arXiv subjects

A. V. Bednyakov

Publications and source records attributed to A. V. Bednyakov.

At least 19 recordsLinked to original sources

arXiv2026

On the renormalization-group analysis of the SM: loops, uncertainties, and vacuum stability

Renormalization-group equations (RGE) is one of the key tools in studying high-energy behavior of the Standard Model (SM). We begin by reviewing one-loop RGE for the dimensionless couplings of the SM and proceed to the state-of-the-art results. Our study focuses on the RGE solutions at different loop orders. We compare not only the standard (``diagonal'') loop counting when one considers gauge, Yukawa, and scalar self-coupling beta functions at the same order but also ``non-diagonal'' ones, inspired by the so-called Weyl consistency conditions. We discuss the initial conditions for RGE (``matching'') for different loop configurations and study the uncertainties of running couplings both related to the limited precision of the experimental input (``parametric'') and the missing high-order corrections (``theoretical''). As an application of our analysis we also estimate the electroweak vacuum decay probability and study how the uncertainties in the running parameters affect the latter. We argue that ``non-diagonal'' beta functions, if coupled with a more consistent ``non-diagonal'' matching, lead to larger theoretical uncertainty than ``diagonal'' ones.

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arXiv2026

On the six-loop scaling dimensions of the $(ϕ^2)^n$ operators in $d=3$

We consider a class of singlet operators $(ϕ^2)^n$ in the three-dimensional $O(N)$ model with $λ^2 ϕ^6$ interaction. Recently, the corresponding anomalous dimensions $γ_{2n}$ were computed by semiclassical methods and the all-loop result for the leading-$n$ corrections in the small $λ$ limit was found. In this paper, we obtain the six-loop expressions not only for the leading-$n$ contribution but also for the subleading one. While the leading correction confirms the predictions of recent semiclassical calculation, the subleading one is a new result and will serve as a future welcome check for all-loop expressions. As an important by-product of our calculation, we provide a full dependence on $n$ of the four-loop $γ_{2n}$ in the $O(N)$ case.

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arXiv2025

On the scalar sector of 2HDM: ring of basis invariants, syzygies, and six-loop renormalization-group equations

We consider a generating set of reparametrization invariants that can be constructed from the couplings and masses entering the scalar potential of the general Two-Higgs-Doublet Model (2HDM). Being independent of higgs-basis rotations, they generate a polynomial ring of basis invariants that represent the physical content of the model. Ignoring for the moment gauge and Yukawa interactions, we derive six-loop renormalization group equations (RGE) for all the invariants entering the set. We do not compute a single Feynman diagram but rely heavily on the general RGE results for scalar theories. We use linear algebra together with techniques from Invariant Theory. The latter not only allow one to compute the number of linearly independent invariants entering beta functions at a certain loop order (via Hilbert series) but also provide a convenient tool for dealing with polynomial relations (so-called syzygies) between invariants from the generating set.

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arXiv2024

Three-loop anomalous dimensions of fixed-charge operators in the SM

In this Letter we consider renormalization of a class of scalar operators with fixed hypercharge $Q$ within the Standard Model. We carry out explicit computation of the corresponding anomalous dimensions up to the three-loop order. In spite of the fact that our result is gauge-dependent, in the Landau gauge and in the limit of vanishing weak isospin coupling the expression can be matched to recent gauge-independent computation based on the large-charge method. Our result serves an important and non-trivial cross-check of new developments in large-charge expansion and applications of the latter to realistic gauge theories. We not only confirm the leading and subleading terms in perturbative $Q$ expansion up to three loops, but also provide the expressions for sub-subleading coefficients that at the moment are not captured by the large-charge approach.

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arXiv2024

Asymptotic safety in the Litim-Sannino model at four loops

We consider a four-dimensional $SU(N_c)$ gauge theory coupled to $N_f$ species of color fermions and $N_f^2$ colorless scalars. The quantum field theory possesses a weakly interacting ultraviolet fixed point that we determine from beta functions computed up to four-loop order in the gauge coupling, and up to three-loop order in the Yukawa and quartic scalar couplings. The fixed point has one relevant direction giving rise to asymptotic safety. We compute fixed point values of dimensionless couplings together with the corresponding scaling exponents up to the first three nontrivial orders in Veneziano parameter $ε$, both for infinite and finite number of colors $N_c$. We also consider anomalous dimensions for fields, scalar mass squared, and a class of dimension-three operators. Contrary to previous studies, we take into account possible mixing of the latter and compute eigenvalues of the corresponding matrix. Further, we investigate the size of the conformal window in the Veneziano limit and its dependence on $N_c$.

