High Energy Physics Lattice

Lefschetz thimbles regularisation of (lattice) field theories was put forward as a possible solution to the sign problem. Despite elegant and conceptually simple, it has many subtleties, a major one boiling down to a plain question: how many thimbles should we take into account? In the original formulation, a single thimble dominance hypothesis was put forward: in the thermodynamic limit, universality arguments could support a scenario in which the dominant thimble (associated to the global minimum of the action) captures the physical content of the field theory. We know by now many counterexamples and we have been pursuing multi-thimble simulations ourselves. Still, a single thimble regularisation would be the real breakthrough. We report on ongoing work aiming at a single thimble formulation of lattice field theories, in particular putting forward the proposal of performing Taylor expansions on the dominant thimble.

In recent years there has been much progress on the investigation of the QCD phase diagram with lattice QCD simulations. In this review I focus on the developments in the last two years. Especially the addition of external influences or new parameter ranges yield an increasing number of interesting results. I discuss the progress for small, finite densities from both analytical continuation and Complex Langevin simulations, for heavy quark bound states (quarkonium), the dependence on the quark masses (Columbia plot) and the influence of a magnetic field. Many of these conditions are relevant for the understanding of both the QCD transition in the early universe and heavy ion collision experiments which are conducted for example at the LHC and RHIC.

The mass shifts for two-fermion bound and scattering P-wave states subject to the long-range interactions due to QED in the non-relativistic regime are derived. Introducing a short range force coupling the spinless fermions to one unit of angular momentum in the framework of pionless EFT, we first calculate both perturbatively and non-perturbatively the Coulomb corrections to fermion-fermion scattering in the continuum and infinite volume context. Motivated by the research on particle-antiparticle bound states, we extend the results to fermions of identical mass and opposite charge. Second, we transpose the system onto a cubic lattice with periodic boundary conditions and we calculate the finite volume corrections to the energy of the lowest bound and unboundT±1eigenstates. In particular, power law corrections proportional to the fine structure constant and resembling the recent results for S-wave states are found. Higher order contributions inαare neglected, since the gapped nature of the momentum operator in the lattice environnement allows for a perturbative treatment of the QED interactions.

We determine the?(1232)resonance parameters using lattice QCD and the Lüscher method. The resonance occurs in elastic pion-nucleon scattering withJP=3/2+in the isospinI=3/2,P-wave channel. Our calculation is performed withNf=2+1flavors of clover fermions on a lattice withL??.8fm. The pion and nucleon masses arem?=255.4(1.6)MeV andmN=1073(5)MeV, and the strong decay channel??�πNis found to be above the threshold. To thoroughly map out the energy-dependence of the nucleon-pion scattering amplitude, we compute the spectra in all relevant irreducible representations of the lattice symmetry groups for total momenta up toP??=2?L(1,1,1), including irreps that mixSandPwaves. We perform global fits of the amplitude parameters to up to 21 energy levels, using a Breit-Wigner model for theP-wave phase shift and the effective-range expansion for theS-wave phase shift. From the location of the pole in theP-wave scattering amplitude, we obtain the resonance massm?=1378(7)(9)MeV and the couplingg?-?N=23.8(2.7)(0.9).

We review the Euclidean path-integral formulation of the nucleon hadronic tensor and classify the gauge invariant and topologically distinct insertions in terms of connected and disconnected insertions and also in terms of leading and higher-twist contributions in the DIS region. Converting the Euclidean hadronic tensor back to the Minkowski space requires solving an inverse problem of the Laplace transform. We have investigated several inverse algorithms and studied the pros and cons of each. We show a result with a relatively large momentum transfer (Q2∼4GeV2) to suppress the elastic scattering and reveal the contributions from the resonance and inelastic region of the neutrino-nucleon scattering. For elastic scattering, the hadronic tensor is the the product of the elastic form factors for the two corresponding currents. We checked numerically for the case of two charge vector currents (V4) with the electric form factor calculated from the three-point function and found they agree within errors.

