arXiv subjects

Zhu-Fang Cui

Publications and source records attributed to Zhu-Fang Cui.

At least 55 records · Page 3Linked to original sources

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

Effective charge from lattice QCD

Using lattice configurations for quantum chromodynamics (QCD) generated with three domain-wall fermions at a physical pion mass, we obtain a parameter-free prediction of QCD's renormalisation-group-invariant process-independent effective charge, $\hatα(k^2)$. Owing to the dynamical breaking of scale invariance, evident in the emergence of a gluon mass-scale, this coupling saturates at infrared momenta: $\hatα(0)/π=0.97(4)$. Amongst other things: $\hatα(k^2)$ is almost identical to the process-dependent (PD) effective charge defined via the Bjorken sum rule; and also that PD charge which, employed in the one-loop evolution equations, delivers agreement between pion parton distribution functions computed at the hadronic scale and experiment. The diversity of unifying roles played by $\hatα(k^2)$ suggests that it is a strong candidate for that object which represents the interaction strength in QCD at any given momentum scale; and its properties support a conclusion that QCD is a mathematically well-defined quantum field theory in four dimensions.

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

Transition form factors: $γ^\ast + p \to Δ(1232)$, $Δ(1600)$

Electroproduction form factors describing the $γ^\ast p \to Δ^+(1232), Δ^+(1600)$ transitions are computed using a fully-dynamical diquark-quark approximation to the Poincaré-covariant three-body bound-state problem in relativistic quantum field theory. In this approach, the $Δ(1600)$ is an analogue of the Roper resonance in the nucleon sector, appearing as the simplest radial excitation of the $Δ(1232)$. Precise measurements of the $γ^\ast p \to Δ^+(1232)$ transition already exist on $0 \leq Q^2 \lesssim 8\,$GeV$^2$ and the calculated results compare favourably with the data outside the meson-cloud domain. The predictions for the $γ^\ast p \to Δ^+(1600)$ magnetic dipole and electric quadrupole transition form factors are consistent with the empirical values at the real photon point, and extend to $Q^2 \approx 6 m_p^2$, enabling a meaningful direct comparison with experiment once analysis of existing data is completed. In both cases, the electric quadrupole form factor is particularly sensitive to deformation of the $Δ$-baryons. Interestingly, whilst the $γ^\ast p \to Δ^+(1232)$ transition form factors are larger in magnitude than those for $γ^\ast p \to Δ^+(1600)$ in some neighbourhood of the real photon point, this ordering is reversed on $Q^2 \gtrsim 2 m_p^2$, suggesting that the $γ^\ast p \to Δ^+(1600)$ transition is more localised in configuration space.

nucl-th↗

arXiv2018

Finite volume effects on the chiral phase transition from Dyson-Schwinger equations of QCD

Within the framework of Dyson-Schwinger equations of QCD, we study the finite volume effects on the chiral phase transition, especially the influence on the position of the possible pseudo-critical end point (pCEP). The results show that in the chiral limit case (the current quark mass $m=0$), the absolute value of quark condensate decreases for smaller volumes, and more interestingly, so does the pseudo-critical temperature $T_c(μ=0)$, which is in agreement with the Polyakov Nambu--Jona-Lasinio model result and opposite to the Polyakov linear sigma model prediction. These conclusions hold for $m>0$ case in our calculations. Moreover, the results of pCEP as a function of different volumes show that $T$ of pCEP also decreases for smaller volumes, but $μ$ of pCEP will increase, which are qualitatively more close to Polyakov linear sigma model results. For our model setup, results for systems with a size larger than (5 fm)$^3$ closely approximate those from infinite volume, but if the volume is smaller, the corrections are non-negligible, even significantly affect signatures of the results from an infinite system. There also exists some possibility that, if the system size is too small, the whole phase transition would be crossover, which means no pCEP exists at all. It is no doubt that, finite volume effects deserve further researches.

hep-ph↗

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↗

arXiv2016

Finite-volume effects on phase transition in the Polyakov-loop extended Nambu-Jona-Lasinio model with a chiral chemical potential

To investigate finite-volume effects on the chiral symmetry restoration and the deconfinement transition and some impacts of possible global topological background for a quantum chromodynamics (QCD) system with $N_f=2$ (two quark flavors), we apply the Polyakov-loop extended Nambu-Jona-Lasinio model by introducing a chiral chemical potential $μ_5$ artificially. The final numerical results indicate that the introduced chiral chemical potential does not change the critical exponents but shifts the location of critical end point (CEP) significantly; the ratios for the chiral chemical potentials and temperatures at CEP, $μ_c/μ_{5c}$ and $T_c/T_{5c}$, are significantly affected by the system size $R$. The behavior is that $T_c$ increases slowly with $μ_5$ when $R$ is large and $T_c$ decreases first and then increases with $μ_5$ when $R$ is small. It is also found that for a fixed $μ_5$, there is a $R_{\text{min}}$, where the critical end point vanishes, and the whole phase diagram becomes a crossover when $R<R_{\text{min}}$. Therefore, we suggest that for the heavy-ion collision experiments, which is to study the possible location of CEP, the finite-volume behavior should be taken into account.

