Origin of logarithms and precision results for SM processes

by Zbigniew Was (Cracow Institute of Nuclear Physics)

Friday 28 Mar 2025, 15:00 → 17:00 US/Eastern

3-192 (Building 510E)

Regardless of whether detectors are used in hadron or electron colliders, the most precisely measured quantities are the directions of muons, followed by the directions of electrons, and then the energies of leptons. The non-negligible lifetime of electroweak (and therefore colorless) bosons allows for the separation of event components from production interactions. These valuable features require careful control over the associated final-state QED bremsstrahlung effects and detector granularity. Even during the LEP era, third-order effects (at least their leading contributions) were necessary to extract the full potential of precision measurements.

Despite its infrared singularities, QED remains solvable at lower energies. This is why YFS exponentiation, along with its exclusive exponentiation variant, provided a foundation for Monte Carlo programs, aiding in the interpretation of precise measurements such as Bhabha scattering for luminosity determination at LEP. However, this came at a cost. While expressing results in terms of next-next-... logarithm formulations was convenient—particularly for renormalization schemes, including those in QCD—it also introduced additional challenges. Standard, off-the-shelf results often required further refinement.

In what follows, we will focus on how the structure induced by the Lorentz group (and its representations), particularly its layers with respect to the rotation subgroup, can be used to reorganize perturbation expansions—analogous to logarithmic structures, but at the level of spin amplitudes. This property, fundamental to QED exponentiation, can also be identified in perturbative results of QCD. This central theme of the talk does not encompass all efforts required for precision. Issues such as distinguishing electroweak contributions into genuinely weak and QED components, as well as expansions involving contact interactions, parametric ambiguities, and anti-analytic constraints in field theory, will also be touched upon. However, these topics warrant further discussion in separate presentations.