Daniel Nogradi

The Yang-Mills gradient flow in finite volume

A bstractThe Yang-Mills gradient flow is considered on the four dimensional torus T4 for SU(N) gauge theory coupled to Nf flavors of massless fermions in arbitrary representations. The small volume dynamics is dominated by the constant gauge fields. The expectation value of the field strength tensor squared TrFμνFμν (t) is calculated for positive flow time t by treating the non-zero gauge modes perturbatively and the zero modes exactly. The finite volume correction to the infinite volume result is found to contain both algebraic and exponential terms. The leading order result is then used to define a one parameter family of running coupling schemes in which the coupling runs with the linear size of the box. The new scheme is tested numerically in SU(3) gauge theory coupled to Nf = 4 flavors of massless fundamental fermions. The calculations are performed at several lattice spacings with a controlled continuum extrapolation. The continuum result agrees with the perturbative prediction for small renormalized coupling as expected.

Twelve massless flavors and three colors below the conformal window

We report new results for a frequently discussed gauge theory with twelve fermion flavors in the fundamental representation of the SU(3) color gauge group. The model, controversial with respect to its conformality, is important in non-perturbative studies searching for a viable composite Higgs mechanism Beyond the Standard Model (BSM). To resolve the controversy, we subject the model to opposite hypotheses inside and outside of the conformal window. In the first hypothesis we test chiral symmetry breaking ( SB) with its Goldstone spectrum, F , the SB condensate, and several composite hadron states as the fermion mass is varied in a limited range with our best e ort to control finite volume e ects and extrapolation to the massless chiral limit. Supporting results for SB from the running coupling based on the force between static sources and some preliminary evidence for the finite temperature transition are also presented. In the second test for the alternate hypothesis we probe conformal behavior driven by a single anomalous mass dimension under the assumption of unbroken chiral symmetry. Our results show a very low level of confidence in the conformal scenario. Staggered lattice fermions with stout-suppressed taste breaking are used throughout the simulations.

Can the nearly conformal sextet gauge model hide the Higgs impostor

Abstract New results are reported from large scale lattice simulations of a frequently discussed strongly interacting gauge theory with a fermion flavor doublet in the two-index symmetric (sextet) representation of the SU(3) color gauge group. We find that the chiral condensate and the mass spectrum of the sextet model are consistent with chiral symmetry breaking in the limit of vanishing fermion mass. In contrast, sextet fermion mass deformations of spectral properties are not consistent with leading conformal scaling behavior near the critical surface of a conformal theory. A recent paper could not resolve the conformal fixed point of the gauge coupling from the slowly walking scenario of a very small nearly vanishing β -function (DeGrand et al. [3] ). It is argued that overall consistency with our new results is resolved if the sextet model is close to the conformal window, staying outside with a very small non-vanishing β -function. The model would exhibit then the simplest composite Higgs mechanism leaving open the possibility of a light scalar state with quantum numbers of the Higgs impostor. It would emerge as the pseudo-Goldstone dilaton state from spontaneous symmetry breaking of scale invariance. We will argue that even without association with the dilaton, the scalar Higgs-like state can be light very close to the conformal window. A new Higgs project of sextet lattice simulations is outlined to resolve these important questions.

QCD thermodynamics with continuum extrapolated Wilson fermions I

A bstractQCD thermodynamics is considered using Wilson fermions in the fixed scale approach. The temperature dependence of the renormalized chiral condensate, quark number susceptibility and Polyakov loop is measured at four lattice spacings allowing for a controlled continuum limit. The light quark masses are fixed to heavier than physical values in this first study. Finite volume effects are ensured to be negligible by using approriately large box sizes. The final continuum results are compared with staggered fermion simulations performed in the fixed Nt approach. The same continuum renormalization conditions are used in both approaches and the final results agree perfectly.

The lattice gradient flow at tree-level and its improvement

A bstractThe Yang-Mills gradient flow and the observable 〈E(t)〉, defined by the square of the field strength tensor at t > 0, are calculated at finite lattice spacing and tree-level in the gauge coupling. Improvement of the flow, the gauge action and the observable are all considered. The results are relevant for two purposes. First, the discretization of the flow, gauge action and observable can be chosen in such a way that O(a2), O(a4) or even O(a6) improvement is achieved. Second, simulation results using arbitrary discretizations can be tree-level improved by the perturbatively calculated correction factor normalized to one in the continuum limit.

Charmonium spectral functions from 2+1 flavour lattice QCD

A bstractFinite temperature charmonium spectral functions in the pseudoscalar and vector channels are studied in lattice QCD with 2+1 flavours of dynamical Wilson quarks, on fine isotropic lattices (with a lattice spacing of 0.057fm), with a non-physical pion mass of mπ ≈ 545 MeV. The highest temperature studied is approximately 1.4Tc. Up to this temperature no significant variation of the spectral function is seen in the pseudoscalar channel. The vector channel shows some temperature dependence, which seems to be consistent with a temperature dependent low frequency peak related to heavy quark transport, plus a temperature independent term at ω > 0. These results are in accord with previous calculations using the quenched approximation.

QCD thermodynamics with dynamical overlap fermions

Abstract We study QCD thermodynamics using two flavors of dynamical overlap fermions with quark masses corresponding to a pion mass of 350 MeV. We determine several observables on N t = 6 and 8 lattices. All our runs are performed with fixed global topology. Our results are compared with staggered ones and a nice agreement is found.

The running coupling of 8 flavors and 3 colors

A bstractWe compute the renormalized running coupling of SU(3) gauge theory coupled to Nf = 8 flavors of massless fundamental Dirac fermions. The recently proposed finite volume gradient flow scheme is used. The calculations are performed at several lattice spacings allowing for a controlled continuum extrapolation. The results for the discrete β-function show that it is monotonic without any sign of a fixed point in the range of couplings we cover. As a cross check the continuum results are compared with the well-known perturbative continuum β-function for small values of the renormalized coupling and perfect agreement is found.

Fate of the conformal fixed point with twelve massless fermions and SU(3) gauge group

We report new results on the conformal properties of an important strongly coupled gauge theory, a building block of composite Higgs models beyond the Standard Model. With twelve massless fermions in the fundamental representation of the SU(3) color gauge group, an infrared fixed point (IRFP) of the

An ideal toy model for confining, walking and conformal gauge theories: the O (3) sigma model with ϑ -term

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