Gauge Coupling Constant Research Articles

Algebraic structure of the renormalization group in the renormalizable QFT theories

In this paper, we consider the group formed by finite renormalizations as an infinite-dimensional Lie group. It is demonstrated that for the finite renormalization of the gauge coupling constant, its generators [Formula: see text] with [Formula: see text] satisfy the commutation relations of the Witt algebra and, therefore, form its subalgebra. The commutation relations are also written for the more general case when finite renormalizations are made for both the coupling constant and matter fields. We also construct the generator of the Abelian subgroup corresponding to the changes of the renormalization scale. The explicit expressions for the renormalization group generators are written in the case when they act on the [Formula: see text]-function and the anomalous dimension. It is explained how the finite changes of these functions under the finite renormalizations can be obtained with the help of the exponential map.

Gravitational corrections to the two-loop beta function in a non-Abelian gauge theory

This paper investigates the coupling of massive fermions to gravity within the context of a non-Abelian gauge theory, utilizing the effective field theory framework for quantum gravity. Specifically, we calculate the two-loop beta function of the gauge coupling constant in a non-Abelian gauge theory, employing the one-graviton exchange approximation. Our findings reveal that gravitational corrections may lead to a nontrivial UV fixed point in the beta function of the gauge coupling constant, contingent upon the specific gauge group and the quantity of fermions involved. Published by the American Physical Society 2024

Féeton (B-L gauge boson) dark matter for the 511-keV gamma-ray excess and the prediction of low-energy neutrino flux* *Supported by the Talent Scientific Start-Up Project of China, the Natural Science Foundation of China (12175134, 12375101, 12090060, 12090064, 12247141), the SJTU Double First Class start-up fund(WF220442604), and the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan

The féeton is the gauge boson of the gauge theory. If the gauge coupling constant is extremely small, the féeton becomes a candidate for dark matter. We show that its decay to a pair of an electron and a positron explains the observed Galactic 511-keV gamma-ray excess in a consistent manner. This féeton dark matter decays mainly into pairs neutrino and anti-neutrino. Future low-energy experiments with improved directional capability will enable capturing these neutrino signals. The seesaw-motivated parameter space predicts a relatively short féeton lifetime that is comparable to the current cosmological constraint.

A model of pseudo-Nambu-Goldstone dark matter with two complex scalars

Pseudo-Nambu-Goldstone (pNG) dark matter (DM) is a promising DM candidate and able to explain the measured DM abundance by the thermal freeze-out mechanism evading the stringent bound from DM direct detection experiments. We propose a new model providing a pNG DM by introducing two Standard-Model-singlet complex scalars with the same charges of a dark U(1) gauge symmetry. They are also charged under a U(1) global symmetry corresponding to their relative phase rotations, which is explicitly broken by a soft-breaking term in the scalar potential. The both U(1) symmetries are spontaneously broken by their vacuum expectation values, giving rise to one real pNG boson. We also introduce a discrete ℤ2 symmetry exchanging the two scalars to stabilize the pNG boson as DM. It is shown that this model reproduces the DM abundance consistently with the current bound from the direct detection experiments. The model has a gauge kinetic mixing between the dark and U(1)Y gauge fields, which allows the dark gauge boson to decay even with a relatively light mass and prevents it from being an additional DM component. The Landau pole is avoided thanks to the small gauge coupling constant. In addition, a DM pair dominantly annihilates into a pair of the dark gauge bosons if the gauge boson mass is lighter than the DM mass, and thus its cross section has significantly different parameter dependence from other pNG DM models. We also calculate the DM-nucleon scattering cross section at the loop level. It turns out that it is necessary to probe region covered by the neutrino fog in order to test this model.

