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Register a new userTwo-Loop QCD Helicity Amplitudes for Higgs Production Associated with a Vector Boson through Bottom Quark Annihilation
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We present the two-loop QCD corrections to the amplitude of the Higgs production associated with a $Z$ boson via the bottom quark-antiquark annihilation channel with a non-vanishing bottom-quark Yukawa coupling. The computation is performed by projecting the D-dimensional scattering amplitude directly onto a set of Lorentz structures related to the linear polarisation states of the $Z$ boson. We cross-check the finite remainders through a computation based on conventional form factor decomposition. We show that for physical observables, an ultimate D-dimensional form factor decomposition of amplitudes is not necessary which has a huge potential to simplify a multiloop computation. We compute numerically the resulting cross sections under the soft-virtual approximation to NNLO and find it three orders of magnitude smaller than that of the s-channel.
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We present a complete set of analytic helicity amplitudes for top quark pair production via gluon fusion at two-loops in QCD. For the first time, we include corrections due to massive fermion loops which give rise to integrals over elliptic curves. We present the results of the missing master integrals needed to compute the amplitude and obtain an analytic form for the finite remainders in terms of iterated integrals using rationalised kinematics and finite field sampling. We also study the numerical evaluation of the iterated integrals.
We present the calculation of next-to-next-to-leading order (NNLO) corrections in perturbative QCD for the production of a Higgs boson decaying into a pair of bottom quarks in association with a leptonically decaying weak vector boson: $mathrm{pp} to V mathrm{H} + X to ellbar{ell};mathrm{bbar{b}} + X$. We consider the corrections to both the production and decay sub-processes, retaining a fully differential description of the final state including off-shell propagators of the Higgs and vector boson. The calculation is carried out using the antenna subtraction formalism and is implemented in the NNLOJET framework. Clustering and identification of $mathrm{b}$-jets is performed with the flavour-$k_t$ algorithm and results for fiducial cross sections and distributions are presented for the LHC at $sqrt{s}=13;text{TeV}$. We assess the residual theory uncertainty by varying the production and decay scales independently and provide scale uncertainty bands in our results, yielding percent-level accurate predictions for observables in this Higgs production mode computed at NNLO. Confronting a naive perturbative expansion of the cross section against the customary re-scaling procedure to a fixed branching ratio reveals that starting from NNLO, the latter could be inadequate in estimating missing higher-order effects through scale variations.
We calculate the two-loop QCD corrections to $gg to ZZ$ involving a closed top-quark loop. We present a new method to systematically construct linear combinations of Feynman integrals with a convergent parametric representation, where we also allow for irreducible numerators, higher powers of propagators, dimensionally shifted integrals, and subsector integrals. The amplitude is expressed in terms of such finite integrals by employing syzygies derived with linear algebra and finite field techniques. Evaluating the amplitude using numerical integration, we find agreement with previous expansions in asymptotic limits and provide ab initio results also for intermediate partonic energies and non-central scattering at higher energies.
We compute the top quark contribution to the two-loop amplitude for on-shell $Z$ boson pair production in gluon fusion, $gg to ZZ$. Exact dependence on the top quark mass is retained. For each phase space point the integral reduction is performed numerically and the master integrals are evaluated using the auxiliary mass flow method, allowing fast computation of the amplitude with very high precision.
We present a precise and efficient computation of the two-loop amplitudes entering the Higgs boson pair production process via gluon fusion. Our approach is based on the small-Higgs-mass expansion while keeping the full dependence on the top quark mass and other kinematic invariants. We compare our results to the up-to-date predictions based on a combination of sector decomposition and high-energy expansion. We find that our method provides precision numeric predictions in the entire phase space, while at the same time is highly efficient as the computation can be easily performed on a normal desktop or laptop computer. Our method is valuable for practical phenomenological studies of the Higgs boson pair production process, and can also be applied to other similar processes.
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