Rapidity distribution of pseudoscalar Higgs boson to NNLOA+NNLL¯

We present the differential predictions for the rapidity distribution of pseudoscalar Higgs boson through gluon fusion at the LHC. These results are obtained taking into account the soft-virtual (SV) as well as the next-to-soft virtual (NSV) resummation effects to next-to-next-to-leading-logarithmic (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mover accent="true"><a:mi>NNLL</a:mi><a:mo stretchy="true">¯</a:mo></a:mover></a:math>) accuracy and matching them to the approximate fixed order next-to-next-to-leading-order (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mrow><e:mi>NNLO</e:mi></e:mrow><e:mi mathvariant="normal">A</e:mi></e:msub></e:math>) computation. We perform the resummation in two-dimensional Mellin space by limiting ourselves to the contributions only from gluon-gluon (<h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mrow><h:mi>g</h:mi><h:mi>g</h:mi></h:mrow></h:math>) initiated channels. The <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msub><j:mrow><j:mi>NNLO</j:mi></j:mrow><j:mi mathvariant="normal">A</j:mi></j:msub></j:math> rapidity distribution of pseudoscalar Higgs is obtained by applying a ratio method on the NNLO rapidity distribution of the scalar Higgs boson. We also present the first analytical results of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi mathvariant="normal">N</m:mi><m:mn>3</m:mn></m:msup><m:mi>LO</m:mi></m:math> rapidity distribution of pseudoscalar Higgs at <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mrow><p:mi>SV</p:mi><p:mo>+</p:mo><p:mi>NSV</p:mi></p:mrow></p:math> accuracy. The phenomenological impacts of <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msub><r:mrow><r:mi>NNLO</r:mi></r:mrow><r:mi mathvariant="normal">A</r:mi></r:msub><r:mo>+</r:mo><r:mover accent="true"><r:mi>NNLL</r:mi><r:mo stretchy="true">¯</r:mo></r:mover></r:math> predictions for 13 TeV LHC are studied. We observe that for <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi>m</w:mi><w:mi>A</w:mi></w:msub><w:mo>=</w:mo><w:mn>125</w:mn><w:mo stretchy="false">(</w:mo><w:mn>700</w:mn><w:mo stretchy="false">)</w:mo><w:mtext> </w:mtext><w:mtext> </w:mtext><w:mi>GeV</w:mi></w:math> the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mrow><ab:mi>SV</ab:mi><ab:mo>+</ab:mo><ab:mi>NSV</ab:mi></ab:mrow></ab:math> resummation at the <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mover accent="true"><cb:mi>NNLL</cb:mi><cb:mo stretchy="true">¯</cb:mo></cb:mover></cb:math> level brings about 14.76% (11.48%) corrections to the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msub><gb:mrow><gb:mi>NNLO</gb:mi></gb:mrow><gb:mi mathvariant="normal">A</gb:mi></gb:msub></gb:math> results at the central scale value of <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:msub><jb:mi>μ</jb:mi><jb:mi>R</jb:mi></jb:msub><jb:mo>=</jb:mo><jb:msub><jb:mi>μ</jb:mi><jb:mi>F</jb:mi></jb:msub><jb:mo>=</jb:mo><jb:msub><jb:mi>m</jb:mi><jb:mi>A</jb:mi></jb:msub></jb:math>. Further, we find that the sensitivity to the renormalization scale gets improved substantially by the inclusion of NSV resummed predictions at <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:mover accent="true"><lb:mi>NNLL</lb:mi><lb:mo stretchy="true">¯</lb:mo></lb:mover></lb:math> accuracy.