Pseudo-Nambu-Goldstone dark matter in SU(7) grand unification

We propose a grand unified theory (GUT) pseudo-Nambu-Goldstone boson (pNGB) dark matter (DM) model based on SU(7) gauge symmetry. In the GUT model, the Standard Model (SM) gauge symmetry GSM≔SU(3)C×SU(2)L×U(1)Y and the “dark” gauge symmetry SU(2)D are unified, where the SU(2)D symmetry plays an important role in the stability of DM. The unification of SM fermions and dark sector fermions is partially realized. The gauge symmetry SU(7) is spontaneously broken to SU(5)×SU(2)×U(1) gauge symmetry at the GUT scale by the nonvanishing vacuum expectation values of an SU(7) adjoint scalar field, where the SU(5) gauge symmetry is not usual SU(5) GUT gauge symmetry. The symmetry is further broken to GSM×SU(2)D at an intermediate scale. Furthermore, the SU(2)D symmetry is broken by the SU(2)D doublet and triplet scalar fields at the TeV scale. In the pNGB DM model based on GSM×SU(2)D, the residual global U(1)V dark custodial symmetry guarantees DM stability. On the other hand, in the SU(7) pNGB DM model, this global symmetry is explicitly broken by the Yukawa interaction and the effective Majorana mass terms. In the scalar sector, the cubic coupling constants of the SU(2)D doublet and triplet scalar fields are the order parameters of the U(1)V symmetry breaking. To maintain U(1)V symmetry and thus the DM stability, we need to tune Yukawa coupling constants and cubic scalar couplings at high accuracy. We find that the allowed DM mass region is quite restricted as the gauge coupling constant of SU(2)D is determined by the condition of the gauge coupling unification. To satisfy gauge coupling unification and the current experimental constraint on proton lifetime, we find that three generations of SU(3)C adjoint fermions and another three generations of SU(2)L adjoint fermions with the intermediate mass scale are required. We also find that there is no other solution to satisfy simultaneously the gauge coupling unification and the proton decay constraint if one assumes the other symmetry breaking schemes. Published by the American Physical Society 2024

Moduli spaces of instantons in flag manifold sigma models. Vortices in quiver gauge theories

In this paper, we discuss lumps (sigma model instantons) in flag manifold sigma models. In particular, we focus on the moduli space of BPS lumps in general Kähler flag manifold sigma models. Such a Kähler flag manifold, which takes the form Un1+⋯+nL+1Un1×⋯×UnL+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{\ extrm{U}\\left({n}_1+\\cdots +{n}_{L+1}\\right)}{\ extrm{U}\\left({n}_1\\right)\ imes \\cdots \ imes \ extrm{U}\\left({n}_{L+1}\\right)} $$\\end{document}, can be realized as a vacuum moduli space of a U(N1) × ··· × U(NL) quiver gauged linear sigma model. When the gauge coupling constants are finite, the gauged linear sigma model admits BPS vortex configurations, which reduce to BPS lumps in the low energy effective sigma model in the large gauge coupling limit. We derive an ADHM-like quotient construction of the moduli space of BPS vortices and lumps by generalizing the quotient construction in U(N) gauge theories by Hanany and Tong. As an application, we check the dualities of the 2d models by computing the vortex partition functions using the quotient construction.

The [formula omitted] vertex in a left–right model

We consider the one-loop corrections to the Zbb¯ vertex in a CP-conserving left–right model (LRM), viz. a model with gauge group SU(2)L×SU(2)R×U(1). We allow the gauge coupling constants of SU(2)L and SU(2)R to be different. The spontaneous symmetry breaking is accomplished only by doublets and/or singlets of SU(2)L and SU(2)R. The lightest massive neutral gauge boson of our LRM is assumed to have the same Yukawa couplings to bottom-quark pairs as the Z of the Standard Model (SM); this assumption has the advantage that, then, the infrared divergences automatically cancel down in the subtraction of the Zbb¯ vertex in the SM from the same vertex in the LRM. We effect a proper renormalization of the Zbb¯ vertex and check explicitly both its gauge invariance and the cancellation of all the ultraviolet divergences. We find out that a LRM with the above assumptions cannot achieve a better fit to the Zbb¯ vertex than a multi-Higgs extension of the SM, viz. both models can only achieve a decent fit when one admits scalar particles with very low masses ≲50 GeV. This is true even when we allow for markedly different gauge coupling constants of SU(2)L and SU(2)R.

