Can the nearly conformal sextet gauge model hide the Higgs impostor?

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.     

Maximal symmetry and mass generation of Dirac fermions and gravitational gauge field theory in six-dimensional spacetime

The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors. A massless Dirac fermion generates new symmetries corresponding to chirality spin and charge spin as well as conformal scaling transformations. With the introduction of intrinsic W-parity, a massless Dirac fermion can be treated as a Majorana-type or Weyl-type spinor in a six-dimensional spacetime that reflects the intrinsic quantum numbers of chirality spin. A generalized Dirac equation is obtained in the six-dimensional spacetime with a maximal symmetry. Based on the framework of gravitational quantum field theory proposed in Ref. [1] with the postulate of gauge invariance and coordinate independence, we arrive at a maximally symmetric gravitational gauge field theory for the massless Dirac fermion in six-dimensional spacetime. Such a theory is governed by the local spin gauge symmetry SP(1,5) and the global Poincar′e symmetry P(1,5)= SO(1,5) P~(1,5) as well as the charge spin gauge symmetry SU(2). The theory leads to the prediction of doubly electrically charged bosons. A scalar field and conformal scaling gauge field are introduced to maintain both global and local conformal scaling symmetries. A generalized gravitational Dirac equation for the massless Dirac fermion is derived in the six-dimensional spacetime. The equations of motion for gauge fields are obtained with conserved currents in the presence of gravitational effects. The dynamics of the gauge-type gravifield as a Goldstone-like boson is shown to be governed by a conserved energy-momentum tensor, and its symmetric part provides a generalized Einstein equation of gravity. An alternative geometrical symmetry breaking mechanism for the mass generation of Dirac fermions is demonstrated.     

Dynamical fermion mass hierarchy and flavour mixing

The chiral symmetry breaking of high colour representations produces dynamical breaking of the standard electroweak gauge symmetry. By enlarging the colour group and subsequently breaking it down toSU(3) _c fermions acquire radiative masses from the chiral breaking. We present attempts to produce realistic fermion mass matrix in two classes of models depending on the way that the colour group is enlarged. A realistic example is found in one of these classes of models.     

Effect of Fermion Velocity on Phase Structure of QED3

Dynamical chiral symmetry breaking (DCSB) in thermal QED₃ with fermion velocity is studied in the framework of Dyson-Schwinger equations. By adopting instantaneous approximation and neglecting the transverse component of gauge boson propagator at finite temperature, we numerically solve the fermion self-energy equation in the rainbow approximation. It is found that both DCSB and fermion chiral condensate are suppressed by fermion velocity. Moreover, the critical temperature decreases as fermion velocity increases.     

QED with vector and axial vector types of interaction and dynamical generation of particle masses

We consider a model of electrodynamics with two types of interaction, the vector \((e\bar \psi (\gamma ^\mu A_\mu )\psi )\) and axial vector \((e_A \bar \psi (\gamma ^\mu \gamma ^5 B_\mu )\psi )\) interactions, i.e., with two types of vector gauge fields, which corresponds to the local nature of the complete massless-fermion symmetry group U(1) ? U _A (1). We present a phenomenological model with spontaneous symmetry breaking through which the fermion and the axial vector field B_μ acquire masses. Based on an approximate solution of the Dyson equation for the fermion mass operator, we demonstrate the phenomenon of dynamical chiral symmetry breaking when the field B_μ has mass. We show the possibility of eliminating the axial anomalies in the model under consideration when introducing other types of fermions (quarks) within the standard-model fermion generations. We consider the polarization operator for the field B_μ and the procedure for removing divergences when calculating it. We demonstrate the emergence of a mass pole in the propagator of the particles that correspond to the field B_03BC when chiral symmetry is broken and consider the problems of regularizing closed fermion loops with axial vector vertices in connection with chiral symmetry breaking.     

A Wilson-Yukawa Model with undoubled chiral fermions in 2D

We consider the fermion mass spectrum in the strong coupling vortex phase (VXS) of a lattice fermion-scalar model with a global U(1)_L × U(1)_R, in two dimensions, in the context of a recently proposed two-cutoff lattice formulation. The fermion doublers are made massive by a strong Wilson-Yukawa coupling, but in contrast with the standard formulation of these type of models, in which the light fermion spectrum was found to be vector-like, we find massless fermions with chiral quantum numbers at finite lattice spacing. When the global symmetry is gauged, this model is expected to give rise to a lattice chiral gauge theory.     