In a Quantum Field Theory, the analytic structure of the 2-points correlation functions, ie the propagators, encloses information about the properties of the corresponding quanta, particularly if they are or not confined. However, in Quantum Chromodynamics (QCD), we can only have an analytic solution in a perturbative picture of the theory. For the non-perturbative propagators, one resorts on numerical solutions of QCD that accesses specific regions of the Euclidean momentum space, as, for example, those computed via Monte Carlo simulations on the lattice. In the present work, we rely on Padé Approximants (PA) to approximate the numerical data for the gluon and ghost propagators, and investigate their analytic structures. In a first stage, the advantages of using PAs are explored when reproducing the properties of a function, focusing on its analytic structure. The use of PA sequences is tested for the perturbative solutions of the propagators, and a residue analysis is performed to help in the identification of the analytic structure. A technique used to approximate a PA to a discrete set of points is proposed and tested for some test data sets. Finally, the methodology is applied to the Landau gauge gluon and ghost propagators, obtained via lattice simulations. The results identify a conjugate pair of complex poles for the gluon propagator, that is associated with the infrared structure of the theory. This is in line with the presence of singularities for complex momenta in theories where confinement is observed. Regarding the ghost propagator, a pole atp2=0is identified. For both propagators, a branch cut is found on the real negativep2-axis, which recovers the perturbative analysis at high momenta.

We present results for the unpolarized parton distribution function of the nucleon computed in lattice QCD at the physical pion mass. This is the first study of its kind employing the method of Ioffe time pseudo-distributions. Beyond the reconstruction of the Bjorken-xdependence we also extract the lowest moments of the distribution function using the small Ioffe time expansion of the Ioffe time pseudo-distribution. We compare our findings with the pertinent phenomenological determinations.

We present a new method, based on Gaussian process regression, for reconstructing the continuousx-dependence of parton distribution functions (PDFs) from quasi-PDFs computed using lattice QCD. We examine the origin of the unphysical oscillations seen in current lattice calculations of quasi-PDFs and develop a nonparametric fitting approach to take the required Fourier transform. The method is tested on one ensemble of maximally twisted mass fermions with two light quarks. We find that with our approach oscillations of the quasi-PDF are drastically reduced. However, the final effect on the light-cone PDFs is small. This finding suggests that the deviation seen between current lattice QCD results and phenomenological determinations cannot be attributed solely on the Fourier transform.

We perform a first calculation for the unpolarized parton distribution function of theΔ+baryon using lattice QCD simulations within the framework of Large Momentum Effective Theory. Two ensembles ofNf=2+1+1twisted mass fermions are utilized with a pion mass of 270 MeV and 360 MeV, respectively. The baryon, which is treated as a stable single-particle state, is boosted with momentumP3with values{0.42,0.83,1.25}GeV, and we utilize momentum smearing to improve the signal. The unpolarized parton distribution function ofΔ+is obtained using a non-perturbative renormalization and a one-loop formula for the matching, with encouraging precision. In particular, we compute thed¯¯¯(x)−u¯¯¯(x)asymmetry and compare it with the same quantity in the nucleon, in a first attempt towards resolving the physical mechanism responsible for generating such asymmetry.

Non-perturbative scale-dependent renormalization problems are ubiquitous in lattice QCD as they enter many relevant phenomenological applications. They require solving non-perturbatively the renormalization group equations for the QCD parameters and matrix elements of interest in order to relate their non-perturbative determinations at low energy to their high-energy counterparts needed for phenomenology. Bridging the large energy separation between the hadronic and perturbative regimes of QCD, however, is a notoriously difficult task. In this contribution we focus on the case of the QCD coupling. We critically address the common challenges that state-of-the-art lattice determinations have to face in order to be significantly improved. In addition, we review a novel strategy that has been recently put forward in order to solve this non-perturbative renormalization problem and discuss its implications for future precision determinations. The new ideas exploit the decoupling of heavy quarks to matchNf-flavor QCD and the pure Yang-Mills theory. Through this matching the computation of the non-perturbative running of the coupling in QCD can be shifted to the computationally much easier to solve pure-gauge theory. We shall present results for the determination of theΛ-parameter ofNf=3-flavor QCD where this strategy has been applied and proven successful. The results demonstrate that these techniques have the potential to unlock unprecedented precision determinations of the QCD coupling from the lattice. The ideas are moreover quite general and can be considered to solve other non-perturbative renormalization problems.