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Register a new userTwo-loop divergences of scattering amplitudes with massive partons
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We complete the study of two-loop infrared singularities of scattering amplitudes with an arbitrary number of massive and massless partons in non-abelian gauge theories. To this end, we calculate the universal functions F_1 and f_2, which completely specify the structure of three-parton correlations in the soft anomalous-dimension matrix, at two-loop order in closed analytic form. Both functions are found to be suppressed like O(m^4/s^2) in the limit of small parton masses, in accordance with mass factorization theorems proposed in the literature. On the other hand, they are unsuppressed and diverge logarithmically near the threshold for pair production of two heavy particles. As an application, we calculate the two-loop anomalous-dimension matrix for q q_bar --> t t_bar near threshold and show that it is not diagonal in the s-channel singlet-octet basis.
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The infrared divergences of QCD scattering amplitudes can be derived from an anomalous dimension Gamma, which is a matrix in color space and depends on the momenta and masses of the external partons. It has recently been shown that in cases where there are at least two massive partons involved in the scattering process, starting at two-loop order Gamma receives contributions involving color and momentum correlations between three (and more) partons. The three-parton correlations can be described by two universal functions F_1 and f_2. In this paper these functions are calculated at two-loop order in closed analytic form and their properties are studied in detail. Both functions are found to be suppressed like O(m^4/s^2) in the limit of small parton masses, in accordance with mass factorization theorems proposed in the literature. On the other hand, both functions are O(1) and even diverge logarithmically near the threshold for pair production of two heavy particles. As an application, we calculate the infrared poles in the q qbar --> t tbar and g g --> t tbar scattering amplitudes at two-loop order.
We present complete analytical ${mathcal O}(epsilon^2)$ results on the one-loop amplitudes relevant for the NNLO quark-parton model description of the hadroproduction of heavy quarks as given by the so-called loop-by-loop contributions. All results of the perturbative calculation are given in the dimensional regularization scheme. These one-loop amplitudes can also be used as input in the determination of the corresponding NNLO cross sections for heavy flavor photoproduction, and in photon-photon reactions.
We present the analytic form of the two-loop four-graviton scattering amplitudes in Einstein gravity. To remove ultraviolet divergences we include counterterms quadratic and cubic in the Riemann curvature tensor. The two-loop numerical unitarity approach is used to deal with the challenging momentum dependence of the interactions. We exploit the algebraic properties of the integrand of the amplitude in order to map it to a minimal basis of Feynman integrals. Analytic expressions are obtained from numerical evaluations of the amplitude. Finally, we show that four-graviton scattering observables depend on fewer couplings than naively expected.
We evaluate the two-loop corrections to Bhabha scattering from fermion loops in the context of pure Quantum Electrodynamics. The differential cross section is expressed by a small number of Master Integrals with exact dependence on the fermion masses me, mf and the Mandelstam invariants s,t,u. We determine the limit of fixed scattering angle and high energy, assuming the hierarchy of scales me^2 << mf^2 << s,t,u. The numerical result is combined with the available non-fermionic contributions. As a by-product, we provide an independent check of the known electron-loop contributions.
We study the asymptotic behaviour of two-loop electroweak corrections at energies Q >> M_W, where logarithms of the type ln(Q/M_W) become dominant. The calculation of the leading and next-to-leading logarithmic terms for massless and massive fermion-scattering processes is summarized. The derivations are performed diagrammatically within the spontaneously broken electroweak theory. We find that the soft and collinear singularities resulting from photons can be factorized into a QED-like term and that, up to logarithms of the Z-W mass ratio, the effects of symmetry breaking cancel. This result supports resummation prescriptions that are based on a symmetric SU(2)xU(1) theory matched with QED at the electroweak scale.
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