arXiv subjects

Matteo Becchetti

Publications and source records attributed to Matteo Becchetti.

29 records · Page 2Linked to original sources

arXiv2021

Two-loop amplitude for mixed QCD-EW corrections to $gg \to Hg$

We report on the two-loop amplitude computation for the mixed QCD-electroweak corrections to the process $gg \to Hg$, with exact dependence on the electroweak boson masses. This amplitude has been employed in the computation of next-to-leading order (NLO) mixed QCD-electroweak corrections to the Higgs-boson production rate in arXiv:2010.09451. The master integrals that appear in the amplitude are evaluated by means of generalized power series expansions, which allows for fast and high-precision numerical evaluation of the amplitude in the physical phase-space, proving to be a powerful tool for phenomenological applications.

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arXiv2021

A differential-geometry approach to operator mixing in massless QCD-like theories and Poincaré-Dulac theorem

We review recent progress on operator mixing in the light of the theory of canonical forms for linear systems of differential equations and, in particular, of the Poincaré-Dulac theorem. We show that the matrix $A(g) = -\frac{γ(g)}{β(g)} =\frac{γ_0}{β_0}\frac{1}{g} + \cdots $ determines which different cases of operator mixing can occur, and we review their classification. We derive a sufficient condition for $A(g)$ to be set in the one-loop exact form $A(g) = \frac{γ_0}{β_0}\frac{1}{g}$. Finally, we discuss the consequences of the unitarity requirement in massless QCD-like theories, and we demonstrate that $γ_0$ is always diagonalizable if the theory is conformal invariant and unitary in its free limit at $g =0$.

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arXiv2021

Operator mixing in massless QCD-like theories and Poincare'-Dulac theorem

Recently, a geometric approach to operator mixing in massless QCD-like theories -- that involves canonical forms based on the Poincare'-Dulac theorem for the linear system that defines the renormalized mixing matrix in the coordinate representation $Z(x,μ)$ -- has been advocated in arXiv:2103.15527 . As a consequence, a classification of operator mixing in four cases -- depending on the canonical forms of $- \frac{γ(g)}{β(g)}$, with $γ(g)=γ_0 g^2+\cdots$ the matrix of the anomalous dimensions and $β(g)=-β_0 g^3 + \cdots$ the beta function -- has been proposed: (I) nonresonant $\frac{γ_0}{β_0}$ diagonalizable, (II) resonant $\frac{γ_0}{β_0}$ diagonalizable, (III) nonresonant $\frac{γ_0}{β_0}$ nondiagonalizable, (IV) resonant $\frac{γ_0}{β_0}$ nondiagonalizable. In particular, in arXiv:2103.15527 a detailed analysis of the case (I) -- where operator mixing reduces to all orders of perturbation theory to the multiplicatively renormalizable case -- has been provided. In the present paper, following the aforementioned approach, we work out in the remaining three cases the canonical forms for $- \frac{γ(g)}{β(g)}$ to all orders of perturbation theory, the corresponding UV asymptotics of $Z(x,μ)$, and the physics interpretation. We also work out in detail physical realizations of the cases (I) and (II).

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arXiv2021

Operator mixing, UV asymptotics of nonplanar/planar $2$-point correlators, and nonperturbative large-$N$ expansion of QCD-like theories

We work out the interplay between lowest-order perturbative computations in the 't Hooft coupling, $g^2=g^2_{YM} N$, operator mixing, renormalization-group (RG) improved ultraviolet (UV) asymptotics of leading-order (LO) nonplanar/planar contributions to $2$-point correlators, and nonperturbative large-$N$ expansion of perturbatively massless QCD-like theories. As concrete examples, we compute to the lowest perturbative order in $SU(N)$ YM theory the ratios, $r_i$, of LO-nonplanar to planar contributions to the $2$-point correlators in the orthogonal basis in the coordinate representation of the gauge-invariant dimension-$8$ scalar operators and all the twist-$2$ operators. We demonstrate that -- if $\frac{γ_0}{β_0}$ has no LO-nonplanar contribution, with $γ_0$ and $β_0$ the one-loop coefficients of the anomalous-dimension matrix and beta function respectively -- $r_i$ actually coincides with the corresponding ratio in the large-$N$ expansion of the RG-improved UV asymptotics of the $2$-point correlators, provided that a certain canonical nonresonant diagonal renormalization scheme exists for the corresponding operators. Contrary to the aforementioned scalar operators, for the first $10^3$ twist-$2$ operators we actually verify the above conditions, and we get the universal value $r_i=-\frac{1}{N^2}$. Hence, nonperturbatively such $r_i$ must coincide with the UV asymptotics of the ratio of the glueball self-energy loop to the glueball tree contribution to the $2$-point correlators above. As a consequence, the universality of $r_i$ reflects the universality of the effective coupling in the nonperturbative large-$N$ YM theory for the twist-$2$ operators in the coordinate representation.

