High Energy Physics Lattice

Lattice QCD calculations of nucleon form factors are restricted to discrete values of the Euclidean four-momentum transfer. Therefore, the extraction of radii typically relies on parametrizing and fitting the lattice QCD data to obtain its slope close to zero momentum transfer. We investigate a new method, which allows to compute the nucleon radius directly from existing lattice QCD data, without assuming a functional form for the momentum dependence of the underlying form factor. The method is illustrated for the case of the isovector mean square charge radius of the nucleon⟨r2isov⟩and the quark-connected contributions to⟨r2p⟩and⟨r2n⟩for the proton and neutron, respectively. Computations are performed using a single gauge ensemble withNf=2+1+1maximally twisted mass clover-improved fermions at physical quark mass and a lattice spacing ofa=0.08fm.

Under the assumption of separable interactions, we illustrate how the few-body quantization condition may be formulated in terms of phase shifts in general, which may be useful for describing and modeling of few-body resonances in finite volume.

We present results on the isovector momentum fraction,⟨x⟩u−d, helicity moment,⟨x⟩Δu−Δd, and the transversity moment,⟨x⟩δu−δd, of the nucleon obtained using nine ensembles of gauge configurations generated by the MILC collaboration using2+1+1-flavors of dynamical highly improved staggered quarks (HISQ). The correlation functions are calculated using the Wilson-Clover action and the renormalization of the three operators is carried out nonperturbatively on the lattice in the RI′-MOM scheme. The data have been collected at lattice spacingsa≈0.15, 0.12, 0.09,and 0.06 fm andMπ≈310, 220and 135 MeV, which are used to obtain the physical values using a simultaneous chiral-continuum-finite-volume fit. The final results, in theMS¯¯¯¯¯¯¯¯¯scheme at 2 GeV, are⟨x⟩u−d=0.173(14)(07),⟨x⟩Δu−Δd=0.213(15)(22)and⟨x⟩δu−δd=0.208(19)(24), where the first error is the overall analysis uncertainty and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with other recent lattice calculations and phenomenological global fit values.

In this thesis, we studied the bosonic BFSS and IKKT matrix models using Monte Carlo simulations. First, we explored some toy models to check the validity of the numerical simulations. Then we simulated the BFSS matrix model using Hamiltonian Monte Carlo (HMC) algorithm. In the BFSS matrix model, we used the Polyakov loop as an order parameter to investigate the large-N behaviour of this model at different temperatures. Our simulations confirmed that the model exhibits a confinement-deconfinement phase transition as the temperature of the system is varied. Besides the Polyakov loop, other observables such as internal energy and extent of space were also computed. In the bosonic IKKT model, we studied the spontaneous symmetry breaking (SSB) of SO(10) symmetry using the moment of inertia tensor and found that there is no SSB of SO(10) symmetry in this model. Besides the eigenvalues of the moment of inertia tensor, other observable such as extent of spacetime was also computed. We also studied the simulation theory of the phase-quenched IKKT model.

We study canonical and affine versions of non-renormalizable euclidean classical scalar field-theory with twelfth-order power-law interactions on three dimensional lattices through the Monte Carlo method. We show that while the canonical version of the model turns out to approach a "free-theory" in the continuum limit, the affine version is perfectly well defined as an interaction model.

Supersymmetric Yang-Mills (SYM) theories in four dimensions exhibit many interesting non-perturbative phenomena that can be studied by means of Monte Carlo lattice simulations. However, the lattice regularization breaks supersymmetry explicitly, and in general a fine tuning of a large number of parameters is required to correctly extrapolate the theory to the continuum limit. From this perspective, it is important to preserve on the lattice as many symmetries of the original continuum action as possible. Chiral symmetry for instance prevents an additive renormalization of the fermion mass. A (modified) version of chiral symmetry can be preserved exactly if the Dirac operator fulfills the Ginsparg-Wilson relation. In this contribution, we present an exploratory non-perturbative study of N=1 supersymmetric Yang-Mills theory using the overlap formalism to preserve chiral symmetry at non-zero lattice spacings. N=1 SYM is an ideal benchmark toward the extension of our studies to more complex supersymmetric theories, as the only parameter to be tuned is the gluino mass. Overlap fermions allow therefore to simulate the theory without fine-tuning. We compare our approach to previous investigations of the same theory, and we present clear evidences for gluino condensation.

We discuss a tensor network formulation for relativistic lattice fermions. The Grassmann tensor is concretely defined with the auxiliary Grassmann fields which play a role of bond degrees of freedom. This formulation is immediately applicable to any lattice theory with only nearest neighbor interactions. We introduce a general formula to derive the tensor network representation for lattice fermions, which is expressed by the singular value decomposition for a given Dirac matrix. We also test this formulation numerically for the free Wilson fermion.

The three-gluon vertex has been found to be a vital ingredient in non-perturbative functional approaches. We present an updated lattice calculation of it in various kinematical configurations for all tensor structures and multiple lattice parameters in three dimensions, and in a subset of those in four dimensions, for SU(2) Yang-Mills theory in minimal Landau gauge. In three dimensions an unambiguous zero crossing for the tree-level form-factor is established, and consistency for all investigated form factors with a power-like divergence towards the infrared. The results in four dimensions are consistent with such a behavior, but do not yet reach deep enough into the infrared to establish it.

A pair of triply charmed baryons,ΩcccΩccc, is studied as an ideal dibaryon system by (2+1)-flavor lattice QCD with nearly physical light-quark masses and the relativistic heavy quark action with the physical charm quark mass. The spatial baryon-baryon correlation is related to their scattering parameters on the basis of the HAL QCD method. TheΩcccΩcccin the1S0channel taking into account the Coulomb repulsion with the charge form factor ofΩcccleads to the scattering lengthaC0?��?19 fmand the effective rangerCeff??.45 fm. The ratiorCeff/aC0?��?0.024, whose magnitude is considerably smaller than that of the dineutron (??.149), indicates thatΩcccΩcccis located in the unitary regime.

The hadronic contribution to the muon anomalous magnetic momentaμ=(gμ−2)/2has to be determined at the per-mille level for the Standard Model prediction to match the expected final uncertainty from the ongoing E989 experiment. This is 3 times better than the current precision from the dispersive approach, and 5-15 times smaller than the uncertainty on the purely theoretical determinations from lattice QCD. So far the stumbling-block is the large statistical error in the Monte Carlo evaluation of the required correlation functions which can hardly be tamed by brute force. Here we propose to solve this problem by multi-level Monte Carlo integration, a technique which reduces the variance of correlators exponentially in the distance of the fields. We test our strategy by computing the Hadronic Vacuum Polarization on a lattice with a linear extension of 3 fm, a spacing of 0.065 fm, and a pion mass of 270 MeV. Indeed the two-level integration makes the contribution to the statistical error from long-distances de-facto negligible by accelerating its inverse scaling with the cost of the simulation. These findings establish multi-level Monte Carlo as a solid and efficient method for a precise lattice determination of the hadronic contribution toaμ. As the approach is applicable to other computations affected by a signal-to-noise ratio problem, it has the potential to unlock many open problems for the nuclear and particle physics community.