We present the first observation of a flavor-singlet scalar meson as light as the pion in $N_f=8$ QCD on the lattice, using the Highly Improved Staggered Quark action. Such a light scalar meson can be regarded as a composite Higgs with mass 125 GeV. In accord with our previous lattice results showing that the theory exhibits walking behavior, the light scalar may be a technidilaton, a pseudo Nambu-Goldstone boson of the approximate scale symmetry in walking technicolor.
Based on lattice simulations using highly improved staggered quarks for twelve-flavor QCD with several bare fermion masses, we observe a flavor-singlet scalar state lighter than the pion in the correlators of fermionic interpolating operators. The same state is also investigated using correlators of gluonic interpolating operators. Combined with our previous study, that showed twelve-flavor QCD to be consistent with being in the conformal window, we infer that the lightness of the scalar state is due to infrared conformality. This result shed some light on the possibility of a light composite …
We present a new lattice study of the discrete beta function for SU(3) gauge theory with Nf=8 massless flavors of fermions in the fundamental representation. Using the gradient flow running coupling, and comparing two different nHYP-smeared staggered lattice actions, we calculate the 8-flavor step-scaling function at significantly stronger couplings than were previously accessible. Our continuum-extrapolated results for the discrete beta function show no sign of an IR fixed point up to couplings of g^2~14. At the same time, we find that the gradient flow coupling runs much more slowly than pre…
We present new lattice investigations of finite-temperature transitions for SU(3) gauge theory with Nf=8 light flavors. Using nHYP-smeared staggered fermions we are able to explore renormalized couplings $g^2 \lesssim 20$ on lattice volumes as large as $48^3 \times 24$. Finite-temperature transitions at non-zero fermion mass do not persist in the chiral limit, instead running into a strongly coupled lattice phase as the mass decreases. That is, finite-temperature studies with this lattice action require even larger $N_T > 24$ to directly confirm spontaneous chiral symmetry breaking.
We present our lattice studies of SU(3) gauge theory with $N_f$ = 8 degenerate fermions in the fundamental representation. Using nHYP-smeared staggered fermions we study finite-temperature transitions on lattice volumes as large as $L^3 \times N_t = 48^3 \times 24$, and the zero-temperature composite spectrum on lattice volumes up to $64^3 \times 128$. The spectrum indirectly indicates spontaneous chiral symmetry breaking, but finite-temperature transitions with fixed $N_t \leq 24$ enter a strongly coupled lattice phase as the fermion mass decreases, which prevents a direct confirmation of spo…
In reference [1] a unified description, both at the effective and fundamental Lagrangian level, of models of composite Higgs dynamics was proposed. In the unified framework the Higgs itself can emerge, depending on the way the electroweak symmetry is embedded, either as a pseudo-Goldstone boson or as a massive excitation of the condensate. The most minimal fundamental description consists of an SU(2) gauge theory with two Dirac fermions transforming according to the defining representation of the gauge group. We therefore provide first principle lattice results for the massive spectrum of this…
In search for a composite Higgs boson (techni-dilaton) in the walking technicolor, we present our preliminary results on the first observation of a light flavor-singlet scalar in a candidate theory for the walking technicolor, the Nf=8 QCD, which was found in our previous paper to have spontaneous chiral symmetry breaking together with remnants of the conformality. Based on simulations with the HISQ-type action on several lattice sizes with various fermion masses, we find evidence of a flavor-singlet scalar meson with mass comparable to that of the Nambu-Goldstone pion in both the small fermio…
We consider measurement of the leading irrelevant scaling exponent $γ_g^\ast$, given by the slope of the beta function, at the fixed point of SU(2) gauge theory with six or eight flavors. We use the running coupling measured using the gradient flow method and perform the continuum extrapolation by interpolating the measured beta function. We study also the dependence of the results on different discretization of the flow. For the eight flavor theory we find $γ_g^\ast=0.19(8)_{-0.09}^{+0.21}$. Applying the same analysis also for the six flavor theory, we find $γ_g^\ast=0.648(97)_{-0.1}^{+0.16}$…
We study an SU(3) gauge theory with Nf=8 degenerate flavors of light fermions in the fundamental representation. Using the domain wall fermion formulation, we investigate the light hadron spectrum, chiral condensate and electroweak S parameter. We consider a range of light fermion masses on two lattice volumes at a single gauge coupling chosen so that IR scales approximately match those from our previous studies of the two- and six-flavor systems. Our results for the Nf=8 spectrum suggest spontaneous chiral symmetry breaking, though fits to the fermion mass dependence of spectral quantities do…
We report on simulations of QCD with many flavors of degenerate quarks, the DBW2 gauge action and naive staggered fermions, using the rational hybrid Monte Carlo algorithm. We primarily focus on eight degenerate quark flavors where a variety of values of the coupling constant and quark mass have been used in the simulations. The scaling behavior of the hadron spectrum and the string tension of the heavy quark potential is studied, to probe whether the zero temperature, continuum limit of the theory breaks chiral symmetry.
