arXiv subjects

Yu-xin Liu

Publications and source records attributed to Yu-xin Liu.

At least 55 records · Page 3Linked to original sources

arXiv2018

A modification of Faddeev-Popov approach free from Gribov ambiguity

We propose a modified version of the Faddeev-Popov quantization approach for non-Abelian gauge field theory to avoid the Gribov ambiguity. We show that by means of introducing a new method to insert the correct identity into the Yang-Mills generating functional and considering the identity generated by an integral through a subgroup of the gauge group, the problem of the Gribov ambiguity can be removed naturally. Meanwhile by handling the absolute value of the Faddeev-Popov determinant with the method introduced by Williams and collaborators, we lift the Jacobian determinant together with the absolute value and obtain a local Lagrangian. The new Lagrangian have a nilpotent symmetry which can be viewed as an analogue of the BRST symmetry.

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arXiv2018

Colour Confinement: a Dynamical Phenomenon of QCD

We study in this Letter the origin of the confinement in QCD by analyzing the colour charge of physics states. We derive the colour charge operator in QCD and compare it with the electromagnetic charge operator in QED. It shows that the two charges have very similar structure, but the dynamical properties of the gauge fields are different. The difference between the behaviours of the gauge boson propagator at zero momentum for QCD and that for QED guarantees that there occurs colour confinement in QCD but there is no confinement in QED. We give then a universal relation between the confinement and the dynamical property of QCD and reveals the origin of the colour confinement, which can be demonstrated as the dynamical effect of QCD or more explicitly the dynamical mass generation of the gluon.

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arXiv2017

Revisiting the Equation of State of Hybrid Stars in the Dyson-Schwinger Equation Approach to QCD

We investigate the equation of state(EoS) and the effect of the hadron-quark phase transition of strong interaction matter in compact stars. The hadron matter is described with the relativistic mean field theory,and the quark matter is described with the Dyson-Schwinger equation approach of QCD. The complete EoS of the hybrid star matter is constructed with not only the Gibbs construction but also the 3-window interpolation. The mass-radius relation of hybrid stars is also investigated. We find that, although the EoSs of both the hadron matter with hyperon and $Δ$-baryon and the quark matter are generally softer than that of the nucleon matter, the 3-window interpolation construction may provide an EoS stiff enough for a hybrid star with mass exceeding 2$M_{\odot}^{}$ and, in turn, solve the so called "hyperon puzzle".

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arXiv2017

A Universal Constraint on the Infrared Behavior of the Ghost Propagator in QCD

With proposing a unified description of the fields variation at the level of generating functional, we obtain a new identity for the quark-gluon interaction vertex based on gauge symmetry, which is similar to the Slavnov-Taylor Identities(STIs) based on the Becchi-Rouet-Stora-Tyutin transformation. With these identities, we find that in Landau gauge, the dressing function of the ghost propagator approaches to a constant as its momentum goes to zero, which provides a strong constraint on the infrared behaviour of ghost propagator.

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arXiv2017

Four-fermion interactions and the chiral symmetry breaking in an external magnetic field

We investigate the chiral symmetry and its spontaneous breaking at finite temperature and in an external magnetic field with four-fermion interactions of different channels. Quantum and thermal fluctuations are included within the functional renormalization group approach, and properties of the set of flow equations for different couplings, such as its fixed points, are discussed. It is found that external parameters, e.g. the temperature and the external magnetic field and so on, do not change the structure of the renormalization group flows for the couplings. The flow strength is found to be significantly dependent on the route and direction in the plane of couplings of different channels. Therefore, the critical temperature for the chiral phase transition shows a pronounced dependence on the direction as well. Given fixed initial ultraviolet couplings, the critical temperature increases with the increasing magnetic field, viz., the magnetic catalysis is observed with initial couplings fixed.

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arXiv2017

Temperature Effect on Shear and Bulk Viscosities of QCD Matter

We investigate the temperature dependence of the shear and bulk viscosities and their ratios to the entropy density via a continuum QCD approach. We calculate the pion mass and decay constant in the framework of Dyson-Schwinger equations of QCD and the pion thermal width by combining with Roy equations. We obtain then the variation behaviors of the viscosities, especially a novel feature of the bulk viscosity, with respect to temperature.

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arXiv2017

Identifying the QCD Phase Transitions via the Gravitational Wave Frequency

We investigate the nonradial oscillations of newly born neutron stars (NSs) and strange quark stars (SQSs). This is done with the relativistic nuclear field theory with hyperon degrees of freedom employed to describe the equation of state for the stellar matter in NSs, and with both the MIT bag model and the Nambu--Jona-Lasinio model adopted to construct the configurations of the SQSs. We find that the gravitational-mode ($g$-mode) eigenfrequencies of newly born SQSs are about one order of magnitude lower than those of NSs, which is independent of models implemented to describe the equation of state for the strange quark matter. Meanwhile the eigenfrequencies of the other modes of nonradial oscillations, e.g., fundamental ($f$)- and pressure ($p$)-modes, are much larger than those of the $g$-mode. In the light of the first direct observation of gravitational waves, it is promising to employ the gravitational waves to identify the QCD phase transition in high density strong interaction matter.

