Origin of Mass and Strong Coupling Gauge Theories (SCGT15)

The following sections are included:

• Preface
• Workshop Organization
• Contents

We analyze three sets of gauge ensembles in our extended physics program of a particularly important BSM gauge theory with a fermion doublet in the two-index symmetric (sextet) representation of the SU(3) BSM color gauge group. Our investigations include chiral symmetry breaking (xSB) in the p-regime and ∊-regime, the mass of the composite 0⁺⁺ scalar, resonance spectroscopy, new physics from gauge anomaly constraints, and the role of stable sextet BSM baryons with Electroweak interactions in dark matter searches. Important new goals include studies of the 0⁺⁺ scalar entangled with Goldstone dynamics in the p-regime and the ∊-regime, the resonance spectrum with particular attention to emerging LHC signals, like recent hints for diphoton excess at 750 GeV or diboson anomalies in the 2 TeV range. All results reported here are preliminary before journal publication including some post-conference material for the discussion.

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 ≈ 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 lighter than the vector resonance and has a mass consistent with the one of the pseudoscalar state for the whole fermion mass range explored. We comment on the existence of such state emerging from our lattice simulations and on the challenges of its analysis. Moreover we highlight the difficulties in pursuing simulations in the chiral regime of this theory using large volumes.

The dynamical origin of electroweak symmetry breaking is an open question with many possible theoretical explanations. Strongly coupled systems predicting the Higgs boson as a bound state of a new gauge-fermion interaction form one class of candidate models. Due to increased statistics, LHC run II will further constrain the phenomenologically viable models in the near future. In the meanwhile it is important to understand the general properties and specific features of the different competing models.

In this work we discuss many-flavor gauge-fermion systems that contain both massless (light) and massive fermions. The former provide Goldstone bosons and trigger electroweak symmetry breaking, while the latter indirectly influence the infrared dynamics. Numerical results reveal that such systems can exhibit a light 0⁺⁺ isosinglet scalar, well separated from the rest of the spectrum. Further, when we set the scale via the vev of electroweak symmetry breaking, we predict a 2 TeV vector resonance which could be a generic feature of SU(3) gauge theories.

The LHC Higgs can be identified as the technidilaton, a composite scalar, arising as a pseudo Nambu-Goldstone boson for the spontaneous breaking of scale symmetry in walking technicolor. One interesting candidate for the walking technicolor is the QCD with the large number of fermion flavors, involving the one-family model having the eight-fermion flavors. The smallness of the technidilaton mass can be ensured by the generic walking feature, Miransky scaling, and the presence of the “anti-Veneziano limit” characteristic to the large-flavor walking scenario. To tell the standard-model Higgs from the technidilaton, one needs to wait for the precise estimate of the Higgs couplings to the standard model particles, which is expected at the ongoing LHC-Run II. In this talk the technidilaton phenomenology in comparison with the LHC Run-I data is summarized with the special emphasis placed on the presence of the anti-Veneziano limit supporting the lightness of technidilaton. Besides the technidilaton, the walking technicolor predicts the rich particle spectrum such as technipions and technirho mesons, arising as composite particles formed by technifermions. The LHC phenomenology of those technihadrons and the discovery channels are also discussed, which are smoking-guns of the walking technicolor, to be accessible at the LHC-Run II.

LatKMI Collaboration discusses the topological insights in many-flavor QCD on the lattice. We explore walking/conformal/confining phase in N_f = 4, 8 and 12 (in particular N_f = 8) lattice QCD via the topological charge and susceptibility, eigenvalues and anomalous dimension.

We present some results for SU(2) with one adjoint Dirac flavour from the lattice studies. Data for the spectroscopy, the static potential, topological charge, and the anomalous dimension of the fermionic condensate are included. Our findings are found to be inconsistent with conventional confining behaviour, instead pointing tentatively towards a theory lying within or very near the onset of the conformal window, with an anomalous dimension of the fermionic condensate of almost 1. Implications of these findings on the building of models of strongly-interacting dynamics beyond the standard model are discussed.

We discuss recent results on renormalization-group evolution of several types of theories. First, we consider asymptotically free vectorial gauge theories with various fermion contents and discuss higher-loop calculations of the UV to IR evolution in these theories, including an IR zero of the beta function and the value of the anomalous dimension γ_m at this point, together with comparisons with lattice measurements. Effects of scheme transformations are discussed. We then present a novel way to determine the value of N_TC in an SU(N_TC) technicolor model from a particular embedding in an extended technicolor theory. Finally, we analyze the renormalization-group behavior of several non-asymptotically free theories, including a U(1) gauge theory, a non-Abelian gauge theory with many fermions, an O(N) $\lambda {\left|\overline{\varphi }\right|}^4$ scalar theory, and Yukawa theories.

