High Energy Physics Lattice

We present a formalism to describe two-π+and three-π+dynamics in finite volume, the formalism is based on combination of a variational approach and the Faddeev method. Both pair-wise and three-body interactions are included in the presentation. Impacts of finite lattice spacing and the cubic lattice symmetry are also discussed. To illustrate application of the formalism, the pair-wise contact interaction that resembles the leading order interaction terms in chiral effective theory is used to analyze recent lattice results.

Critical slowing down for the Krylov Dirac solver presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. We propose a new multi-grid approach for chiral fermions, applicable to both the 5-d domain wall or 4-d Overlap operator. The central idea is to directly coarsen the 4-d Wilson kernel, giving an effective domain wall or overlap operator on each level. We provide here an explicit construction for the Shamir domain wall formulation with numerical tests for the 2-d Schwinger prototype, demonstrating near ideal multi-grid scaling. The framework is designed for a natural extension to 4-d lattice QCD chiral fermions, such as the Möbius, Zolotarev or Borici domain wall discretizations or directly to a rational expansion of the 4-d Overlap operator. For the Shamir operator, the effective overlap operator is isolated by the use of a Pauli-Villars preconditioner in the spirit of the Kähler-Dirac spectral map used in a recent staggered MG algorithm [1].

Monte Carlo simulations of quantum field theories on a lattice become increasingly expensive as the continuum limit is approached since the cost per independent sample grows with a high power of the inverse lattice spacing. Simulations on fine lattices suffer from critical slowdown, the rapid growth of autocorrelations in the Markov chain. This causes a strong increase in the number of lattice configurations that have to be generated to obtain statistically significant results. This paper discusses hierarchical sampling methods to tame the growth in autocorrelations. Combined with multilevel variance reduction, this significantly reduces the computational cost of simulations for given tolerancesϵdiscon the discretisation error andϵstaton the statistical error. For observables with lattice errors of orderαand integrated autocorrelation times that grow likeτint∝a−z, multilevel Monte Carlo (MLMC) reduces the cost fromO(ϵ−2statϵ−(1+z)/αdisc)toO(ϵ−2stat|logϵdisc|2+ϵ−1/αdisc)orO(ϵ−2stat+ϵ−1/αdisc). Higher gains are expected for simulations of quantum field theories inDdimensions. The efficiency of the approach is demonstrated on two model systems, including a topological oscillator that is badly affected by critical slowdown from topological charge freezing. On fine lattices, the new methods are orders of magnitude faster than standard Hybrid Monte Carlo sampling. For high resolutions, MLMC can be used to accelerate even the cluster algorithm for the topological oscillator. Performance is further improved through perturbative matching which guarantees efficient coupling of theories on the multilevel hierarchy.

In this notes, we illustrate why the infinite volume scattering amplitude is in fact dispensable when it comes to formulating few-body quantization condition in finite volume. Only subprocess interactions or interactions associated subprocess amplitudes are essential and fundamental ingredients of quantization conditions. After these ingredients are determined, infinite volume scattering amplitude can be computed separately. The underlying reasons are rooted in facts that (1) the final physical process is generated by all subprocess or interactions among particles; (2) the ultimate goal of quantization condition in finite volume is to find stationary solutions of few-body system. That is to say, in the end, it all comes down to the solving of eigenvalue problem,H^|n⟩=En|n⟩.

We study the nature of the finite temperature phase transition for three-flavor QCD. In particular we investigate the location of the critical endpoint along the three flavor symmetric line in the light quark mass region of the Columbia plot. In the study, the Iwasaki gauge action and the nonperturvatively O(a) improved Wilson-Clover fermion action are employed. We newly generate data atNt=12and set an upper bound of the critical pseudoscalar meson mass in the continuum limitmPS,E≲110MeV.

The appearance of large, none-Gaussian cumulants of the baryon number distribution is commonly discussed as a signal for the QCD critical point. We review the status of the Taylor expansion of cumulant ratios of baryon number fluctuations along the freeze-out line and also compare QCD results with the corresponding proton number fluctuations as measured by the STAR Collaboration at RHIC. To further constrain the location of a possible QCD critical point we discuss poles of the baryon number fluctuations in the complex plane. Here we use not only the Taylor coefficients obtained at zero chemical potential but perform also calculations of Taylor expansion coefficients of the pressure at purely imaginary chemical potentials.