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arXiv2016

Two Photon Transition Form Factor of $\bar{c}c $ Quarkonia

The two photon transition of $\bar{c}c$ quarkonia are studied within a covariant approach based on the consistent truncation scheme of the quantum chromodynamics Dyson-Schwinger equation for the quark propagator and the Bethe--Salpeter equation for the mesons. We find the decay widths of $η_{c}^{} \to γγ$ and $χ_{c0,2}^{} \to γγ$ in good agreement with experimental data. The obtained transition form factor of $η_{c}^{} \to γγ^{\ast}$ for a wide range of space-like photon momentum transfer squared is also in agreement with the experimental findings of the BABAR experiment. As a by-product, the decay widths of $η_{b}^{},χ_{b0,2}^{} \to γγ$ and the transition form factor of $η_{b}^{}, χ_{c0,b0}^{} \toγγ^{\ast}$ are predicted, which await for experimental test.

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arXiv2016

A Novel Algorithm for Extracting the Parton Distribution Amplitude from the Euclidean Bethe-Salpeter Wave Function

We propose a new numerical method to compute parton distribution amplitude(PDA) from the Euclidean Bethe-Salpeter wave function. The essential step is to extract the weight function in the Nakanishi representation of the Bethe-Salpeter wave function in Euclidean space, which is an ill-posed inversion problem, via the maximum entropy method(MEM). The Nakanishi weight function as well as the corresponding light-front PDA can be well determined. We confirm the previous works on PDA computation therein the different method has been performed.

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arXiv2016

Interface Effect in QCD Phase Transitions via Dyson-Schwinger Equation Approach

With the chiral susceptibility criterion we obtain the phase diagram of strong-interaction matter in terms of temperature and chemical potential in the framework of Dyson-Schwinger equations (DSEs) of QCD.After calculating the pressure and some other thermodynamic properties of the matter in the DSE method, we get the phase diagram in terms of temperature and baryon number density. We also obtain the interface tension and the interface entropy density to describe the inhomogeneity of the two phases in the coexistence region of the first order phase transition. After including the interface effect, we find that the total entropy density of the system increases in both the deconfinement (dynamical chiral symmetry restoration) and the hadronization (dynamical chiral symmetry breaking) processes of the first order phase transitions and thus solve the entropy puzzle in the hadronization process.

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arXiv2016

QCD phase transitions via a refined truncation of Dyson-Schwinger equations

We investigate both the chiral and deconfinement phase transitions of QCD matter in a refined scheme of Dyson-Schwinger equations, which have been shown to be successful in giving the meson mass spectrum and matching the interaction with the results from ab initio computation. We verify the equivalence of the chiral susceptibility criterion with different definitions for the susceptibility and confirm that the chiral susceptibility criterion is efficient to fix not only the chiral phase boundary but also the critical end point (CEP), especially when one could not have the effective thermodynamical potential. We propose a generalized Schwinger function criterion for the confinement. We give the phase diagram of both phase transitions and show that in the refined scheme the position of the CEP shifts to lower chemical potential and higher temperature. Based on our calculation and previous results of the chemical freeze out conditions, we propose that the CEP locates in the states of the matter generated by the Au--Au collisions with $\sqrt{s_{NN}^{}}=9\sim15$ GeV.

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arXiv2016

Properties of Mesons in a Strong Magnetic Field

By extending the $Φ$-derivable approach in Nambu-Jona-Lasinio model to finite magnetic field we calculate the properties of pion, $σ$ and $ρ$ mesons in a magnetic field at finite temperature in not only the quark-antiquark bound state scheme but also the pion-pion scattering resonant state scenario. Our calculation results manifest that the masses of $π^{0}$ and $σ$ meson can be nearly degenerate at the pseudo-critical temperature which increases with increasing the magnetic field strength, and the $π^{\pm}$ mass ascends suddenly at almost the same critical temperature. While the $ρ$ mesons' masses decrease with the temperature but increase with the magnetic field strength. We also check the Gell-Mann-Oakes-Renner relation and find that the relation can be violated obviously with increasing the temperature, and the effect of the magnetic field becomes pronounced around the critical temperature. With different criteria, we analyze the effect of the magnetic field on the chiral phase transition and find that the pseudo-critical temperature of the chiral phase cross, $T_{c}^χ$, is always enhanced by the magnetic field. Moreover our calculations indicate that the $ρ$ mesons will get melted as the chiral symmetry has not yet been restored, but the $σ$ meson does not disassociate even at very high temperature. Particularly, it is the first to show that there does not exist vector meson condensate in the QCD vacuum in the pion-pion scattering scheme.

