Resummation of Double-Differential Cross Sections and Fully-Unintegrated Parton Distribution Functions

Abstract

LHC measurements involve cuts on several observables, but resummed calculations are mostly restricted to single variables. We show how the resummation of a class of double-differential measurements can be achieved through an extension of Soft-Collinear Effective Theory (SCET). A prototypical application is $pp\to Z+0$ jets, where the jet veto is imposed through the beam thrust event shape $\mathcal{T}$, and the transverse momentum $p_T$ of the $Z$ boson is measured. A standard SCET analysis suffices for $p_T\sim m_Z^{1/2}{\mathcal{T}}^{1/2}$ and $p_T\sim \mathcal{T}$, but additional collinear-soft modes are needed in the intermediate regime. We show how to match the factorization theorems that describe these three different regions of phase space, and discuss the corresponding relations between fully-unintegrated parton distribution functions, soft functions and the newly defined collinear-soft functions. The missing ingredients needed at NNLL/NLO accuracy are calculated, providing a check of our formalism. We also revisit the calculation of the measurement of two angularities on a single jet in JHEP 1409 (2014) 046, finding a correction to their conjecture for the NLL cross section at $\mathcal{O}({\alpha }_s^2)$.

43 pages, 3 figures. v2: JHEP version, discussion on non-global logarithms added

References in corpus (13)

• PYTHIA 6.4 Physics and Manual
• Matching NLO QCD computations with Parton Shower simulations: the POWHEG method
• Herwig++ Physics and Manual
• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• Boosted objects: a probe of beyond the Standard Model physics
• Strategies to Identify Boosted Tops
• Power Counting to Better Jet Observables
• Gaining (Mutual) Information about Quark/Gluon Discrimination
• The Quark Beam Function at NNLL
• Resummation of Threshold Logarithms in Effective Field Theory For DIS, Drell-Yan and Higgs Production
• On jet mass distributions in Z+jet and dijet processes at the LHC
• Glauber Gluons and Multiple Parton Interactions
• The Fully-Differential Quark Beam Function at NNLO

Cited by in corpus (6)

• Sudakov Safety in Perturbative QCD
• New Angles on Energy Correlation Functions
• Collinear expansion for color singlet cross sections
• ChiliPDF: Chebyshev Interpolation for Parton Distributions
• The Fully-Differential Gluon Beam Function at NNLO
• Double-charming Higgs identification using machine-learning assisted jet shapes