High Energy Physics Lattice

In this paper we study thermodynamic properties of dense coldSU(2)QCD within lattice simulation with dynamical rooted staggered quarks which in the continuum limit correspond toNf=2quark flavours. We calculate baryon density, renormalized chiral and diquark condensates for various baryon chemical potentials in the regionμ∈(0,2000)MeV. It is found, that in the regionμ∈(0,540)MeV the system is well described by the ChPT predictions. In the regionμ>540MeV the system becomes sufficiently dense and ChPT is no longer applicable to describe lattice data. For chemical potentialsμ>900MeV we observe formation of the Fermi sphere, and the system is similar to the one described by the Bardeen-Cooper-Schrieffer theory where the the diquarks play a role of Cooper pairs. In order to study how nonzero baryon density influences the gluon background we calculate chromoelectric and chromomagnetic fields, as well as the topological susceptibility. We find that the chromoelectric field and the topological susceptibility decrease, whereas the chromomagnetic field increases with rising of baryon chemical potential. Finally we study the equation of state of dense two-color quark matter.

The transverse-momentum-dependent (TMD) soft function is a key ingredient in QCD factorization of Drell-Yan and other processes with relatively small transverse momentum. We present a lattice QCD study of this function at moderately large rapidity on a 2+1 flavor CLS dynamic ensemble witha=0.098fm. We extract the rapidity-independent (or intrinsic) part of the soft function through a large-momentum-transfer pseudo-scalar meson form factor and its quasi-TMD wave function using leading-order factorization in large-momentum effective theory. We also investigate the rapidity-dependent part of the soft function---the Collins-Soper evolution kernel---based on the large-momentum evolution of the quasi-TMD wave function.

The Casimir effect arises from the zero-point energy of particles in momentum space deformed by the existence of two parallel plates. For degrees of freedom on the lattice, its energy-momentum dispersion is determined so as to keep a periodicity within the Brillouin zone, so that its Casimir effect is modified. We study the properties of Casimir effect for lattice fermions, such as the naive fermion, Wilson fermion, and overlap fermion based on the Möbius domain-wall fermion formulation, in the1+1-,2+1-, and3+1-dimensional space-time with the periodic or antiperiodic boundary condition. An oscillatory behavior of Casimir energy between odd and even lattice size is induced by the contribution of ultraviolet-momentum (doubler) modes, which realizes in the naive fermion, Wilson fermion in a negative mass, and overlap fermions with a large domain-wall height. Our findings can be experimentally observed in condensed matter systems such as topological insulators and also numerically measured in lattice simulations.

I discuss recent progress in lattice calculations ofB→D(∗)ℓνform factors, important for the precision determination of|Vcb|in the Standard Model (SM), and for testing SM expectations of lepton flavor universality in observablesR(D(∗)). I also discuss progress in calculations of the relatedb→csemileptonic decaysBs→D(∗)sℓνandBc→J/ψℓνnow experimentally accessible at the LHC.

We compute the leading order hadronic vacuum polarization (LO-HVP) contribution to the anomalous magnetic moment of the muon,(gμ−2), using lattice QCD. Calculations are performed with four flavors of 4-stout-improved staggered quarks, at physical quark masses and at six values of the lattice spacing down to 0.064~fm. All strong isospin breaking and electromagnetic effects are accounted for to leading order. The infinite-volume limit is taken thanks to simulations performed in volumes of sizes up to 11~fm. Our result for the LO-HVP contribution to(gμ−2)has a total uncertainty of 0.8\%. Compared to the result of the dispersive approach for this contribution, ours significantly reduces the tension between the standard model prediction for(gμ−2)and its measurement.

We present recent progress in the lattice calculation of leptonic decay constants forB(s)andD(s)mesons using the Oktay-Kronfeld (OK) action for charm and bottom valence quarks, whose masses are tuned non-perturbatively. The calculations are done on 6 HISQ ensembles generated by the MILC collaboration withNf=2+1+1flavors. We also use the HISQ action for the light spectator quarks. Results are presented for the ratiosfBs/fBandfDs/fD, which reflectSU(3)flavor symmetry breaking, and are independent of the renormalization constants of the axial currents.

