Pseudo-scalar Higgs boson production at N $$^3$$ 3 LO $$_{\text {A}}$$ A +N $$^3$$ 3 LL $$'$$ ′

Abstract

We consider the production of a pseudo-scalar particle A at the LHC, and present accurate theoretical predictions for its inclusive cross section in gluon fusion. The prediction is based on combining fixed-order perturbation theory and all-order threshold resummation. At fixed order we include the exact next-to-next-to-leading order (NNLO) plus an approximate next-to-next-to-next-to-leading order (NLO) which is based on the recent computation at this order for the scalar case. We then add threshold resummation at next-to-next-to-next-to leading logarithmic accuracy (NLL). Various forms of threshold resummation are considered, differing by the treatment of subleading terms, allowing a robust estimate of the theoretical uncertainties due to missing higher orders. With particular attention to pseudo-scalar masses of 200 and 750 GeV, we also observe that perturbative convergence is much improved when resummation is included. Additionally, results obtained with threshold resummation in direct QCD are compared with analogous results as computed in soft-collinear effective theory, which turn out to be in good agreement. We provide precise predictions for pseudo-scalar inclusive cross section at 13 TeV LHC for a wide range of masses. The results are available through updated versions of the public codes ggHiggs and TROLL.

Two loop QCD amplitudes for di-pseudo scalar production in gluon fusion

“…The renormalisation of O J is related to the renormalisation of the singlet axial vector current J µ 5 which needs the standard overall UV renormalisation constant Z s M S and a finite renormalisation constant Z s 5 . The later is necessary in dimensional regularisation in order to ensure the nature of operator relation resulting from axial anomaly [48] [∂ µ J µ 5 ] = a s 23) which is true in Pauli-Villars, a 4-dimensional regularisation. To preserve eq.…”

“…The three loop form factor thus obtained was later combined with appropriate soft distribution function [19][20][21] and mass factorisation kernels to obtain soft plus virtual contribution at N 3 LO in QCD [22]. Later, the process dependent resummation constants from the three loop form factors were used to perform threshold resummation in [23] and also make approximate prediction at N 3 LO level. This was possible due to the similarity of the interaction vertices of scalar and pseudo scalar Higgs bosons with the gluons.…”

Cornering pseudoscalar-mediated dark matter with the LHC and cosmology

“…For the gluon fusion channel, we multiply the LO cross sections returned by MadGraph5 aMC@NLO by N 3 LO A + N 3 LL K-factors for pseudoscalar mediators [67,68], so that the total rate includes the matching of approximate next-to-next-to-next-to-leading order predictions with the resummation of soft and collinear gluon radiation close to threshold at the next-to-next-to-next-to-leading logarithmic accuracy. In the case of the associated production of the mediator with a bottom quark pair, we consider instead NLO production rates multiplied by LO branching ratios.…”

Pseudo-scalar Higgs form factor at 3 loops and QCD N3LO threshold corrections to its production at the LHC

“…Since the IR poles in QCD become UV ones in Soft Collinear Effective Theory (SCET) ( [46,47,48,49,50,51,52]), a suitable renormalisation constant can be used to absorb all residual IR poles to obtain finite results. The resulting finite part is the matching coefficient required to perform N 3 LL resummation in SCET for the pseudo-scalar Higgs boson production at the LHC [12].…”

“…The recent discovery of a Standard-Model-like Higgs boson at the LHC [9,10] prompted the community to study the properties of the discovered boson in order to identify either with lightest scalar or pseudo-scalar Higgs bosons of extended models. These corrections can be used to obtain the next-to-next-to-next-to leading order and leading log (N 3 LO and N 3 LL) gluon fusion cross sections [11,12] for pseudo-scalar Higgs boson production, thereby reducing the theoretical uncertainities resulting from renormalisation and factorisation scales. We use the universal infra-red (IR) pole structure of the form factors to determine the ultraviolet (UV) renormalisation constants and mixing of the effective operators up to three loop level.…”