Spin structure of the pion

We present the first calculation of the transverse spin structure of the pion in lattice QCD. Our simulations are based on two flavors of nonperturbatively improved Wilson fermions, with pion masses as low as 400 MeV in volumes up to (2.1 fm)(3) and lattice spacings below 0.1 fm. We find a characteristic asymmetry in the spatial distribution of transversely polarized quarks. This asymmetry is very similar in magnitude to the analogous asymmetry we previously obtained for quarks in the nucleon. Our results support the hypothesis that all Boer-Mulders functions are alike.     

Pion condensation in a medium with massive quarks in an external spherically symmetrical non-Abelian chromomagnetic field

We consider pion condensation in a flavor asymmetric quark medium with massive quarks in the external spherically symmetric non-Abelian chromomagnetic field. It is shown that the external field is a catalyzing factor for the occurrence of pion condensation, while the finite quark masses prevent the emergence of this phenomenon.     

Pion condensation in a medium with massive quarks in the external chromomagnetic field

Pion condensation in a flavor-asymmetric quark medium with massive quarks in the external chromomagnetic field is considered. It is shown that the external field catalyzes pion condensation while the finite quark mass does not impede the onset of this phenomenon.     

On the scaling behavior of the chiral phase transition in QCD in finite and infinite volume

We study the scaling behavior of the two-flavor chiral phase transition using an effective quark–meson model. We investigate the transition between infinite-volume and finite-volume scaling behavior when the system is placed in a finite box. We can estimate effects that the finite volume and the explicit symmetry breaking by the current quark masses have on the scaling behavior which is observed in full QCD lattice simulations. The model allows us to explore large quark masses as well as the chiral limit in a wide range of volumes, and extract information about the scaling regimes. In particular, we find large scaling deviations for physical pion masses and significant finite-volume effects for pion masses that are used in current lattice simulations.     

Pion mass dependence of the <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">l</Emphasis>3</Subscript> semileptonic scalar form factor within finite volume

We calculate the scalar semileptonic kaon decay in finite volume at the momentum transfer t _m =(m _K −m _π )², using chiral perturbation theory. At first we obtain the hadronic matrix element to be calculated in finite volume. We then evaluate the finite size effects for two volumes with L=1.83 fm and L=2.73 fm and find that the difference between the finite volume corrections of the two volumes are larger than the difference as quoted in Boyle et al. (Phys. Rev. Lett. 100:141601, 2008). It appears then that the pion masses used for the scalar form factor in ChPT are large which result in large finite volume corrections. If appropriate values for pion mass are used, we believe that the finite size effects estimated in this paper can be useful for lattice data to extrapolate at large lattice size.     

On the phase structure of QCD in a finite volume

The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case.     

Pion properties at finite isospin chemical potential with isospin symmetry breaking

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI 0 and μI 0 in the phase diagram, and different values for the charged pion mass(or decay constant) and neutral pion mass(or decay constant) at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses.     

手征胶子修正夸克平均场模型

这项工作利用考虑π介子与胶子效应的夸克平均场模型研究原子核结构的基本性质。在夸克平均场中,核子由三个束缚在谐振子势场中的组分夸克构成。描述强相互作用的量子色动力学必须满足手征对称性,此外夸克之间也需要通过交换胶子相互作用。因此,在夸克平均场模型中,对利用夸克势获得的核子质量考虑π介子修正与胶子修正。通过少数稳定有限核的结合能与半径实验值确定模型中的未知参数,获得了一组夸克平均场相互作用参数,QMF-NK。利用该组参数计算40Ca和208Pb的电荷密度分布,发现与实验值符合很好。随后获得了与经验值一致的对称核物质的饱和性质。包含π介子修正和胶子修正的夸克平均场模型能够更好地描述有限核和核物质的性质。The basic properties of nuclear structure are studied within the quark mean field (QMF) model by taking the effects of pions and gluons into account. In QMF, the nucleon is made up of three constituent quarks confined by a harmonic oscillator potential. The quantum chromodynamics describing the strong interaction must satisfy the chiral symmetry and quarks interact with each other through exchange of gluons. Therefore pion correction and gluon correction are included in the nucleon mass obtained by using quark confinement potential in quark mean field model. We determine the unknown parameters in the model by fitting the experimental data of the binding energies and radii of several stable finite nuclei and obtain a set of parameters of quark mean field interaction, named QMF-NK. The charge density distributions of 40Ca and 208Pb are calculated, which are in good agreement with the experimental data. Later the saturation properties of symmetric nuclear matter which are consistent with the empirical data are obtained. With the pion and gluon corrections, the QMF model could treat finite nuclei and nuclear matter better.     

Phase Structure of the Semi-Classical Linear Sigma Model

In order to establish a quantitative framework for assessing the reliability of dynamical simulations of DCC phenomena with the semi-classical mean-field treatment of the linear model, we determine and discuss the phase structure implied by this approximate treatment. While the results appear to be physically reasonable for realistic scenarios, where the pion mass and the volume are finite, the approximate treatment might be less appropriate for idealized scenarios involving small masses and large volumes.     

