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Title: Two-reggeon exchange to all loop orders
Author: Reichel, Joscha
ISNI:       0000 0004 7969 4497
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2019
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In the limit of very large centre-of-mass energy s the two-parton scattering amplitude is well approximated by the exchange of reggeons in the t channel. In particular, the leading contributions to the signature-even two-reggeon exchange are described by the famous Balitsky-Fadeev-Kuraev-Lipatov (BFKL) evolution equation. In this thesis we demonstrate that it is possible to solve this equation iteratively, and in this way calculate the associated amplitude to any loop order in perturbative QCD. The key idea is to analyse the evolution of the two-reggeon wavefunction in two complementary regions. The so-called soft region is characterised by the small momentum of one of the reggeons. There, the wavefunction obeys a simplified evolution equation and evaluates to a polynomial in the soft momentum. This region is the exclusive source of the singularities of the signature-even amplitude. Consequently, the complementary region is described by purely finite integrals which can be evaluated without dimensional regularisation, directly in terms of a class of iterated polylogarithms. The contributions from both regions are combined and shown to recover the result of the full BFKL evolution. All the above methods are algorithmic and work to any loop order. We resum the singularities of the amplitude to all loop orders and match the result to the predictions made by the soft factorisation theorem to shed light on the universal infrared behaviour of two-parton scattering. This lets us extract the all-order soft anomalous dimension in the high-energy limit whose properties we analyse in detail. In particular, it turns out to be an entire function of the coupling which can be approximated by a simple oscillating function well beyond the perturbative regime. The finite terms of the signature-even amplitude show intricate combinations of transcendental numbers. At low loop orders they are the well-known values of the Riemann zeta function evaluated at integer arguments. However, examining the amplitude at eleven loops and beyond reveals that a broader class of numbers - so-called single-valued multiple zeta values - is needed to describe the two-reggeon exchange. Moreover, finite terms that originate in the soft region are readily resummed and allow us to derive a modified evolution equation for the complementary hard region. In fact, there are more hints of all-order resummation which we discuss towards the end of this thesis hoping they will inspire future research in this area.
Supervisor: Gardi, Einan ; O'Connell, Donal Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: scattering amplitudes ; perturbation theory ; forward scattering ; Large Hadron Collider ; reggeons ; long-distance singularities ; Quantum Chromodynamics ; Riemann zeta function