Abstract
The coupling of a pseudo-scalar Higgs boson to gluons is mediated through a heavy quark loop. In the limit of large quark mass, it is described by an effective Lagrangian that only admits light degrees of freedom. In this effective theory, we compute the three-loop massless QCD corrections to the form factor that describes the coupling of a pseudo-scalar Higgs boson to gluons. Due to the axial anomaly, the pseudo-scalar operator for the gluonic field strength mixes with the divergence of the axial vector current. Working in dimensional regularization and using the 't~Hooft-Veltman prescription for the axial vector current, we compute the three-loop pseudo-scalar form factors for massless quarks and gluons. Using the universal infrared factorization properties, we independently derive the three-loop operator mixing and finite operator renormalisation from the renormalisation group equation for the form factors, thereby confirming recent results in the operator product expansion. The finite part of the three-loop form factor is an important ingredient to the precise prediction of the pseudo-scalar Higgs boson production cross section at hadron colliders. We discuss potential applications and derive the hard matching coefficient in soft-collinear effective theory.
Highlights
In [13], it was shown that the single pole term in quark and gluon form factors up to two loop level can be shown to decompose into UV and universal collinear (BI ), color singlet soft anomalous dimensions, later on observed to hold even at three loop level in [22]
The three-loop quark and gluon form factors through to finite terms were computed in [30,31,32,33] and subsequently extended to higher powers in the expansion [34]. These results were enabled by modern techniques for multi-loop calculations in quantum field theory, in particular integral reduction methods. These are based on integration-by-parts (IBP) [35, 36] and Lorentz invariance (LI) [37] identities which reduce the set of thousands of multi-loop integrals to the one with few integrals, so called master integrals (MIs) in dimensional regularisation
The three-loop corrections to the pseudo-scalar form factors computed in this article are an important ingredient to the N3LO and N3LL gluon fusion cross sections [81] for pseudoscalar Higgs boson production, thereby enabling predictions at the same level of precision that is attained in the scalar case
Summary
A pseudo-scalar Higgs boson couples to gluons only indirectly through a virtual heavy quark loop. This loop can be integrated out in the limit of infinite quark mass. The Wilson coefficients CG and CJ are obtained by integrating out the heavy quark loop, and CG does not receive any QCD corrections beyond one loop due to the Adler-Bardeen theorem [84], while CJ starts only at second order in the strong coupling constant. As ≡ as μ2R is the strong coupling constant renormalised at the scale μR which is related to the unrenormalised one, ˆas ≡ gs2/(16π2) through μ2 /2.
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