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arXiv2023

Impact of a non-universal $Z^\prime$ on the $B\to K^{()}l^+l^-$ and $B \to K^{()}ν\barν$ processes

We perform a study of the new physics effects in semileptonic FCNC processes within a low-energy approximation of the anomaly-free supersymmetic extension of the SM with additional $Z'$ vector field. The key feature of the model is the non-diagonal structure of $Z'$ couplings to fermions, which is parameterized by few new-physics parameters in addition to well-known mixing matrices for quarks and leptons in the SM. We not only consider CP-conserving scenarios with real parameters, but also account for possible CP violation due to new physical weak phases. We analyse the dependence of the $b\to s$ observables on the parameters together with correlations between the observables predicted in the model. Special attention is paid to possible enhancement of $B \to K^{(*)} ν\barν$ rates and to CP-odd angular observables in $B \to K^* ll$ decays.

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arXiv2018

On the electroweak contribution to the matching of the strong coupling constant in the SM

The effective renormalizable theory describing electromagnetic and strong interactions of quarks of five light flavors ($n_f = 5$ QCD$\times$QED) is considered as a low-energy limit of the full Standard Model. Two-loop relation between the running strong coupling constants $α_s$ defined in either theories is found by simultaneous decoupling of electroweak gauge and Higgs bosons in addition to the top quark. The relation potentially allows one to confront "low-energy determination of $α_s$ with a high-energy one with increased accuracy. Numerical impact of new $\mathcal{O}(α_sα)$ terms is studied at the $M_Z$ scale. It is shown that the corresponding contribution, although being suppressed with respect to $\mathcal{O}(α_s^2)$ terms, is an order of magnitude larger than the three-loop QCD corrections $\mathcal{O}(α_s^3)$ usually taken into account in four-loop renormalization group evolution of $α_s$. The dependence on the matching scale is also analyzed numerically.

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arXiv2018

On three-loop RGE for the Higgs sector of 2HDM

We discuss renormalization group equations (RGE) for the parameters of the Higgs sector in general Two-Higgs-Doublet Model (2HDM). We present the three-loop results but consider only contributions due to self-couplings of the Higgs doublets. We study the structure of RGE and express beta-functions in terms of reparametrization invariants with respect to higgs-basis rotations. The Cayley-Hamilton theorem is utilized to reduce both the number of independent tensor structures in matrix RGE and the number of invariants to a minimal set. As a by-product of our calculation we discovered that two-loop RGE of the scalar sector in general QFT with multiple higgses were not properly implemented in a number of public packages. The latter give rise to a wrong result when mixing in the scalar sector is allowed.

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arXiv2018

On the $b$-quark running mass in QCD and the SM

We consider electroweak corrections to the relation between the running $\overline{\mathrm{MS}}$ mass $m_b$ of the $b$ quark in the five-flavor QCD$\times$QED effective theory and its counterpart in the Standard Model (SM). As a bridge between the two parameters, we use the pole mass $M_b$ of the $b$ quark, which can be calculated in both models. The running mass is not a fundamental parameter of the SM Lagrangian, but the product of the running Yukawa coupling $y_b$ and the Higgs vacuum expectation value. Since there exist different prescriptions to define the latter, the relations considered in the paper involve a certain amount of freedom. All the definitions can be related to each other in perturbation theory. Nevertheless, we argue in favor of a certain gauge-independent prescription and provide a relation which can be directly used to deduce the value of the Yukawa coupling of the $b$ quark at the electroweak scale from its effective QCD running mass. This approach allows one to resum large logarithms $\ln(m_b/M_t)$ systematically. Numerical analysis shows that, indeed, the corrections to the proposed relation are much smaller than those between $y_b$ and $M_b$.