Pion polarizabilities at finite temperature

A first calculation of pion polarizabilities at finite temperature is presented. Compton scattering off a pion is examined in the Nambu-Jona-Lasinio model and an expansion in the inverse number of colors N _c is used. Quark loop, σ-pole and vector meson contributions to the invariant amplitude are considered. The calculated polarizabilities of the charged and neutral pions at T = 0 agree fairly well with experiment. For increasing temperature, the polarizabilities stay fairly constant until they diverge at the Mott temperature (T _M = 202.2 MeV), above which the pion can decay into two quarks.     

A single quark model for single pion photoproduction at threshold

Single pion photoproduction is studied in a single quark model in which a quark absorbs the photon and then emits the pion, propagating as a quark between the two interactions. Two different chiral bag models are used which allow for the coupling of the quarks to the pion. Surprisingly, the single quark model reproduces the results of phenomenological models and agrees with the experimental amplitudes to within 30% at threshold.     

Spin structure of the pion from the instanton vacuum

We investigate the spin structure of the pion within the framework of the nonlocal chiral quark model from the instanton vacuum. We first evaluate the tensor form factors of the pion for the first and second moment (n=1,2)$(n=1,2)$ and compare it with the lattice data. Combining the tensor form factor of the pion with the electromagnetic one, we determine the impact-parameter dependent probability density of transversely polarized quarks inside the pion. It turns out that the present numerical results for the tensor form factor as well as those for the probability density are in good agreement with the lattice data. We also discuss the distortion of the spatial distribution of the quarks in the transverse plane inside the pion.     

QCD with two colors at finite baryon density at next-to-leading order

We study QCD with two colors and quarks in the fundamental representation at finite baryon density in the limit of light-quark masses. In this limit the free energy of this theory reduces to the free energy of a chiral Lagrangian which is based on the symmetries of the microscopic theory. In earlier work this Lagrangian was analyzed at the mean-field level and a phase transition to a phase of condensed diquarks was found at a chemical potential of half the diquark mass (which is equal to the pion mass). In this article we analyze this theory at next-to-leading order in chiral perturbation theory. We show that the theory is renormalizable and calculate the next-to-leading order free energy in both phases of the theory. By deriving a Landau–Ginzburg theory for the order parameter we show that the finite one-loop contribution and the next-to-leading order terms in the chiral Lagrangian do not qualitatively change the phase transition. In particular, the critical chemical potential is equal to half the next-to-leading order pion mass, and the phase transition is of second order.     

Pion Decay Constant and Masses of Light Quarks and In-medium Goldstone Bosons

Based on the fully dressed confining quark propagator, the pion decay constant f_π, local quark vacuum condensate, and the masses of light quarks and in-medium Goldstone bosons are investigated. The pion decay constant f_π is predicted and compared with its value of experimental measurement. A great agreement is obtained. With the predicted f_π and values of Goldstone boson masses measured by experiments in free configuration the current masses of light quarks and the masses of in-medium Goldstone bosons are obtained.     

Charged pion condensation in anti-parallel electromagnetic fields and nonzero isospin density

The formation of charged pion condensate in anti-parallel electromagnetic fields and in the presence of the isospin chemical potential is studied in the two-flavor Nambu-Jona-Lasinio model.The method of Schwinger proper time is extended to explore the quantities in the off-diagonal flavor space,i.e.the charged pion.In this framework,π^± are treated as bound states of quarks and not as point-like charged particles.The isospin chemical potential plays the role of a trigger for charged pion condensation.We obtain the associated effective potential as a function of the strength of the electromagnetic fields and find that it contains a sextic term which possibly induces a weak first order phase transition.The dependence of pion condensation on model parameters is investigated.     

Parton Distribution Functions from Lattice QCD

We present recent results on the first moments of parton distributions using gauge configurations generated with two degenerate flavors of light twisted mass quarks with pion mass fixed approximately to its physical value. We also present a first study of the vector parton distribution function using a twisted mass ensemble at pion mass of 373 MeV.     

Chiral symmetry breaking and pion properties at finite temperatures

Spontaneous and explicit chiral symmetry breaking is analyzed in Coulomb gauge QCD at finite temperatures, using an instantaneous approximation for the quark interaction and incorporating confinement through a running coupling constant. The thermodynamics of the quarks is treated approximatively by assuming that the momentum-dependent constituent quark mass sets the scale for thermodynamic fluctuations of colour singlet excitations. We investigate the class of a temperature independent and a temperature dependent interaction between quarks. In the chiral limit both temperature independent and a smooth temperature dependent interaction yields a second order chiral phase transition with critical exponents close to the values for a BCS super-conductor. For explicit chiral symmetry breaking we find a nearly constant pion mass below the transition temperature, but a strongly overdamped mode above. For a first order deconfining transition in the gluonic sector also the quark sector shows a first order chiral phase transition. The relevance of our results for relativistic heavy ion collisions is briefly discussed.     

The equation of state of quarks and mesons in a renormalization group flow picture

Non-perturbative flow equations within an effective linear sigma model coupled to constituent quarks for two quark flavours are derived and solved. A heat kernel regularization is employed for a renormalization group improved effective potential. We determine the initial values of the coupling constants in the effective potential at zero temperature. Solving the evolution equations with the same initial values at finite temperature in the chiral limit, we find a second-order phase transition at T_c≈150 MeV. Due to the smooth decoupling of massive modes, we can directly link the low-temperature four-dimensional theory to the three-dimensional high-temperature theory. We calculate the equation of state in the chiral limit and for finite pion masses and determine universal critical exponents.