A fully dynamical origin for the masses of weak gauge bosons and heavy quarks of the Standard Model is considered. Electroweak symmetry breaking and the gauge boson masses arise from new strong dynamics, which leads to the appearance of a composite scalar in the spectrum of excitations. In order to generate mass for the Standard Model fermions, we consider extended gauge dynamics, effectively represented by four fermion interactions at presently accessible energies. By systematically treating these interactions, we show that they lead to a large reduction of the mass of the scalar resonance. Therefore, interpreting the scalar as the recently observed 125 GeV state, implies that the mass originating solely from new strong dynamics can be much heavier, of the order of 1 TeV. The couplings of the scalar resonance with the Standard Model gauge bosons and fermions are evaluated, and found to be compatible with the current LHC results.

We discuss the Top-Mode Pseudo-Nambu-Goldstone boson Higgs (TMpNGBH) model which has recently been proposed as a variant of the top quark condensate model in light of the 125 GeV Higgs boson discovered at the LHC. In this talk, we focus on the vacuum alignment and the phenomenologies of characteristic particles of the TMpNGBH model.

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.

In the functional renormalization group (FRG), the introduction of a momentum cutoff often breaks symmetry present in a theory. The most important example is the gauge symmetry. However a symmetry survives in the presence of a cutoff in a modified form. We apply our understanding to QED as the simplest case. A modified version of the Ward-Takahashi identity is solved partially to constrain the Wilson action. Furthermore, we study the flow equation for the photon 2-point function and find its analytical expression for the regulator function of the exponential type.

I discuss how to access dense baryonic matter of compact stars by combining hidden local symmetry (HLS) of light-quark vector mesons with spontaneously broken scale invariance of a (pseudo) Nambu-Goldstone boson, dilaton, in a description that parallels the approach to dilatonic Higgs. Some of the surprising observations are that the bulk of proton mass is not Nambu-Goldstonian, parity doubling emerges at high density and the EoS of baryonic matter can be soft enough for heavy-ion processes at low density and stiff enough at high density for ∼ 2 solar mass neutron stars.

We present the calculations of isospin splitting mass of pions and nucleons in the Sakai- Sugimoto model of holographic QCD. We find that m_π± − m_π0 ≃ 1.8 MeV and the electromagnetic mass difference of nucleons, (M_p − M_n)_QED = 0.48 MeV, taking the Kaluza-Klein scale, M_KK = 949 MeV.

The following sections are included:

• Introduction
• Sigma meson as two-quark state
• Sigma meson as four-quark state
• Summary
• References

First, we give a gauge-independent definition of chromomagnetic monopoles in SU(N) Yang-Mills theory which is derived through a non-Abelian Stokes theorem for the Wilson loop operator. Then we discuss how such magnetic monopoles can give a nontrivial contribution to the Wilson loop operator for understanding the area law of the Wilson loop average. Next, we discuss how the magnetic monopole condensation picture are compatible with the vortex condensation picture as another promising scenario for quark confinement. We analyze the profile function of the magnetic flux tube as the non-Abelian vortex solution of U(N) gauge-Higgs model, which is to be compared with numerical simulations of the SU(N) Yang-Mills theory on a lattice. This analysis gives an estimate of the string tension based on the vortex condensation picture, and possible interactions between two non-Abelian vortices.

In the preceeding works, we have given a non-Abelian dual superconductivity picture for quark confinement, and demonstrated the numerical evidences on the lattice. In this talk, we discuss the confinement and deconfinement phase transition at finite temperature in view of the dual superconductivity. We investigate chromomagnetic monopole currents induced by chromoelectric flux in both confinement and deconfinement phase by the numerical simulations on a lattice at finite temperature, and discuss the role of the chromomagnetic monopole in the confinement/deconfinement phase transition.

We discuss holographic QCD in the Veneziano limit (the V-QCD models), concentrating on phenomena near the “conformal” phase transition taking place at a critical value of the ratio x ≡ N_f/N_c. In particular, we review the results for the S-parameter, the technidilaton, and the masses of the mesons.

The duality conjecture states that p + 1-dimensional maximally supersymmetric Yang- Mills theory at finite temperature is expected to be dual to the non extremal black p-brane at large N. We perform the lattice simulations of SYM for p = 0, 1 to investigate the validity of the conjecture. We show that the conjecture is qualitatively valid by comparing lattice results of the black p-branes mass with analytic expectations in the gravity side.

