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Vladyslav Shtabovenko

Publications and source records attributed to Vladyslav Shtabovenko.

At least 19 recordsLinked to original sources
arXiv2026

FeynCalc 10.2 and FeynHelpers 2: Multiloop calculations streamlined

We present new versions of the Mathematica package FeynCalc and the FeynHelpers add-on that represent an important contribution to the collection of public codes for semi-automatic evaluation of multiloop Feynman diagrams. FeynHelpers enables interfacing between FeynCalc and selected programs routinely used in multiloop calculations such as QGRAF, FIRE, KIRA, FIESTA or pySecDec. In addition to that FeynCalc now supports parallelizing the execution of selected routines on multicore CPUs and can handle tensor integrals with zero Gram determinants where the traditional tensor reduction breaks down.

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arXiv2026

$B_c \to η_c$ form factors at large recoil: SCET analysis and a three-loop consistency check

The double-logarithmic series of non-relativistic $B_c \to η_c$ form factors at large recoil is governed by a coupled set of integral equations, reflecting an intricate interplay between arbitrarily many soft-quark and soft-gluon exchanges. Whereas we previously derived these integral equations with diagrammatic resummation techniques, we analyze the form factors in the limit $m_b \gg m_c \gg Λ_{\rm QCD}$ with methods from Soft-Collinear Effective Theory (SCET) in this work. Although the resulting factorization theorem for the so-called soft-overlap contribution is known to be spoilt by endpoint divergences, it can still be used at the level of bare (regularized) quantities at any fixed order in perturbation theory. By calculating the required ingredients, we show that the SCET analysis confirms the predictions of the integral equations up to three-loop order. We also argue that the iterative structure and the intertwined soft-quark and soft-gluon effects can be derived from standard renormalization-group equations of the $B_c$-meson light-cone distribution amplitudes, provided their inverse moments are regularized with an appropriate cutoff.

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arXiv2025

Complete next-to-next-to-leading order QCD corrections to the decay matrix in $\boldsymbol{B}$-meson mixing at leading power

We compute next-to-next-to-leading order corrections to the decay width difference of mass eigenstates and the charge-parity (CP) asymmetry $a_{\rm fs}$ in flavour-specific decays of neutral $B$ mesons. We include both current-current and penguin operators at three-loop order. All input integrals in the transition amplitude are reduced to a small set of master integrals which depend on the ratio of the charm and bottom quark masses. The latter are computed using semi-analytic methods which provide deep expansions around properly selected values of $m_c/m_b$. We provide numerical results for $ΔΓ$ and $ΔΓ/ΔM$, both for the $B_d$ and $B_s$ system, including a detailed uncertainty analysis. Using the experimental value for the mass difference $ΔM_s$ we predict $ΔΓ_s=(0.078 \pm 0.015) ~\mbox{ps}^{-1}$. For the CP asymmetries we find $ a_{\rm fs}^s = (2.27 \pm 0.13 ) \times 10^{-5}$ and $a_{\rm fs}^d = -(5.19 \pm 0.30)~\times~10^{-4}$. Furthermore, we show that the ratios $(ΔΓ_s/ΔM_s) / (ΔΓ_d/ΔM_d)$ and $ΔΓ_d / ΔΓ_s$ can be predicted with high precision. The former quantity permits the prediction $ΔΓ_d=(0.00215\pm 0.00013)~\mbox{ps}^{-1}$ from the measurements of $ΔM_{d,s}$ and $ΔΓ_s$. We further discuss the impact of $ΔΓ_d/ΔΓ_s$ on the CKM unitarity triangle and present ready-to-use formulae which permit improved predictions once updated results for the operator matrix elements are available.

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arXiv2025

$B_c \to η_c$ form factors at large recoil: Interplay of soft-quark and soft-gluon dynamics

We perform an all-order analysis of double-logarithmic corrections to the so-called soft-overlap contribution to heavy-to-light transition form factors at large hadronic recoil. Specifically, we study $B_c \to η_c$ transitions within a perturbative non-relativistic framework, treating both the bottom and charm quarks as heavy with the hierarchy $m_b \gg m_c \ggΛ_{\rm QCD}$. Our diagrammatic analysis shows that double-logarithmic corrections arise from two distinct sources: Exponentiated soft-gluon effects described by standard Sudakov factors, and rapidity-ordered soft-quark configurations, leading to implicit integral equations, which so far have only been studied in the context of energetic muon-electron backward scattering. We find that the all-order structure of the double logarithms is governed by a novel type of coupled integral equations, which encode the non-trivial interplay between these two effects. Whereas a closed-form solution to these equations is currently unknown, we present useful iteration formulas, and derive the asymptotic behaviour of the soft-overlap form factor for infinitely large recoil energies, showing that the Sudakov suppression is somewhat weakened by the intertwined soft-quark and soft-gluon corrections. In a broader context, our findings shed light onto the physical origin and mathematical structure of endpoint divergences arising from soft-collinear factorization and the related Feynman mechanism for power-suppressed hard exclusive processes.

