Abstract
We present the first results on the production of pseudo-scalar through gluon fusion at the LHC to N$^3$LO in QCD taking into account only soft gluon effects. We have used the effective Lagrangian that describes the coupling of pseudo-scalar with the gluons in the large top quark mass limit. We have used recently available quantities namely the three loop pseudo-scalar form factor and the third order universal soft function in QCD to achieve this. Along with the fixed order results, we also present the process dependent resummation coefficient for threshold resummation to N$^3$LL in QCD. Phenomenological impact of these threshold N$^3$LO corrections to pseudo-scalar production at the LHC is presented and their role to reduce the renormalisation scale dependence is demonstrated.
Highlights
The effective LagrangianA pseudo-scalar Higgs boson couples to gluons only indirectly through a virtual heavy quark loop which can be integrated out in the infinite quark mass limit
Like the scalar Higgs boson in the SM, the leading order prediction of the pseudo-scalar Higgs boson production at the hadron colliders suffers from theoretical uncertainties that are large, due to the renormalization scale μR arising from the strong coupling constant, and are mild due to the factorization scale μF in the parton distribution functions
We have exploited the universal structure of the soft function that appears in scalar Higgs boson production at the LHC
Summary
A pseudo-scalar Higgs boson couples to gluons only indirectly through a virtual heavy quark loop which can be integrated out in the infinite quark mass limit. The effective Lagrangian [73] describing the interaction between pseudoscalar Higgs boson χ A and the QCD particles in the infinitely large top quark mass limit is given by. CJ starts only at second order in the strong coupling constant These Wilson coefficients are given by [73]. M A and mt symbolize the masses of the pseudo-scalar Higgs boson and top quark (heavy quark), respectively. The strong coupling constant as ≡ as(μ2R) is renormalized at the mass scale μR and is related to the unrenormalized one, as ≡ gs2/16π 2, through μ2 /2. Βi ’s are the coefficients of the QCD β function [75]
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