Two-loop Renormalization Group Analysis Research Articles

The Higgs Trilinear Coupling and the Scale of New Physics for the SM-Axion-Seesaw-Higgs Portal Inflation (SMASH) Model

In the extended scalar sector of the SMASH (Standard Model - Axion-Seesaw-Higgs portal inflation) framework, we conduct a phenomenological investigation of the observable effects. In a suitable region of the SMASH scalar parameter spaces, we solve the vacuum metastability problem and discuss the one-loop correction to the triple Higgs coupling, λHHH. The λHHH and SM Higgs quartic coupling λH corrections are found to be proportional to the threshold correction. A large λHHH correction (≳5%) implies vacuum instability in the model and thus limits the general class of theories that use threshold correction. We performed a full two-loop renormalization group analysis of the SMASH model. The SMASH framework has also been used to estimate the evolution of lepton asymmetry in the universe.

Generalized multifractality in the spin quantum Hall symmetry class with interaction

Scaling of various local observables with a system size at Anderson transition criticality is characterized by a generalized multifractality. We study the generalized multifractality in the spin quantum Hall symmetry class (class C) in the presence of interaction. We employ Finkel'stein nonlinear sigma model and construct the pure scaling derivativeless operators for class C in the presence of interaction. Within the two-loop renormalization group analysis we compute the anomalous dimensions of the pure scaling operators and demonstrate that they are affected by the interaction. We find that the interaction breaks exact symmetry relations between generalized multifractal exponents known for a noninteracting problem.

Renormalization group analysis of Dirac fermions with a random mass

Two-dimensional (2D) disordered superconductor (SC) in class D exhibits a disorder-induced quantum multicritical phenomenon among diffusive thermal metal (DTM), topological superconductor (TS), and conventional localized (AI) phases. To characterize the quantum tricritical point where these three phases meet, we carry out a two-loop renormalization group (RG) analysis for 2D Dirac fermion with random mass in terms of the $\epsilon$-expansion in the spatial dimension $d=2-\epsilon$. In 2D ($\epsilon=0$), the random mass is marginally irrelevant around a clean-limit fixed point of the gapless Dirac fermion, while there exists an IR unstable fixed point at finite disorder strength that corresponds to the tricritical point. The critical exponent, dynamical exponent, and scaling dimension of the (uniform) mass term are evaluated around the tricritical point by the two-loop RG analysis. Using a mapping between an effective theory for the 2D random-mass Dirac fermion and the (1+1)-dimensional Gross-Neveu model, we further deduce the four-loop evaluation of the critical exponent, and the scaling dimension of the uniform mass around the tricritical point. Both the two-loop and four-loop results suggest that criticalities of a AI-DTM transition line as well as TS-DTM transition line are controlled by other saddle-point fixed point(s) at finite uniform mass.

Model building from asymptotic safety with Higgs and flavor portals

We perform a comprehensive search for Standard Model extensions inspired by asymptotic safety. Our models feature a singlet matrix scalar field, three generations of vector-like leptons, and direct links to the Higgs and flavor sectors via new Yukawa and portal couplings. A novel feature is that the enlarged scalar sector may spontaneously break lepton flavor universality. We provide a complete two-loop renormalization group analysis of the running gauge, Yukawa, and quartic couplings to find ultraviolet fixed points and the BSM critical surface of parameters, $i.e.$ the set of boundary conditions at the TeV scale for which models remain well-behaved and predictive up to the Planck scale without encountering Landau poles or instabilities. This includes templates for asymptotically safe Standard Model extensions which match the measured values of gauge couplings and the Higgs, top, and bottom masses. We further detail the phenomenology of our models covering production, decay, fermion mixing, anomalous magnetic moments, effects from scalar mixing and chiral enhancement, and constraints on model parameters from data. Signatures at proton-proton and lepton colliders such as lepton flavor violation and displaced vertices, and the prospect for electric dipole moments or charged lepton-flavor-violating type processes, are also indicated.

