Chao Shi

Kaon and pion parton distribution amplitudes to twist-three

We compute all kaon and pion parton distribution amplitudes (PDAs) to twist-three and find that only the pseudotensor PDA can reasonably be approximated by its conformal limit expression. At terrestrially accessible energy scales, the twist-two and pseudoscalar twist-three PDAs differ significantly from those functions commonly associated with their forms in QCDs conformal limit. In all amplitudes studied, SU(3) flavour-symmetry breaking is typically a 13% effect. This scale is determined by nonperturbative dynamics; namely, the current-quark-mass dependence of dynamical chiral symmetry breaking. The heavier-quark is favoured by this distortion, for example, support is shifted to the s-quark in the negative kaon. It appears, therefore, that at energy scales accessible with existing and foreseeable facilities, one may obtain reliable expectations for experimental outcomes by using these strongly dressed PDAs in formulae for hard exclusive processes. Following this procedure, any discrepancies between experiment and theory will be significantly smaller than those produced by using the conformal-limit PDAs. Moreover, the magnitude of any disagreement will either be a better estimate of higher-order, higher-twist effects or provide more realistic constraints on the Standard Model.

Flavour symmetry breaking in the kaon parton distribution amplitude

Abstract We compute the kaons valence-quark (twist-two parton) distribution amplitude (PDA) by projecting its Poincare-covariant Bethe–Salpeter wave-function onto the light-front. At a scale ζ = 2 GeV , the PDA is a broad, concave and asymmetric function, whose peak is shifted 12–16% away from its position in QCDs conformal limit. These features are a clear expression of SU ( 3 ) -flavour-symmetry breaking. They show that the heavier quark in the kaon carries more of the bound-states momentum than the lighter quark and also that emergent phenomena in QCD modulate the magnitude of flavour-symmetry breaking: it is markedly smaller than one might expect based on the difference between light-quark current masses. Our results add to a body of evidence which indicates that at any energy scale accessible with existing or foreseeable facilities, a reliable guide to the interpretation of experiment requires the use of such nonperturbatively broadened PDAs in leading-order, leading-twist formulae for hard exclusive processes instead of the asymptotic PDA associated with QCDs conformal limit. We illustrate this via the ratio of kaon and pion electromagnetic form factors: using our nonperturbative PDAs in the appropriate formulae, F K / F π = 1.23 at spacelike- Q 2 = 17 GeV 2 , which compares satisfactorily with the value of 0.92 ( 5 ) inferred in e + e − annihilation at s = 17 GeV 2 .

Locate QCD critical end point in a continuum model study

A bstractWith a modified chemical potential dependent effective model for the gluon propagator, we try to locate the critical end point (CEP) of strongly interacting matter in the framework of Dyson-Schwinger equations (DSE). Beyond the chiral limit, we find that Nambu solution and Wigner solution could coexist in some area. Using the CornwallJackiw-Tomboulis (CJT) effective action, we show that these two phases are connected by a first order phase transition. We then locate CEP as the end point of the first order phase transition line. Meanwhile, based on CJT effective action, we give a direct calculation for the chiral susceptibility and thereby study the crossover.

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

Within the Dyson-Schwinger equation framework, a gluon propagator model incorporating a quarks feedback through operator product expansion is introduced to investigate the QCD phase diagram in the temperature-chemical-potential (T - mu) plane. Partial restoration of chiral symmetry at zero temperature and finite temperature are both studied, suggesting a first order phase transition point on the mu axis and a critical end point at (T-E,mu(E))/T-c = (0.85,1.11), where T-c is the pseudocritical temperature. In addition, we find the pseudocritical line can be well parametrized with the curvature parameter. and a consistent decrease in., with more of the gluon propagator distributed to the quarks feedback.

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.

Chiral crossover transition in a finite volume

Finite volume effects on the chiral crossover transition of strong interactions at finite temperature are studied by solving the quark gap equation within a cubic volume of finite size L. With the anti-periodic boundary condition, our calculation shows the chiral quark condensate, which characterizes the strength of dynamical chiral symmetry breaking, decreases as L decreases below 2.5 fm. We further study the finite volume effects on the pseudo transition temperature T-c of the crossover, showing a significant decrease in T-c as L decreases below 3 fm.