One-loop Renormalization Group Research Articles

Leading-logarithmic approximation by one-loop renormalization group within Matsubara formalism

Leading-logarithmic approximation by one-loop renormalization group within Matsubara formalism

Complete one-loop renormalization-group equations in the seesaw effective field theories

In this paper, we derive the complete set of one-loop renormalization-group equations (RGEs) for the operators up to dimension-six (dim-6) in the seesaw effective field theories (SEFTs). Two kinds of contributions to those RGEs are identified, one from double insertions of the dimension-five (dim-5) Weinberg operator and the other from single insertions of the tree-level dim-6 operators in the SEFTs. A number of new results are presented. First, as the dim-5 Weinberg operator is unique in the standard model effective field theory (SMEFT), its contributions to the RGEs for the SEFTs are equally applicable to the SMEFT. We find the full contributions from the Weinberg operator to one-loop RGEs in the SMEFT, correcting the results existing in previous works, and confirm that those from dim-6 operators are consistent with the results in the literature. Second, in the type-I SEFT, we give the explicit expressions of the RGEs of all the physical parameters involved in the charged- and neutral-current interactions of leptons. Third, the RGEs are numerically solved to illustrate the running behaviors of the non-unitary parameters, mixing angles and CP-violating phases in the non-unitary leptonic flavor mixing matrix. Together with the one-loop matching results of the dim-5 and dim-6 operators and their Wilson coefficients, the present work has established a self-consistent framework up to dim-6 to investigate low-energy phenomena of three types of seesaw models at the one-loop level.

Interface Roughening in Nonequilibrium Phase-Separated Systems.

Interfaces of phase-separated systems roughen in time due to capillary waves. Because of fluxes in the bulk, their dynamics is nonlocal in real space and is not described by the Edwards-Wilkinson or Kardar-Parisi-Zhang (KPZ) equations, nor their conserved counterparts. We show that, in the absence of detailed balance, the phase-separated interface is described by a new universality class that we term |q|KPZ. We compute the associated scaling exponents via one-loop renormalization group and corroborate the results by numerical integration of the |q|KPZ equation. Deriving the effective interface dynamics from a minimal field theory of active phase separation, we finally argue that the |q|KPZ universality class generically describes liquid-vapor interfaces in two- and three-dimensional active systems.

One-loop algebras and fixed flow trajectories in adjoint multi-scalar gauge theory

We study the one loop renormalisation of 4d SU(N) Yang-Mills theory with M adjoint representation scalar multiplets related by O(M) symmetry. General M are of field theoretic interest, and the 4d one loop beta function of the gauge coupling g2 vanishes for the case M = 22, which is intriguing for string theory. This case is related to D3 branes of critical bosonic string theory in D = 22 + 4 = 26. An RG fixed point could have provided a definition for a purely bosonic AdS/CFT, but we show that scalar self-couplings λ ruin one-loop conformal invariance in the large N limit. There are real fixed flows (fixed points of λ/g2) only for M ≥ 406, rendering one-loop fixed points of the gauge coupling and scalar couplings incompatible.We develop and check an algebraic approach to the one-loop renormalisation group which we find to be characterised by a non-associative algebra of marginal couplings. In the large N limit, the resulting RG flows typically suffer from strong coupling in both the ultraviolet and the infrared. Only for M ≥ 406 fine-tuned solutions exist which are weakly coupled in the infrared.

The translational μ-τ reflection symmetry of Majorana neutrinos

The present neutrino oscillation data allow [Formula: see text] (or [Formula: see text]) for the neutrino mass spectrum and support [Formula: see text] and [Formula: see text] as two good approximations for the PMNS lepton flavor mixing matrix [Formula: see text]. We show that these intriguing possibilities can be a very natural consequence of the translational[Formula: see text]-[Formula: see text] reflection symmetry — the effective Majorana neutrino mass term keeps invariant under the transformations [Formula: see text], [Formula: see text] and [Formula: see text] (for [Formula: see text] or 3), where [Formula: see text] is the charge conjugation of a constant spinor field [Formula: see text]. By extending such a working flavor symmetry to the canonical seesaw mechanism at a superhigh-energy scale, we calculate its soft breaking effects at the electroweak scale by using the one-loop renormalization-group equations.

