Leading Order Chiral Perturbation Theory Research Articles

QCD with light Wilson quarks on fine lattices (I): first experiences and physics results

Recent conceptual, algorithmic and technical advances allow numerical simulations of lattice QCD with Wilson quarks to be performed at significantly smaller quark masses than was possible before. Here we report on simulations of two-flavour QCD at sea-quark masses from slightly above to approximately 1/4 of the strange-quark mass, on lattices with up to 64x32^3 points and spacings from 0.05 to 0.08 fm. Physical sea-quark effects are clearly seen on these lattices, while the lattice effects appear to be quite small, even without O(a) improvement. A striking result is that the dependence of the pion mass on the sea-quark mass is accurately described by leading-order chiral perturbation theory up to meson masses of about 500 MeV.

Density resummation of perturbation series in a pion gas to leading order in chiral perturbation theory

The mean field (MF) approximation for the pion matter, being equivalent to the leading order chiral perturbation theory, involves no dynamical loops and, if self-consistent, produces finite renormalizations only. The weight factor of the Haar measure of the pion fields, entering the path integral, generates an effective Lagrangian $\ensuremath{\delta}{\mathcal{L}}_{H}$ which is generally singular in the continuum limit. There exists only one parametrization of the pion fields, for which the weight factor is equal to unity and $\ensuremath{\delta}{\mathcal{L}}_{H}=0$, respectively. This unique parametrization ensures self-consistency of the MF approximation. We use it to calculate thermal Green functions of the pion gas in the MF approximation as a power series over the density. The Borel transforms of thermal averages of a function $\mathcal{J}({\ensuremath{\chi}}^{\ensuremath{\alpha}}{\ensuremath{\chi}}^{\ensuremath{\alpha}})$ of the pion fields ${\ensuremath{\chi}}^{\ensuremath{\alpha}}$ with respect to the scalar pion density are found to be $\frac{2}{\sqrt{\ensuremath{\pi}}}\mathcal{J}(4t)$. The perturbation series over the scalar pion density for basic characteristics of the pion matter, such as the pion propagator, the pion optical potential, the scalar quark condensate $⟨\overline{q}q⟩$, the in-medium pion decay constant $\stackrel{\texttildelow{}}{F}$, and the equation of state of pion matter, appear to be asymptotic ones. These series are summed up using the contour-improved Borel resummation method. The quark scalar condensate decreases smoothly until ${T}_{\mathrm{max}}\ensuremath{\simeq}310\text{ }\text{ }\mathrm{MeV}$. The temperature ${T}_{\mathrm{max}}$ is the maximum temperature admissible for the thermalized nonlinear sigma model at zero pion chemical potentials. The estimate of ${T}_{\mathrm{max}}$ is above the chemical freeze-out temperature $T\ensuremath{\simeq}170\text{ }\text{ }\mathrm{MeV}$ in relativistic heavy-ion collisions and above the phase transition to two-flavor quark matter ${T}_{c}\ensuremath{\simeq}175\text{ }\text{ }\mathrm{MeV}$, predicted by lattice gauge theories.

Note on the power divergence in lattice calculations ofΔI=1/2K→ππamplitudes atMK=Mπ

In this Brief Report, we clarify a point concerning the power divergence in lattice calculations of $\ensuremath{\Delta}I=1/2\stackrel{\ensuremath{\rightarrow}}{K}\ensuremath{\pi}\ensuremath{\pi}$ decay amplitudes. There have been worries that this divergence might show up in the Minkowski amplitudes at ${M}_{K}{=M}_{\ensuremath{\pi}}$ with all the mesons at rest. Here we demonstrate, via an explicit calculation in leading-order chiral perturbation theory, that the power divergence is absent at the above kinematic point, as predicted by CPS symmetry.

Topological susceptibility with the improved Asqtad action

Chiral perturbation theory predicts that in quantum chromodynamics light dynamical quarks suppress the topological (instanton) susceptibility. We investigate this suppression through direct numerical simulation using the Asqtad improved lattice fermion action. This action holds promise for carrying out nonperturbative simulations over a range of quark masses for which chiral perturbation theory is expected to converge. To test the effectiveness of the action in capturing instanton physics, we measure the topological susceptibility as a function of quark masses with $2+1$ dynamical flavors. Our results, when extrapolated to zero lattice spacing, are consistent with predictions of leading order chiral perturbation theory. Included in our study is a comparison of three methods for analyzing the topological susceptibility: (1) the Boulder hypercubic blocking technique with the Boulder topological charge operator, (2) the more traditional Wilson cooling method with the twisted plaquette topological charge operator and (3) the improved cooling method of de Forcrand, Perez, and Stamatescu and their improved topological charge operator. We show in one comparison at nonzero lattice spacing that the largest difference between methods (1) and (2) can be attributed to the operator, rather than the smoothing method.

Topological susceptibility with the improved Asqtad action

As a test of the chiral properties of the improved Asqtad (staggered fermion) action, we have been measuring the topological susceptibility as a function of quark masses for 2 + 1 dynamical flavors. We report preliminary results, which show reasonable agreement with leading order chiral perturbation theory for lattice spacing less than 0.1 fm. The total topological charge, however, shows strong persistence over Monte Carlo time.

Cross section for γγ → π+π−π0 in chiral perturbation theory

We give the amplitude for γγ → π+π−π0 in leading order chiral perturbation theory. For the case of real photons we calculate the total and differential cross section. Furthermore, we give the dependence of the total cross section on the invariant mass of one of the photons.