High Energy Physics Lattice

Lattice QCD with staggered fermions can be formulated in dual variables to address the finite baryon density sign problem. In the past we have performed simulations in the strong coupling regime, including leading order gauge corrections. In order to vary the temperature for fixedβit was necessary to introduce a bare anisotropy. In this talk we will extend our work to include results from a non-perturbative determination of the physical anisotropyaσ/aτ=ξ(γ,β), which is necessary to unambiguously locate the critical end point and the first order line of the chiral transition.

We consider a gauge-invariant, mass-independent prescription for renormalizing composite operators, regularized on the lattice, in the spirit of the coordinate space (X-space) renormalization scheme. The prescription involves only Green's functions of products of gauge-invariant operators, situated at distinct space-time points, in a way as to avoid potential contact singularities. Such Green's functions can be computed nonperturbatively in numerical simulations, with no need to fix a gauge: thus, renormalization to this "intermediate" scheme can be carried out in a completely nonperturbative manner.Expressing renormalized operators in theMS¯¯¯¯¯¯¯scheme requires the calculation of corresponding conversion factors. The latter can only be computed in perturbation theory, by the very nature of theMS¯¯¯¯¯¯¯; however, the computations are greatly simplified by virtue of the following attributes: i) In the absense of operator mixing, they involve only massless, two-point functions; such quantities are calculable to very high perturbative order. ii) They are gauge invariant; thus, they may be computed in a convenient gauge. iii) Where operator mixing may occur, only gauge-invariant operators will appear in the mixing pattern: Unlike other schemes, involving mixing with gauge-variant operators (which may contain ghost fields), the mixing matrices in the present scheme are greatly reduced. Still, computation of some three-point functions may not be altogether avoidable.We exemplify the procedure by computing, to lowest order, the conversion factors for fermion bilinear operators of the form?¯??in QCD. We also employ the gauge-invariant scheme in the study of mixing between gluon and quark energy-momentum tensor operators: We compute to one loop the conversion factors relating the nonperturbative mixing matrix to theMS¯¯¯¯¯¯¯scheme.

We present a generalization of the relativistic, finite-volume, three-particle quantization condition for non-identical pions in isosymmetric QCD. The resulting formalism allows one to use discrete finite-volume energies, determined using lattice QCD, to constrain scattering amplitudes for all possible values of two- and three-pion isospin. As for the case of identical pions considered previously, the result splits into two steps: The first defines a non-perturbative function with roots equal to the allowed energies,En(L), in a given cubic volume with side-lengthL. This function depends on an intermediate three-body quantity, denotedKdf,3, which can thus be constrained from lattice QCD input. The second step is a set of integral equations relatingKdf,3to the physical scattering amplitude,M3. Both of the key relations,En(L)↔Kdf,3andKdf,3↔M3, are shown to be block-diagonal in the basis of definite three-pion isospin,Iπππ, so that one in fact recovers four independent relations, corresponding toIπππ=0,1,2,3. We also provide the generalized threshold expansion ofKdf,3for all channels, as well as parameterizations for all three-pion resonances present forIπππ=0andIπππ=1. As an example of the utility of the generalized formalism, we present a toy implementation of the quantization condition forIπππ=0, focusing on the quantum numbers of theωandh1resonances.

We determine spins of more than 100 low lying glueball states inD=2+1dimensionalSU(4)gluodynamics by a lattice calculation. We go up toJ=8in the spin value. We compare the resulting spectrum with predictions of the Axionic String Ansatz (ASA). We find a perfect match for 39 lightest states, corresponding to the first four string levels. In particular, this resolves tensions between the ASA predictions and earlier spin determinations. The observed spins of heavier glueballs are also in a good agreement with the ASA. We did not identify any sharp tension between lattice data and the ASA, but more work is needed to fully test the ASA predictions for the spins of 64 states at the fifth string level.

