Abstract
The cross section for top quark pair production factorizes at small transverse momentum of the heavy quark pair, qT. One of the key ingredients that appears in the factorization formula is the soft function, which mediates soft gluon exchanges between particles and gives rise to colour correlations. We present the complete result for the small-qT soft function at the next-to-next-to-leading order. This is the last missing element needed to calculate the NNLO cross section for top quark pair production by means of the qT slicing method. In order to evaluate divergent integrals appearing in the calculation, we develop methods based on sector decomposition and differential equations. We present an extensive validation of our framework. In particular, we recover results predicted by the renormalization group, which constitutes a direct demonstration of validity of the small-qT factorization at NNLO. We provide complete results for the real and imaginary part of the soft function, which are ready for application in the calculation of the toverline{t} cross section at NNLO.
Highlights
One of the most important classes of measurements studied at the Large Hadron Collider (LHC) concern processes which involve the production of the top quark
In order to evaluate divergent integrals appearing in the calculation, we develop methods based on sector decomposition and differential equations
A second, independent calculation of the next-to-next-toleading order (NNLO) correction for top quark pair production in proton-proton collisions would be of great value
Summary
One of the most important classes of measurements studied at the Large Hadron Collider (LHC) concern processes which involve the production of the top quark. The new fields decouple in the Lagrangian and this separation largely facilitates proofs of factorization theorems One of such factorizations [25] lies at the basis of the formalism used in our calculation, and the only missing piece needed to use it to evaluate the cross section for top pair production at the next-to-next-to-leading order is the NNLO, small-qT soft function. The result for the latter is presented in this work.
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