High Energy Physics Lattice

I present a numerical study of the crossover between the low temperature chirally broken phase and the high temperature chirally restored phase inSU(Nc)gauge theory withNc=3??colors andNf=2degenerate fermion flavors. Fermion masses span a range of intermediate values (represented by the squared ratio of pseudoscalar to vector meson masses(mPS/mV)2??.25to 0.63). Observables include the temperature dependent chiral condensate and screening masses. At each fermion mass these quantities show nearly identical temperature dependence acrossNc.

We calculate the spin-averaged amplitude for doubly virtual forward Compton scattering off nucleons in the framework of manifestly Lorentz invariant baryon chiral perturbation theory at complete one-loop orderO(p4). The calculations are carried out both in the infinite and in a finite volume. The obtained results allow for a detailed estimation the finite-volume corrections to the amplitude which can be extracted on the lattice using the background field technique.

Using numerical simulations of lattice QCD with physical quark masses, we reveal the influence of magnetic-field background on chiral and deconfinement crossovers in finite-temperature QCD at low baryonic density. In the absence of thermodynamic singularity, we identify these transitions with inflection points of the approximate order parameters: normalized light-quark condensate and renormalized Polyakov loop, respectively. We show that the quadratic curvature of the chiral transition temperature in the ``temperature--chemical potential'' plane depends rather weakly on the strength of the background magnetic field. At weak magnetic fields, the thermal width of the chiral crossover gets narrower as the density of the baryon matter increases, possibly indicating a proximity to a real thermodynamic phase transition. Remarkably, the curvature of the chiral thermal width flips its sign ateBfl≃0.6GeV2, so that above the flipping pointB>Bfl, the chiral width gets wider as the baryon density increases. Approximately at the same strength of magnetic field, the chiral and deconfining crossovers merge together atT≈140MeV. The phase diagram in the parameter space ``temperature-chemical potential-magnetic field'' is outlined, and single-quark entropy and single-quark magnetization are explored. The curvature of the chiral thermal width allows us to estimate an approximate position of the chiral critical endpoint at zero magnetic field:(TCEPc,μCEPB)=(100(25)MeV, 800(140)MeV).

The leading finite-volume and thermal effects, arising in numerical lattice QCD calculations ofaHVP,LOμ≡(g−2)HVP,LOμ/2, are determined to all orders with respect to the interactions of a generic, relativistic effective field theory of pions. In contrast to earlier work based in the finite-volume Hamiltonian, the results presented here are derived by formally summing all Feynman diagrams contributing to the Euclidean electromagnetic-current two-point function, with any number of internal pion loops and interaction vertices. As was already found in our previous publication, the leading finite-volume corrections toaHVP,LOμscale asexp[−mL]wheremis the pion mass andLis the length of the three periodic spatial directions. In this work we additionally control the two sub-leading exponentials, scaling asexp[−2–√mL]andexp[−3–√mL]. As with the leading term, the coefficient of these is given by the forward Compton amplitude of the pion, meaning that all details of the effective theory drop out of the final result. Thermal effects are additionally considered, and found to be sub-percent-level for typical lattice calculations. All finite-volume corrections are presented both foraHVP,LOμand for each time slice of the two-point function, with the latter expected to be particularly useful in correcting small to intermediate current separations, for which the series of exponentials exhibits good convergence.

In Ref. [1], a method was proposed to calculate QED corrections to hadronic self energies from lattice QCD without power-law finite-volume errors. In this paper, we extend the method to processes which occur at second-order in the weak interaction and in which there is a massless (or almost massless) leptonic propagator. We demonstrate that, in spite of the presence of the propagator of an almost massless electron, such an infinite-volume reconstruction procedure can be used to obtain the amplitude for the rare kaon decayK+→π+νν¯from a lattice quantum chromodynamics computation with only exponentially small finite-volume corrections.

Using the framework of non-relativistic effective field theory, the finite-volume ground-state energy shift is calculated up-to-and-includingO(L−6)for the system of three pions in the channel with the total isospinI=1. The relativistic corrections are included perturbatively, up to the same order in the inverse of the box sizeL. The obtained explicit expression, together with the known result for the system with maximal isospinI=3, can be used for the extraction of two independent effective three-body couplings from the measured ground-state spectrum of three pions.

The dynamics of multi-kaon systems are of relevance for several areas of nuclear physics. However, even the simplest systems, two and three kaons, are hard to prepare and study experimentally. Here we show how to extract this information using first-principle lattice QCD results. We (1) extend the relativistic three-body quantization condition to the strangeness sector, predicting for the first time the excited level finite-volume spectrum of three kaon systems at maximal isospin, and (2) present a first lattice QCD calculation of the excited levels of this system in a finite box. We compare our predictions with the lattice results reported here and with previous ground state calculations and find very good agreement.

We present the formalism for connecting a second-order electroweak2−→−−−HI+HI2transition amplitudes in the finite volume (with two hadrons in the initial and final states) to the physical amplitudes in the infinite volume. Our study mainly focus on the case where the low-lying intermediate state consists of two scattering hadrons. As a side product we also reproduce the finite-volume formula for2−→HI2transition, originally obtained by Briceño and Hansen. With the available finite-volume formalism, we further discuss how to treat with the finite-volume problem in the double beta decaysnn→ppeeν¯ν¯andnn→ppee.

We consider one-plaquette unitary matrix model at finiteNusing exact expression of the partition function for both SU(N) and U(N) groups.

We present a non-perturbative lattice calculation of the form factors which contribute to the amplitudes for the radiative decaysP→ℓν¯ℓγ, wherePis a pseudoscalar meson andℓis a charged lepton. Together with the non-perturbative determination of the corrections to the processesP→ℓν¯ℓdue to the exchange of a virtual photon, this allows accurate predictions atO(αem)to be made for leptonic decay rates for pseudoscalar mesons ranging from the pion to theDsmeson. We are able to separate unambiguously and non-pertubatively the point-like contribution, from the structure-dependent, infrared-safe, terms in the amplitude. The fully non-perturbativeO(a)improved calculation of the inclusive leptonic decay rates will lead to the determination of the corresponding Cabibbo-Kobayashi-Maskawa (CKM) matrix elements also atO(αem). Prospects for a precise evaluation of leptonic decay rates with emission of a hard photon are also very interesting, especially for the decays of heavyDandBmesons for which currently only model-dependent predictions are available to compare with existing experimental data.