arXiv subjects

P. Mastrolia

Publications and source records attributed to P. Mastrolia.

47 records · Page 3Linked to original sources

arXiv2004

Two-Loop QCD Corrections to the Heavy Quark Form Factors: Axial Vector Contributions

We consider the Z Q Qbar vertex to second order in the QCD coupling for an on-shell massive quark-antiquark pair and for arbitrary momentum transfer of the Z boson. We present closed analytic expressions for the two parity-violating form factors of that vertex at the two-loop level in QCD, excluding the contributions from triangle diagrams. These form factors are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.

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arXiv2004

Two-loop QCD Corrections to the Heavy Quark Form Factors: the Vector Contributions

We present closed analytic expressions of the electromagnetic vertex form factors for heavy quarks at the two-loop level in QCD for arbitrary momentum transfer. The calculation is carried out in dimensional regularization. The electric and magnetic form factors are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.

hep-ph↗

arXiv2004

Planar box diagram for the (N_F = 1) 2-loop QED virtual corrections to Bhabha scattering

In this paper we present the master integrals necessary for the analytic calculation of the box diagrams with one electron loop (N_{F}=1) entering in the 2-loop (α^3) QED virtual corrections to the Bhabha scattering amplitude of the electron. We consider on-shell electrons and positrons of finite mass m, arbitrary squared c.m. energy s, and momentum transfer t; both UV and soft IR divergences are regulated within the continuous D-dimensional regularization scheme. After a brief overview of the method employed in the calculation, we give the results, for s and t in the Euclidean region, in terms of 1- and 2-dimensional harmonic polylogarithms, of maximum weight 3. The corresponding results in the physical region can be recovered by analytical continuation. For completeness, we also provide the analytic expression of the 1-loop scalar box diagram including the first order in (D-4).

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arXiv2004

Vertex diagrams for the QED form factors at the 2-loop level

We carry out a systematic investigation of all the 2-loop integrals occurring in the electron vertex in QED in the continuous $D$-dimensional regularization scheme, for on-shell electrons, momentum transfer $t=-Q^2$ and finite squared electron mass $m_e^2=a$. We identify all the Master Integrals (MI's) of the problem and write the differential equations in $Q^2$ which they satisfy. The equations are expanded in powers of $ε= (4-D)/2$ and solved by the Euler's method of the variation of the constants. As a result, we obtain the coefficients of the Laurent expansion in $ε$ of the MI's up to zeroth order expressed in close analytic form in terms of Harmonic Polylogarithms.

hep-ph↗

arXiv2004

The analytic value of a 4-loop sunrise graph in a particular kinematical configuration

The 4-loop sunrise graph with two massless lines, two lines of equal mass M and a line of mass m, for external invariant timelike and equal to m^2 is considered. We write differential equations in x=m/M for the Master Integrals of the problem, which we Laurent-expand in the regularizing continuous dimension d around d=4, and then solve exactly in x up to order (d-4)^3 included; the result is expressed in terms of Harmonic PolyLogarithms of argument x and maximum weight 7. As a by product, we obtain the x=1 value, expected to be relevant in QED 4-loop static quantities like the electron (g-2). The analytic results were checked by an independent precise numerical calculation

hep-ph↗

arXiv2004

Master Integrals for the 2-loop QCD virtual corrections to the Forward-Backward Asymmetry

We present the Master Integrals needed for the calculation of the two-loop QCD corrections to the forward-backward asymmetry of a quark-antiquark pair produced in electron-positron annihilation events. The abelian diagrams entering in the evaluation of the vector form factors were calculated in a previous paper. We consider here the non-abelian diagrams and the diagrams entering in the computation of the axial form factors, for arbitrary space-like momentum transfer Q^2 and finite heavy quark mass m. Both the UV and IR divergences are regularized in the continuous D-dimensional scheme. The Master Integrals are Laurent-expanded around D=4 and evaluated by the differential equation method; the coefficients of the expansions are expressed as 1-dimensional harmonic polylogarithms of maximum weight 4.

hep-ph↗

arXiv2003

QED vertex form factors at two loops

We present the closed analytic expression of the form factors of the two-loop QED vertex amplitude for on-shell electrons of finite mass $m$ and arbitrary momentum transfer $S=-Q^2$. The calculation is carried out within the continuous $D$-dimensional regularization scheme, with a single continuous parameter $D$, the dimension of the space-time, which regularizes at the same time UltraViolet (UV) and InfraRed (IR) divergences. The results are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.

hep-ph↗

arXiv2003

Two-Loop Form Factors in QED

We evaluate the on shell form factors of the electron for arbitrary momentum transfer and finite electron mass, at two loops in QED, by integrating the corresponding dispersion relations, which involve the imaginary parts known since a long time. The infrared divergences are parameterized in terms of a fictitious small photon mass. The result is expressed in terms of Harmonic Polylogarithms of maximum weight 4. The expansions for small and large momentum transfer are also given

hep-ph↗

arXiv2002

The analytic value of a 3-loop sunrise graph in a particular kinematical configuration

We consider the scalar integral associated to the 3-loop sunrise graph with a massless line, two massive lines of equal mass $M$, a fourth line of mass equal to $Mx$, and the external invariant timelike and equal to the square of the fourth mass. We write the differential equation in $x$ satisfied by the integral, expand it in the continuous dimension $d$ around $d=4$ and solve the system of the resulting chained differential equations in closed analytic form, expressing the solutions in terms of Harmonic Polylogarithms. As a byproduct, we give the limiting values of the coefficients of the $(d-4)$ expansion at $x=1$ and $x=0$.

hep-ph↗

arXiv2002

Analytic evaluation of Feynman graph integrals

We review the main steps of the differential equation approach to the analytic evaluation of Feynman graphs, showing at the same time its application to the 3-loop sunrise graph in a particular kinematical configuration.

hep-ph↗

arXiv2002

The analytic value of the sunrise self-mass with two equal masses and the external invariant equal to the third squared mass

We consider the two-loop self-mass sunrise amplitude with two equal masses $M$ and the external invariant equal to the square of the third mass $m$ in the usual $d$-continuous dimensional regularization. We write a second order differential equation for the amplitude in $x=m/M$ and show as solve it in close analytic form. As a result, all the coefficients of the Laurent expansion in $(d-4)$ of the amplitude are expressed in terms of harmonic polylogarithms of argument $x$ and increasing weight. As a by product, we give the explicit analytic expressions of the value of the amplitude at $x=1$, corresponding to the on-mass-shell sunrise amplitude in the equal mass case, up to the $(d-4)^5$ term included.

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