light-front wave functions (LFWFs), parton distribution amplitudes (PDAs), quasi-PDAs (qPDAs), valence parton distribution functions (PDFs), and quasi-PDFs (qPDFs). The LFWFs are broad, concave functions; and the scale of flavour-symmetry violation in the kaon is roughly 15%, being set by the ratio of emergent masses in the $s$-and $u$-quark sectors. qPDAs computed with longitudinal momentum $P_z =1.75\,$GeV provide a semiquantitatively accurate representation of the objective PDA; but even with $P_z=3\,$GeV, they cannot provide information about this amplitude's endpoint behaviour. On the valence-quark domain, similar outcomes characterise qPDFs. In this connection, however, the ratio of kaon-to-pion $u$-quark qPDFs is found to provide a good approximation to the true PDF ratio on $0.3\lesssim x \lesssim 0.8$, suggesting that with existing resources computations of ratios of quasi-parton-distributions can yield results that support empirical comparison.

nucl-th↗

arXiv2017

Parity partners in the baryon resonance spectrum

We describe a calculation of the spectrum of flavour-SU(3) octet and decuplet baryons, their parity partners, and the radial excitations of these systems, made using a symmetry-preserving treatment of a vector-vector contact interaction as the foundation for the relevant few-body equations. Dynamical chiral symmetry breaking generates nonpointlike diquarks within these baryons and hence, using the contact interaction, flavour-antitriplet scalar, pseudoscalar and vector, and flavour-sextet axial-vector quark-quark correlations can all play an active role. The model yields reasonable masses for all systems studied, and Faddeev amplitudes for ground states and associated parity partners that sketch a realistic picture of their internal structure: ground-state, even parity baryons are constituted, almost exclusively, from like-parity diquark correlations; but orbital angular momentum plays an important role in the rest-frame wave functions of odd-parity baryons, whose Faddeev amplitudes are dominated by odd-parity diquarks.

nucl-th↗

arXiv2016

Critical endpoint in the presence of a chiral chemical potential

A class of Polyakov-loop-modified Nambu--Jona-Lasinio (PNJL) models have been used to support a conjecture that numerical simulations of lattice-regularized quantum chromodynamics (QCD) defined with a chiral chemical potential can provide information about the existence and location of a critical endpoint in the QCD phase diagram drawn in the plane spanned by baryon chemical potential and temperature. That conjecture is challenged by conflicts between the model results and analyses of the same problem using simulations of lattice-regularized QCD (lQCD) and well-constrained Dyson-Schwinger equation (DSE) studies. We find the conflict is resolved in favor of the lQCD and DSE predictions when both a physically-motivated regularization is employed to suppress the contribution of high-momentum quark modes in the definition of the effective potential connected with the PNJL models and the four-fermion coupling in those models does not react strongly to changes in the mean-field that is assumed to mock-up Polyakov loop dynamics. With the lQCD and DSE predictions thus confirmed, it seems unlikely that simulations of lQCD with $μ_5>0$ can shed any light on a critical endpoint in the regular QCD phase diagram.

nucl-th↗

arXiv2016

Continuum study on QCD phase diagram through an OPE-modified gluon propagator

Within the Dyson-Schwinger equations (DSEs) framework, a gluon propagator model incorporating quark's feedback through operator product expansion (OPE) is introduced to investigate the QCD phase diagram in the temperature--chemical-potential ($T-μ$) plane. Partial restoration of chiral symmetry at zero temperature and finite temperature are both studied, suggesting a first order phase transition point on the $μ$ axis and a critical end point at $(T_E,μ_E)/T_c = (0.85,1.11)$, where $T_c$ is the pseudo-critical temperature. In addition, we find the pseudo-critical line can be well parameterized with the curvature parameter $κ$ and a consistent decrease in $κ$ with more of gluon propagator distributed to quark's feedback.

hep-ph↗

arXiv2015

Contact-interaction Faddeev equation and, inter alia, proton tensor charges

A confining, symmetry-preserving, Dyson-Schwinger equation treatment of a vector-vector contact interaction is used to formulate Faddeev equations for the nucleon and Delta-baryon in which the kernel involves dynamical dressed-quark exchange and whose solutions therefore provide momentum-dependent Faddeev amplitudes. These solutions are compared with those obtained in the static approximation and with a QCD-kindred formulation of the Faddeev kernel. They are also used to compute a range of nucleon properties, amongst them: the proton's sigma-term; the large Bjorken-x values of separate ratios of unpolarised and longitudinally-polarised valence u- and d-quark parton distribution functions; and the proton's tensor charges, which enable one to directly determine the effect of dressed-quark electric dipole moments (EDMs) on neutron and proton EDMs.

nucl-th↗