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arXiv2016

On the four-loop strong coupling beta-function in the SM

In the talk the leading four-loop contribution to the beta-function of the strong coupling in the SM is discussed. Some details of calculation techniques are provided. Special attention is paid to the ambiguity due to utilized $γ_5$ treatment and a particular prescription with anticommuting $γ_5$ is advocated. As a by-product of our computation the four-loop beta-function in QCD with "gluino" is also obtained.

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arXiv2016

An advanced precision analysis of the SM vacuum stability

The talk is devoted to the problem of stability of the Standard Model vacuum. The effective potential for the Higgs field, which can potentialy exhibit additional, deeper minimum, is considered as a convenient tool for addressing the problem. Different methods and approximations used to calculate the potential are considered. Special attention is paid to the renomalization-group approach that allows one to carry out three-loop analysis of the problem. By means of an explicit gauge-independent procedure the absolute stability bounds on the observed Higgs and top-quark masses are derived. The importance of high-order corrections is demonstrated. In addition, potential metastablity of the SM is discussed together with modifications of the analysis due to some New Physics.

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arXiv2016

Four-loop strong coupling beta-function in the Standard Model

In this letter we present our results for the four-loop beta-function of the strong coupling in the Standard Model of fundamental interactions. We take top-Yukawa and self-Higgs interactions into account, but neglect electroweak gauge couplings.

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arXiv2015

Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision

We perform a manifestly gauge-independent analysis of the vacuum stability in the Standard Model (SM) including two-loop matching, three-loop renormalization group evolution, and pure QCD corrections through four loops. All these ingredients are exact, except that light-fermion masses are neglected. We in turn apply the criterion of nullifying the $\overline{\mathrm{MS}}$ Higgs self-coupling and its beta function and a recently proposed consistent method for determining the true minimum of the effective Higgs potential that also avoids gauge dependence. Exploiting our knowledge of the Higgs-boson mass, we derive an upper bound on the pole mass of the top quark by requiring that the SM be stable all the way up to the Planck mass scale and conservatively estimate the theoretical uncertainty. This bound is compatible with Monte Carlo mass quoted by the Particle Data Group at the $1.3σ$ level.

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arXiv2014

Three-loop SM RGEs with general Yukawa matrices

The results for the three-loop renormalization group equations for all fundamental parameters of the SM Lagrangian are presented. Special attention is paid to the Flavor sector of the SM, which parameterized by general complex non-diagonal Yukawa couplings. Some details of calculation techniques are given. In addition, ambiguities in the beta-functions for the matrix couplings are discussed.

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arXiv2014

Three-loop SM beta-functions for matrix Yukawa couplings

We present the extension of our previous results for three-loop Yukawa coupling beta-functions to the case of complex Yukawa matrices describing the flavour structure of the SM. The calculation is carried out in the context of unbroken phase of the SM with the help of the MINCER program in a general linear gauge and cross-checked by means of MATAD/BAMBA codes. In addition, ambiguities in Yukawa matrix beta-functions are studied.

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arXiv2014

A Mathematica Package for Calculation of One-Loop Penguins in FCNC Processes

In this work, we present a Mathematica package Peng4BSM@LO which calculates the contributions to the Wilson Coefficients of certain effective operators originating from the one-loop penguin Feynman diagrams. Both vector and scalar external legs are considered. The key feature of our package is the ability to find the corresponding expressions in almost any New Physics model which extends the SM and has no flavour changing neutral current (FCNC) transitions at the tree level.

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arXiv2013

Three-loop Higgs self-coupling beta-function in the Standard Model with complex Yukawa matrices

Three-loop renormalization group equations for the Higgs self-coupling and Higgs mass parameter are recalculated in the case of complex Yukawa matrices, which encompass general flavour structure of the Standard Model. In addition, the anomalous dimensions both for the quantum Higgs field and its vacuum expectation value are presented in the $\overline{MS}$-scheme. A numerical study of the latter quantities is carried out for a certain set of initial parameters.

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arXiv2013

Three-loop beta-functions and anomalous dimensions in the Standard Model

In this talk the methods and computer tools which were used in our recent calculation of the three-loop Standard Model renormalization group coefficients are discussed. A brief review of the techniques based on special features of dimensional regularization and minimal subtraction schemes is given. Our treatment of gamma5 is presented in some details. In addition, for a reasonable set of initial parameters the numerical estimates of the obtained three-loop contributions are presented.

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