J. Gluza

Quest for precision in hadronic cross sections at low energy: Monte Carlo tools vs. experimental data

We present the achievements of the last years of the experimental and theoretical groups working on hadronic cross section measurements at the low-energy e+e− colliders in Beijing, Frascati, Ithaca, Novosibirsk, Stanford and Tsukuba and on τ decays. We sketch the prospects in these fields for the years to come. We emphasise the status and the precision of the Monte Carlo generators used to analyse the hadronic cross section measurements obtained as well with energy scans as with radiative return, to determine luminosities and τ decays. The radiative corrections fully or approximately implemented in the various codes and the contribution of the vacuum polarisation are discussed.

AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals

Abstract The Mathematica toolkit AMBRE derives Mellin–Barnes (MB) representations for Feynman integrals in d = 4 − 2 e dimensions. It may be applied for tadpoles as well as for multi-leg multi-loop scalar and tensor integrals. The package uses a loop-by-loop approach and aims at lowest dimensions of the final MB representations. The present version works fine for planar Feynman diagrams. The output may be further processed by the package MB for the determination of its singularity structure in e. The AMBRE package contains various sample applications for Feynman integrals with up to six external particles and up to four loops. Program summary Program title:AMBRE Catalogue identifier:ADZR_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADZR_v1_0.html Program obtainable from:CPC Program Library, Queens University, Belfast, N. Ireland Licensing provisions:standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.:21 387 No. of bytes in distributed program, including test data, etc.:100 004 Distribution format:tar.gz Programming language:MATHEMATICA v.5.0 and later versions Computer:all Operating system:all RAM:sufficient for a typical installation of MATHEMATICA Classification:5; 11.1 External routines:The examples in the package use: – MB.m [M. Czakon, Comput. Phys. Commun. 175 (2006) 559 (CPC Cat. Id. ADYG)], for expansions in e; – CUBA [T. Hahn, Comput. Phys. Commun. 168 (2005) 78 (CPC Cat. Id. ADVH)], for numerical evaluation of multidimensional integrals; – CERNlib [CERN Program Library, http://cernlib.web.cern.ch/cernlib/ ], for the implementation of Γ and Ψ functions in Fortran. Nature of problem:Derivation of a representation for a Feynman diagram with L loops and N internal lines in d dimensions by Mellin–Barnes integrals; the subsequent evaluation, after an analytical continuation in e = ( 4 − d ) / 2 , has to be done with other packages. Solution method:Introduction of N Feynman parameters x i , integration over the loop momenta, and subsequent integration over x, introducing thereby representations of sums of monomials in x by Mellin–Barnes integrals. Restrictions:Limited by the size of the available storage space. Running time:Depending on the problem; usually seconds.

Master integrals for massive two-loop Bhabha scattering in QED

We present a set of scalar master integrals (MIs) needed for a complete treatment of massive two-loop corrections to Bhabha scattering in QED, including integrals with arbitrary fermionic loops. The status of analytical solutions for the MIs is reviewed and examples of some methods to solve MIs analytically are worked out in more detail. Analytical results for the pole terms in {epsilon} of so far unknown box MIs with five internal lines are given.

Towards a basis for planar two-loop integrals

The existence of a finite basis of algebraically independent one-loop integrals has underpinned important developments in the computation of one-loop amplitudes in field theories and gauge theories, in particular. We give an explicit construction reducing integrals with massless propagators to a finite basis for planar integrals at two loops, both to all orders in the dimensional regulator {epsilon}, and also when all integrals are truncated to O({epsilon}). We show how to reorganize integration-by-parts equations to obtain elements of the first basis efficiently, and how to use Gram determinants to obtain additional linear relations reducing this all-orders basis to the second one. The techniques we present should apply to nonplanar integrals, to integrals with massive propagators, and beyond two loops as well.

Heavy neutrinos and the pp→lljj CMS data

Abstract We show that the excess in the p p → e e j j CMS data can be naturally interpreted within the Minimal Left–Right Symmetric model (MLRSM), keeping g L = g R , if CP phases and non-degenerate masses of heavy neutrinos are taken into account. As an additional benefit, a natural interpretation of the reported ratio ( 14 : 1 ) of the opposite-sign (OS) p p → l ± l ∓ j j to the same-sign (SS) p p → l ± l ± j j lepton signals is possible. Finally, a suppression of muon pairs with respect to electron pairs in the p p → l l j j data is obtained, in accordance with experimental data. If the excess in the CMS data survives in the future, it would be a first clear hint towards presence of heavy neutrinos in right-handed charged currents with specific CP phases, mixing angles and masses, which will have far reaching consequences for particle physics directions.

Numerical evaluation of tensor Feynman integrals in Euclidean kinematics

For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently ‘simple’ numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4−2ε dimensions. One method uses Mellin–Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A.V. Smirnov and V.A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop ε-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sector_decomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin–Barnes representations and sector decompositions, is compared. The computational packages are publicly available.

The planar four-point master integrals for massive two-loop Bhabha scattering

Abstract We present the values of the complete set of planar four-point Master Integrals needed for massive Bhabha scattering in the limit of fixed angle and high energy at the two-loop level. The integrals have been calculated using direct expansions of Mellin–Barnes representations, followed by a resummation of resulting harmonic series.

Two-loop fermionic corrections to massive Bhabha scattering

Abstract 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 m e , m f and the Mandelstam invariants s , t , u . We determine the limit of fixed scattering angle and high energy, assuming the hierarchy of scales m e 2 ≪ m f 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.

Matter effects and CP violating neutrino oscillations with nondecoupling heavy neutrinos

The evolution equation for active and sterile neutrinos propagating in a general anisotropic or polarized background environment is found and solved for a special case when heavy neutrinos do not decouple, resulting in nonunitary mixing among light neutrino states. Then new

Complete reduction of one-loop tensor 5- and 6-point integrals

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