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

A lattice study of a chirally invariant Higgs-Yukawa model including a higher dimensional Φ6\Phi^6-term

We discuss the non-thermal phase structure of a chirally invariant Higgs-Yukawa model on the lattice in the presence of a higher dimensional $\Phi^6$-term. For the exploration of the phase diagram we use analytical, lattice perturbative calculations of the constraint effectice potential as well as numerical simulations. We also present first results of the effects of the $\Phi^6$-term on the lower Higgs boson mass bounds

Lattice study of infrared behaviour in SU(3) gauge theory with twelve massless flavours

We present details of a lattice study of infrared behaviour in SU(3) gauge theory with twelve massless fermions in the fundamental representation. Using the step-scaling method, we compute the coupling constant in this theory over a large range of scale. The renormalisation scheme in this work is defined by the ratio of Polyakov loops in the directions with different boundary conditions. We closely examine systematic effects, and find that they are dominated by errors arising from the continuum extrapolation. Our investigation suggests that SU(3) gauge theory with twelve flavours contains an infrared fixed point.Comment: 29 pages, 15 figures, 4 tables. Minor revision. Published versio

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

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

Matrix elements of the complete set of \Delta B = 2 and \Delta C = 2 operators in heavy meson chiral perturbation theory

Using heavy meson chiral perturbation theory, we consider the light quark-mass and spatial volume dependence of the matrix elements of \Delta B=2 and \Delta C=2 four-quark operators relevant for B^{0}_{(s)}{-}\bar{B}^{0}_{(s)} and D^{0}{-}\bar{D}^{0} mixing, and the B_{s} meson width difference. Our results for these matrix elements are obtained in the N_{f}=2+1 partially quenched theory, which becomes full QCD in the limit where sea and valence quark masses become equal. They can be used in extrapolation of lattice calculations of these matrix elements to the physical light quark masses and to infinite volume. An important conclusion of this paper is that the chiral extrapolations for matrix elements of heavy-light meson mixing beyond the Standard Model, and those relevant for the B_s width difference are more complicated than that for the Standard Model mixing matrix elements.Comment: 13 pages; version accepted for publicatio