Matchmakereft: automated tree-level and one-loop matching

We introduce matchmakereft, a fully automated tool to compute the tree-level and one-loop matching of arbitrary models onto arbitrary effective theories. Matchmakereft performs an off-shell matching, using diagrammatic methods and the background field method (BFM) when gauge theories are involved. The large redundancy inherent to the off-shell matching together with explicit gauge invariance offers a significant number of non-trivial checks of the results provided. These results are given in the physical basis but several intermediate results, including the matching in the Green basis before and after canonical normalization, are given for flexibility and the possibility of further cross-checks. As a non-trivial example we provide the complete matching in the Warsaw basis up to one loop of an extension of the Standard Model with a charge $-1$ vector-like lepton singlet. Matchmakereft has been built with generality, flexibility and efficiency in mind. These ingredients allow matchmakereft to have many applications beyond the matching between models and effective theories. Some of these applications include the one-loop renormalization of arbitrary theories (including the calculation of the one-loop renormalization group equations for arbitrary theories); the translation between different Green bases for a fixed effective theory or the check of (off-shell) linear independence of the operators in an effective theory. All these applications are performed in a fully automated way by matchmakereft.

Exploiting the scheme dependence of the renormalization group improvement in infrared Yang–Mills theory

Within the refined Gribov–Zwanziger scenario for four-dimensional Yang–Mills theory in the Landau gauge, a gluon mass term is generated from the restriction of the gauge field configurations to the first Gribov region. Tissier and Wschebor have pointed out that adding a gluon mass term to the usual Faddeev–Popov action yields one-loop renormalization group improved gluon and ghost propagators which are in reasonable agreement with the lattice data even in the infrared regime. In this work, we extend their analysis to several alternative renormalization schemes and show how the renormalization scheme dependence can be used to achieve an almost perfect matching to the lattice data for the gluon and ghost propagators.

Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation

Higher rank symmetry and higher moment conservation have been drawn considerable attention from, e.g., subdiffusive transport to fracton topological order. In this paper, we perform a one-loop renormalization group (RG) analysis and show how these phenomena emerge at low energies. We consider a $d$-dimensional model of interacting bosons of d components. At higher-rank-symmetric points with conserved angular moments, the $a$-th bosons have kinetic energy only along the $x^a$ direction. Therefore, the symmetric points look highly anisotropic and fine-tuned. By studying RG in a wide vicinity of the symmetric points, we find that symmetry-disallowed kinetic terms tend to be irrelevant within the perturbative regime, which potentially leads to emergent higher-rank symmetry and higher-moment conservation at the deep infrared limit. While non-perturbative analysis is called for in the future, by regarding higher-rank symmetry as an emergent phenomenon, the RG analysis presented in this paper holds alternative promise for realizing higher-rank symmetry and higher-moment conservation in experimentally achievable systems.

The smallest neutrino mass revisited

As is well known, the smallest neutrino mass turns out to be vanishing in the minimal seesaw model, since the effective neutrino mass matrix Mν is of rank two due to the fact that only two heavy right-handed neutrinos are introduced. In this paper, we point out that the one-loop matching condition for the effective dimension-five neutrino mass operator can make an important contribution to the smallest neutrino mass. By using the available one-loop matching condition and two-loop renormalization group equations in the supersymmetric version of the minimal seesaw model, we explicitly calculate the smallest neutrino mass in the case of normal neutrino mass ordering and find m1 ∈ [10−8, 10−10] eV at the Fermi scale ΛF = 91.2 GeV, where the range of m1 results from the uncertainties on the choice of the seesaw scale ΛSS and on the input values of relevant parameters at ΛSS.

Higgs-electroweak chiral Lagrangian: One-loop renormalization group equations

Starting from the one-loop divergences we obtained previously, we work out the renormalization of the Higgs-electroweak chiral Lagrangian explicitly and in detail. This includes the renormalization of the lowest-order Lagrangian, as well as the decomposition of the remaining divergences into a complete basis of next-to-leading-order counterterms. We provide the list of the corresponding beta functions. We show how our results match the one-loop renormalization of some of the dimension-6 operators in SMEFT. We further point out differences with related work in the literature and discuss them. As an application of the obtained results, we evaluate the divergences of the vacuum expectation value of the Higgs field at one loop and show that they can be appropriately removed by the corresponding renormalization. We also work out the finite renormalization required to keep the no-tadpole condition on the Higgs field at one loop.