Concept of the basic standard model and a relation between the three gauge coupling constants

Among the known elementary particles, 15 are not massless. In the Lagrangian of the standard model, the Higgs particle couples to all 15 of them to give them their respective masses. In this paper, a new model is proposed, where in the Lagrangian, the Higgs particle couples only to the four heaviest known elementary particles [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], all with masses in the vicinity of [Formula: see text], but not to the other 11. In this model, the masses of these 11 elementary particles that do not couple directly to the Higgs particle are generated by radiative corrections. Because of the reduction of the number of terms in the Lagrangian, this model is referred to as the basic standard model. By studying how the bottom quark can acquire a mass, it is found that there must be a relation between the three gauge coupling constants of the gauge group [Formula: see text]. This relation between these coupling constants is the first prediction, on purely theoretical grounds without using any experimental input, of the basic standard model, and is studied in some detail. In particular, this new prediction is found to be in good agreement with experimental measurements.

Non-supersymmetric SO(10) models with Gauge and Yukawa coupling unification

We study a non-supersymmetric SO(10) Grand Unification Theory with a very high energy intermediate symmetry breaking scale in which not only gauge but also Yukawa coupling unification are enforced via suitable threshold corrections and matching conditions. For gauge unification, we focus on a few symmetry breaking patterns with the intermediate gauge groups text {SU}(4)_{textrm{C}} times text {SU}(2)_{textrm{L}} times text {SU}(2)_{textrm{R}} (Pati–Salam) and text {SU}(3)_{textrm{C}} times text {SU}(2)_{textrm{L}} times text {SU}(2)_{textrm{R}}times text {U}(1)_{{textrm{B}}-{textrm{L}}} (minimal left-right symmetry) assuming an additional global U(1) Peccei–Quinn symmetry, and having the Standard Model supplemented by a second Higgs doublet field at the electroweak scale. We derive the conditions as well as the approximate analytical solutions for the unification of the gauge coupling constants at the two-loop level and discuss the constraints from proton decay on the resulting high scale. Specializing to the case of the Pati–Salam intermediate breaking pattern, we then impose also the unification of the Yukawa couplings of third generation fermions at the high scale, again at the two-loop level. In the considered context, Yukawa unification implies a relation between the fermion couplings to the 10- and 126-dimensional scalar representations of the SO(10) group. We consider one such possible relation which is obtainable in an text {E}_6 model where the previous two scalar fields are part of a single multiplet. Taking into account some phenomenological features such as the absence of flavor changing neutral currents at tree-level, we derive constraints on the parameters of the low energy model, in particular on the ratio of the two Higgs doublets vacuum expectation values tan beta .

Wilson loops in the abelian lattice Higgs model

We consider the lattice Higgs model on $\mathbb{Z}^4$, with structure group given by $ \mathbb{Z}_n $ for $ n \geq 2 $. We compute the expected value of the Wilson loop observable to leading order when the gauge coupling constant and hopping parameter are both sufficiently large. The leading order term is expressed in terms of a quantity arising from the related but much simpler $ \mathbb{Z}_n $ model, which reduces to the Ising model when $n=2$. As part of the proof, we construct a coupling between the lattice Higgs model and the $ \mathbb{Z}_n $ model.

The anomalous shift of the weak boson mass and the quintessence electroweak axion

One of the simplest ways to account for the observed W-boson mass shift is to introduce the SU(2) L triplet Higgs boson with zero hypercharge, whose vacuum expectation value is about 3 GeV. If the triplet is heavy enough at TeV, it essentially contributes only to T parameter without any conflict with the observation. The presence of a complex triplet Higgs boson raises the SU(2) L gauge coupling constant to α 2(M PL) ≃ 1/44 at the Planck scale. Thanks to this larger gauge coupling constant, we show that the electroweak axion vacuum energy explains the observed cosmological constant provided that the axion field is located near the hill top of the potential at present.

