Higgs boson production through bbˉb \bar b annihilation at threshold in N3^3LO QCD

We present threshold enhanced N$^3$LO QCD corrections to inclusive Higgs production through bottom anti-bottom annihilation at hadron colliders using threshold resummed cross section. The resummed cross section is obtained using factorization properties and Sudakov resummation of the inclusive cross section. We use the recent results on threshold N$^3$LO corrections in QCD for Drell-Yan production and three loop QCD corrections to Higgs form factor with bottom anti-bottom quark to achieve this task. This is the first step towards the evaluation of complete N$^3$LO result. We have numerically demonstrated the importance of such corrections at the LHC.Comment: 15 pages, 1 figur

High energy behaviour of form factors

We solve renormalization group equations that govern infrared divergences of massless and massive form factors. By comparing to recent results for planar massive three-loop and massless four-loop form factors in QCD, we give predictions for the high-energy limit of massive form factors at the four- and for the massless form factor at five-loop order. Furthermore, we discuss the relation which connects infrared divergences regularized dimensionally and via a small quark mass and extend results present in the literature to higher order.Comment: 21 page

Polarized qqˉ→Z+q \bar{q} \rightarrow Z +Higgs amplitudes at two loops in QCD: the interplay between vector and axial vector form factors and a pitfall in applying a non-anticommuting γ5\gamma_5

We consider QCD corrections to two loops for the polarized amplitudes of $q{\bar q}\to Z +$ Higgs boson. First we show how the polarized amplitudes of $b \bar{b} \rightarrow Z h$ associated with a non-vanishing $b$-quark Yukawa coupling and a scalar or pseudoscalar Higgs boson $h$ can be built up solely from vector form factors (FF) of properly grouped classes of diagrams, bypassing completely the need of explicitly manipulating $\gamma_5$ in dimensional regularization (up to a few "anomalous", i.e., triangle diagrams). We determine the contributions of the triangle diagrams in the heavy top limit. We present the analytic results of the vector FF and the triangle-diagram contributions to the axial vector FF, which are sufficient for deriving the two-loop QCD amplitudes for $b \bar{b} \rightarrow Z h$ with a CP-even and CP-odd Higgs boson $h$. We derive the respective Ward identity for these amplitudes, which are subsequently verified to two-loop order in QCD using these FF. In addition, the FF of a class of corrections to $q \bar{q} \rightarrow ZH$ proportional to the top-Yukawa coupling are obtained analytically to two-loop order in QCD in the heavy-top limit using the Higgs-gluon effective Lagrangian where the top quark is integrated out. We address a pitfall that occurs when applying the non-anticommutating $\gamma_5$ prescription to this class of contributions that has been overlooked so far in the literature. We attribute this issue to the fact that the absence of certain heavy-mass expanded diagrams in the infinite-mass limit of a scattering amplitude with an axial vector current depends on the particular $\gamma_5$ prescription in use.Comment: A few typos fixed along with minor typographic edits, references in the manuscript and the ReadMe.txt updated, matched with the version accepted by JHE

Two-Loop QCD Corrections to Higgs →b+bˉ+g\rightarrow b + \bar{b} + g Amplitude

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 $H\rightarrow b+\overline b+g$ 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.Comment: Published version; 25 pages, 2 figures; v2: analytically continued result added, typos are correcte

Pseudo-scalar Higgs Boson Production at Threshold N3^3LO and N3^3LL QCD

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.Comment: 34 pages, 17 figure