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arXiv2020

NLO Corrections to Light-Quark Mixed QCD-EW Contributions to Higgs Production

We present for the first time the exact NLO QCD corrections to the light-quark part of the mixed QCD-EW contributions to Higgs production via gluon fusion at LHC13, with exact EW-boson mass dependence. The relevant two-loop real-emission matrix element is computed using a dynamic one-dimensional series expansion strategy whose stability and speed allows for a numerical phase-space integration using local IR subtraction counterterms. For $μ_R=μ_F=M_H$, we find: \begin{equation}σ^{(α_s^2α^2+α_s^3α^2)}_{g g\rightarrow H+X} = 1.467(2)^{\;+18.7\%}_{\;-14.6\%}\;(μ_R\;\text{var.})\;\pm 2\%\;(\text{PDF}) \ \textrm{pb},\end{equation} which we use to provide the best result including an estimate of suppressed contributions: \begin{equation}σ^{(\text{EW},\textrm{best})}_{p p\rightarrow H+X} = 2.11 \pm 0.28 \ (\textrm{theory}) \ \mathrm{pb}.\end{equation}

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arXiv2019

Two-loop non-planar master integrals for top-pair production in the quark-annihilation channel

We present the analytic computation of the master integrals associated to certain two-loop non-planar topologies, which are needed to complete the evaluation of the last two color coefficients for the top-pair production in the quark-annihilation channel, which are not yet known analytically. The master integrals have been computed exploiting the differential equations method in canonical form. The solution is given as a series expansion in the dimensional regularization parameter through to weight four, the expansion coefficients are given in terms of multiple polylogarithms.

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arXiv2019

Three-loop contributions to the $ρ$ parameter and iterated integrals of modular forms

We compute fully analytic results for the three-loop diagrams involving two different massive quark flavours contributing to the $ρ$ parameter in the Standard Model. We find that the results involve exactly the same class of functions that appears in the well-known sunrise and banana graphs, namely elliptic polylogarithms and iterated integrals of modular forms. Using recent developments in the understanding of these functions, we analytically continue all the iterated integrals of modular forms to all regions of the parameter space, and in each region we obtain manifestly real and fast-converging series expansions for these functions.

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arXiv2019

Master Integrals for the two-loop, non-planar QCD corrections to top-quark pair production in the quark-annihilation channel

We present the analytic calculation of the Master Integrals for the two-loop, non-planar topologies that enter the calculation of the amplitude for top-quark pair hadroproduction in the quark-annihilation channel. Using the method of differential equations, we expand the integrals in powers of the dimensional regulator $ε$ and determine the expansion coefficients in terms of generalized harmonic polylogarithms of two dimensionless variables through to weight four.

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arXiv2019

OPE and a low-energy theorem in QCD-like theories

We verify, both perturbatively and nonperturbatively asymptotically in the ultraviolet (UV), a special case of a low-energy theorem of the NSVZ type in QCD-like theories, recently derived in arXiv:1701.07833, that relates the logarithmic derivative with respect to the gauge coupling, or the logarithmic derivative with respect to the renormalization-group (RG) invariant scale, of an $n$-point correlator of local operators in one side to an $n+1$-point correlator with the insertion of $Tr F^2$ at zero momentum in the other side. Our computation involves the operator product expansion (OPE) of the scalar glueball operator, $Tr F^2$, in massless QCD, worked out perturbatively in arXiv:1209.1516 -- and in its RG-improved form in the present paper -- by means of which we extract both the perturbative divergences and the nonperturbative UV asymptotics in both sides. We also discuss the role of the contact terms in the OPE, both finite and divergent, discovered some years ago in arXiv:1209.1516, in relation to the low-energy theorem. Besides, working the other way around by assuming the low-energy theorem for any 2-point correlator of a multiplicatively renormalizable gauge-invariant operator, we compute in a massless QCD-like theory the corresponding perturbative OPE to the order of $g^2$ and nonperturbative asymptotics. The low-energy theorem has a number of applications: to the renormalization in asymptotically free QCD-like theories, both perturbatively and nonperturbatively in the large-$N$ 't Hooft and Veneziano expansions, and to the way the open/closed string duality may or may not be realized in the would-be solution by canonical string theories for QCD-like theories, both perturbatively and in the 't Hooft large-$N$ expansion. Our computations will also enter further developments based on the low-energy theorem.

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arXiv2018

Planar master integrals for the two-loop light-fermion electroweak corrections to Higgs plus jet production

We present the analytic calculation of the planar master integrals which contribute to compute the two-loop light-fermion electroweak corrections to the production of a Higgs boson in association with a jet in gluon-gluon fusion. The complete dependence on the electroweak-boson mass is retained. The master integrals are evaluated by means of the differential equations method and the analytic results are expressed in terms of multiple polylogarithms up to weight four.

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arXiv2017

Two-Loop Master Integrals for the Planar QCD Massive Corrections to Di-photon and Di-jet Hadro-production

We present the analytic calculation of the Master Integrals necessary to compute the planar massive QCD corrections to Di-photon (and Di-jet) production at hadron colliders. The masters are evaluated by means of the differential equations method and expressed in terms of multiple polylogarithms and one- or two-fold integrals of polylogarithms and irrational functions, up to transcendentality four.

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