Anomalous Dimensions of Leading Composite Operators in the Kinematic MHD Turbulence: Two-Loop Renormalization Group Analysis

Using the field theoretic renormalization group technique and the operator product expansion, the kinematic MHD turbulence is investigated in the second order (two-loop) approximation of the corresponding perturbative expansion. The anomalous dimensions of the leading composite operators, which drive the anomalous scaling of the single-time two-point correlation functions of the passive magnetic field, are calculated. It is shown that the two-loop corrections to these anomalous dimensions are significant and lead to the more anomalous (more negative) values of the total two-loop anomalous dimensions. It also means that the anomalous scaling at the two-loop level of approximation is much more pronounced in the present model of passive vector advection than in the analogous model of passive scalar quantity advected by the turbulent velocity field driven by the stochastic Navier–Stokes equation.

Pati-Salam axion

I discuss the implementation of the Peccei-Quinn mechanism in a minimal realization of the Pati-Salam partial unification scheme. The axion mass is shown to be related to the Pati-Salam breaking scale and it is predicted via a two-loop renormalization group analysis to be in the window ma ∈ [10−11, 3 × 10−7] eV, as a function of a sliding Left-Right symmetry breaking scale. This parameter space will be fully covered by the late phases of the axion Dark Matter experiments ABRACADABRA and CASPEr-Electric. A Left-Right symmetry breaking scenario as low as 20 TeV is obtained for a Pati-Salam breaking of the order of the reduced Planck mass.

Influence of Finite-Time Velocity Correlations on Scaling Properties of the Magnetic Field in the Kazantsev-Kraichnan Model: Two-Loop Renormalization Group Analysis

Using the field theory renormalization group method and the operator product expansion technique in the two-loop approximation, we investigate the influence of the finite-time correlations of a turbulent velocity field on the anomalous scaling behavior of the single-time two-point correlation functions of the passive magnetic field in the framework of the generalized kinematic Kazantsev-Kraichnan model with the presence of large-scale anisotropy in the three-dimensional case. We briefly discuss the scaling regimes of the model and find two-loop expressions for the anomalous dimensions of the leading composite operators in the operator product expansion as explicit functions of the parameter determining the finite-time correlations of the velocity field in the studied model. We show that the anomalous dimensions of the composite operators near the isotropic shell play a central role in the scaling properties of the model and this allows uniquely determining the two-loop expressions for the scaling exponents of all single-time two-point correlation functions of the magnetic field that drive their scaling properties deep inside the inertial interval. We show that the presence of the finite-time correlations of the velocity field leads to a significantly more pronounced anomalous scaling of the magnetic correlation functions compared with the standard Kazantsev-Kraichnan rapid-change model with the δ-time correlated Gaussian velocity field.

Turbulent Prandtl Number in Two Spatial Dimensions: Two-Loop Renormalization Group Analysis

Using the field theory renormalization group technique in the framework of the so-called double-expansion scheme, which takes additional divergences that appear in two dimensions into account, we calculate the turbulent Prandtl number in two spatial dimensions in the two-loop approximation in the model of a passive scalar field advected by the turbulent environment driven by the stochastic Navier–Stokes equation. We show that in contrast to the three-dimensional case, where the two-loop correction to the one-loop value of the turbulent Prandtl number is very small (less than 2% of the one-loop value), the two-loop value of the turbulent Prandtl number in two spatial dimensions, Prt = 0.27472, is considerably smaller than the corresponding value Prt(1) = 0.64039 obtained in the one-loop approximation, i.e., the two-loop correction to the turbulent Prandtl number in the two-dimensional case represents about 57% of its one-loop value and must be seriously taken into account. This result also means that there is a significant difference (at least quantitatively) between diffusion processes in two- and three-dimensional turbulent environments.