We report the calculation of the flavor-singlet scalar in the SU(3) gauge theory with the degenerate twelve fermions in the fundamental representation using a HISQ-type action at a fixed $β$. In order to reduce the large statistical error coming from the vacuum-subtracted disconnected correlator, we employ a noise reduction method and a large number of configurations. We observe that the flavor-singlet scalar is lighter than the pion in this theory from the calculations with the fermion bilinear and gluonic operators. This peculiar feature is considered to be due to the infrared conformality o…
The many open questions concerning the existence of IR and UV fixed points in gauge theories as a function of the number of fermion flavors and bare coupling are briefly reviewed and discussed. It is pointed out that only a small subset of potential IR-conformal gauge theories, i.e. theories whose IR behavior is determined by an IR fixed point, has so far been examined. It is suggested that the naturally light scalar composites that seem to appear generically as lowest states in the non-QCD-like spectrum of such theories provide a natural basis for composite Higgs models, where the composite H…
I present first results from large-scale lattice investigations of SU(3) gauge theory with eight light flavors in the fundamental representation. Using leadership computing resources at Argonne, we are generating gauge configurations with lattice volumes up to $64^3\times128$ at relatively strong coupling, in an attempt to access the chiral regime. We use nHYP-improved staggered fermions, carefully monitoring finite-volume effects and other systematics. Here I focus on analyses of the light hadron spectrum and chiral condensate, measured on lattice volumes up to $48^3\times96$ with fermion mas…
We present our preliminary study of the SU(2) gauge theory with 8 flavors of fermions in fundamental representation. This theory could be a candidate of the gauge theory with conformal fixed point. By using Wilson/Polyakov loop in a finite volume with twisted boundary conditions, we study the renormalization group flow of the gauge coupling constant. Our calculation gives consistent result with the perturbative prediction of the running coupling in the weak coupling region. We investigate a possible signal for conformal behavior in the strong coupling region.
In the search for a composite Higgs boson in walking technicolor models, many flavor QCD, in particular with $N_f=8$, is an attractive candidate, and has been found to have a composite flavor-singlet scalar as light as the pion. Based on lattice simulations of this theory with the HISQ action, we will present our preliminary results on the scalar decay constant using the fermionic bilinear operator, and on the mass of the lightest baryon state which could be a dark matter candidate. Combining these two results, implications for dark matter direct detection are also discussed.
Beyond Standard Model theories describing the electro-weak sector must exhibit a large separation of scales (or "walking") to account for a light, 125 GeV Higgs boson and the fact that so far no other resonances have been observed. Large separation of scales arises naturally and in a tunable manner in mass-split models that are built on a conformal fixed point in the ultraviolet. Splitting the fermion masses into "light" (massless) and "heavy" flavors, the system shows conformal behavior in the ultraviolet but is chirally broken in the infrared. Due to the presence of a conformal fixed point, …
We report on an investigation into the low energy dynamics of walking gauge theory. Taking $SU(3)$ Yang Mills with eight flavors of fundamental fermions as an example, we discuss the light flavor singlet scalar appearing in the spectrum and its implications for low energy physics. We compute the maximal isospin $ππ$ scattering length at the lightest quark masses yet investigated for the eight flavor theory. The validity of chiral perturbation theory is assessed, and we discuss motivations for a more extensive effective field theory analysis to be carried out in future work.
