International Journal of Modern Physics A

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 $(\chi \mathrm{\text{SB}})$ in the p-regime and $𝜖$-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 $𝜖$-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 $M_{\rho }/M_{\pi }\approx 2.2$. 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 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 $N_{\mathrm{\text{f}}}=4,8$ and 12 (in particular $N_{\mathrm{\text{f}}}=8$) 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 ${\gamma }_m$ 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 $\mathrm{\text{SU}}(N_{TC})$ 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 $\mathrm{\text{O}}(N)$ $\lambda |\overrightarrow{\varphi }{|}^4$ 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 $\sim 2$ 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 $m_{{\pi }^{\pm }}-m_{{\pi }^0}\simeq 1.8\mathrm{\text{MeV}}$ and the electromagnetic mass difference of nucleons, ${(M_p-M_n)}_{\mathrm{\text{QED}}}=0.48\mathrm{\text{MeV}}$, taking the Kaluza–Klein scale, $M_{\mathrm{\text{KK}}}=949\mathrm{\text{MeV}}$.

In this short review we describe some aspects of $\kappa$-deformation. After discussing the algebraic and geometric approaches to $\kappa$-Poincaré algebra we construct the free scalar field theory, both on noncommutative $\kappa$-Minkowski space and on curved momentum space. Finally, we make a few remarks concerning the interacting scalar field.

We show that due to the large coupling constant of the monopole–photon interaction the annihilation of monopole–antimonopole and monopolium into many photons must be considered experimentally. For monopole–antimonopole annihilation and lightly bound monopolium, even in the less favorable scenario, multiphoton events (four and more photons in the final state) are dominant, while for strongly bound monopolium, although two photon events are important, four- and six-photon events are also sizable.

The strong coupling constants not only are important to understand the strong interactions of the heavy baryons, but can also help us reveal the nature and structure of these baryons. Additionally, researchers indeed have made great efforts to calculate some of the strong coupling constants, $g_{{\mathrm{\Omega }}_c^{\ast }{\mathrm{\Omega }}_c^{\ast }\varphi }$, $g_{{\mathrm{\Omega }}_c^{\ast }{\mathrm{\Xi }}_c^{\ast }{K}^{\ast }}$, $g_{{\mathrm{\Xi }}_c^{\ast }{\mathrm{\Sigma }}_c^{\ast }{K}^{\ast }}$, $g_{{\mathrm{\Omega }}_b^{\ast }{\mathrm{\Omega }}_b^{\ast }\varphi }$, $g_{{\mathrm{\Xi }}_b^{\ast }{\mathrm{\Sigma }}_b^{\ast }{K}^{\ast }}$, $g_{{\mathrm{\Xi }}_b^{\ast }{\mathrm{\Xi }}_b\pi }$, $g_{{\mathrm{\Xi }}_c^{\ast }{\mathrm{\Xi }}_c\pi }$, $g_{{\mathrm{\Lambda }}_{b}N{B}^{\ast }}$, $g_{{\mathrm{\Lambda }}_b{N}^{\ast }{B}^{\ast }}$, $g_{{\mathrm{\Lambda }}_{c}N{D}^{\ast }}$, $g_{{\mathrm{\Lambda }}_c{N}^{\ast }{D}^{\ast }}$, $g_{{\mathrm{\Sigma }}_{c}N{D}^{\ast }}$, $g_{{\mathrm{\Sigma }}_b{N}^{\ast }{B}^{\ast }}$, $g_{{\mathrm{\Sigma }}_{b}N{B}^{\ast }}$, $g_{{\mathrm{\Sigma }}_c{N}^{\ast }{D}^{\ast }}$, etc. In this paper, we analyze the strong vertices ${\mathrm{\Sigma }}_c^{\ast }ND$ and ${\mathrm{\Sigma }}_b^{\ast }NB$ using the three-point QCD sum rules under the Dirac structure of $q/p//{\gamma }_{\mu }$. We perform our analysis by considering the contributions of the perturbative part and the condensate terms of $〈\bar{q}q〉$ and $〈\frac{{\alpha }_s}{\pi }GG〉$. After the form factors are calculated, they are then fitted into analytical functions which are used to get the strong coupling constants for these two vertices. The final results are $g_{{\mathrm{\Sigma }}_c^{\ast }ND}=7.19_{-3.11}^{+8.49}\pm 1.76$ and $g_{{\mathrm{\Sigma }}_b^{\ast }NB}=10.54_{-5.23}^{+15.59}\pm 1.82$.

The phase transition and critical behaviors of charged AdS black holes in $f(R)$ gravity with a conformally invariant Maxwell (CIM) source and constant curvature are further investigated. As a highlight, this research is carried out by employing new state parameters $(T,Q,\mathrm{\Phi })$ and contributes to deeper understanding of the thermodynamics and phase structure of black holes. Our analyses manifest that the charged $f(R)$-CIM AdS black hole undergoes a first-order small–large black hole phase transition, and the critical behaviors qualitatively behave like a Van der Waals liquid–vapor system. However, differing from the case in Einstein’s gravity, phase structures of the black holes in $f(R)$ theory exhibit an interesting dependence on gravity modification parameters. Moreover, we adopt the thermodynamic geometry to probe the black hole microscopic properties. The results show that, on the one hand, both the Ruppeiner curvature and heat capacity diverge exactly at the critical point, on the other hand, the $f(R)$-CIM AdS black hole possesses the property as ideal Fermi gases. Of special interest, we discover a microscopic similarity between the black holes and a Van der Waals liquid–vapor system.

A canonical relativistic quantization of the electromagnetic field is introduced in the presence of an anisotropic conductor magneto-dielectric medium in a standard way in the Gupta–Bleuler framework. The medium is modeled by a continuum collection of the vector fields and a continuum collection of the antisymmetric tensor fields of the second rank in Minkowski space–time. The collection of vector fields describes the conductivity property of the medium and the collection of antisymmetric tensor fields describes the polarization and the magnetization properties of the medium. The conservation law of the total electric charges, induced in the anisotropic conductor magneto-dielectric medium, is deduced using the antisymmetry conditions imposed on the coupling tensors that couple the electromagnetic field to the medium. Two relativistic covariant constitutive relations for the anisotropic conductor magneto-dielectric medium are obtained. The constitutive relations relate the antisymmetric electric–magnetic polarization tensor field of the medium and the free electric current density four-vector, induced in the medium, to the strength tensor of the electromagnetic field, separately. It is shown that for a homogeneous anisotropic medium the susceptibility tensor of the medium satisfies the Kramers–Kronig relations. Also it is shown that for a homogeneous anisotropic medium the real and imaginary parts of the conductivity tensor of the medium satisfy the Kramers–Kronig relations and a relation other than the Kramers–Kronig relations.