Resummed Higgs boson cross section at next-to SV to $${\mathrm{NNLO}}+ {\overline{\mathrm{NNLL}}}$$

Abstract

Abstract We present the resummed predictions for inclusive cross section for the production of Higgs boson at next-to-next-to leading logarithmic ( $${\overline{\mathrm{NNLL}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>NNLL</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> ) accuracy taking into account both soft-virtual ( $$\mathrm{SV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>SV</mml:mi> </mml:math> ) and next-to SV ( $$\mathrm{NSV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>NSV</mml:mi> </mml:math> ) threshold logarithms. We derive the N -dependent coefficients and the N -independent constants in Mellin- N space for our study. Using the minimal prescription we perform the inverse Mellin transformation and match it with the corresponding fixed order results. We report in detail the numerical impact of N -independent part of resummed result and explore the ambiguity involved in exponentiating them. By studying the K factors at different logarithmic accuracy, we find that the perturbative expansion shows better convergence improving the reliability of the prediction at $${\mathrm{NNLO}} + {\overline{\mathrm{NNLL}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>NNLO</mml:mi> <mml:mo>+</mml:mo> <mml:mover> <mml:mi>NNLL</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> accuracy. For instance, the cross-section at $${\mathrm{NNLO}} + {\overline{\mathrm{NNLL}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>NNLO</mml:mi> <mml:mo>+</mml:mo> <mml:mover> <mml:mi>NNLL</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> accuracy reduces by $$3.15\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>3.15</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> as compared to the $$\mathrm{NNLO}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>NNLO</mml:mi> </mml:math> result for the central scale $$\mu _R = \mu _F = m_H/2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>μ</mml:mi> <mml:mi>R</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>μ</mml:mi> <mml:mi>F</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>H</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> at 13 TeV LHC. We also observe that the resummed $$\mathrm{SV} + \mathrm{NSV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>SV</mml:mi> <mml:mo>+</mml:mo> <mml:mi>NSV</mml:mi> </mml:mrow> </mml:math> result improves the renormalisation scale uncertainty at every order in perturbation theory. The uncertainty from the renormalisation scale $$\mu _R$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>μ</mml:mi> <mml:mi>R</mml:mi> </mml:msub> </mml:math> ranges between $$(+8.85\% ,-10.12\%)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>+</mml:mo> <mml:mn>8.85</mml:mn> <mml:mo>%</mml:mo> <mml:mo>,</mml:mo> <mml:mo>-</mml:mo> <mml:mn>10.12</mml:mn> <mml:mo>%</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> at $$\mathrm{NNLO}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>NNLO</mml:mi> </mml:math> whereas it goes down to $$(+6.54\% , - 8.32\%)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>+</mml:mo> <mml:mn>6.54</mml:mn> <mml:mo>%</mml:mo> <mml:mo>,</mml:mo> <mml:mo>-</mml:mo> <mml:mn>8.32</mml:mn> <mml:mo>%</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> at $${\mathrm{NNLO}} + {\overline{\mathrm{NNLL}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>NNLO</mml:mi> <mml:mo>+</mml:mo> <mml:mover> <mml:mi>NNLL</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> accuracy. However, the factorisation scale uncertainty is worsened by the inclusion of these NSV logarithms hinting the importance of resummation beyond $$\mathrm{NSV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>NSV</mml:mi> </mml:math> terms. We also present our predictions for $$\mathrm{SV} + \mathrm{NSV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>SV</mml:mi> <mml:mo>+</mml:mo> <mml:mi>NSV</mml:mi> </mml:mrow> </mml:math> resummed result at different collider energies.

Topics & Concepts