NNLO zero-jettiness beam and soft functions to higher orders in the dimensional-regularization parameter $$\epsilon $$
Daniel Baranowski
Abstract
Abstract We present the calculation of the next-to-next-to-leading order (NNLO) zero-jettiness beam and soft functions, up to the second order in the expansion in the dimensional regularization parameter $$\epsilon $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ϵ</mml:mi></mml:math> . These higher order terms are needed for the computation of the next-to-next-to-next-to-leading order ( $$\hbox {N}^3\hbox {LO}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mtext>N</mml:mtext><mml:mn>3</mml:mn></mml:msup><mml:mtext>LO</mml:mtext></mml:mrow></mml:math> ) zero-jettiness soft and beam functions. As a byproduct, we confirm the $${\mathcal {O}}{(\epsilon ^0)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>ϵ</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> results for NNLO beam and soft functions available in the literature by Gaunt et al. (JHEP 4:113, 2014), Gaunt et al. (JHEP 8:20, 2014), Boughezal et al. (Phys Rev D 96:34001, 2017), Monni et al. (JHEP 8:10, 2011) and Kelley et al. (Phys Rev D 84:45022, 2011).