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O. L. Veretin

Publications and source records attributed to O. L. Veretin.

At least 19 recordsLinked to original sources
arXiv2026

Renormalization of three-quark operators with up to two derivatives at three loops

We study in QCD the $\overline{\mathrm{MS}}$ renormalization of three-quark operators with up to two covariant derivatives, which are related to $N=0,1,2$ Mellin moments of baryonic light-cone distributions amplitudes. Apart from general three-quark operators, we also consider those corresponding to spin 3/2 and 1/2 states. We present in analytic form the renormalization constants and anomalous dimensions of these operators through three loops, confirming previous two- and three-loop results for $N=0$. Furthermore, we evaluate through two loops their amputated four-point Green's functions with RI${}^\prime$/MOM four-momentum assignment, which are required for the matching of lattice results with perturbative calculations. We work in linear covariant gauge and find the anomalous dimensions to be gauge independent as expected.

hep-ph↗
arXiv2026

Numerical analytical continuation of multivariate hypergeometric functions

We present a general framework for the high-precision numerical evaluation of multivariate hypergeometric functions defined as solutions of holonomic systems of partial differential equations. Our approach adapts and extends methods originally developed for multi-loop Feynman integrals to the setting of hypergeometric functions of many variables. In particular, we construct Pfaffian systems for arbitrary multivariate hypergeometric functions by applying the Laporta reduction algorithm to suitable systems of differential relations. Next, we construct a numerical scheme based on the Frobenius method, which allows us to compute local power-series solutions with controlled precision and to transport them along prescribed paths in the space of variables. A central part of the paper is devoted to a systematic analysis of multivaluedness and branch structure: we show how the Frobenius method can be used to access different Riemann sheets in a controlled way and to track changes of the solution under analytic continuation around singular loci.

math-ph↗
arXiv2025

Updated determination of light-cone distribution amplitudes of octet baryons in lattice QCD

We present updated results on the wave function normalization constants and the first moments of the light cone distribution amplitudes for the lowest-lying baryon octet. The analysis is carried out on a large number of $n_f=2+1$ lattice gauge ensembles, including ensembles at physical pion (and kaon) masses. These are spread across five different lattice spacings, enabling a controlled continuum limit. The main differences with respect to our earlier work are the use of two-loop conversion factors to an $\overline{\mathrm{MS}}$-like scheme and of an updated set of low-energy constants in the parametrization of the quark mass dependence. As a byproduct, for the first time, the anomalous dimensions for local three-quark operators with one derivative are obtained.

hep-lat↗
arXiv2025

$\texttt{PrecisionLauricella}$: package for numerical computation of Lauricella functions depending on a parameter

We introduce the $\texttt{PrecisionLauricella}$ package, a computational tool developed in Wolfram Mathematica for high-precision numerical evaluations of Lauricella functions with indices linearly dependent on a parameter, $\varepsilon$. The package leverages a method based on analytical continuation via Frobenius generalized power series, providing an efficient and accurate alternative to conventional approaches relying on multi-dimensional series expansions or Mellin--Barnes representations. This one-dimensional approach is particularly advantageous for high-precision calculations and facilitates further optimization through $\varepsilon$-dependent reconstruction from evaluations at specific numerical values, enabling efficient parallelization. The underlying mathematical framework for this method has been detailed in our previous work, while the current paper focuses on the design, implementation, and practical applications of the $\texttt{PrecisionLauricella}$ package.

cs.MS↗
arXiv2025

High-precision numerical evaluation of Lauricella functions

We present a method for high-precision numerical evaluations of Lauricella functions, whose indices are linearly dependent on some parameter $\varepsilon$, in terms of their Laurent series expansions at zero. This method is based on finding analytic continuations of these functions in terms of Frobenius generalized power series. Being one-dimensional, these series are much more suited for high-precision numerical evaluations than multi-dimensional sums arising in approaches to analytic continuations based on re-expansions of hypergeometric series or Mellin--Barnes integral representations. To accelerate the calculation procedure further, the $\varepsilon$ dependence of the result is reconstructed from the evaluations of given Lauricella functions at specific numerical values of $\varepsilon$, which, in addition, allows for efficient parallel implementation. The method has been implemented in the $\texttt{PrecisionLauricella}$ package, written in Wolfram Mathematica language.

hep-th↗
arXiv2020

Massive kite diagrams with elliptics

We present the results for two-loop massive kite master integrals with elliptics in terms of iterated integrals with algebraic kernels. The key ingredients are new integral representations for sunset subgraphs in $d=4-2ε$ and $d=2-2ε$ dimensions together with differential equations for considered kite master integrals in $A+Bε$ form. The obtained results can be easily generalized to all orders in $ε$-expansion and show that the class of functions defined as iterated integrals with algebraic kernels may be large enough for writing down results for a large class of massive Feynman diagrams.

hep-ph↗
arXiv2019

Two-loop diagrams in non-relativistic QCD with elliptics

In this paper we consider two-loop two-, three- and four-point diagrams with elliptic structure in the case of two different masses $m$ and $M$. The latter diagrams generally arise within NRQCD matching procedures and are relevant for parapositronium decay and top pair production at threshold. We present the obtained results in several different representations: series solution with binomial coefficients, integral representation and representation in terms of generalized hypergeometric functions. The results are valid up to $\mathcal{O}(\varepsilon)$ terms in $d=4-2\varepsilon$ space-time dimensions. In the limit of equal masses $m=M$ the obtained results are written in terms of elliptic constants with explicit series representation.