Motivated in part by the pseudo-Nambu Goldstone Boson mechanism of electroweak symmetry breaking in Composite Higgs Models, in part by dark matter scenarios with strongly coupled origin, as well as by general theoretical considerations related to the large-N extrapolation, we perform lattice studies of the Yang-Mills theories withSp(2N)gauge groups. We measure the string tension and the mass spectrum of glueballs, extracted from appropriate 2-point correlation functions of operators organised as irreducible representations of the octahedral symmetry group. We perform the continuum extrapolation and study the magnitude of finite-size effects, showing that they are negligible in our calculation. We present new numerical results forN=1,2,3,4, combine them with data previously obtained forN=2, and extrapolate towardsN→∞. We confirm explicitly the expectation that, as already known forN=1,2also forN=3,4a confining potential rising linearly with the distance binds a static quark to its antiquark. We compare our results to the existing literature on other gauge groups, with particular attention devoted to the large-Nlimit. We find agreement with the known values of the mass of the0++,0++∗and2++glueballs obtained taking the large-Nlimit in theSU(N)groups. In addition, we determine for the first time the mass of some heavier glueball states at finiteNinSp(2N)and extrapolate the results towardsN→+∞taking the limit in the latter groups. Since the large-Nlimit ofSp(2N)is the same as inSU(N), our results are relevant also for the study of QCD-like theories.

Efficient digitization is required for quantum simulations of gauge theories. Schemes based on discrete subgroups use fewer qubits at the cost of systematic errors. We systematize this approach by deriving a single plaquette action for approximating general continuous gauge groups through integrating out field fluctuations. This provides insight into the effectiveness of these approximations, and how they could be improved. We accompany the scheme by simulations of pure gauge over the largest discrete subgroup ofSU(3)up to the third order.

The static longitudinal and transverse gluon propagators in the Landau gauge are studied in2+1lattice QCD with nonzero isospin chemical potentialμI. Parameterization of the momentum dependence of the propagators is provided for all values of the chemical potential under study. We find that the longitudinal propagator is infrared suppressed at nonzeroμIwith suppression increasing with increasingμI. It is found, respectively, that the electric screening mass is increasing with increasingμI. Additionally, we analyze the difference between two propagators as a function of the momentum and thus compare interactions in chromoelectric and chromomagnetic sectors.

We study the gluon sector in pure Yang-Mills theories via the computation of two, three and four point Landau gauge gluon correlation functions via LQCD using the Wilson action for Monte-Carlo simulations. The first goal was to use lattice tensor representations for the propagator in four dimensions to understand/quantify deviations of the lattice propagator from its continuum form. We also identified classes of kinematic configurations where these deviations are minimal and the continuum description of lattice tensors is improved. These tensor structures also allow to verify that the continuum Slavnov-Taylor identity for the propagator is is fulfilled, with good accuracy, on the lattice. The computation of the three gluon vertex served to explore the so-called zero crossing, a property related to the ghost dominance at the infrared scales that restricts the behaviour of the three gluon vertex. We also explore the possible existence of a ghost mass preventing the IR divergence. Functional forms were used to model the lattice data and explore the two different possibilities for the IR behaviour. In the first case we estimate the mass scale associated with the crossing and search for a possible sign of the divergence. Secondly, we study the possibility of a sign change and a finite zero momentum value of the vertex. A last topic is the calculation of the four gluon vertex. A suitable choice of kinematics allows to eliminate the unwanted contributions from lower order functions while large statistical fluctuations hinder the precise computation of this object. Our investigation is a proof of concept, we show that the lattice computation of the four gluon correlation function is feasible with reasonable computational resources. An increase in statistics is necessary to provide a clearer signal on the complete correlation function and to compute the one particle irreducible function.

We present the first study of the Abelian-projected gluonic-excitation energies for the static quark-antiquark (QQ¯) system in SU(3) lattice QCD at the quenched level, using a324lattice atβ=6.0. We investigate ground-state and three excited-state QQ¯potentials, using smeared link variables on the lattice. We find universal Abelian dominance for the quark confinement force of the excited-state QQ¯potentials as well as the ground-state potential. Remarkably, in spite of the excitation phenomenon in QCD, we find Abelian dominance for the first gluonic-excitation energy of about 1 GeV at long distances in the maximally Abelian gauge. On the other hand, no Abelian dominance is observed for higher gluonic-excitation energies even at long distances. This suggests that there is some threshold between 1 and 2 GeV for the applicable excitation-energy region of Abelian dominance. Also, we find that Abelian projection significantly reduces the short-distance1/r-like behavior in gluonic-excitation energies.

Landau gauge longitudinal and transverse gluon propagators are studied in lattice QCD with gauge groupSU(2)at varying temperature and quark density. In particular, it is found that the longitudinal propagator decreases with increasing quark chemical potential at all temperatures under study, whereas the transverse propagator increases with increasing quark chemical potential atT<200MeV and does not depend on it at higher temperatures. The relative strength of chromoelectric and chromomagnetic interactions is also discussed.