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arXiv2015

Chemical Freeze-out Parameters via a Non-perturbative QCD Approach

By analyzing the calculated baryon number susceptibility ratios ${χ_{1}^{B}}/{χ_{2}^{B}}$ and ${χ_{3}^{B}}/{χ_{1}^{B}}$ in two-flavor system via the Dyson-Schwinger equation approach of QCD, we determine the chemical freeze-out temperature and baryon chemical potential in cases of both thermodynamic limit and finite size. We calculate the center-of-mass energy dependence of the ${χ_{4}^{B}}/{χ_{2}^{B}}\, (κσ^{2})$ at the freeze-out line and find an excellent agreement with experimental data in $\sqrt{S_{NN}^{}} \geq 19.6\,$GeV region when taking into account the finite size effect. Our calculations indicate that the $κσ^{2}$ exhibits a non-monotonic behavior in lower collision energy region.

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arXiv2014

The emergent dynamical symmetry at the triple point of nuclear deformations

Based on the boson realization of the Euclidean algebras, it is shown that the five-dimensional Euclidean dynamical symmetry may emerge at the triple point of the shape phase diagram of the interacting boson model, which thus offers a symmetry-based understanding of this isolated point. It is further shown that the low-lying dynamics in $^{108}$Pd, $^{134}$Ba, $^{64}$Zn, and $^{114}$Cd may be dominated by the Euclidean dynamical symmetry.

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arXiv2013

Interface Tension and Interface Entropy in 2+1 Flavour Nambu-Jona-Lasino Model

We study the QCD phases and their transitions in 2+1 flavour NJL model, with focus on the interface effects such as the interface tension, the interface entropy and critical bubble size in the coexistence region of the first order phase transitions. Our results show that, under the thin-wall approximation, interface contribution to total entropy density changes its discontinuity scale in the first order phase transition. However, the entropy density of dynamical chiral symmetry (DCS) phase is always greater than that of the dynamical chiral symmetry broken (DCSB) phase in both heating and hadronization processes. To address this entropy puzzle, the thin-wall approximation is evaluated in the present work. We find that the puzzle can be attributed to a drastic overestimate of the critical bubble size at low temperature in the hadronization process. With an improvement on the thin-wall approximation, the entropy puzzle is well solved with the total entropy density of the hadron-DCSB phase exceeding apparently that of the DCS-quark phase at low temperature.

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arXiv2013

Practical corollaries of transverse Ward-Green-Takahashi identities

The gauge principle is fundamental in formulating the Standard Model. Fermion--gauge-boson couplings are the inescapable consequence and the primary determining factor for observable phenomena. Vertices describing such couplings are simple in perturbation theory and yet the existence of strong-interaction bound-states guarantees that many phenomena within the Model are nonperturbative. It is therefore crucial to understand how dynamics dresses the vertices and thereby fundamentally alters the appearance of fermion--gauge-boson interactions. We consider the coupling of a dressed-fermion to an Abelian gauge boson, and describe a unified treatment and solution of the familiar longitudinal Ward-Green-Takahashi identity and its less well known transverse counterparts. Novel consequences for the dressed-fermion--gauge-boson vertex are exposed.

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arXiv2013

Baryon and meson screening masses

In a strongly-coupled quark-gluon plasma, collective excitations of gluons and quarks should dominate over the excitation of individual quasi-free gluon and quark modes. To explore this possibility, we computed screening masses for ground-state light-quark mesons and baryons at leading-order in a symmetry-preserving truncation scheme for the Dyson-Schwinger equations using a confining formulation of a contact-interaction at nonzero temperature. Meson screening masses are obtained from Bethe-Salpeter equations; and baryon analogues from a novel construction of the Faddeev equation, which employs an improved quark-exchange approximation in the kernel. Our treatment implements a deconfinement transition that is coincident with chiral symmetry restoration in the chiral limit, when both transitions are second order. Despite deconfinement, in all T=0 bound-state channels, strong correlations persist above the critical temperature, T>T_c; and, in the spectrum defined by the associated screening masses, degeneracy between parity-partner correlations is apparent for T >1.3T_c. Notwithstanding these results, there are reasons (including Golberger-Treiman relations) to suppose that the inertial masses of light-quark bound-states, when they may be defined, vanish at the deconfinement temperature; and that this is a signal of bound-state dissolution. Where a sensible comparison is possible, our predictions are consistent with results from contemporary numerical simulations of lattice-regularised QCD.

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arXiv2012

Existence and stability of multiple solutions to the gap equation

We argue by way of examples that, as a nonlinear integral equation, the gap equation can and does possess many physically distinct solutions for the dressed-quark propagator. The examples are drawn from a class that is successful in describing a broad range of hadron physics observables. We apply the homotopy continuation method to each of our four exemplars and thereby find all solutions that exist within the interesting domains of light current-quark masses and interaction strengths; and simultaneously provide an explanation of the nature and number of the solutions, many of which may be associated with dynamical chiral symmetry breaking. Introducing a stability criterion based on the scalar and pseudoscalar susceptibilities we demonstrate, however, that for any nonzero current-quark mass only the regular Nambu solution of the gap equation is stable against perturbations. This guarantees that the existence of multiple solutions to the gap equation cannot complicate the description of phenomena in hadron physics.

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