hep-ph↗
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 $M_b$.

hep-ph↗
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.

hep-ph↗
arXiv2015

Electroweak corrections to $Z$-boson hadroproduction at finite transverse momentum

We calculate the full one-loop electroweak radiative corrections, of ${\cal O}(α^2α_s)$, to the cross section of single $Z$-boson inclusive hadroproduction at finite transverse momentum ($p_T$). This includes the ${\cal O}(α)$ corrections to $Z+j$ production, the ${\cal O}(α_s)$ corrections to $Z+γ$ production, and certain QCD-electroweak interference contributions involving a single quark trace. We recover the QCD and purely weak corrections and study the QED corrections and the QCD-electroweak interference contributions for the first time. We also consider direct and resolved photoproduction in elastic and inelastic scattering. We present $p_T$ and rapidity distributions for the experimental conditions at the Fermilab Tevatron and the CERN LHC and assess the significance of the various contributions.

hep-ph↗
arXiv2009

Orthopositronium lifetime at O(alpha) and O(alpha^3 ln(alpha)) in closed form

Recently, the O(alpha) and O(alpha^3 ln(alpha)) radiative corrections to the orthopositronium lifetime have been presented in closed analytical form, in terms of basic irrational numbers that can be evaluated numerically to arbitrary precision [Phys. Rev. Lett. 101, 193401 (2008)]. Here, we present the details of this calculation and reveal the nature of these new constants. We also list explicit transformation formulas for generalized polylogarithms of weight four, which may be useful for other applications.

hep-ph↗
arXiv2009

Heavy-quark pair production in polarized photon-photon collisions at next-to-leading order: Fully integrated total cross sections

We consider the production of heavy-quark pairs in the collisions of polarized and unpolarized on-shell photons and present, in analytic form, the fully integrated total cross sections for total photon spins $J_z=0, \pm 2$ at next-to-leading-order in QCD. Phenomenological applications include $b\bar b$ production, which represents an irreducible background to standard-model intermediate-mass Higgs-boson production, as well as $t\bar t$ production.

hep-ph↗
arXiv2008

Irrational constants in positronium decays

We establish irrational constants, that contribute to the positronium lifetime at $O(α)$ and $O(α^2)$ order. In particular we show, that a new type of constants appear, which are not related to Euler--Zagier sums or multiple $ζ$ values.

hep-ph↗
arXiv2006

Strong-Coupling Constant with Flavor Thresholds at Five Loops in the MS-bar Scheme

We present in analytic form the matching conditions for the strong-coupling constant alpha_s^(n_f)(mu) at the flavor thresholds to four loops in the modified minimal-subtraction scheme. Taking into account the present knowledge on the coefficient beta_4 of the Callan-Symanzik beta function of quantum chromo-dynamics, we thus derive a five-loop formula for alpha_s^(n_f)(mu) together with appropriate relationships between the asymptotic scale parameters Lambda^(n_f) for different numbers of flavors n_f.

hep-ph↗
arXiv2003

Heavy mass expansion, light-by-light scattering and the anomalous magnetic moment of the muon

Contributions from light-by-light scattering to (g_μ-2)/2, the anomalous magnetic moment of the muon, are mediated by the exchange of charged fermions or scalar bosons. Assuming large masses M for the virtual particles and employing the technique of large mass expansion, analytical results are obtained for virtual fermions and scalars in the form of a series in (m_μ/M)^2. This series is well convergent even for the case M=m_μ. For virtual fermions, the expansion confirms published analytical formulae. For virtual scalars, the result can be used to evaluate the contribution from charged pions. In this case our result confirms already available numerical evaluations, however, it is significantly more precise.

hep-ph↗
arXiv1999

Analytical Results for Dimensionally Regularized Massless On-shell Double Boxes with Arbitrary Indices and Numerators

We present an algorithm for the analytical evaluation of dimensionally regularized massless on-shell double box Feynman diagrams with arbitrary polynomials in numerators and general integer powers of propagators. Recurrence relations following from integration by parts are solved explicitly and any given double box diagram is expressed as a linear combination of two master double boxes and a family of simpler diagrams. The first master double box corresponds to all powers of the propagators equal to one and no numerators, and the second master double box differs from the first one by the second power of the middle propagator. By use of differential relations, the second master double box is expressed through the first one up to a similar linear combination of simpler double boxes so that the analytical evaluation of the first master double box provides explicit analytical results, in terms of polylogarithms $\Li{a}{-t/s}$, up to $a=4$, and generalized polylogarithms $S_{a,b}(-t/s)$, with $a=1,2$ and $b=2$, dependent on the Mandelstam variables $s$ and $t$, for an arbitrary diagram under consideration.

hep-ph↗
arXiv1999

Two-loop QCD corrections of the massive fermion propagator

The off-shell two-loop correction to the massive quark propagator in an arbitrary covariant gauge is calculated and results for the bare and renormalized propagator are presented. The calculations were performed by means of a set of new generalized recurrence relations proposed recently by one of the authors. From the position of the pole of the renormalized propagator we obtain the relationship between the pole mass and the \bar{MS} mass. This relation confirms the known result by Gray et al.. The bare amplitudes are given for an arbitrary gauge group and for arbitrary space-time dimensions.

hep-ph↗