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تسجيل مستخدم جديدNew DoS approaches to finite density lattice QCD
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We present two new suggestions for density of states (DoS) approaches to finite density lattice QCD. Both proposals are based on the recently developed and successfully tested DoS FFA technique, which is a DoS approach for bosonic systems with a complex action problem. The two different implementations of DoS FFA we suggest for QCD make use of different representations of finite density lattice QCD in terms of suitable pseudo-fermion path integrals. The first proposal is based on a pseudo-fermion representation of the grand canonical QCD partition sum, while the second is a formulation for the canonical ensemble. We work out the details of the two proposals and discuss the results of exploratory 2-d test studies for free fermions at finite density, where exact reference data allow one to verify the final results and intermediate steps.
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We discuss two new DoS approaches for finite density lattice QCD. The paper extends a recent presentation of the new techniques based on Wilson fermions, while here we now discuss and test the case of finite density QCD with staggered fermions. The f
irst of our two approaches is based on the canonical formulation where observables at a fixed net quark number $N$ are obtained as Fourier moments of the vacuum expectation values at imaginary chemical potential $theta$. We treat the latter as densities which can be computed with the recently developed FFA method. The second approach is based on a direct grand canonical evaluation after rewriting the QCD partition sum in terms of a suitable pseudo-fermion representation. In this form the imaginary part of the pseudo-fermion action can be identified and the corresponding density may again be computed with FFA. We develop the details of the two approaches and discuss some exploratory first tests for the case of free fermions where reference results for assessing the new techniques may be obtained from Fourier transformation.
We pursue the idea of adding the naive $mu N$ term, where $mu$ is the quark chemical potential and $N$ is the conserved quark number, to the lattice QCD action. While computations of higher order susceptibilities, required for estimating the location
of the QCD critical point, need a lot fewer number of quark propagators at any order as a result, it has its problem. We discuss a solution, and examine if it works.
We explore the phase space spanned by the temperature and the chemical potential for 4-flavor lattice QCD using the Wilson-clover quark action. In order to determine the order of the phase transition, we apply finite size scaling analyses to gluonic
and quark observables including plaquette, Polyakov loop and quark number density, and examine their susceptibility, skewness, kurtosis and Challa-Landau-Binder cumulant. Simulations were carried out on lattices of a temporal size fixed at $N_{text{t}}=4$ and spatial sizes chosen from $6^3$ up to $10^3$. Configurations were generated using the phase reweighting approach, while the value of the phase of the quark determinant were carefully monitored. The $mu$-parameter reweighting technique is employed to precisely locate the point of the phase transition. Among various approximation schemes for calculating the ratio of quark determinants needed for $mu$-reweighting, we found the Taylor expansion of the logarithm of the quark determinant to be the most reliable. Our finite-size analyses show that the transition is first order at $(beta, kappa, mu/T)=(1.58, 0.1385, 0.584pm 0.008)$ where $(m_pi/m_rho, T/m_rho)=(0.822, 0.154)$. It weakens considerably at $(beta, kappa, mu/T)=(1.60, 0.1371, 0.821pm 0.008)$ where $(m_pi/m_rho, T/m_rho)=(0.839, 0.150)$, and a crossover rather than a first order phase transition cannot be ruled out.
This an English translation of a review of finite-density lattice QCD. The original version in Japanese appeared in Soryushiron Kenkyu Vol 31 (2020) No. 1.
We demonstrate that the leading and next-to-leading finite-volume effects in the evaluation of leptonic decay widths of pseudoscalar mesons at $O(alpha)$ are universal, i.e. they are independent of the structure of the meson. This is analogous to a s
imilar result for the spectrum but with some fundamental differences, most notably the presence of infrared divergences in decay amplitudes. The leading non-universal, structure-dependent terms are of $O(1/L^2)$ (compared to the $O(1/L^3)$ leading non-universal corrections in the spectrum). We calculate the universal finite-volume effects, which requires an extension of previously developed techniques to include a dependence on an external three-momentum (in our case, the momentum of the final state lepton). The result can be included in the strategy proposed in Ref.,cite{Carrasco:2015xwa} for using lattice simulations to compute the decay widths at $O(alpha)$, with the remaining finite-volume effects starting at order $O(1/L^2)$. The methods developed in this paper can be generalised to other decay processes, most notably to semileptonic decays, and hence open the possibility of a new era in precision flavour physics.
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