On the character of chiral symmetry breaking and fermion vacuum structure in QED<Subscript>3</Subscript>

Equation for the Bethe-Salpeter wave function of the Goldstone boson in QED₃ is considered in the ladder approximation with the use of the Landau gauge for the photon propagator. With the help of standard simplifications, the existence of nonzero solutions for this equation is demonstrated, which testifies to the production of the above-described boson in the process of chiral symmetry breaking. At the same time, it is demonstrated that only one of the entire set of solutions describing the Goldstone boson corresponds to the stable ground state; this solution has the greatest fermion mass. In the remaining cases, the compound boson state with zero mass is excited, and all other states having smaller energies appear tachyon states and hence are unstable. The fermion condensate is calculated; it is demonstrated that in the examined case, it is finite. Based on the foregoing, conclusions are drawn about spontaneous rather than dynamic character of chiral symmetry breaking in QED₃, complex structure of fermion vacuum for the examined model, and at the same time, simple structure of the massive phase vacuum.     

On the critical behavior of (2 + 1)-dimensional QED

It is shown the analysis [1] for QED in (2 + 1) dimensions with N four-component fermions in the leading and next-to-leading orders of the 1/N expansion. As it was demonstrated in [1], the range of the admissible values N, where the dynamical fermion mass exists, decreases strongly with the increasing of the gauge charge. So, in Landau gauge the dynamical chiral symmetry breaking appears forN < 3.78, that is very close to the results of the leading order and in Feynman gauge dynamical mass is completely absent.     

Chiral phase structure of QCD with many flavors

We investigate QCD with a large number of massless flavors with the aid of renormalization group flow equations. We determine the critical number of flavors separating the phases with and without chiral symmetry breaking in SU(N_c) gauge theory with many fermion flavors. Our analysis includes all possible fermionic interaction channels in the pointlike four-fermion limit. Constraints from gauge invariance are resolved explicitly and regulator-scheme dependencies are studied. Our findings confirm the existence of an N_f window where the system is asymptotically free in the ultraviolet, but remains massless and chirally invariant on all scales, approaching a conformal fixed point in the infrared. Our prediction for the critical number of flavors of the zero-temperature chiral phase transition in SU(3) is N_f^cr=10.0±0.29 (fermion)^+1.55_-0.63 (gluon), with the errors arising from approximations in the fermionic and gluonic sectors, respectively. PACS 11.10.Hi, 11.15.Tk, 11.30.Rd     

Influence of Finite Chemical Potential on Critical Boson Mass in QED3

Using the coupled Dyson-Schwinger equation for the fermion propagator at finite chemical potential μ, we investigate the fermion chiral condensate when the gauge boson mass is nonzero in QED3. We show that the chiral symmetry restores when the boson mass is large enough, and the critical boson mass depends little on μ.     

Instantons and the U(1) problem

If instantons spontaneously break the chiral SU(N) × SU(N) symmetry of a non-abelian gauge theory, they break U(1) symmetry in a manner consistent with the chiral Ward identities of the theory. Excitations of the fermion vacuum play a crucial role in this process. A model calculation of the symmetry breaking effect shows a phenomenological structure which differs from that provided by models with many color degrees of freedom.     

Gauge independence and chiral symmetry breaking in a strong magnetic field

The gauge independence of the dynamical fermion mass generated through chiral symmetry breaking in QED in a strong, constant external magnetic field is critically examined. We present a (first, to the best of our knowledge) consistent truncation of the Schwinger-Dyson equations in the lowest Landau level approximation. We demonstrate that the dynamical fermion mass, obtained as the solution of the truncated Schwinger-Dyson equations evaluated on the fermion mass shell, is manifestly gauge independent.     

Lattice study of the conformal window in QCD-like theories

We study the extent of the conformal window for an SU(3) gauge theory with N{f} Dirac fermions in the fundamental representation. We present lattice evidence for 12相似文献   

Scaling behaviour of charged spin-one partons in a gauge model

In a hadron model in which the fermion constituents are bound by vector-isovector gauge fields, electromagnetism is introduced; by spontaneously breaking the strong (SU(2)) gauge symmetry, the gauge fields become massive. We identify the spinors and vectors with partons, and, assuming the naive parton model hypothesis, we calculate the cross section e⁺e^?→ hadrons and the structure functions of the nucleon; scaling is obtained desoite induces presence of an anomalous magnetic moment term in the coupling of the photon with the charged vector fields; the reason is that the spontaneous breaking of the symmetry indices a vector-meson dominance type of coupling between the photon and the neutral vector, which is just what is necessary to restore scaling.     

