Abstract
Small-x resummation has been proven recently to be a crucial ingredient for describing small-x HERA data, and the inclusion of small-x resummation in parton distribution function (PDF) determination has a sizeable effect on the PDFs even at the electroweak scale. In this work we explore the implications of small-x resummation at the large hadron collider (LHC) and at a future circular collider (FCC). We construct the theoretical machinery for resumming physical inclusive observables at hadron colliders, and describe its implementation in the public code HELL 3.0. We focus on Higgs production in gluon fusion as a prototypical example, both because it is sensitive to small-x gluons and because of its importance for the LHC physics programme. We find that adding small-x resummation to the hbox {N}^3LO Higgs production cross section can lead to an increase of up to 10% at FCC, while the effect is smaller (+1%) at LHC but still important to achieve a high level of precision.
Highlights
We find that adding small-x resummation to the N3LO Higgs production cross section can lead to an increase of up to 10% at future circular collider (FCC), while the effect is smaller (+1%) at large hadron collider (LHC) but still important to achieve a high level of precision
We investigate the phenomenological implications of small-x resummation in Higgs production at the LHC, and to enlarge the sensitivity to the parton distribution function (PDF) at small x at higherenergy colliders, namely high-energy LHC (HE-LHC) and a future circular hadron-hadron collider (FCC-hh)
While we believe that this effect is spurious, it is interesting to see how it affects the physical cross section. This is interesting because the PDF sets of Ref. [1] have been obtained using resummation based on the LL anomalous dimension.19 (the instability of the LL anomalous dimension appears when expanded to O(αs3), which is not the case for the NNLO + NLL resummation used in the PDFs, for which the use of the LL formulation can be considered reliable.) in the left plot of Fig. 5 we show the LL version of the resummed prediction
Summary
The first manifest instability appears at NNLO, and PDFs determined with NNLO theory are rather different to those determined with NNLO theory improved by NLL small-x resummation. This difference, determined at low Q2 where the small-x HERA data lie, persists and is enlarged by DGLAP evolution at larger scales. While NNLO + NLL PDFs are available, resummed predictions for LHC observables did not exist, or at least not in a format which makes them immediately usable for phenomenology It is the goal of this paper to provide the theoretical setup to perform this resummation for inclusive observables with the public code. We investigate the phenomenological implications of small-x resummation in Higgs production at the LHC, and to enlarge the sensitivity to the PDFs at small x at higherenergy colliders, namely high-energy LHC (HE-LHC) and a future circular hadron-hadron collider (FCC-hh)
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