Influence of finite-time velocity correlations on scaling properties of the magnetic field in the Kazantsev-Kraichnan model: Two-loop renormalization group analysis

В рамках обобщенной кинематической модели Казанцева-Крейчнана при наличии крупномасштабной анизотропии в трехмерном случае исследовано влияние конечновременных корреляций турбулентного поля скоростей на аномальное скейлинговое поведение одновременны́х двухточечных корреляционных функций пассивного магнитного поля. Для анализа использован метод теоретико-полевой ренормгруппы и техника операторного разложения в двухпетлевом приближении. Кратко обсуждаются режимы скейлинга модели, найдены двухпетлевые выражения для аномальных размерностей ведущих составных операторов в операторном разложении в виде явных функций параметра, который определяет в исследуемой модели временны́е корреляции поля скоростей при конечных временах. Показано, что центральную роль в скейлинговых свойствах модели играют аномальные размерности составных операторов вблизи изотропной оболочки, что позволяет однозначно определить двухпетлевые выражения для скейлинговых показателей всех одновременны́х двухточечных корреляционных функций магнитного поля, которые управляют скейлинговыми свойствами глубоко внутри инерционного интервала. Также показано, что наличие конечновременных корреляций поля скоростей приводит к значительно более ярко выраженному аномальному скейлингу магнитных корреляционных функций, чем в стандартной модели быстрых изменений Казанцева-Крейчнана с $\delta$-коррелированным по времени гауссовым полем скоростей.

Orbital selectivity versus Pomeranchuk instability in the iron–chalcogenide superconductors: A two-loop renormalization group study

We perform a two-loop renormalization group (RG) analysis of a 2D effective multiband model, which is relevant for describing the low-energy properties of some iron–chalcogenide superconducting materials. Crucial ingredients in this analysis are the calculation of higher-order contributions in the RG scheme that go beyond the widely-used parquet approximation and the consequent inclusion of nontrivial self-energy effects of the model that yield an anisotropic renormalization of the quasiparticle weight in the system. The motivation of our work is the experimental discovery by Sprau et al. (2017) that orbitally-selective renormalization of the quasiparticle weight in the Hund’s metal phase at moderate temperatures underpins the highly unusual gap in the superconducting phase of the FeSe compound at lower temperatures. One prediction we arrive here is that the underlying origin of nematicity in these systems may indeed come from orbital-selectivity, instead of a Pomeranchuk instability in the d± channel. This orbital selectivity is driven by the presence of stripe-type antiferromagnetic fluctuations in the model. Therefore, we argue that the present RG results may provide a scenario from a weak-to-moderate coupling perspective, in which the role of orbital selectivity to describe the physical properties of some iron–chalcogenide superconductors is emphasized.

Anomalous scaling in the Kazantsev-Kraichnan model with finite time correlations: two-loop renormalization group analysis of relevant composite operators

The field theoretic renormalization group technique together with the operator product expansion in the second order of the perturbation theory (in the two-loop approximation) is used for the investigation of the influence of the finite time correlations of the velocity field on the anomalous dimensions of the leading set of composite operators, which drive the anomalous scaling of correlation functions of a weak magnetic field in the framework of the kinematic Kazantsev–Kraichnan model in the presence of a large scale anisotropy. The system of possible scaling regimes of the model is found and two important special limits of the model are briefly discussed. The general two-loop expressions for the anomalous and critical dimensions of the leading composite operators are found as functions of the spatial dimension d and of the renormalization group fixed point value of the parameter u, which drives the presence of the finite time correlations of the velocity field in the model. The anisotropic hierarchies among various anomalous dimensions are investigated and it is shown that, regardless of the fixed point value of the parameter u as well as regardless of the spatial dimension of the system, the leading role in the anomalous scaling properties of the model is played by the anomalous dimensions of the composite operators near the isotropic shell, in accordance with the Kolmogorov’s local isotropy restoration hypothesis. The properties of the anomalous dimensions of the leading composite operators in the Kazantsev–Kraichnan model with finite time correlations of the velocity field are compared to the properties of the corresponding anomalous dimensions of the composite operators relevant in the framework of the Kraichnan model of passively advected scalar field with finite time correlations. It is shown that, regardless of the fixed point value of the parameter u, the two-loop corrections to the anomalous dimensions are much more important in the framework of the Kazantsev–Kraichnan vector model than in the Kraichnan model of a passive scalar advection. At the same time, again regardless of the strength of time correlations, the two-loop values of the leading anomalous dimensions in the Kazantsev–Kraichnan model of the passive magnetic field are significantly more negative than the corresponding two-loop values of the relevant anomalous dimensions in the framework of the Kraichnan model. It means that the anomalous scaling of the correlation functions of the passive magnetic field, deep inside the inertial interval of the turbulent environment with finite time correlations of the velocity field, must be much more pronounced than in the case of the correlation functions of the passively advected scalar field.