有限温下三维QED中费米速度对费米子手征凝聚的影响（英文）

三维QED 具有两个和QCD类似的性质:动力学手征对称破缺和禁闭。为了研究动力学手征对称破缺,基于彩虹近似,在Dyson-Schwinger 方程框架下,通过迭代求解有限温下的费米子自能方程,讨论了不同的费米速度下费米子手征凝聚与费米子味数之间的关系。发现在有限温下,对于固定的费米子味数,费米手征凝聚随费米速度的变大而单调减小。Analogous to Quantum QCD, QED₃ has two interesting features: dynamical chiral symmetry breaking (DCSB) and confinement. By adopting the rainbow approximation, we numerically solve the fermion self-energy equation at finite temperature in the framework of Dyson-Schwinger equations and discuss the relation between chiral condensate and fermion flavor for several fermion velocities in the finite temperature QED₃. It is found that the fermion chiral condensate decreases monotonically with the fermion velocity increasing for a fixed N at finite temperature.     

Nearly conformal gauge theories in finite volume

We report new results on nearly conformal gauge theories with fermions in the fundamental representation of the SU(3)$\mathit{SU}(3)$ color gauge group as the number of fermion flavors is varied in the Nf=4–16$N_f=4\text{–}16$ range. To unambiguously identify the chirally broken phase below the conformal window we apply a comprehensive lattice tool set in finite volumes which includes the test of Goldstone pion dynamics, the spectrum of the fermion Dirac operator, and eigenvalue distributions of random matrix theory. We also discuss the theory inside the conformal window and present our first results on the running of the renormalized gauge coupling and the renormalization group beta function. The importance of understanding finite volume zero momentum gauge field dynamics inside the conformal window is illustrated. Staggered lattice fermions are used throughout the calculations.     

Studies of chiral symmetry breaking in SU(2) lattice gauge theory

We study chiral symmetry breaking (_χSB) in SU(2) lattice gauge theory with quarks in the $\text{l =}\text{1}\text{2}\text{, l = 1, l =}\text{3}\text{2}$, and l = 2 representations of the color group. We perform Monte Carlo evaluations of $\text{〈}\text{ψ}\text{ψ〉}$ in the quenched approximation and extract the relevant length scales for _χSB. We revise a previous estimate for the ratio between the chiral symmetry restoration temperatures for fundamental and adjoint quarks and obtain $\text{T}{}_{\mathrm{l\; =\; 1}}\text{/T}{}_{\mathrm{l}}\text{=}\text{1}\text{2}\text{～ 8}$. Our results for the higher representations, $\text{l =}\text{3}\text{2}\text{and}\text{l = 2}$, are consistent with Casimir scaling and give C₂g_mom² ～ 4. Many aspects of our calculational method are explained in detail. The issues discussed include the relation between _χSB in the quenched approximation and the spectrum of the Dirac operator, the flavor symmetries of euclidean staggered fermions, estimates of finite-size effects and the reliability of m → 0 extrapolations on finite lattices.     

Chiral quarks,chiral limit,nonanalytic terms and baryon spectroscopy

It is shown that the principal pattern in baryon spectroscopy, which is associated with the flavor-spin hyperfine interactions, is due to the spontaneous breaking of chiral symmetry in QCD and persists in the chiral limit. All corrections, which are associated with a finite quark (Goldstone boson) mass are suppressed by the factor (μ/Λ_χ)² and higher.     

Effective lagrangian analysis of the chiral phase transition at finite density

Introducing a finite chemical potential μ for the quark number density ψ^°ψ, we study analytically the restoration of Π^° chiral symmetry as μ is varied. In the strong coupling limit, the effective lagrangian for SU(N) gauge theories coupled to fermion fields in d dimensions is derived for all N. In the case of SU(2) we predict a second order chiral symmetry restoration phase transition, whereas for all N?3 the transition is first order. Predictions are given for the critical values of the chemical potential μ.     

Dynamical mass generation in QED_3 beyond the instantaneous approximation

In this paper, we investigate dynamical mass generation in(2+1)-dimensional quantum electrodynamics at finite temperature. Many studies are carried out within the instantaneous-exchange approximation, which ignores all but the zero-frequency component of the boson propagator and fermion self-energy function. We extend these studies by taking the retardation effects into consideration. In this paper, we get the explicit frequency n and momentum p dependence of the fermion self-energy function and identify the critical temperature for different fermion flavors in the chiral limit. Also, the phase diagram for spontaneous symmetry breaking in the theory is presented in T_c-N_f space. The results show that the chiral condensate is just one-tenth of the scale of previous results, and the chiral symmetry is restored at a smaller critical temperature.