We summarize recent progress in lattice studies of four-dimensional N = 4 supersymmetric Yang–Mills theory and present preliminary results from ongoing investigations. Our work is based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing, and we review a new procedure to regulate flat directions by modifying the moduli equations in a manner compatible with this supersymmetry. This procedure defines an improved lattice action that we have begun to use in numerical calculations. We discuss some highlights of these investigations, including the static potential and an update on the question of a possible sign problem in the lattcie theory.

We discuss a new mechanism of D-term dynamical supersymmetry breaking in the context of Dirac gaugino scenario. The existence of a nontrivial solution of the gap equation for D-term is shown. It is also shown that an observed 126 GeV Higgs mass is realized by tree level D-term effects in a broad range of parameters.

We explore the generation of large-scale magnetic fields in the so-called moduli inflation. The hypercharge electromagnetic fields couple to not only a scalar field but also a pseudoscalar one, so that the conformal invariance of the hypercharge electromagnetic fields can be broken. We explicitly analyze the strength of the magnetic fields on the Hubble horizon scale at the present time, the local non-Gaussianity of the curvature perturbations originating from the massive gauge fields, and the tensor-to-scalar ratio of the density perturbations. As a consequence, we find that the local non-Gaussianity and the tensor-to-scalar ratio are compatible with the recent Planck results.

A new heavy di-jet resonance could be discovered at the 14 TeV LHC. In this talk we present a strategy to reveal the nature of such a particle; in particular to discern whether it is a quark-antiquark (q$\overline{q}$), quark-gluon (qg), or gluon-gluon (gg) resonance. The strategy is based on the study of the energy profiles of the two leading jets in the dijet channel. Including statistical uncertainties in the signal and the QCD backgrounds, we show that one can distinguish between gg, qg, and q$\overline{q}$ resonances; an evaluation of systematic uncertainties in the measurement of the jet energy profile will require a detailed detector study once sufficient 14 TeV di-jet data is in hand.

Color-singlet and color-octet vector bosons predicted in theories beyond the Standard Model have the potential to be discovered as dijet resonances at the LHC. A color-singlet resonance that has leptophobic couplings needs further investigation to be distinguished from a color-octet one. In previous work, we introduced a method for discriminating between the two kinds of resonances when their couplings are flavor-universal, using measurements of the dijet resonance mass, total decay width and production cross-section. Here, we describe two extensions of that work. First, we broaden the method to the case where the vector resonances have flavor non-universal couplings, by incorporating measurements of the heavy-flavor decays of the resonance. Second, we apply the method to separating vector bosons from color-octet scalars and excited quarks.

We apply the orbifold grand unified theory (GUT) mechanism to the noncommutative Higgs model. An assignment of Z₂ parity to the “constituent fields” induces parity assignments of both the gauge and Higgs bosons, because these bosons are treated as some kind of composite fields in this formalism.

We discuss properties of non-Abelian gauge theories that change significantly across the lower edge of the conformal window. Their probes are the topological observables, the meson spectrum and the scalar glueball operator. The way these quantities change tells about the way conformal symmetry is lost.

The first Nagoya SCGT workshop back in 1988 (SCGT 88) was motivated by the walking technicolor and technidilaton. Now at SCGT15 I returned to the “old wine” in “a new bottle”, the recently discovered 125 Higgs boson as the technidilaton. We show that the Standard Model (SM) Higgs Lagrangian is identical to the nonlinear realization of both the scale and chiral symmetries (“scale-invariant nonlinear sigma model”), and is further gauge equivalent to the “scale-invariant Hidden Local Symmetry (HLS) model” having possible new vector bosons as the HLS gauge bosons with scaleinvariant mass: SM Higgs is nothing but a (pseudo) dilaton. The effective theory of the walking technicolor has precisely the same type of the scale-invariant nonlinear sigma model, thus further having the scale-invariant HLS gauge bosons (technirho’s, etc.). The technidilaton mass M_ϕ comes from the trace anomaly, which yields $M_{\varphi }^2{F}_{\varphi }^2\simeq \left[\frac{8}{N_F}\frac{4}{N_C}\right]\cdot$ (2.5)² ·v⁴ via PCDC, in the underlying walking SU(N_C) gauge theory with N_F massless flavors, where F_ϕ is the the decay constant and v = 246 GeV. This implies F_ϕ ≃ 5 v for $M_{\varphi }\simeq 125\text{GeV}\simeq \frac{1}{2}v$ in the one-family walking technicolor model (N_C = 4, N_F = 8), in good agreement with the current LHC Higgs data. In the anti-Veneziano limit, N_C → ∞, with N_Cα = fixed and N_F /N_C = fixed(≫ 1), we have a result: $M_{\varphi }^2/v^2\sim M_{\varphi }^2/F_{\varphi }^2\sim 1/\left(N_F{N}_C\right)\to 0.$ Then the technidilaton is a naturally light composite Higgs out of the strongly coupled conformal dynamics, with its couplings even weaker than the SM Higgs. Related holographic and lattice results are also discussed. In particular, such a light flavor-singlet scalar does exists in the lattice simulations in the walking regime.

