Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop

172

194

Abstract:We analyze the production of Higgs particles at the early stage of the CERN large Hadron Collider with a 7 TeV center of mass energy (lHC). We first consider the case of the Standard Model Higgs boson that is mainly produced in the gluon-gluon fusion channel and to be detected in its decays into electroweak gauge bosons, gg → H → W W, ZZ, γγ. The production cross sections at √ s = 7 TeV and the decay branching ratios, including all relevant higher order QCD and electroweak corrections, are evaluated. An emphasis is put on the various theoretical uncertainties that affect the production rates: the significant uncertainties from scale variation and from the parametrization of the parton distribution functions as well as the uncertainties which arise due to the use of an effective field theory in the calculation of the next-to-next-to-leading order corrections. The parametric uncertainties stemming from the values of the strong coupling constant and the heavy quark masses in the Higgs decay branching ratios, which turn out to be non-negligible, are also discussed. The implications for different center of mass energies of the proton collider, √ s = 8-10 TeV as well as for the design energy √ s = 14 TeV, are briefly summarized. We then discuss the production of the neutral Higgs particles of the Minimal Supersymmetric extension of the Standard Model in the two main channels: gluon-gluon and bottom quark fusion leading to Higgs bosons which subsequently decay into tau lepton or b-quark pairs, gg, bb → Higgs → τ + τ − , bb. The Higgs production cross sections at the lHC and the decay branching ratios are analyzed. The associated theoretical uncertainties are found to be rather large and will have a significant impact on the parameter space of the model that can be probed.

Section: The Production Cross Sections At the Lhcmentioning

confidence: 99%

Higgs production at the lHC

Baglio

Djouadi

2011

172

194

“…Equations exact in m 2 could also be useful to study integrals appearing in realistic amplitudes involving massive particles, see e.g. [56]. It should be possible to derive such equations at least in some cases, perhaps by noticing that four-dimensional massive propagators are formally identical to AdS bulk-to-boundary propagators [52].…”

Section: Jhep04(2011)083mentioning

confidence: 99%

New differential equations for on-shell loop integrals

Drummond

Henn

Trnka

2011

155

We present a novel type of differential equations for on-shell loop integrals. The equations are second-order and importantly, they reduce the loop level by one, so that they can be solved iteratively in the loop order. We present several infinite series of integrals satisfying such iterative differential equations. The differential operators we use are best written using momentum twistor space. The use of the latter was advocated in recent papers discussing loop integrals in N = 4 super Yang-Mills. One of our motivations is to provide a tool for deriving analytical results for scattering amplitudes in this theory. We show that the integrals needed for planar MHV amplitudes up to two loops can be thought of as deriving from a single master topology. The master integral satisfies our differential equations, and so do most of the reduced integrals. A consequence of the differential equations is that the integrals we discuss are not arbitrarily complicated transcendental functions. For two specific two-loop integrals we give the full analytic solution. The simplicity of the integrals appearing in the scattering amplitudes in planar N = 4 super Yang-Mills is strongly suggestive of a relation to the conjectured underlying integrability of the theory. We expect these differential equations to be relevant for all planar MHV and non-MHV amplitudes. We also discuss possible extensions of our method to more general classes of integrals.

“…In particular we develop tools and understanding that will be valuable for the N 2 LO computation: (i) we introduce a systematic method of expansion of Feynman integrals based on differential equations and (ii) we explore how the phase-space integration create non-trivial analytic behaviour of the inclusive integrals as m b → 0 and we were able to obtain the correct small m 2 b expansion. Note that the two-loop amplitudes needed at NLO along with the corresponding master integrals are already known in the literature with full m b dependence [4,[9][10][11][12] and that the real radiation matrix elements have been obtained in references [13][14][15]. While the known two-loop virtual master integrals will merely serve as a check of our method of expansion, we present analytic results for the cut two-loop real master integrals for the first time.…”

Section: Jhep08(2016)055mentioning

confidence: 97%

On the computation of finite bottom-quark mass effects in Higgs boson production

Mueller

Öztürk

2016

We present analytic results for the partonic cross-sections contributing to the top-bottom interference in Higgs production via gluon fusion at hadron colliders at NLO accuracy in QCD. We develop a method of expansion in small bottom-mass for master integrals and combine it with the usual infinite top-mass effective theory. Our method of expansion admits a simple algorithmic description and can be easily generalized to any small parameter. These results for the integrated cross-sections will be needed in the computation of the renormalization counter-terms entering the computation of finite bottom-quark mass effects at NNLO.