Recent lattice data onππ-scattering phase shifts in the vector-isovector channel, pseudoscalar meson masses and decay constants for strange-quark masses smaller or equal to the physical value allow us to study the strangeness dependence of these observables for the first time. We perform a global analysis on two kind of lattice trajectories depending on whether the sum of quark masses or the strange-quark mass is kept fixed to the physical point. The quark mass dependence of these observables is extracted from unitarized coupled-channel one-loop Chiral Perturbation Theory. This analysis guides new predictions on theρ(770)meson properties over trajectories where the strange-quark mass is lighter than the physical mass, as well as on the SU(3) symmetric line. As a result, the light- and strange-quark mass dependence of theρ(770)meson parameters are discussed and precise values of the Low Energy Constants present in unitarized one-loop Chiral Perturbation Theory are given. Finally, the current discrepancy between two- and three-flavor lattice results for theρ(770)meson is studied.

We study the finite temperature localization transition in the spectrum of the overlap Dirac operator. Simulating the quenched approximation of QCD, we calculate the mobility edge, separating localized and delocalized modes in the spectrum. We do this at several temperatures just above the deconfining transition and by extrapolation we determine the temperature where the mobility edge vanishes and localized modes completely disappear from the spectrum. We find that this temperature, where even the lowest Dirac eigenmodes become delocalized, coincides with the critical temperature of the deconfining transition. This result, together with our previously obtained similar findings for staggered fermions shows that quark localization at the deconfining temperature is independent of the fermion discretization, suggesting that deconfinement and localization of the lowest Dirac eigenmodes are closely related phenomena.

Neutrinoless double beta decay, if detected, would prove that neutrinos are Majorana fermions and provide the direct evidence for lepton number violation. If such decay would exist in nature, thenπ−π−→eeandπ−→π+ee(or equivalentlyπ−e+→π+e−) are the two simplest processes accessible via first-principle lattice QCD calculations. In this work, we calculate the long-distance contributions to theπ−→π+eetransition amplitude using four ensembles at the physical pion mass with various volumes and lattice spacings. We adopt the infinite-volume reconstruction method to control the finite-volume effects arising from the (almost) massless neutrino. Providing the lattice QCD inputs for chiral perturbation theory, we obtain the low energy constantgππν(mρ)=−10.89(28)stat(74)sys, which is close togππν(mρ)=−11.96(31)statdetermined from the crossed-channelπ−π−→eedecay.

The interactions between two octet baryons are studied at low energies using lattice QCD (LQCD) with larger-than-physical quark masses corresponding to a pion mass ofmπ∼450MeV and a kaon mass ofmK∼596MeV. The two-baryon systems that are analyzed range from strangenessS=0toS=−4and include the spin-singlet and tripletNN,ΣN(I=3/2), andΞΞstates, the spin-singletΣΣ(I=2) andΞΣ(I=3/2) states, and the spin-tripletΞN(I=0) state. Thes-wave scattering phase shifts, low-energy scattering parameters, and binding energies when applicable, are extracted using Lüscher's formalism. While the results are consistent with most of the systems being bound at this pion mass, the interactions in the spin-tripletΣNandΞΞchannels are found to be repulsive and do not support bound states. Using results from previous studies at a larger pion mass, an extrapolation of the binding energies to the physical point is performed and is compared with experimental values and phenomenological predictions. The low-energy coefficients in pionless EFT relevant for two-baryon interactions, including those responsible forSU(3)flavor-symmetry breaking, are constrained. TheSU(3)symmetry is observed to hold approximately at the chosen values of the quark masses, as well as theSU(6)spin-flavor symmetry, predicted at largeNc. A remnant of an accidentalSU(16)symmetry found previously at a larger pion mass is further observed. TheSU(6)-symmetric EFT constrained by these LQCD calculations is used to make predictions for two-baryon systems for which the low-energy scattering parameters could not be determined with LQCD directly in this study, and to constrain the coefficients of all leadingSU(3)flavor-symmetric interactions, demonstrating the predictive power of two-baryon EFTs matched to LQCD.