Electroweak Sudakov Logarithms Research Articles

Mass gap effects and higher order electroweak Sudakov logarithms

The infrared structure of spontaneously broken gauge theories is phenomenologically very important and theoretically a challenging problem. Various attempts have been made to calculate the higher-order behavior of large double-logarithmic (DL) corrections originating from the exchange of electroweak gauge bosons resulting in contradictory claims. We present results from two-loop electroweak corrections for the process g→f R f ̄ L to DL accuracy. This process is ideally suited as a theoretical model reaction to study the effect of the mass gap of the neutral electroweak gauge bosons at the two-loop level. Contrary to recent claims in the literature, we find that the calculation performed with the physical Standard Model fields is in perfect agreement with the results from the infrared evolution equation method. In particular, we can confirm the exponentiation of the electroweak Sudakov logarithms through two loops.

Electroweak Sudakov logarithms in the Coulomb gauge

We describe a formalism for calculating electroweak Sudakov logarithms in the Coulomb gauge. This formalism is applicabl to arbitrary electroweak processes. For illustration we focus on the specific reactions e +e − → f f and e + e − → W T + W T −, W L + W L −, which contain all the salient details of dealing with the various types of particles. We discuss an explicit two-loop calculation and have a critical look at the (non-) exponentiation and factorisation properties of the Sudakov logarithms in the Standard Model.

New insights into the perturbative structure of electroweak Sudakov logarithms

To match the expected experimental precision at future linear colliders, improved theoretical predictions beyond next-to-leading order are required. At the anticipated energy scale of s =1 TeV the electroweak virtual corrections are strongly enhanced by collinear-soft Sudakov logarithms of the form log 2( s/ M 2), with M being the generic mass scale of the W and Z bosons. By choosing an appropriate gauge, we have developed a formalism to calculate such corrections for arbitrary electroweak processes. As an example we consider in this letter the process e +e −→f f ̄ and study the perturbative structure of the electroweak Sudakov logarithms by means of an explicit two-loop calculation. In this way we investigate how the Standard Model, with its mass gap between the photon and Z boson in the neutral sector, compares to unbroken theories like QED and QCD. In contrast to what is known for unbroken theories we find that the Sudakov logarithms are not exclusively given by the so-called rainbow diagrams, owing to the mass gap and the charged-current interactions. In spite of this, we nevertheless observe that the two-loop corrections are consistent with an exponentiation of the one-loop corrections. In this sense the Standard Model behaves like an unbroken theory at high energies.