We continue our study of spectroscopy data for the SU(3) gauge theory with eight fundamental fermions, motivated by the effective field theory framework of dilaton chiral perturbation theory (dChPT). At leading order dChPT predicts a constant mass anomalous dimension $γ_m$, consistent with the assumed proximity of an infrared fixed point. For the relatively large fermion masses simulated by the LatKMI collaboration, the influence of the infrared fixed point diminishes, and our fits suggest that $γ_m$ starts running. Since a complete higher-order analysis is not feasible with presently availabl…
We propose to construct a chirally broken model based on the infrared fixed point of a conformal system by raising the mass of some flavors while keeping the others massless. In the infrared limit the massive fermions decouple and the massless fermions break chiral symmetry. The running coupling of this system "walks" and the energy range of walking can be tuned by the mass of the heavy flavors. Renormalization group considerations predict that the spectrum of such a system shows hyperscaling. We have studied a model with four light and eight heavy flavors coupled to SU(3) gauge fields and ver…
The Lattice Strong Dynamics collaboration is investigating the properties of a SU(3) gauge theory with $N_f = 8$ light fermions on the lattice. We measure the masses of the lightest pseudoscalar, scalar and vector states using simulations with the nHYP staggered-fermion action on large volumes and at small fermion masses, reaching $M_ρ/M_π \approx 2.2$. The axial-vector meson and the nucleon are also studied for the same range of fermion masses. One of the interesting features of this theory is the dynamical presence of a light flavor-singlet scalar state with $0^{++}$ quantum numbers that is …
Mass-split composite Higgs models naturally accommodate the experimental observation of a light 125 GeV Higgs boson and predict a large scale separation to other heavier resonances. We explore the SU(3) gauge system with four light (massless) and six heavy (massive) flavors by performing numerical simulations. Since the underlying system with degenerate and massless ten flavors appears to be infrared conformal, this system inherits conformal hyperscaling and allows to study near-conformal dynamics. Carrying out nonperturbative lattice field theory simulations, we present the low-lying particle…
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 calculate the $m_\varrho / f_π$ ratio in the chiral and continuum limit for $SU(3)$ gauge theory coupled to $N_f = 2,3,4,5,6$ fermions in the fundamental representation. Keeping all systematic effects under full control we find no statistically significant $N_f$-dependence; $m_\varrho / f_π= 7.95(15)$. Assuming the KSRF-relations we conclude that 3 other low energy quantities related to the vector meson are also $N_f$-independent within errors including the $\varrhoππ$ coupling $g_{\varrhoππ}$. If the model is thought of as a strong dynamics inspired composite Higgs model our results indica…
We consider the most general fractional background fluxes in the color, flavor, and baryon number directions, compatible with the faithful action of the global symmetry of a given theory. We call the obstruction to gauging symmetries revealed by such backgrounds the baryon-color-flavor (BCF) 't Hooft anomaly. We apply the BCF anomaly to vector-like theories, with fermions in higher-dimensional representations of arbitrary N-ality, and derive non-trivial constraints on their IR dynamics. In particular, this class of theories enjoys an independent discrete chiral symmetry and one may ask about t…
The appearance of a light composite $0^+$ scalar resonance in nearly conformal gauge-fermion theories motivates further study of the low energy structure of these theories. To this end, we present a nonperturbative lattice calculation of s-wave scattering of Goldstone bosons in the maximal-isospin channel in SU(3) gauge theory with $N_f=8$ light, degenerate flavors. The scattering phase shift is measured both for different values of the underlying fermion mass and for different values of the scattering momentum. We examine the effect of a light flavor-singlet scalar (reported in earlier studie…
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 ($χ{\rm SB}$) with its Goldstone spectrum, $F_π$, the $χ{\rm SB}$ condensate, and several…
Studying SU(3) gauge theories with increasing number of light fermions is relevant both for understanding the strong dynamics of QCD and for constructing strongly interacting extensions of the Standard Model (e.g. UV completions of composite Higgs models). In order to contrast these many-flavors strongly interacting theories with QCD, we study the flavor-singlet spectrum as an interesting probe. In fact, some composite Higgs models require the Higgs boson to be the lightest flavor-singlet scalar in the spectrum of a strongly interacting new sector with a well defined hierarchy with the rest of…
The scale-dependent renormalized coupling of SU(3) gauge theory coupled to Nf = 2 flavors of massless Dirac flavors in the sextet representation is presented in the range 0 < g^2 < 6.5. This range includes the location where the beta-function turns zero in the MSbar scheme to 3-loop and 4-loop approximations, however our non-perturbative result shows a monotonically increasing beta-function. Our lattice calclulations are carried out at several lattice spacings allowing for a controlled continuum extrapolation. We also comment on a recent similar calculation by Hasenfratz tet al.
We construct renormalizable Standard Model extensions, valid up to the Planck scale, that give a composite Higgs from a new fundamental strong force acting on fermions and scalars. Yukawa interactions of these particles with Standard Model fermions realize the partial compositeness scenario. Under certain assumptions on the dynamics of the scalars, successful models exist because gauge quantum numbers of Standard Model fermions admit a minimal enough 'square root'. Furthermore, right-handed SM fermions have an SU(2)$_R$-like structure, yielding a custodially-protected composite Higgs. Baryon a…
We present the phase diagram and the fluctuations of different conserved charges like quark number, charge and strangeness at vanishing chemical potential for the 2+1 flavor Polyakov Loop extended Nambu--Jona-Lasinio model with eight-quark interaction terms using three-momentum cutoff regularisation. The main effect of the higher order interaction term is to shift the critical end point to the lower value of the chemical potential and higher value of the temperature. The fluctuations show good qualitative agreement with the lattice data.
The strongly coupled near-conformal gauge theory with two fermion flavors in the two-index symmetric (sextet) representation of SU(3) is potentially a minimal realization of the composite Higgs mechanism. We discuss the staggered fermion construction of baryonic states, present our first numerical results and comment on implications for dark matter.
