N3LL resummation of one-jettiness for Z -boson plus jet production at hadron colliders

We present the resummation of one-jettiness for the color-singlet plus jet production process <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>p</a:mi><a:mi>p</a:mi><a:mo stretchy="false">→</a:mo><a:mo stretchy="false">(</a:mo><a:msup><a:mi>γ</a:mi><a:mo>*</a:mo></a:msup><a:mo>/</a:mo><a:mi>Z</a:mi><a:mo stretchy="false">→</a:mo><a:msup><a:mo>ℓ</a:mo><a:mo>+</a:mo></a:msup><a:msup><a:mo>ℓ</a:mo><a:mo>−</a:mo></a:msup><a:mo stretchy="false">)</a:mo><a:mo>+</a:mo><a:mtext>jet</a:mtext></a:math> at hadron colliders up to the fourth logarithmic order (<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi mathvariant="normal">N</g:mi><g:mn>3</g:mn></g:msup><g:mi>LL</g:mi></g:math>). This is the first resummation at this order for processes involving three colored partons at the Born level. We match our resummation formula to the corresponding fixed-order predictions, extending the validity of our results to regions of the phase space where further hard emissions are present. This result paves the way for the construction of next-to-next-to-leading order simulations for color-singlet plus jet production matched to parton showers in the framework.