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@PHDTHESIS{Saragnese:481508,
      author       = {Saragnese, Marco},
      othercontributors = {Blümlein, Johannes and Moch, Sven-Olaf},
      title        = {{M}assive 2- and 3-loop corrections to hard scattering
                      processes in {QCD}},
      school       = {Universität Hamburg},
      type         = {Dissertation},
      address      = {Hamburg},
      publisher    = {Verlag Deutsches Elektronen-Synchrotron DESY},
      reportid     = {PUBDB-2022-04411, DESY-THESIS-2022-016},
      series       = {DESY-THESIS},
      pages        = {258},
      year         = {2022},
      note         = {Dissertation, Universität Hamburg, 2022},
      abstract     = {This thesis deals with calculations of higher-order
                      corrections in perturbative quantum chromodynamics(QCD). The
                      two-mass contributions to the 3-loop, polarized twist-two
                      operator matrixelements (OMEs) A(3),PSQq and A(3)gg,Q are
                      calculated. The N-space result for A(3)gg,Q is obtained
                      analyticallyas a function of the quark mass ratio, which for
                      A(3),PSQq is not yet possible. In thez-space representation,
                      one obtains for both matrix elements semi-analytical
                      representations interms of iterated integrals, whereby for
                      reasons of efficiency an additional integral is necessaryfor
                      some terms.These universal (process-independent) massive
                      OMEs govern the asymptotic behaviour ofthe Wilson
                      coefficients in deep-inelastic scattering at large
                      virtualities Q2 ≫ m2c,b, with mc,bthe charm and bottom
                      quark masses. These corrections are also required to define
                      the variableflavour number scheme. This scheme describes the
                      transition from massive quark corrections tothe massless
                      ones for very high momentum scales, which is relevant to the
                      description of colliderdata.In the single-mass, polarized
                      case, we derive the logarithmic corrections for the Wilson
                      coefficientsof the structure function g1 in the asymptotic
                      region Q2 ≫ m2c,b. This is done using theknown OMEs and
                      massless Wilson coefficients, using the renormalization
                      group equations.For the non-singlet structure functions FNS2
                      and gNS1 we revisit the scheme-invariant evolutionoperator
                      known for massless quarks and extend it to the massive case
                      with single- and two-masscorrections. In this case, the
                      evolution can effectively be described up to O(a3s) in the
                      Wilsoncoefficients, where as = αs/(4π) denotes the strong
                      coupling constant. The influence of thehitherto not fully
                      known 4-loop non-singlet anomalous dimension can be
                      described effectively.It turns out that the effect of the
                      theory error in question can be completely controlled.
                      Arepresentation by a Pad´e approximant proves to be
                      sufficient.We consider the class of functions of
                      multivariate hypergeometric series and study systemsof
                      differential equations obeyed by them. We describe an
                      algorithmic method to solve someclasses of such differential
                      systems which delivers a hypergeometric series solution
                      having nestedhypergeometric products as summand; we discuss
                      the relationship between these products andPochhammer
                      symbols. For a number of classical hypergeometric series we
                      derive differentialsystems and their associated difference
                      equations. We present some examples of series expansionsof
                      such functions and of the mathematical objects which arise
                      therein. We also present aMathematica package which
                      implements algorithms related to the solution of partial
                      linear differenceequations, focusing in particular on
                      bounding the degree of the denominator of solutionswhich are
                      rational functions. These methods are of particular
                      importance when solving multi-legcalculations for Feynman
                      diagrams, but also come into play when hypergeometric
                      methods formulti-loop integrals are used.We describe a
                      numerical implementation of an N-space library for the
                      calculation of scalingviolations for structure functions,
                      which can perform the evolution of parton
                      distributionfunctions up to NNLO from a parametrization
                      chosen by the user, and encodes massless andmassive Wilson
                      coefficients for the structure functions F2 and g1 in the
                      case of photon exchange,and for the structure functions
                      FW+±W−3 in the case of charged-current exchange. The
                      librarycontains analytic continuation of the relevant
                      harmonic sums in Mellin-space up to weight 5 andmany
                      weight-6 harmonic sums. The numerical representation in x
                      space is performed by contourintegration around the
                      singularities of the solution of the evolution equations in
                      N space.},
      cin          = {$Z_ZPPT$},
      cid          = {$I:(DE-H253)Z_ZPPT-20210408$},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611) / SAGEX -
                      Scattering Amplitudes: from Geometry to Experiment (764850)},
      pid          = {G:(DE-HGF)POF4-611 / G:(EU-Grant)764850},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)3 / PUB:(DE-HGF)11},
      doi          = {10.3204/PUBDB-2022-04411},
      url          = {https://bib-pubdb1.desy.de/record/481508},
}