Towards the renormalisation of the Standard Model effective field theory to dimension eight: Bosonic interactions I

We compute the one-loop renormalisation group running of the bosonic Standard Model effective operators to order v^4/\Lambda^4v4/Λ4, with v\sim 246v∼246 GeV being the electroweak scale and \LambdaΛ the unknown new physics threshold. We concentrate on the effects triggered by pairs of the leading dimension-six interactions, namely those that can arise at tree level in weakly-coupled ultraviolet completions of the Standard Model. We highlight some interesting consequences, including the interplay between positivity bounds and the form of the anomalous dimensions; the non-renormalisation of the SS and UU parameters; or the importance of radiative corrections to the Higgs potential for the electroweak phase transition. As a byproduct of this work, we provide a complete Green basis of operators involving only the Higgs and derivatives at dimension-eight, comprising 13 redundant interactions.

Effective field theory interpretation of lepton magnetic and electric dipole moments

We perform a model-independent analysis of the magnetic and electric dipole moments of the muon and electron. We give expressions for the dipole moments in terms of operator coefficients of the low-energy effective field theory (LEFT) and the Standard Model effective field theory (SMEFT). We use one-loop renormalization group improved perturbation theory, including the one-loop matching from SMEFT onto LEFT, and one-loop lepton matrix elements of the effective-theory operators. Semileptonic four-fermion operators involving light quarks give sizable non-perturbative contributions to the dipole moments, which are included in our analysis. We find that only a very limited set of the SMEFT operators is able to generate the current deviation of the magnetic moment of the muon from its Standard Model expectation.

Quenched disorder at antiferromagnetic quantum critical points in two-dimensional metals

We study spin density wave quantum critical points in two dimensional metals with a quenched disorder potential coupling to the electron density. Adopting an $\epsilon$-expansion around three spatial dimensions, where both disorder and the Yukawa-type interaction between electrons and bosonic order parameter fluctuations are marginal, we present a perturbative, one-loop renormalization group analysis of this problem, where the interplay between fermionic and bosonic excitations is fully incorporated. Considering two different Gaussian disorder models restricted to small-angle scattering, we show that the non-Fermi liquid fixed point of the clean SDW hot-spot model is generically unstable and the theory flows to strong coupling due to a mutual enhancement of interactions and disorder. We study properties of the asymptotic flow towards strong coupling, where our perturbative approach eventually breaks down. Our results indicate that disorder dominates at low energies, suggesting that the ground-state in two dimensions is Anderson-localized.

Interplay of New Physics effects in (g \u2212 2)\u2113 and h \u2192 \u2113+\u2113\u2212 \u2014 lessons from SMEFT

We explore the interplay of New Physics (NP) effects in (g− 2)ℓ and h→ℓ+ℓ− within the Standard Model Effective Field Theory (SMEFT) framework, including one-loop Renormalization Group (RG) evolution of the Wilson coefficients as well as matching to the observables below the electroweak symmetry breaking scale. We include both the leading dimension six chirality flipping operators including a Higgs and SU(2)L gauge bosons as well as four-fermion scalar and tensor operators, forming a closed operator set under the SMEFT RG equations. We compare present and future experimental sensitivity to different representative benchmark scenarios. We also consider two simple UV completions, a Two Higgs Doublet Model and a single scalar LeptoQuark extension of the SM, and show how tree level matching to SMEFT followed by the one-loop RG evolution down to the electroweak scale can reproduce with high accuracy the (g−2)ℓ and h→ℓ+ℓ− contributions obtained by the complete one- and even two-loop calculations in the full models.

Parquet approximation and one-loop renormalization group: Equivalence on the leading-logarithmic level

We investigate the functional renormalization group (FRG) flow of the two-particle vertex function of a model for x-ray absorption in metals. Concerning the appearance of logarithmic divergences, the model is prototypical for an important class of mostly zero- and one-dimensional systems which includes the Kondo model and the interacting one-dimensional Fermi gas. For our analysis, we formulate the FRG in the framework of the real-time zero-temperature formalism, in which the model was studied before with a parquet-based approach. We establish that a reasonably crafted, purely fermionic one-loop FRG approximation is fully equivalent on a detailed level to the leading-logarithmic parquet approximation. These two approximation schemes are thus found to just represent different perspectives on the same technical steps. This finding also reconfirms the traditional understanding of the capabilities of one-loop RG approximations for such models, which was recently put into question by an investigation of the x-ray-absorption model with multiloop FRG.