Neutrinoless double beta decay (\( 0 \nu \beta \beta \)) is a hypothetical nuclear decay mode with important implications. In particular, observation of this decay would demonstrate that the neutrino is a Majorana particle and that lepton number conservation is violated in nature. Relating experimental constraints on \(0 \nu \beta \beta\) decay rates to the neutrino masses requires theoretical input in the form of non-perturbative nuclear matrix elements which remain difficult to calculate reliably. This work marks a first step toward providing a general lattice QCD framework for computing long-distance \(0 \nu \beta \beta\) matrix elements in the case where the decay is mediated by a light Majorana neutrino. The relevant formalism is developed and then tested by computing the simplest such matrix element describing an unphysical \( \pi^{-} \rightarrow \pi^{+} e^{-} e^{-} \) transition on a series of domain wall fermion ensembles. The resulting lattice data is then fit to next-to-leading-order chiral perturbation theory, allowing a fully-controlled extraction of the low energy constant governing the transition rate, \(g_{\nu}^{\pi \pi}(\mu = 770 \,\, \mathrm{MeV}) = -10.78(12)_{\rm stat}(51)_{\rm sys}\). Finally, future prospects for calculations of more complicated processes, such as the phenomenologically important \(n^{0} n^{0} \rightarrow p^{+} p^{+} e^{-} e^{-}\) decay, are discussed.

We present preliminary results for the contributions to the neutron EDM arising from the QCDθ-term, the Weinberg three-gluon and the quark chromo-EDM operators from our ongoing lattice calculations using clover valence quarks on the MILC HISQ lattices. We use the gradient-flow technique to smooth the lattices and renormalize the gluonic operators, and use the Schwinger source method to incorporate the quark chromo-EDM interactions in the quark propagator. For the QCDθ-term and the Weinberg three-gluon operator, we report results in the gradient-flow scheme from 8 ensembles at four lattice spacings and three pion masses, including 2 physical pion mass ensembles. For the quark chromo-EDM, unrenormalized results are presented at two lattice spacings,a=0.12and0.09fm, and two pion masses,Mπ=310MeV and220MeV.

We extract the neutron electric dipole moment|d→N|within the lattice QCD formalism. We analyse one ensemble ofNf=2+1+1twisted mass clover-improved fermions with lattice spacing ofa≃0.08 fmand physical values of the quark masses corresponding to a pion massmπ≃139 MeV. The neutron electric dipole moment is extracted by computing theCP-odd electromagnetic form factorF3(Q2→0)through smallθ-expansion of the action. This approach requires the calculation of the topological charge for which we employ a fermionic definition by means of spectral projectors while we also provide a comparison with the gluonic definition accompanied by the gradient flow. We show that using the topological charge from spectral projectors leads to absolute errors that are more than two times smaller than those provided when the field theoretic definition is employed. We find a value of|d→N|=0.0009(24) θ e⋅fmwhen using the fermionic definition, which is statistically consistent with zero.

Violation of non-Abelian Bianchi identity can be regarded asN2−1Abelian-like monopole currents in the continuum SU(N) QCD. Three Abelian-like monopoles, when defined in SU(2) gluodynamics on the lattice à la DeGrand-Toussaint, are shown to have the continuum limit with respect to the color-invariant monopole density and the effective monopole action. Since each Abelian-like monopole is not gauge invariant, we have introduced various partial gauge fixing for the purpose of reducing lattice artifact monopoles in the thermalized vacuum. Here we investigate Abelian and monopole dominances and the Abelian dual Meissner effects adopting the same gauges like the maximal center gauge (MCG) in comparison with the maximal Abelian gauge (MAG). Abelian and monopole contributions to the string tension in these gauges are observed to be a little smaller than the non-Abelian string tension. However, we find that the monopole dominance is improved well when use is made of the block-spin transformations with respect to Abelian-like monopoles. We find each electric field is squeezed by the corresponding colored Abelian-like monopole in such gauges and the Abelian dual Meissner effect is observed independently for each color. Moreover, we confirm the dual Ampère's law in these new gauges as well as in MAG. The SU(2) vacuum is shown to be near the border between the type 1 and type 2 dual superconductors. The penetration length is almost equal for the four gauge fixings and the vacuum type in MCG is almost the same value as the previous results. These results are consistent with the previous results suggesting the continuum limit and the gauge-independence of Abelian monopoles.