Superconducting versus semiconducting electronic ground state in chirality-specific double-wall carbon nanotubes

By using two-loop renormalization group analysis, we explore the phase diagram with respect to the electron–phonon and Coulomb interaction strengths in the two (3,3)@(8,8) and (5,0)@(15,0) double-wall carbon nanotube systems (DWCNTs). Using estimation of the two types of coupling strengths from ab initio calculations, both systems are shown to scale to the superconducting fixed point as temperature decreases to zero. This is in contrast to the (3,3) and (5,0) single-wall carbon nanotubes, which scales to the Peierls-distorted semiconducting ground state. While the superconducting transition temperature can be quite low in the (3,3)@(8,8) system, the (5,0)@(15,0) promises observable superconducting behavior. Our result is in support of recent experimental observation of superconductivity in DWCNTs.

Breakdown of Fermi liquid behavior near the hot spots in a two-dimensional model: A two-loop renormalization group analysis

Motivated by a recent experimental observation of a nodal liquid on both single crystals and thin films of Bi2Sr2CaCu2O8+δ by Chatterjee et al. [Nature Phys. 6 (2010) 99], we perform a field-theoretical renormalization group (RG) analysis of a two-dimensional model such that only eight points located near the “hot spots” on the Fermi surface are retained, which are directly connected by spin density wave ordering wavevector. We derive RG equations up to two-loop order describing the flow of renormalized couplings, quasiparticle weight, several order-parameter response functions, and uniform spin and charge susceptibilities of the model. We find that while the order-parameter susceptibilities investigated here become non-divergent at two loops, the quasiparticle weight vanishes in the low-energy limit, indicating a breakdown of Fermi liquid behavior at this RG level. Moreover, both uniform spin and charge susceptibilities become suppressed in the scaling limit which indicate gap openings in both spin and charge excitation spectra of the model.

Erratum: Anomalous scaling and large-scale anisotropy in magnetohydrodynamic turbulence: Two-loop renormalization-group analysis of the Kazantsev-Kraichnan kinematic model [Phys. Rev. E85, 065301(R) (2012)

Erratum: Anomalous scaling and large-scale anisotropy in magnetohydrodynamic turbulence: Two-loop renormalization-group analysis of the Kazantsev-Kraichnan kinematic model [Phys. Rev. E<b>85</b>, 065301(R) (2012)

Rings and Coulomb boxes in dissipative environments

We study a particle on a ring in the presence of a dissipative Caldeira-Leggett environment and derive its response to a dc field. We show how this non-equilibrium response is related to a flux averaged equilibrium response. We find, through a two-loop renormalization group analysis, that a large dissipation parameter $\ensuremath{\eta}$ flows to a fixed point ${\ensuremath{\eta}}^{R}=\ensuremath{\hbar}/(2\ensuremath{\pi})$. We also reexamine the mapping of this problem to that of the Coulomb box and show that the relaxation resistance, of recent interest, is quantized for large $\ensuremath{\eta}$. For finite $\ensuremath{\eta}&gt;{\ensuremath{\eta}}^{R}$ we find that a certain average of the relaxation resistance is quantized. We propose a Coulomb-box experiment to measure a quantized noise.

Anomalous scaling and large-scale anisotropy in magnetohydrodynamic turbulence: Two-loop renormalization-group analysis of the Kazantsev-Kraichnan kinematic model

The field theoretic renormalization group and operator product expansion are applied to the Kazantsev-Kraichnan kinematic model for the magnetohydrodynamic turbulence. The anomalous scaling emerges as a consequence of the existence of certain composite fields ("operators") with negative dimensions. The anomalous exponents for the correlation functions of arbitrary order are calculated in the two-loop approximation (second order of the renormalization-group expansion), including the anisotropic sectors. The anomalous scaling and the hierarchy of anisotropic contributions become stronger due to those second-order contributions.