In this brief talk, I will try to focus on the things that happened at the conference that seemed very important, but that I didn’t understand.

We study the deviation of yukawa coupling in the gauge-Higgs unification scenario from the Standard Model one. Applying the obtained results to the tau and bottom yukawa couplings, we numerically calculate the signal strength of $gg\to H\to b\overline{b},\tau \overline{\tau }$ in the gauge-Higgs unification.

We find a new evidence of a gauge/gravity duality: an explicit correspondence between eigenvalue densities and geometries. We examine the duality between IIA supergravity solutions and SU(2|4) symmetric gauge theories, which are BMN matrix model, N = 8 super Yang-Mills theory on R × S² and N = 4 super Yang-Mills theory on R × S³/Z_k. We show that the corresponding geometries are realized as the solution to the saddle point equations in the gauge theories, and that typical scales of the geometries are characterized by the range of the eigenvalue distribution.

We explore the descriptions for the three observables of the inflationary universe: the spectral index of curvature perturbations, the tensor-to-scalar ratio, and the running of the spectral index, in the context of scalar field theories, perfect fluid models, and F(R) gravity theories with the methods of reconstruction. By comparing the descriptions of these three observables with the recent cosmological observations, we explicitly show that the inflationary universe represented in scalar field theories, perfect fluid models, and F(R) gravity theories can explain the Planck results.

In this presentation we review our work on Abelian Maxwell-Chern-Simons theory in three-dimensional AdS black brane backgrounds, with both integer and non-integer Chern-Simons coupling. Such theories can be derived from several string theory constructions, and we found exact solutions in the low frequency, low momentum limit (ω, k ≪ T, the hydrodynamic limit). Our results are translated into correlation functions of vector operators in the dual strongly coupled 1 + 1-dimensional quantum field theory with a chiral anomaly at non-zero temperature T, via the holographic correspondence. The applicability of the hydrodynamic limit is discussed, together with the comparison between an exact field theoretic computation and the found holographic correlation functions in the conformal case.

In recent years, many kinds of modified gravity theories are suggested to get over problems in the general relativity. We consider a kind of modified gravity theories “Born- Infeld gravity in the Palatini formalism” and apply this theory to the black hole formation by considering the spherically symmetric collapse of the dust ball. We find the condition for the mass that the black hole horizon is formed.

LatKMI Collaboration has been studying SU(3) gauge theories with large numbers of fermion flavors, N_f. Here, we report results of lattice simulations for SU(3) gauge theory with four fundamental fermions. We first show fermion mass dependence of F_π,$〈\overline{q}q〉$ M_π, M_ρ and chiral extrapolations of them, showing the evidence of chiral symmetry breaking. Then, we show preliminary result of the measurement of the mass of the flavor-singlet scalar bound state.

The supersymmetric grand unified theories (SUSY GUTs) are the promising models beyond the standard model for particle physics. The standard SUSY GUTs predict that there exist the baryon-number violating processes, such as proton decay. It is important to estimate RGE effects on these processes in order to predict precise nucleon lifetime since there exists a large scale running between the GUT scale and 1GeV where the nucleon matrix elements are calculated. In this work, we have evaluated the GUT scale threshold corrections to the Wilson coefficients of the dimension-six baryon-number violating operators, and then we have estimated the effect of the threshold corrections on the decay rate in the minimal SUSY SU(5) GUT setup and its vector-like extensions.

Motivated by the scenario of electroweak baryogenesis in the walking technicolor (WTC) model, we investigate thermodynamic properties of 8-flavor QCD by using Monte Carlo simulations in the lattice gauge theory framework. We adopt HISQ and tree-level Symanzik improved actions. We show that the chiral susceptibility has a peak structure, and that the ratio of chiral to pion susceptibilities starts showing an inflection point with decreasing fermion mass. These results suggest the existence of a chiral phase transition in 8-flavor QCD.