Improving efficiency of the path optimization method for a gauge theory

We investigate efficiency of a gauge-covariant neural network and an approximation of the Jacobian in optimizing the complexified integration path toward evading the sign problem in lattice field theories. For the construction of the complexified integration path, we employ the path optimization method. The $2$-dimensional $\text{U}(1)$ gauge theory with the complex gauge coupling constant is used as a laboratory to evaluate the efficiency. It is found that the gauge-covariant neural network, which is composed of the Stout-like smearing, can enhance the average phase factor, as the gauge-invariant input does. For the approximation of the Jacobian, we test the most drastic case in which we perfectly drop the Jacobian during the learning process. It reduces the numerical cost of the Jacobian calculation from ${\cal O}(N^3)$ to ${\cal O}(1)$, where $N$ means the number of degrees of freedom of the theory. The path optimization using this Jacobian approximation still enhances the average phase factor at expense of a slight increase of the statistical error.

Minimal Nambu-Goldstone-Higgs model in supersymmetric SU(5) revisited

We revisit the minimal Nambu-Goldstone (NG) Higgs supersymmetric (SUSY) SU(5) grand unified model and study its phenomenological implications. The Higgs sector of the model possesses a global SU(6) symmetry, which is spontaneously broken and results in the Higgs doublets of the minimal SUSY Standard Model (MSSM) as NG chiral superfields. Therefore, the model naturally leads to light Higgs doublets and solves the doublet-triplet splitting problem. Because of the SU(6) symmetry, the couplings of the Higgs sector are tightly restricted, and thus the model is more predictive than the minimal SUSY SU(5). We determine all the grand-unified-theory parameters via the matching conditions of the gauge coupling constants at the unification scale and calculate proton lifetime, confronting this with current experimental bounds. We discuss that this model is incompatible with the constrained MSSM, whilst it has a large viable parameter space in the high-scale SUSY scenario. The perturbativity condition on the trilinear coupling of the adjoint Higgs field imposes an upper (lower) limit on the wino (gluino) mass, implying a hierarchical mass pattern for these gauginos. Future proton-decay searches can probe a large part of the parameter space, especially if the SUSY-breaking scale is $\lesssim 100$~TeV.

New conformal field theories by gauging electric and magnetic currents

Old folklore says that there is no nontrivial renormalization group fixed point with [Formula: see text] gauge symmetry in four dimensions, but it can be circumvented by the existence of magnetic monopoles. We propose to construct (potentially infinitely many) novel types of field theories with [Formula: see text] gauge symmetry by gauging [Formula: see text] global symmetry electrically and magnetically. If the construction is consistent, the resulting theory will most likely possess a nontrivial renormalization group fixed point for the [Formula: see text] gauge coupling constant and it will be a nontrivial conformal field theory without the [Formula: see text] global symmetry in the infrared upon tunings of other relevant deformations. If the construction is CP-violating, a renormalization of the [Formula: see text]-parameter is accompanied.

Gravitational production of dark photon dark matter with mass generated by the Higgs mechanism

We study the gravitational production of dark photon dark matter during inflation, when dark photons acquire mass by the Higgs mechanism. In the previous study, it was assumed that the dark photon has a Stückelberg mass, or a mass generated by the Higgs mechanism with a sufficiently heavy Higgs boson. In this paper we consider a case in which the Higgs boson is not fully decoupled; the Higgs field changes its vacuum expectation value after inflation. Then, the dark photon mass also changes with time after inflation, and the time evolution of the longitudinal mode is different from the case with a Stückelberg mass. Consequently, the spectrum of the dark photon energy density can have two peaks at an intermediate scale and a small scale. We show that the dark photon can explain the dark matter if its current mass is larger than 6 μeV × (HI /1014 GeV)-4 and smaller than 0.8 GeV × (HI /1014 GeV)-3/2, with HI being the Hubble parameter during inflation. A higher mass is required if one considers a larger gauge coupling constant. The result for the Stückelberg mass can be reproduced in the limit of a small gauge coupling constant. We also comment on the constraints set by various conjectures in quantum gravity theory.

