Factorization at the LHC: From PDFs to Initial State Jets (Ph.D. thesis)

TL;DR

This thesis develops a factorization framework for initial state jets at the LHC, introducing beam functions that enable summing large logarithms in event shape observables for improved theoretical predictions.

Contribution

It introduces beam functions and a factorization theorem for initial state jet vetoes, allowing resummation of large logarithms in LHC processes, with one-loop matching calculations.

Findings

Derived a factorization theorem for pp -> XL with jet vetoes.

Calculated one-loop matching coefficients for beam functions.

Applied the framework to Drell-Yan and Higgs production at NNLL order.

Abstract

New physics searches at the LHC or Tevatron typically look for a specific number of hard jets, leptons and photons. To obtain an exclusive N-jet sample, one can measure the event shape "N-jettiness" \tau_N and veto additional undesired jets by requiring \tau_N <<1. However, this leads to large logarithms of \tau_N in the cross section, that need to be summed for reliable theory predictions. For N=0 in hadronic collisions, \tau_N reduces to the "beam thrust" eventshape \tau_B. We derive a factorization theorem for pp -> XL, where a central jet veto \tau_B<<1 is imposed on the hadronic final state X and L is non-hadronic. This factorization theorem enables us to sum large logarithms of \tau_B in the cross section. The initial state is described by "beam functions", which depend on the momentum fraction x and the (transverse) virtuality t of the colliding partons. The dependence on t can be calculated in perturbation theory by matching beam functions onto the parton distribution functions (PDFs) at the intermediate scale \mu_B^2 ~ t, and we have calculated all one-loop matching coefficients. Unlike the PDFs, the evolution of the beam function is in t and does not affect x or the parton type. We show results for the beam thrust cross section for Drell-Yan and Higgs production through gluon fusion at next-to-next-to-leading-logarithmic order. For N>0, we obtain a factorization formula with inclusive jet and beam functions that allows us to sum the large logarithms of \tau_N.