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arXiv2025

Current-current operator contribution to the decay matrix in $B$-meson mixing at next-to-next-to-leading order of QCD

We compute next-to-next-to-leading order perturbative corrections to the decay width difference of mass eigenstates and the charge-parity asymmetry $a_{\rm fs}$ in flavour-specific decays of neutral $B$ mesons. In our calculation we take into account the full dependence on the charm and bottom quark masses for the current-current operator contributions up to three-loop order. Special emphasis is put on the proper construction of the so-called $|ΔB|=2$ theory such that Fierz symmetry is preserved. We provide updated phenomenological predictions, for $ΔΓ$, $ΔΓ/ΔM$ and $a_{\rm fs}$ for the $B_d$ and $B_s$ system, including a detailed analysis of the uncertainties of our predictions. The calculated NNLO correction reduce the perturbative uncertainty of the leading term of the $1/m_b$ expansion of the width difference $\dg_s$ in the $B_s$ system to the level of the current experimental error. The uncertainty of our prediction $\dg_s=({0.077}\pm 0.016)\,\mbox{ps}^{-1}$ is dominated by the sub-leading term of this expansion. We further illustrate how better future measurements of $\dg_d$ and $a_{\rm fs}^d$ will help to gain a better understanding of $B_d$-$\bar B_d$ mixing.

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arXiv2024

FeynCalc 10: Do multiloop integrals dream of computer codes?

In this work we report on a new version of FeynCalc, a Mathematica package widely used in the particle physics community for manipulating quantum field theoretical expressions and calculating Feynman diagrams. Highlights of the new version include greatly improved capabilities for doing multiloop calculations, including topology identification and minimization, optimized tensor reduction, rewriting of scalar products in terms of inverse denominators, detection of equivalent or scaleless loop integrals, derivation of Symanzik polynomials, Feynman parametric as well as graph representation for master integrals and initial support for handling differential equations and iterated integrals. In addition to that, the new release also features completely rewritten routines for color algebra simplifications, inclusion of symmetry relations between arguments of Passarino--Veltman functions, tools for determining matching coefficients and quantifying the agreement between numerical results, improved export to LaTeX and first steps towards a better support of calculations involving light-cone vectors.

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arXiv2024

New multiloop capabilities of FeynCalc 10

We briefly introduce new multiloop capabilities of the Mathematica package FeynCalc 10 and a collection of interfaces connecting FeynCalc to such popular tools as QGRAF, Fiesta, pySecDec, LoopTools, KIRA, FIRE or Fermat. In addition to that, we showcase the application of these codes to the ongoing study of the soft-overlap contribution to $B_c \to η_c$ transition form factors at large hadronic recoil.

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arXiv2024

$B$ meson mixing at NNLO: technical aspects

We provide details to several technical aspects which are important for the calculation of next-to-next-to-leading order corrections to the mixing of neutral $B$ mesons. This includes the computation of the master integrals for finite charm and bottom quark masses, traces over products of up to 22 $γ$ matrices and tensor integrals with up to rank 11.

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arXiv2024

NNLO QCD corrections to $ΔΓ_s$ in the $B_s-\overline{B}_s$ system

This report summarises recent advances made in the calculation of the NNLO QCD corrections to the width difference $ΔΓ_s$ in the $B_s-\overline{B}_s$ system. The inclusion of the effects due to current-current operators leads to an updated prediction of $ΔΓ_s = (0.076\pm 0.017)\,\text{ps}^{-1}$, which narrows the gap between theory and experiment.

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arXiv2023

Soft-overlap contribution to $B_c \to η_c$ form factors: diagrammatic resummation of double logarithms

Using diagrammatic resummation techniques, we investigate the double-logarithmic series of the "soft-overlap" contribution to $B_c \to η_c$ transition form factors at large hadronic recoil, assuming the scale hierarchy $m_b \gg m_c \gg Λ_{\rm QCD}$. In this case, the hadronic bound states can be treated in the non-relativistic approximation and the relevant hadronic matrix elements can be computed perturbatively. This setup defines one of the simplest examples to study the problem of endpoint singularities appearing in the factorization of exclusive $B$-decay amplitudes. We find that the leading double logarithms arise from a peculiar interplay of soft-quark "endpoint logarithms" from ladder diagrams with energy-ordered spectator-quark propagators, as well as standard Sudakov-type soft-gluon corrections. We elucidate the all-order systematics, and show that their resummation proceeds via a novel type of integral equations. The current status of the calculation, which includes all double logarithms in the Abelian limit, is reported.