The AdS𝜃2/CFT1 correspondence and noncommutative geometry III: Phase structure of the noncommutative AdS𝜃2 × 𝕊N2

The near-horizon noncommutative geometry of black holes, given by [Formula: see text], is discussed and the phase structure of the corresponding Yang–Mills matrix models is presented. The dominant phase transition as the system cools down, i.e. as the gauge coupling constant is decreased is an emergent geometry transition between a geometric noncommutative [Formula: see text] phase (discrete spectrum) and a Yang–Mills matrix phase (continuous spectrum) with no background geometrical structure. We also find a possibility for topology change transitions in which space or time directions grow or decay as the temperature is varied. Indeed, the noncommutative near-horizon geometry [Formula: see text] can evaporate only partially to a fuzzy sphere [Formula: see text] (emergence of time) or to a noncommutative anti-de Sitter space–time [Formula: see text] (topology change).

A road towards a beyond the Standard Model model

In this talk we describe examples of renormalizable strongly interacting field theories where chiral symmetry, broken at the UV cutoff by the presence of some irrelevant d > 4 operators in the fundamental Lagrangian, is recovered at low energy owing to the tuning of certain Lagrangian parameters. The interference of UV effects with IR features coming from the spontaneous breaking of the recovered chiral symmetry yields non perturbatively generated elementary fermion masses parametrically expressed by formulae of the kind mq ~ Cq(α)ΛRGI with α the gauge coupling constant and ΛRGI the RGI scale of the theory. Upon introducing EW interactions, this mechanism can be extended to give mass to EW bosons and leptons and can thus be used as an alternative to the Higgs scenario. In order to give the top quark and the weak gauge bosons a mass of the phenomenologically correct order of magnitude, the model must necessarily include (yet unobserved) super-strongly interacting massive fermions endowed, besides ordinary Standard Model interactions, with super-strong interactions with a RGI scale, ΛT ΛQCD in the few TeV range. Though limited in its scope (here we ignore hypercharge and leptons and discuss only the case of one family neglecting weak isospin splitting), the model opens the way to a solution of the naturalness problem and an understanding of the fermion mass hierarchy.

Breakdown of hydrodynamics from holographic pole collision

We study the breakdown of diffusive hydrodynamics in holographic systems dual to neutral dilatonic black holes with extremal near horizon geometries conformal to AdS2 × R2. We find that at low temperatures by tuning the effective gauge coupling constant in the infra-red, the lowest non-hydrodynamic mode, which collides with the charge diffusive mode and sets the scales at which diffusive hydrodynamics breaks down, could be either an infra-red mode or a slow mode, resulting in different scaling behaviors of the local equilibrium scales. We confirm that the upper bound for the charge diffusion constant is always satisfied using the velocity and timescale of local equilibration from the pole collision. We also examine the breakdown of hydrodynamics at general temperature and find that the convergence radius has nontrivial dependence on temperature, in addition to the effective gauge coupling constant.

Universality of gauge coupling constant in the Einstein-QED system

In this paper, we discuss the universality of the renormalization of the gauge coupling constant in the quantum electrodynamics coupled to the Einstein's gravity in the framework of effective field theory in an arbitrary gauge. We observe that the renormalization of the three-point functions with different particles receive different contributions from the gravitational sector. Despite that, the universality of the gauge coupling constants is guaranteed by the Ward identity that makes the renormalized electric charge receive no contribution from the gravitational sector at one-loop order.

Mass corrections to the hard thermal or dense loops

We compute corrections to the hard thermal (or dense) loop photon polarization tensor associated to a small mass $m$ of the fermions of an electromagnetic plasma at high temperature $T$ (or chemical potential $\mu$). To this aim we use the on-shell effective field theory, amended with mass corrections. We also carry out the computation using transport theory, reaching to the same result. Interemediate steps in the computations reveal the presence of potential infrared divergencies. We use dimensional regularization, as it is respectful with the gauge symmetry, and then show that all infrared divergencies cancel in the final result. We compare the mass corrections with both the power and two-loop corrections, and claim that they are equally important if the mass is soft, that is, of order $e T$ (or $e \mu$), where $e$ is the gauge coupling constant, but are dominat if the mass obeys $ e T < m \ll T $ (or $e \mu < m \ll \mu)$.