Zoltan Fodor, Kieran Holland, Julius Kuti, Daniel Nogradi, Chris Schroeder
备注：
28 pages, based on contributions from K. Holland, J. Kuti, D. Nogradi, and C. Schroeder at The XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, Germany
We report the first results from our comprehensive lattice tool set to explore non-perturbative aspects of Higgs physics in the Standard Model. We demonstrate in Higgs-Yukawa models that Higgs mass lower bounds and upper bounds can be determined in lattice simulations when triviality requires the necessity of a finite cutoff to maintain non-zero interactions. The vacuum instability problem is investigated and the lattice approach is compared with the traditional renormalization group procedure which sets similar goals to correlate lower and upper Higgs mass bounds with the scale of new physics. A novel feature of our lattice simulations is the use of Ginsparg-Wilson fermions to represent the effects of Top quark loops in Higgs dynamics. The need for chiral lattice fermions is discussed and the approach is extended to full Top-Higgs-QCD dynamics. We also report results from our large $N_F$ analysis of Top-Higgs Yukawa models to gain analytic insight and to verify our new lattice tool set which is deployed in the simulations. The role of non-perturbative lattice studies to investigate heavy Higgs particle scenarios is illustrated in extensions of the Standard Model.
Working in a two-representation lattice gauge theory that is close to a composite Higgs model, we calculate the low-energy constant CLR which controls the contribution of the electroweak gauge bosons to the Higgs potential. In QCD, the corresponding low-energy constant governs the mass splitting of the pion multiplet. Taking the continuum and chiral limits, we find that CLR, in units of the pseudoscalar decay constant, is roughly of the same size as its QCD counterpart.
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…
We present the first calculation of the scattering amplitude in the singlet channel beyond QCD. The calculation is performed in $SU(2)$ gauge theory with $N_f=2$ fundamental Dirac fermions and based on a finite-volume scattering formalism. The theory exhibits a $SU(4) \to Sp(4)$ chiral symmetry breaking pattern that is used to design minimal composite Higgs models currently tested at the LHC. Our results show that, for the range of underlying fermion mass considered, the lowest flavour singlet state is stable.
As a first step towards a quantitative understanding of the SU(4)/Sp(4) composite Higgs model through lattice calculations, we discuss the low energy effective field theory resulting from the SU(4) $\to$ Sp(4) global symmetry breaking pattern. We then consider an Sp(4) gauge theory with two Dirac fermion flavours in the fundamental representation on a lattice, which provides a concrete example of the microscopic realisation of the SU(4)/Sp(4) composite Higgs model. For this system, we outline a programme of numerical simulations aiming at the determination of the low-energy constants of the ef…
We investigate the spectrum of the SU(2) gauge theory with $N_f$ = 2 flavors of fermions in the fundamental representation, in the continuum, using lattice simulations. This model provides a minimal template which has been used for different strongly coupled extensions of the Standard Model ranging from composite (Goldstone) Higgs models to intriguing types of dark matter candidates, such as the SIMPs. Here we will focus on the composite Goldstone Higgs paradigm, for which this model provides a minimal UV complete realization in terms of a new strong sector with fermionic matter. After introdu…
We study the resonant decay of the primordial Standard Model Higgs condensate after inflation into $SU(2)$ gauge bosons on the lattice. We find that the non-Abelian interactions between the gauge bosons quickly extend the momentum distribution towards high values, efficiently destroying the condensate after the onset of backreaction. For the inflationary scale $H = 10^8$ GeV, we find that 90% of the Higgs condensate has decayed after $n \sim 10$ oscillation cycles. This differs significantly from the Abelian case where, given the same coupling strengths, most of the condensate would persist af…
The Sp(4) gauge theory with two Dirac fundamental flavours provides a candidate for the microscopic origin of composite-Higgs models based on the SU(4)/Sp(4) coset. We employ a combination of two different, complementary strategies for the numerical lattice calculations, based on the Hybrid Monte Carlo and on the Heat Bath algorithms. We perform pure Yang-Mills, quenched computations and exploratory studies with dynamical Wilson fermions. We present the first results in the literature for the spectrum of glueballs of the pure Sp(4) Yang-Mills theory, an EFT framework for the interpretation of …
We investigate a recently proposed UV-complete composite Higgs scenario in the light of the first LHC runs. The model is based on a $SU(4)$ gauge group with global flavour symmetry breaking $SU(5) \to SO(5)$, giving rise to pseudo Nambu-Goldstone bosons in addition to the Higgs doublet. This includes a real and a complex electroweak triplet with exotic electric charges. Including these, as well as constraints on other exotic states, we show that LHC measurements are not yet sensitive enough to significantly constrain the model's low energy constants. The Higgs potential is described by two par…
Several UV complete models of physics beyond the Standard Model are currently under scrutiny, their low-energy dynamics being compared with the experimental data from the LHC. Lattice simulations can play a role in these studies by providing a first principles computations of the low-energy constants that describe this low-energy dynamics. In this work, we study in detail a specific model recently proposed by Ferretti, and discuss the potential impact of lattice calculations.