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arXiv2022

The width difference in the $B-\bar{B}$ system at next-to-next-to-leading order of QCD

We extend the theoretical prediction for the width difference $ΔΓ_q$ in the mixing of neutral $B$ mesons in the Standard Model to next-to-next-to-leading order in $α_s$. To this aim we calculate three-loop diagrams with two $|ΔB|=1$ current-current operators analytically. In the matching between $|ΔB|=1$ and $|ΔB|=2$ effective theories we regularize the infrared divergences dimensionally and take into account all relevant evanescent operators. Further elements of the calculation are the two-loop renormalization matrix $Z_{ij}$ for the $|ΔB|=2$ operators and the $\mathcal{O}(α_s^2)$ corrections to the finite renormalization that ensures the $1/m_b$ suppression of the operator $R_0$ at two-loop order. Our theoretical prediction reads $ΔΓ_s/ΔM_s = {(4.33\pm 0.93)\cdot 10^{-3}}$ if expressed in terms of the bottom mass in the $\overline{\rm MS}$ scheme and $ΔΓ_s/ΔM_s = {(4.20\pm 0.95)\cdot 10^{-3}}$ for the use of the potential-subtracted mass. While the controversy on $|V_{cb}|$ affects both $ΔΓ_s$ and $ΔM_s$, the ratio $ΔΓ_s/ΔM_s$ is not affected by the uncertainty in $|V_{cb}|$ .

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arXiv2022

Bound-state formation, dissociation and decays of darkonium with potential non-relativistic Yukawa theory for scalar and pseudoscalar mediators

Dark matter models with light mediators featuring sizable interactions among dark particles enjoy an increasing attention in the model building community due to the elegance with which they can potentially explain the scaling relations governing galactic halos and clusters of galaxies. In the present work we continue our study of such models using non-relativistic and potential non-relativistic effective field theories (NREFTs and pNREFTs) and explore the properties of a Yukawa-type model with scalar and pseudoscalar interactions between a low-energetic scalar mediator and heavy dark matter fermions. In particular, we make first steps towards the formulation of such theories at finite temperature by providing the thermal bound-state formation rate and the thermal break-up of bound states from the self-energies of the dark-pair fields, that interact with the thermal environment. We estimate numerically bound-state effects on the dark matter energy density, that provide up to a $35\%$ correction depending on the relative size of the model couplings.

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arXiv2022

The width difference in \bbm\ at order $α_s$ and beyond

We complete the calculation of the element $Γ_{12}^q$ of the decay matrix in $B_q-\bar{B}_q$ mixing, $q=d,s$, to order $α_s$ in the leading power of the Heavy Quark Expansion. To this end we compute one- and two-loop contributions involving two four-quark penguin operators. Furthermore, we present two-loop QCD corrections involving a chromomagnetic operator and either a current-current or four-quark penguin operator. Such contributions are of order $α_s^2$, i.e. next-to-next-to-leading-order. We also present one-loop and two-loop results involving two chromomagnetic operators which are formally of next-to-next-to-leading and next-to-next-to-next-to-leading-order, respectively. With our new corrections we obtain the Standard-Model prediction $ΔΓ_s/ΔM_s= (5.20\pm 0.69)\cdot 10^{-3}$ if $Γ_{12}^s$ is expressed in terms of the $\overline{\rm MS}$ b-quark mass, while we find $ΔΓ_s/ΔM_s= (4.70\pm 0.96)\cdot 10^{-3}$ instead for the use of the pole mass.

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arXiv2021

FeynCalc goes multiloop

We report on the new functionality of the open-source Mathematica package FeynCalc relevant for multiloop calculations. In particular, we focus on such tasks as topology identification by means of the Pak algorithm, search for equivalent master integrals and their graph representations as well as automatic derivations of Feynman parametric representations for a wide class of multiloop integrals. The functions described in this report are expected to be finalized with the official release of FeynCalc 10. The current development snapshot of the package including the documentation is publicly available on the project homepage. User feedback is highly encouraged.

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arXiv2021

NNLO QCD corrections to $B$-meson mixing

We report on the calculation of next-to-next-to-leading order (NNLO) QCD corrections to the width difference $ΔΓ_s$ in the neutral $B$-meson mixing process $B^0_s - \bar{B}^0_s$. These contributions represent an important step in the task of reducing the existing large perturbative errors in the theory prediction for $ΔΓ_s$ and approaching the current experimental uncertainties. We explain the theoretical framework employed in this computation and point out important subtleties in the treatment of evanescent operators and the renormalization. Part of our new results is already available in the literature, while the remaining pieces are expected to be published later this year.

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arXiv2021

Towards two- and three-loop QCD corrections to the width difference in $B_s-\bar{B}_s$ mixing

In this work we address the issue of large perturbative uncertainties in the theory prediction for $ΔΓ_s$, the width difference in the $B^0_s - \bar{B}^0_s$ mixing process. To this aim we complete important steps towards the full analytic result for the previously unknown Wilson coefficients from the matching between $|ΔB|=1$ and $|ΔB|=2$ effective Hamiltonians at next-to-next-leading order (NNLO) in the strong coupling constant. We provide a thorough discussion of technical and conceptual difficulties behind this computation and give an outlook regarding the availability of the new NNLO theory prediction for $ΔΓ_s$.

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