Abstract
Exclusive observables involving Higgs boson in association with jets are often well suited to study the Higgs boson properties. They are rates involving cuts on the final state jets or differential distributions of rapidity, transverse momentum of the observed Higgs boson. While they get dominant contributions from gluon initiated partonic subprocesses, it is important to include the subdominant ones coming from other channels. In this article, we study one such channel namely the Higgs production in association with a jet in bottom anti-bottom annihilation process. We compute relevant amplitude H → b+ $$ \overline{b} $$ +g up to two loop level in QCD where Higgs couples to bottom quark through Yukawa coupling. We use projection operators to obtain the coefficients for each tensorial structure appearing in this process. We have demonstrated that the renormalized amplitudes do have the right infrared structure predicted by the QCD factorization in dimensional regularization. The finite parts of the one and two loop amplitudes are presented after subtracting the infrared poles using Catani’s subtraction operators.
Highlights
Associated production of Higgs with vector bosons and top anti-top pairs and bottom antibottom annihilation
Inclusive cross section for Higgs production in association with bottom quark to NNLO level accuracy is known in the variable flavour scheme (VFS) [18,19,20,21,22,23], while it is known only up to NLO level in the fixed flavour scheme (FFS) [24,25,26,27,28,29]
The differential distributions for Higgs production and its decay to pair of photons [30] or massive vector bosons [31, 32] have been known at NNLO level in QCD in the infinite top quark mass limit
Summary
The interaction part of the action involving bottom quarks and Higgs boson is given by SIb = −λ d4x φ(x)ψb(x)ψb(x). Where, ψb(x) d√enotes the bottom quark field and φ(x) the scalar field. Λ is the Yukawa coupling given by 2mb/υ, with the bottom quark mass mb and the vacuum expectation value υ ≈ 246 GeV. For the pseudoscalar Higgs of MSSM, we need to replace λφ(x)ψb(x)ψb(x) by λφ(x)ψb(x)γ5ψb(x) in the above equation. The angle α is the measure of mixing of weak and mass eigenstates of neutral. In the VFS scheme, except in the Yukawa coupling, mb is taken to be zero like other light quarks in the theory. The number of active flavours is taken to be nf = 5.
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