We study perturbative unitarity and electroweak oblique corrections in the electroweak symmetry breaking models including an arbitrary number of neutral Higgs bosons. Requiring the perturbative unitarity of the high energy scattering amplitudes of weak gauge bosons and the neutral Higgs bosons at tree level, we obtain a set of conditions among the Higgs coupling strengths (unitarity sum rules). It is shown that the one-loop finiteness of the electroweak oblique corrections is automatically ensured once the unitarity sum rules are imposed among the Higgs coupling strengths. Applying the unitarity sum rules, we obtain severe constraints on the mass of the second lightest neutral Higgs boson and the lightest neutral Higgs (a 125GeV Higgs) coupling strength from the results of the electroweak precision tests.

We study the Seiberg dualities with an adjoint matter for the SU(N) gauge groups in three- and four-spacetime dimensions with four supercharges. We derive the three-dimensional duality from four-dimensional one by the dimensional reduction including the non-perturbative effect of the 𝕊¹-compactification, where the twisted instantons play a crucial role.

We summarize the main points of our work on the study of the pion condensation in asymmetric nuclear matter by using a holographic QCD model. We show that the phase transition from the normal hadron phase to the pion condensation phase is delayed in asymmetric matter.

We introduce an explicit supersymmetric unification model where grand unified gauge symmetry breaking and supersymmetry (SUSY) breaking are caused by the same field. Besides, the SM-charged particles are also predicted by the symmetry breaking sector, and their loop corrections induce the soft SUSY breaking terms. Especially, nonzero A-term and B-term are generated at one-loop level according to the mediation via the vector superfields, so that the electro-weak symmetry breaking and 125 GeV Higgs mass could be achieved even if the stop mass is around 1 TeV.

We present new lattice investigations of finite-temperature transitions for SU(3) gauge theory with N_f = 8 light flavors. Using nHYP-smeared staggered fermions we are able to explore renormalized couplings g² ≲ 20 on lattice volumes as large as 48³ × 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.

Motivated by the recent progress on many flavor QCD on a lattice, we investigate conformal/walking dynamics by using Schwinger-Dyson (SD) equation within an improved ladder approximation for two-loop running coupling. By numerically solving the SD equation, we obtain a pole mass (m_p), pion decay constant (f_π), and investigate the chiral symmetry breaking and mass anomalous dimension (γ_m) in the presence of IR cutoffs (Λ_IR). We find that the chiral symmetry breaking is suppressed if IR cutoff (Λ_IR) becomes larger than the critical value near the dynamical mass $\left({\text{Λ}}_{\text{IR}}^{*}\sim m_D\right).$ In the conformal phase the γ_m is strongly suppressed by IR cutoffs for Λ_IR ≳ m_p. We, then, obtain finite size hyperscaling (FSS) relation by adapting a linearized approximation for the SD equation, and examine the γ_m. The results offer valuable insight and suggestion for analyses in lattice gauge theories.

We show that the sizable D-term contributions to the sfermion mass spectrum can be signatures of a certain grand unified theory (GUT), E₆×SU(2)_F×U(1)_A GUT. Note that these D-term contributions destroy the degeneracy of sfermion masses among different generations in this model. Such D-terms are strongly constrained by the FCNC processes if the SUSY breaking scale is the weak scale. However, in E₆×SU(2)_F×U(1)_A, natural SUSY type sfermion mass spectrum is obtained, and if the masses of 10₃ sfermions are larger than O(1) TeV to realize 125 GeV Higgs and the other sfermion masses are O(10) TeV, then sizable D-term contribution is allowed. If the deviations by these D-terms can be observed in future experiments like 100 TeV proton collider or muon collider, we may confirm the E₆×SU(2)_F×U(1)_A GUT.

We report tests and results from a new approach to the spectral density and the mode number distribution of the Dirac operator in lattice gauge theories. The algorithm generates the spectral density of the lattice Dirac operator as a continuous function over all scales of the complete eigenvalue spectrum. This is distinct from an earlier method where the integrated spectral density (mode number) was calculated efficiently for some preselected fixed range of the integration. The new algorithm allows global studies like the chiral condensate from the Dirac spectrum at any scale including the cutoff-dependent IR and UV range of the spectrum. Physics applications include the scale-dependent mass anomalous dimension, spectral representation of composite fermion operators, and the crossover transition from the ∊-regime of Random Matrix Theory to the p-regime in chiral perturbation theory. We present thorough tests of the algorithm in the 2-flavor sextet SU(3) gauge theory that we continue to pursue for its potential as a minimal realization of the composite Higgs scenario.

The following sections are included:

• Workshop Timetable
• Photo Gallery
• List of Participants
• Author Index