Renormalization group analysis of a spin-1 Kondo dot: Nonequilibrium transport and relaxation dynamics

We study non-equilibrium transport through a spin-1 Kondo dot in a local magnetic field. To this end we perform a two-loop renormalization group analysis in the weak-coupling regime yielding analytic results for (i) the renormalized magnetic field and the g-factor, (ii) the time evolution of observables and the relevant decay rates, (iii) the magnetization and anisotropy as well as (iv) the current and differential conductance in the stationary state. In particular, we find that compared to a spin-1/2 Kondo dot there exist three additional decay rates resulting in an enhanced broadening of the logarithmic features observed in stationary quantities. Additionally, we study the effect of anisotropic couplings between reservoir and impurity spin.

Improvedεexpansion for three-dimensional turbulence: Two-loop renormalization near two dimensions

An improved epsilon expansion in the d -dimensional (d > 2) stochastic theory of turbulence is constructed at two-loop order, which incorporates the effect of pole singularities at d--> 2 in coefficients of the epsilon expansion of universal quantities. For a proper account of the effect of these singularities, two different approaches to the renormalization of the powerlike correlation function of the random force are analyzed near two dimensions. By direct calculation, it is shown that the approach based on the mere renormalization of the nonlocal correlation function leads to contradictions at two-loop order. On the other hand, a two-loop calculation in the renormalization scheme with the addition to the force correlation function of a local term to be renormalized instead of the nonlocal one yields consistent results in accordance with the ultraviolet (UV) renormalization theory. The latter renormalization prescription is used for the two-loop renormalization-group analysis amended with partial resummation of the pole singularities near two dimensions, leading to a significant improvement of the agreement with experimental results for the Kolmogorov constant.

Critical, crossover and correction-to-scaling exponents for isotropic Lifshitz points to order (8 $ndash$ d)2

A two-loop renormalization group analysis of the critical behaviour at an isotropic Lifshitz point is presented. Using dimensional regularization and minimal subtraction of poles, we obtain the expansions of the critical exponents ? and ?, the crossover exponent , as well as the (related) wave vector exponent ?q and the correction-to-scaling exponent ? to second order in 8 = 8 ? d. They are compared with the authors' recent -expansion results (2000 Phys. Rev. B 62 12338, 2001 Nucl. Phys. B 612 340) for the general case of an m-axial Lifshitz point. It is shown that the expansions obtained here by a direct calculation for the isotropic (m = d) Lifshitz point all follow from the latter upon setting m = 8 ? 8. This is so despite recent claims to the contrary by de Albuquerque and Leite (2002 J. Phys. A: Math. Gen. 35 1807).

Two-loop renormalization-group analysis of critical behavior at m-axial Lifshitz points

We investigate the critical behavior that d-dimensional systems with short-range forces and an n-component order parameter exhibit at Lifshitz points whose wave-vector instability occurs in an m-dimensional isotropic subspace of R d . Utilizing dimensional regularization and minimal subtraction of poles in d=4+ m 2 −ϵ dimensions, we carry out a two-loop renormalization-group (RG) analysis of the field-theory models representing the corresponding universality classes. This gives the beta function β u ( u) to third order, and the required renormalization factors as well as the associated RG exponent functions to second order, in u. The coefficients of these series are reduced to m-dependent expressions involving single integrals, which for general (not necessarily integer) values of m∈(0,8) can be computed numerically, and for special values of m analytically. The ϵ expansions of the critical exponents η l2 , η l4 , ν l2 , ν l4 , the wave-vector exponent β q , and the correction-to-scaling exponent are obtained to order ϵ 2. These are used to estimate their values for d=3. The obtained series expansions are shown to encompass both isotropic limits m=0 and m= d.