Ugo Aglietti

Two-loop light fermion contribution to Higgs production and decays

We compute the electroweak corrections due to the light fermions to the production cross section σ(gg ! H) and to the partial decay widths ( H ! γ γ) and ( H ! g g). We present analytic results for these corrections that are expressed in terms of Generalized Harmonic Polylogarithms. We find that for the gluon fusion production cross section and for the decay width ( H ! gg) the corrections are large in the Higgs mass region below 160 GeV where they reach up to 9% of the lowest order term. For the decay width ( H ! γγ) the corrections for Higgs mass above 160 GeV can reach 10% of the lowest order term.

Analytic results for virtual QCD corrections to Higgs production and decay

We consider the production of a Higgs boson via gluon-fusion and its decay into two photons. We compute the NLO virtual QCD corrections to these processes in a general framework in which the coupling of the Higgs boson to the external particles is mediated by a colored fermion and a colored scalar. We present compact analytic results for these two-loop corrections that are expressed in terms of Harmonic Polylogarithms. The expansion of these corrections in the low and high Higgs mass regimes, as well as the expression of the new Master Integrals which appear in the reduction of the two-loop amplitudes, are also provided. For the fermionic contribution, we provide an independent check of the results already present in the literature concerning the Higgs boson and the production and decay of a pseudoscalar particle.

Master integrals with 2 and 3 massive propagators for the 2-loop electroweak form factor - Planar case

Abstract We compute the master integrals containing 2 and 3 massive propagators entering the planar amplitudes of the 2-loop electroweak form factor. By this me mean the process f f ¯ → X , where f f ¯ is an on-shell massless fermion pair and X is a singlet under the electroweak gauge group SU ( 2 ) L × U ( 1 ) Y . This work is a continuation of our previous evaluation of master integrals containing at most 1 massive propagator. The masses of the W , Z and Higgs bosons are assumed to be degenerate. The 1 / e poles and the finite parts are computed exactly in terms of a new class of 1-dimensional harmonic polylogarithms of the variable x = − s / m 2 , with e = 2 − D / 2 , D the space–time dimension and s the center-of-mass energy squared. Since thresholds and pseudothresholds in s = ± 4 m 2 do appear in addition to the old ones in s = 0 , ± m 2 , an extension of the basis function set involving complex constants and radicals is introduced, together with a set of recursion equations to reduce integrals with semi-integer powers. It is shown that the basic properties of the harmonic polylogarithms are maintained by the generalization. We derive small-momentum expansions | s | ≪ m 2 of all the 6-denominator amplitudes. Comparison with previous results in the literature is performed finding complete agreement.

Master integrals with one massive propagator for the two-loop electroweak form factor

Abstract We compute the master integrals containing one massive propagator entering the two-loop electroweak form factor, i.e., the process f f →X , where f f is an on-shell massless fermion pair and X is a singlet particle under SU (2) L × U (1) Y , such as a virtual gluon or an hypothetical Z ′. The method used is that of the differential equation in the evolution variable x =− s / m 2 , where s is the c.m. energy squared and m is the mass of the W or Z bosons (assumed to be degenerate). The 1/ ϵ poles and the finite parts are computed exactly in terms of one-dimensional harmonic polylogarithms of the variable x , H( w → ;x) , with ϵ =2− D /2 and D the space–time dimension. We present large-momentum expansions of the master integrals, i.e., expansions for | s |⪢ m 2 , which are relevant for the study of infrared properties of the Standard Model. We also derive small-momentum expansions of the master integrals, i.e., expansions in the region | s |⪡ m 2 , related to the threshold behaviour of the form factor (soft probe). Comparison with previous results in the literature is performed finding complete agreement.

Analytic integration of real-virtual counterterms in NNLO jet cross sections. I.

We present analytic expressions of all integrals required to complete the explicit evaluation of the real-virtual integrated counterterms needed to define a recently proposed subtraction scheme for jet cross sections at next-to-next-to-leading order in QCD. We use the Mellin-Barnes representation of these integrals in 4 − 2ǫ dimensions to obtain the coefficients of their Laurent expansions around ǫ = 0. These coefficients are given by linear combinations of multidimensional Mellin-Barnes integrals. We compute the coefficients of such expansions in ǫ both numerically and analytically by complex integration over the Mellin-Barnes contours.We present analytic expressions of all integrals required to complete the explicit evaluation of the real-virtual integrated counterterms needed to define a recently proposed subtraction scheme for jet cross sections at next-to-next-to-leading order in QCD. We use the Mellin-Barnes representation of these integrals in

Master integrals for the two-loop light fermion contributions to gg→H and H→γγ

4-2\epsilon

Master integrals for the two-loop light fermion contributions to

dimensions to obtain the coefficients of their Laurent expansions around

gg \to H

\epsilon=0

and

. These coefficients are given by linear combinations of multidimensional Mellin-Barnes integrals. We compute the coefficients of such expansions in

H \to \gamma\gamma

\epsilon