hep-ph↗

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↗

arXiv2015

Susceptibilities and critical exponents within the Nambu--Jona-Lasinio model

In the mean field approximation of (2+1)-flavor Nambu--Jona-Lasinio model, we strictly derive several sets of coupled equations for the chiral susceptibility, the quark number susceptibility, etc. at finite temperature and quark chemical potential. The critical exponents of these susceptibilities in the vicinity of the QCD critical end point (CEP) are presented in SU(2) and SU(3) cases, respectively. It is found that these various susceptibilities share almost the same critical behavior near the CEP. The comparisons between the critical exponents for the order parameters and the theoretical predictions are also included.

hep-ph↗

arXiv2015

Critical behaviors near the (tri-)critical end point of QCD within the NJL model

We investigate the dynamical chiral symmetry breaking and its restoration at finite density and temperature within the two-flavor Nambu-Jona-Lasinio model, and mainly focus on the critical behaviors near the critical end point (CEP) and tricritical point (TCP) of quantum chromodynamics. The multi-solution region of the Nambu and Wigner ones is determined in the phase diagram for the massive and massless current quark, respectively. We use the various susceptibilities to locate the CEP/TCP and then extract the critical exponents near them. Our calculations reveal that the various susceptibilities share the same critical behaviors for the physical current quark mass, while they show different features in the chiral limit.

hep-ph↗

arXiv2015

2+1 flavors QCD equation of state at zero temperature within Dyson-Schwinger equations

Within the framework of Dyson-Schwinger equations (DSEs), we discuss the equation of state (EOS) and quark number densities of 2+1 flavors, that is to say, $u$, $d$, and $s$ quarks. The chemical equilibrium and electric charge neutrality conditions are used to constrain the chemical potential of different quarks. The EOS in the cases of 2 flavors and 2+1 flavors are discussed, and the quark number densities, the pressure, and energy density per baryon are also studied. The results show that there is a critical chemical potential for each flavor of quark, at which the quark number density turns to nonzero from 0; and furthermore, the system with 2+1 flavors of quarks is more stable than that with 2 flavors in the system. These discussion may provide some useful information to some research fields, such as the studies related to the QCD phase transitions or compact stars.

hep-ph↗

arXiv2015

Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD

The QCD vacuum condensates and various vacuum susceptibilities are all important parameters which characterize the nonperturbative properties of the QCD vacuum. In the QCD sum rules external field formula, various QCD vacuum susceptibilities play important roles in determining the properties of hadrons. In this paper, we review the recent progress in studies of vacuum susceptibilities together with their applications to the chiral phase transition of QCD. The results of the tensor, the vector, the axial-vector, the scalar, and the pseudo-scalar vacuum susceptibilities are shown in detail in the framework of Dyson-Schwinger equations.

hep-ph↗

arXiv2015

The chiral phase transition with a chiral chemical potential in the framework of Dyson-Schwinger equations

Within the framework of Dyson-Schwinger equations (DSEs), we discuss the chiral phase transition of QCD with a chiral chemical potential $μ_5$ as an additional scale. We focus especially on the issues related to the widely accepted as well as interested critical end point (CEP). With the help of a scalar susceptibility, we find that there might be no CEP$_5$ in the $T-μ_5$ plane, and the phase transition in the $T-μ_5$ plane might be totally crossover when $μ<50$ MeV, which has apparent consistency with the Lattice QCD calculation. Our study may also provide some useful hints to some other studies related to $μ_5$.

hep-ph↗

arXiv2015

Dynamical chiral symmetry breaking in the NJL model with a constant external magnetic field

In this paper we develop a new method that is different from Schwinger proper time method to deduce the fermion propagator with a constant external magnetic field. In the NJL model, we use this method to find out the gap equation at zero and non-zero temperature, and give the numerical results and phase diagram between magnetic field and temperature. Beside these, we also introduce current mass to study the susceptibilities, because there is a new parameter (the strength of external magnetic field) in this problem, corresponding this new parameter, we have defined a new susceptibility $χ_B$ to compare with the other two susceptibilities $χ_c$ (chiral susceptibility) and $χ_T$ (thermal susceptibility), and all of the three susceptibilities show than when current mass is not zero, the phase transition is a crossover, while for comparison, in the chiral limit, the susceptibilities show a second order phase transition. At last, we give out the critical coefficients of different susceptibilities in the chiral limit.

hep-ph↗

arXiv2014

Nonlinear susceptibilities under the framework of Dyson-Schwinger equations

Since the baryon-number susceptibilities are correlated with the cumulant of baryon-number fluctuations in experiments, we do calculations of the susceptibilities and compare them with the experimental fluctuation data under the framework of the Dyson-Schwinger equations (DSEs) approach. We compare our results with lattice QCD and experimental data at RHIC. The fitness of the results indicates that under the framework of DSEs, we can deal with the problems of heavy ion collisions properly.

hep-ph↗

arXiv2014

Influence of gauge boson mass on the staggered spin susceptibility

Based on the study of the linear response of the fermion propagator in the presence of an external scalar field, we calculate the staggered spin susceptibility in the low energy limit in the framework of the Dyson-Schwinger approach. We analyze the effect of a finite gauge boson mass on the staggered spin susceptibility in both Nambu phase and Wigner phase. It is found that the gauge boson mass suppresses the staggered spin susceptibility in Wigner phase. In addition, we try to give an explanation for why the antiferromagnetic spin correlation increases when the doping is lowered.

hep-ph↗