Higgs-Yukawa model on the lattice

We present results from two projects on lattice calculations for the Higgs-Yukawa model. First we report progress on the search of first-order thermal phase transitions in the presence of a dimension-six operator, with the choices of bare couplings that lead to viable phenomenological predictions. In this project the simulations are performed using overlap fermions to implement the required chiral symmetry. Secondly, our study for applying finite-size scaling techniques near the Gaussian fixed point of the Higgs-Yukawa model is presented. We discuss the analytical formulae for the Higgs Yukawa model and show results for a first numerical study in the pure $O(4)$ scalar sector of the theory.Comment: 8 pages, 4 figures; Contribution to the proceedings of the 35th International Symposium on Lattice Field Theory, 18 - 24 June 2017, Granada, Spai

The Yang-Mills gradient flow and SU(3) gauge theory with 12 massless fundamental fermions in a colour-twisted box

We perform the step-scaling investigation of the running coupling constant, using the gradient-flow scheme, in SU(3) gauge theory with twelve massless fermions in the fundamental representation. The Wilson plaquette gauge action and massless unimproved staggered fermions are used in the simulations. Our lattice data are prepared at high accuracy, such that the statistical error for the renormalised coupling, g_GF, is at the subpercentage level. To investigate the reliability of the continuum extrapolation, we employ two different lattice discretisations to obtain g_GF. For our simulation setting, the corresponding gauge-field averaging radius in the gradient flow has to be almost half of the lattice size, in order to have this extrapolation under control. We can determine the renormalisation group evolution of the coupling up to g^2_GF ~ 6, before the onset of the bulk phase structure. In this infrared regime, the running of the coupling is significantly slower than the two-loop perturbative prediction, although we cannot draw definite conclusion regarding possible infrared conformality of this theory. Furthermore, we comment on the issue regarding the continuum extrapolation near an infrared fixed point. In addition to adopting the fit ansatz a'la Symanzik for performing this task, we discuss a possible alternative procedure inspired by properties derived from low-energy scale invariance at strong coupling. Based on this procedure, we propose a finite-size scaling method for the renormalised coupling as a means to search for infrared fixed point. Using this method, it can be shown that the behaviour of the theory around g^2_GF ~ 6 is still not governed by possible infrared conformality.Comment: 24 pages, 6 figures; Published version; Appendix A added for tabulating data; One reference included; Typos correcte

Stabilizing the electroweak vacuum by higher dimensional operators in a Higgs-Yukawa model

The Higgs boson discovery at the LHC with a mass of approximately 126 GeV suggests, that the electroweak vacuum of the standard model may be metastable at very high energies. However, any new physics beyond the standard model can change this picture. We want to address this important question within a lattice Higgs-Yukawa model as the limit of the standard model (SM). In this framework we will probe the effect of a higher dimensional operator for which we take a $(\phi^{\dagger}\phi)^3$-term. Such a term could easily originate as a remnant of physics beyond the SM at very large scales. As a first step we investigate the phase diagram of the model including such a $(\phi^{\dagger}\phi)^3$ operator. Exploratory results suggest the existence of regions in parameter space where first order transitions turn to second order ones, indicating the existence of a tri-critical line. We will explore the phase structure and the consequences for the stability of the SM, both analytically by investigating the constraint effective potential in lattice perturbation theory, and by studying the system non-perturbatively using lattice simulations.Comment: 7 pages, 6 figures; Proceedings of the 31st International Symposium on Lattice Field Theory - LATTICE 201

Heavy meson chiral perturbation theory in finite volume

We present the first step towards the estimation of finite volume effects in heavy-light meson systems using heavy meson chiral perturbation theory. We demonstrate that these effects can be amplified in both light-quark and heavy-quark mass extrapolations (interpolations) in lattice calculations. As an explicit example, we perform a one-loop calculation for the neutral B meson mixing system and show that finite volume effects, which can be comparable with currently quoted errors, are not negligible in both quenched and partially quenched QCD.Comment: Talk presented at Lattice2004(heavy), Fermilab, June 21st-26th, 2004. Three pages, two figure

Deep-inelastic scattering and the operator product expansion in lattice QCD

We discuss the determination of deep-inelastic hadron structure in lattice QCD. By using a fictitious heavy quark, direct calculations of the Compton scattering tensor can be performed in Euclidean space that allow the extraction of the moments of structure functions. This overcomes issues of operator mixing and renormalisation that have so far prohibited lattice computations of higher moments. This approach is especially suitable for the study of the twist-two contributions to isovector quark distributions, which is practical with current computing resources. While we focus on the isovector unpolarised distribution, our method is equally applicable to other quark distributions and to generalised parton distributions. By looking at matrix elements such as $$ (where $V^\mu$ and $A^\nu$ are vector and axial-vector heavy-light currents) within the same formalism, moments of meson distribution amplitudes can also be extracted.Comment: 10 pages, 5 figures, version accepted for publicatio

Λb→pl−νˉ\Lambda_b \to p l^- \bar{\nu} form factors from lattice QCD with static b quarks

We present a lattice QCD calculation of form factors for the decay $\Lambda_b \to p \mu^- \bar{\nu}$, which is a promising channel for determining the CKM matrix element $|V_{ub}|$ at the Large Hadron Collider. In this initial study we work in the limit of static b quarks, where the number of independent form factors reduces to two. We use dynamical domain-wall fermions for the light quarks, and perform the calculation at two different lattice spacings and at multiple values of the light-quark masses in a single large volume. Using our form factor results, we calculate the $\Lambda_b \to p \mu^- \bar{\nu}$ differential decay rate in the range $14 GeV^2 \leq q^2 \leq q^2_{max}$, and obtain the integral $\int_{14 GeV^2}^{q^2_{max}} [d\Gamma/dq^2] dq^2 / |V_{ub}|^2 = 15.3 \pm 4.2 ps^{-1}$. Combined with future experimental data, this will give a novel determination of $|V_{ub}|$ with about 15\% theoretical uncertainty. The uncertainty is dominated by the use of the static approximation for the b quark, and can be reduced further by performing the lattice calculation with a more sophisticated heavy-quark action.Comment: 14 pages, 5 figure

Investigation of the 1+1 dimensional Thirring model using the method of matrix product states

We present preliminary results of a study on the non-thermal phase structure of the (1+1) dimensional massive Thirring model, employing the method of matrix product states. Through investigating the entanglement entropy, the fermion correlators and the chiral condensate, it is found that this approach enables us to observe numerical evidence of a Kosterlitz-Thouless phase transition in the model.Comment: 7 pages, 4 figures; contribution to the proceedings of Lattice 2018 conferenc