DsixTools 2.0: the effective field theory toolkit

DsixTools is a Mathematica package for the handling of the standard model effective field theory (SMEFT) and the low-energy effective field theory (LEFT) with operators up to dimension six, both at the algebraic and numerical level. DsixTools contains a visually accessible and operationally convenient repository of all operators and parameters of the SMEFT and the LEFT. This repository also provides information concerning symmetry categories and number of degrees of freedom, and routines that allow to implement this information on global expressions (such as decay amplitudes and cross-sections). DsixTools also performs weak basis transformations, and implements the full one-loop Renormalization Group Evolution in both EFTs (with SM beta functions up to five loops in QCD), and the full one-loop SMEFT-LEFT matching at the electroweak scale.

Running in the ALPs

The couplings of axion-like particles are probed by different experiments across a huge range of energy scales. Accordingly, a consistent analysis of the corresponding constraints requires the use of the renormalization group equations. We compute the full one-loop renormalization group evolution of all – relevant and marginal – parameters in the effective field theory for axion-like particles up to dimension five, above and below the electroweak scale, assuming only that new physics does not violate CP. We also include a detailed discussion of the different bases used in the literature, the relations among them and the interplay of the CP and shift symmetries.

New scenario for aligned Higgs couplings originated from the twisted custodial symmetry at high energies

We investigate a new scenario of the two Higgs doublet model, where the current experimental data for the electroweak rho parameter and those for the Higgs boson couplings can be simultaneously explained. In this scenario, the two Higgs doublet model is supposed to be a low energy effective theory up to a high energy scale Λ, above which a fundamental theory should appear. It is assumed that the Higgs potential respects a global symmetry at Λ (the twisted custodial symmetry), which is to be given as a consequence of the global symmetry structure of the fundamental theory above Λ. By the analysis using one-loop renormalization group equations, the above experimental data can be explained in a natural way even when the masses of the extra Higgs bosons are near the electroweak scale. We also discuss the predictions on the mass spectrum of the additional Higgs bosons and also those on the coupling constants of the standard-model-like Higgs boson, which make it possible to test this scenario at the current and future collider experiments.

Fate of a multiple-band Fermi liquid that is coupled with critical ϕ4 bosons

Multiple-band nature of electronic energy bands leads to novel physical effects in solids. In this paper, we clarify physical properties of a Fermi system with a pair of electron and hole Fermi surfaces (FSs), whose coupling is mediated by a critical U(1) boson field. By using a one-loop renormalization group analysis, we show that when the boson field undergoes a quantum phase transition with broken U(1) symmetry, the multiple-band Fermi system shows a non-Fermi liquid (non-FL) behaviour in its thermodynamic and magnetic properties. At a quantum critical point (QCP), Fermi velocities of the two FSs are renormalized into a same critical velocity as a boson velocity, and the fermion's density of states (DOS) shows a pseudo-gap behaviour with a logarithmic energy dependence at the QCP.

Integral solutions to the one-loop renormalization-group equations for lepton flavor mixing parameters and the Jarlskog invariant

Working in the basis where the charged-lepton Yukawa matrix is diagonal and making the τ-dominance approximations, we analytically derive integral solutions to the one-loop renormalization-group equations (RGEs) for neutrino masses, flavor mixing angles, CP-violating phases and the Jarlskog invariant under the standard parametrization of the PMNS matrix in the standard model or its minimal supersymmetric extension for both Majorana and Dirac neutrinos. With these integral solutions, we carry out numerical calculations to investigate the RGE running of lepton flavor mixing parameters and the Jarlskog invariant, and also compare these integral solutions with the exact results obtained by numerically solving the one-loop RGEs. It is shown that these integral solutions coincide with the exact results and can well describe the evolution of lepton flavor mixing parameters and the Jarlskog invariant in most cases. Some important features of our integral solutions and the evolution behaviours of relevant flavor parameters are also discussed in detail both analytically and numerically.