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Springer

Received: June 24, 2020 Accepted: August 18, 2020 Published: September 22, 2020

Markus A. Ebert,a Bernhard Mistlbergerb and Gherardo Vitaa a

Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, U.S.A. b SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94039, U.S.A.

E-mail: [email protected], [email protected], [email protected] Abstract: We present the first complete calculation for the quark and gluon N -jettiness (TN ) beam functions at next-to-next-to-next-to-leading order (N3 LO) in perturbative QCD. Our calculation is based on an expansion of the differential Higgs boson and Drell-Yan production cross sections about their collinear limit. This method allows us to employ cutting edge techniques for the computation of cross sections to extract the universal building blocks in question. The class of functions appearing in the matching coefficents for all channels includes iterated integrals with non-rational kernels, thus going beyond the one of harmonic polylogarithms. Our results are a key step in extending the TN subtraction methods to N3 LO, and to resum TN distributions at N3 LL0 accuracy both for quark as well as for gluon initiated processes. Keywords: Perturbative QCD, Resummation ArXiv ePrint: 2006.03056

c The Authors. Open Access, Article funded by SCOAP3 .

https://doi.org/10.1007/JHEP09(2020)143

JHEP09(2020)143

N -jettiness beam functions at N3LO

Contents 1

2 Beam functions from the collinear limit of cross sections

3

3 Results

4

4 Conclusions

9

A Ingredients for the calculation of the beam function A.1 Renormalization group equations A.2 Structure of the beam function counterterm A.3 αs renormalization and IR counterterms

10 10 10 11

B High-energy limit of the beam function kernels

12

1

Introduction

Experimental measurements at the LHC have provided remarkably precise measurements for a multitude of observables, most notably weak gauge boson production, an important benchmark for the Standard Model which has been measured at percent level accuracy [1– 4]. Strong constraints on physics beyond the Standard Model are also provided by precision measurements of Higgs boson production and diboson processes [5–9]. To make full use of these results, it is crucial to confront them with equally-precise theory predictions, which in particular requires to include higher-order corrections in QCD. So far, only inclusive Drell-Yan and Higgs production have been calculated at next-tonext-to-next-to-leading order (N3 LO) in QCD [10–17], while significant progress is being made to reach the same precision for differential distributions [18, 19]. A key challenge for such calculations is the cancellation of infrared divergences between real and virtual corrections, and hence a necessary prerequisite is a profound understanding of the infrared singular structure at three loops. N -jettiness (TN ) is an infrared-sensitive N -jet resolution observable and thus provides a way to study the singular structure of QCD [20