We perform a manifestly gauge-independent analysis of the vacuum stability in standard model 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 neglected. turn apply criterion nullifying Higgs self-coupling its beta function modified minimal-subtraction scheme recently proposed consistent method for determining true minimum effective potential also avoids gauge...

We present the results for three-loop beta-functions Yukawa couplings of heavy Standard Model fermions calculated within unbroken phase model. The calculation is carried out with help MINCER program in a general linear gauge, and final result independent gauge-fixing parameters. In order to calculate three-point functions, we made use infrared rearrangement (IRR) trick. Due chiral structure SM careful treatment loops required perform calculation. It turns that gauge anomaly cancellation...

We study the relationships between basic parameters of on-shell renormalization scheme and their counterparts in $\overline{\mathrm{MS}}$ at full order ${\cal O}(\alpha^2)$ Standard Model. These enter as threshold corrections group analyses underlying, e.g., investigation vacuum stability. To ensure gauge invariance parameters, particular masses, we work $R_\xi$ systematically include tadpole contributions. also consider gaugeless-limit approximation compare it with two-loop electroweak calculation.

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

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

A bstract We consider general renormalizable scalar field theory and derive six-loop beta functions for all parameters in d = 4 dimensions within the $$ \overline{\mathrm{MS}} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>MS</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> -scheme. do not explicitly compute relevant loop integrals but utilize O( n )-symmetric model counter-terms available literature. dimensionless couplings with a mass scale, ranging from...

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

We present five-loop results for the renormalization of various models with a cubic interaction (in ${d = 6 - 2 \varepsilon}$ dimensions). For scalar model and its ${O(n)}$-symmetric extension we provide constants, anomalous dimensions critical exponents. discuss in detail method calculation, all counterterms up to five loops. This allows one consider generalizations ${\varphi^3}$ theory other symmetries.

We present the beta functions of gauge and Yukawa couplings in general four-dimensional quantum field theory, at four three loops, respectively. The essence our approach is fixing unknown coefficients most ansatz for beta-functions by direct calculation several simplified models. apply results to Standard Model its extension with an arbitrary number Higgs doublets provide expressions all four-loop matrix interactions.

We consider electroweak corrections to the relation between running $\overline{\mathrm{MS}}$ mass $m_b$ of $b$ quark in five-flavor QCD$\times$QED effective theory and its counterpart Standard Model (SM). As a bridge two parameters, we use pole $M_b$ quark, which can be calculated both models. The is not fundamental parameter SM Lagrangian, but product Yukawa coupling $y_b$ Higgs vacuum expectation value. Since there exist different prescriptions define latter, relations considered paper...

We consider the Sudakov form factor in planar N=4 supersymmetric Yang-Mills theory off shell kinematical regime, which can be achieved by considering on its Coulomb branch. demonstrate that for up to three loops both infrared-divergent as well finite terms do exponentiate, with coefficient accompanying log^{2}(m^{2}) determined octagon anomalous dimension Γ_{oct}. This behavior is stark contrast previous conjectural accounts literature. Together we observe logarithm of identical twice null...

We evaluate the three-loop massive vacuum bubble diagrams in terms of polylogarithms up to weight six. also construct basis irrational constants being harmonic polylgarithms arguments $e^{k i π/3}$.

A bstract Among the unitarity cuts of 4-loop massless propagators two kinds are currently fully known: 2-particle with 3 loops corresponding to form-factors, and 5-particle phase-space integrals. In this paper we calculate master integrals for remaining ones: 3-particle 2 loops, 4-particle 1 loop. The calculated by solving dimensional recurrence relations. integrated directly using → amplitudes which also re-derive here up transcendentality weight 7. results verified both numerically,...

We use dimensional recurrence relations and analyticity to calculate four-loop propagator-type master integrals in the heavy-quark effective theory. Compared previous applications of DRA method, we apply a new technique fixing homogeneous solutions from pole parts evaluated different rational space-time dimension points. The latter were calculated integration-by-parts reduction finite shifted and/or with increased propagators powers. provide results for epsilon expansions near $d = 4$ 3$...

We present an analytic calculation of the one-loop correction to double-real emission contribution zero-jettiness soft function at N3LO in QCD, accounting for both gluon-gluon and quark-antiquark final-state partons. explain all relevant steps computation including reduction phase-space integrals master presence Heaviside functions, methods we employed compute them.

A bstract We present an analytic calculation of the one-loop correction to double-real emission contribution zero-jettiness soft function at N3LO in QCD, accounting for both gluon-gluon and quark-antiquark final-state partons. explain all relevant steps computation including reduction phase-space integrals master presence Heaviside functions, methods we employed compute them.

The LHC data on the forward heavy-flavour hadron production can be a new unique source for estimation of intrinsic charm and bottom contributions to proton. For example, we analyze heavy-baryon production, namely Λb-baryon, within soft QCD quark gluon string model present predictions observables which could measured at LHC. We also some D-meson in pp collisions made perturbative including proton that verified

We analytically compute the three-loop corrections to relation between renormalized quark masses defined in minimal-subtraction ($\overline{\mathrm{MS}}$) and regularization-invariant symmetric momentum-subtraction (RI/SMOM) schemes. Our result is valid Landau gauge can be used reduce uncertainty a lattice determination of $\overline{\mathrm{MS}}$ masses.

A technique of large-charge expansion provides a novel opportunity for calculation critical dimensions operators $\phi^Q$ with fixed charge $Q$. In the small-coupling regime polynomial structure anomalous can be from number direct perturbative calculations At six-loop level one needs to include new diagrams that correspond five or more legs. The latter never appeared before in scalar-theory calculations. Here we show how compute dimension operator $\phi^{Q=5}$ at order. combination results...

A bstract We calculate the small angle expansion of four-loop QCD cusp anomalous dimension. As a byproduct our calculation, we also obtain dimension heavy-quark field in HQET. The validity calculational setup is cross-checked by independent calculation beta-function from heavy-quark-gluon vertex renormalization check obtained results for and against available analytical numerical results. Finally, find that maximal transcendentality contribution to Bremsstrahlung function coincides, up...

We present analytical expressions for the 31 five-particle phase-space master integrals in massless QCD as an $\epsilon$-series with coefficients being multiple zeta values of weight up to 12. In addition, we provide computer code Monte-Carlo integration higher dimensions, based on RAMBO algorithm, that has been used numerically cross-check obtained results 4, 6, and 8 dimensions.

For the first time, we compute three-loop contributions to all triple vertices in QCD at symmetric point. The analytic results are obtained massless with an arbitrary color group Landau gauge. All new loop integrals expressed terms of harmonic polylogarithms sixth root unity. These corrections allow us derive expressions for four-loop beta function a set momentum-subtraction schemes.