We present the bulk thermodynamic properties and phase diagram of strongly interacting matter in an extension of the 3-flavor NJL and PNJL models of QCD. Using a three momentum cut-off scheme, we have extended the multiquark interaction terms up to eight order so that the stability of the vacuum is ensured in these models. We explore the effects of various combinations of the two eight-quark couplings $g_1$ and $g_2$ and present a comparative study between the NJL and PNJL models as well as Lattice QCD data. The main effect of the eight-quark interaction term is to shift the critical end point…
Here I summarize some of the salient features of technicolor theories with technifermions in higher dimensional representations of the technicolor gauge group. The expected phase diagram as function of number of flavors and colors for the two index (anti)symmetric representation of the gauge group is reviewed. After having constructed the simplest walking technicolor theory one can show that it is not at odds with the precision measurements. The simplest theory also requires, for consistency, a fourth family of heavy leptons. The latter may result in an interesting signature at LHC. In the cas…
We evaluate the pseudoscalar-meson octet-baryon coupling constants and the corresponding axial charges in eight channels ($πN\N$, $πΣΣ$, $πΛΣ$, $KΛN$, $K ΣN $, $πΞΞ$, $KΛΞ$ and $KΣΞ$) in lattice QCD with two flavors of dynamical quarks. The parameter $α\equiv F/(F+D)$ representing the SU(3)-flavor symmetry is computed at each u,d-quark hopping parameter and at the flavor-SU(3) symmetric point where the three quark flavors are degenerate at the physical $s$-quark mass. In particular, we obtain $α=0.395(6)$ at the SU(3) symmetric limit. The quark-mass dependences of the coupling constants are ob…
The 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 is investigated. In previous studies the chiral condensate and the mass spectrum were shown to be consistent with chiral symmetry breaking ($χ$SB) at vanishing fermion mass. The recently reported $β$-function is not inconsistent with this observation, suggesting that the model is very close to the conformal window and a light "Higgs impostor" could emerge as a composite state. In this work we describe the methodology and prel…
Mass-split systems based on a conformal infrared fixed point provide a low-energy effective description of beyond the standard model systems with large scale separation. We report results of exploratory investigations with four light and eight heavy flavors using staggered fermions, and up to five different values for the light flavor mass, five different heavy flavor masses, and two values of the bare gauge coupling.
Recently $SU(2)$ Yang-Mills theory with one massless adjoint Dirac quark flavor emerges as a novel critical theory that can describe the evolution between a trivial insulator and a topological insulator in AIII class in $3+1$ dimensions. There are several classes of conjectured infrared dynamics for this theory. One possibility is that the theory undergoes spontaneous chiral symmetry breaking, with two massless Goldstone bosons (the scalar diquark and its antiparticle) in the infrared. Another scenario, which is suggested by previous lattice studies by Athenodorou et al., is that the IR sector…
We revisit 2D $\mathcal{N}=(2,2)$ super Yang-Mills lattice formulation (Sugino model) to investigate its fermion action with two (Majorana) fermion flavors and exact chiral-$U(1)_{R}$ symmetry. We show that the reconcilement of chiral symmetry and absence of further species-doubling originates in the 4D clifford algebra structure of the action, where 2D two flavors are spuriously treated as a single 4D four-spinor with four 4D gamma matrices introduced into kinetic and Wilson terms. This fermion construction based on the higher-dimensional clifford algebra is extended to four dimensions in two…
The light Higgs boson of the Standard Model could arise as the consequence of the weakly broken conformal symmetry in a strongly interacting gauge theory. Here we present a novel idea to study the transition from conformal to confining behavior using an SU(3) gauge theory with four light and eight heavy flavors. This system interpolates between the 12-flavor conformal and the 4 flavor chirally broken theory as the mass of the heavy flavors are varied. We show first results on our determination of the iso-singlet 0++ state.
We present our progresses in the use of the non-perturbative renormalization framework based on considering QCD at finite temperature with shifted and twisted (for quarks only) boundary conditions in the compact direction. We report our final results in the application of this method for the non-perturbative renormalization of the flavor-singlet local vector current. We then discuss the more challenging case of the renormalization of the energy-momentum tensor, and show preliminary results on the relevant one-point functions for the computation of the renormalization constants of its non-singl…
The SU(4) gauge theory with two flavors of Dirac fermions in the sextet representation shares features of a candidate for a composite Higgs model. The analogue of the Higgs multiplet of the Standard Model lives in the Goldstone manifold resulting from spontaneous breaking of the global symmetry SU(4) to SO(4). The Higgs potential arises from interaction with the particles of the Standard Model. We have computed the gauge boson contribution to the Higgs potential, using valence overlap fermions on a Wilson-clover sea. The calculation is similar to that of the electromagnetic mass splitting of t…
