High Energy Physics Lattice

We discuss the lattice formulation of the 't Hooft surface, that is, the two-dimensional surface operator of a dual variable. The 't Hooft surface describes the world sheets of topological vortices. We derive the formulas to calculate the expectation value of the 't Hooft surface in the multiple-charge lattice Abelian Higgs model and in the lattice non-Abelian Higgs model. As the first demonstration of the formula, we compute the intervortex potential in the charge-2 lattice Abelian Higgs model.

We study the promising idea of using dipolar molecular systems as analog quantum simulators for quantum link models, which are discrete versions of lattice gauge theories. In a quantum link model the link variables have a finite number of degrees of freedom and discrete values. We construct the effective Hamiltonian of a system of dipolar molecules with electric dipole-dipole interactions, where we use the tunable parameters of the system to match it to the target Hamiltonian describing a U(1) quantum link model in 1+1 dimensions.

Quantum chromodynamics (QCD) claims that the major source of the nucleon invariant mass is not the Higgs mechanism but the trace anomaly in QCD energy momentum tensor. Although experimental and theoretical results support such conclusion, a direct demonstration is still absent. We present the first Lattice QCD calculation of the quark and gluon trace anomaly contributions to the hadron masses, using the overlap fermion on the 2+1 flavor dynamical Domain wall quark ensemble atm?=340MeV and lattice spacinga=0.1105 fm. The result shows that the gluon trace anomaly contributes to most of the nucleon mass, and the contribution in the pion state is smaller than that in others nearly by a factor??10 since the gluon trace anomaly density inside pion is different from the other hadrons and the magnitude is much smaller. The gluon trace anomaly coefficientβ/g3=??.056(6)we obtained is consistent with its regularization independent leading order value(??1+2Nf3)/(4?)2perfectly.

In this exploratory study, two photon decay widths of pseudo-scalar (ηc) and scalar (χc0) charmonium are computed using two ensembles ofNf=2twisted mass lattice QCD gauge configurations. The simulation is performed two lattice ensembles with lattice spacingsa=0.067fm with size323×64anda=0.085fm with size243×48, respectively. The results for the decay widths for the two charmonia are obtained which are in the right ballpark however smaller than the experimental ones. Possible reasons for these discrepancies are discussed.

We explore the feasibility of determining Mellin moments of the pion's light cone distribution amplitude using the heavy quark operator product expansion (HOPE) method. As the first step of a proof of principle study we pursue a determination of the second Mellin moment. We discuss our choice of kinematics which allows us to successfully extract the moment at low pion momentum. We describe the numerical simulation, and describe the data analysis, which leads us to a preliminary determination of the second Mellin moment in the continuum limit in the quenched approximation as⟨ξ2⟩=0.19(7)in theMS¯scheme at 2 GeV.

In a non-perturbative gauge-invariant formulation of grand-unified theories all low energy vector states need to be composite with respect to the high-scale gauge group, including the photon. We investigate this by using lattice methods to spectroscopically analyze the vector channel in a toy grand-unified theory, an SU(2) adjoint Higgs model. Our results support indeed the existence of a massless composite vector particle.

We apply the Linear Logarithmic Relaxation (LLR) method, which generalizes the Wang-Landau algorithm to quantum systems with continuous degrees of freedom, to the fermionic Hubbard model with repulsive interactions on the honeycomb lattice. We compute the generalized density of states of the average Hubbard field and divise two reconstruction schemes to extract physical observables from this result. By computing the particle density as a function of chemical potential we assess the utility of LLR in dealing with the sign problem of this model, which arises away from half filling. We show that the relative advantage over brute-force reweighting grows as the interaction strength is increased and discuss possible future improvements.

Above the pseudocritical temperature T_c of chiral symmetry restoration a chiral spin symmetry (a symmetry of the color charge and of electric confinement) emerges in QCD. This implies that QCD is in a confining mode and there are no free quarks. At the same time correlators of operators constrained by a conserved current behave as if quarks were free. This explains observed fluctuations of conserved charges and the absence of the rho-like structures seen via dileptons. An independent evidence that one is in a confining mode is very welcome. Here we suggest a new tool how to distinguish free quarks from a confining mode. If we put the system into a finite box, then if the quarks are free one necessarily obtains a remarkable diffractive pattern in the propagator of a conserved current. This pattern is clearly seen in a lattice calculation in a finite box and it vanishes in the infinite volume limit as well as in the continuum. In contrast, the full QCD calculations in a finite box show the absence of the diffractive pattern implying that the quarks are confined.

In this paper we improve the existing order parameter for monopole condensation in gauge theory vacuum, making it gauge-invariant from scratch and free of the spurious infrared problems which plagued the old one. Computing the new parameter on the lattice will unambiguously detect weather dual superconductivity is the mechanism for color confinement.As a byproduct we relate confinement to the existence of a finite correlation length in the gauge-invariant correlator of chromo-electric field strengths.

Atiyah-Singer index theorem on a lattice without boundary is well understood owing to the seminal work by Hasenfratz et al. But its extension to the system with boundary (the so-called Atiyah- Patodi-Singer index theorem), which plays a crucial role in T-anomaly cancellation between bulk- and edge-modes in 3+1 dimensional topological matters, is known only in the continuum theory and no lattice realization has been made so far. In this work, we try to non-perturbatively define an alternative index from the lattice domain-wall fermion in 3+1 dimensions. We will show that this new index in the continuum limit, converges to the Atiyah-Patodi-Singer index defined on a manifold with boundary, which coincides with the surface of the domain-wall.