Large Top Mass Limit Research Articles

Benchmarking di-Higgs production in various extended Higgs sector models

We present a comprehensive study on Higgs pair production in various archetypical extended Higgs sectors such as the real and the complex 2-Higgs-Doublet Model, the 2-Higgs-Doublet Model augmented by a real singlet field and the Next-to-Minimal Supersymmetric extension of the Standard Model. We take into account all relevant theoretical and experimental constraints, in particular the experimental limits on non-resonant and resonant Higgs pair production. We present the allowed cross sections for Standard Model (SM)-like Higgs pair production and the ranges of the SM-like Yukawa and trilinear Higgs self-coupling that are still compatible with the applied constraints. Furthermore, we give results for the pair production of a SM-like with a non-SM-like Higgs boson and for the production of a pair of non-SM-like Higgs bosons. We find that di-Higgs production in the models under investigation can exceed the SM rate substantially, not only in the non-resonance region but also due to resonant enhancement. We give several benchmarks with interesting features such as large cross sections, the possibility to test CP violation, Higgs-to-Higgs cascade decays or di-Higgs production beating single Higgs production. In all of our benchmark points, the next-to-leading order QCD corrections are included in the large top-mass limit. For these points, we found that, depending on the model and the Higgs pair final state, the corrections increase the leading order cross section by a factor of 1.79 to 2.24. We also discuss the relation between the description of Higgs pair production in an effective field theory approach and in the specific models investigated here.

The complete singlet contribution to the massless quark form factor at three loops in QCD

It is well known that the effect of top quark loop corrections in the axial part of quark form factors (FF) does not decouple in the large top mass or low energy limit due to the presence of the axial-anomaly type diagrams. The top-loop induced singlet-type contribution should be included in addition to the purely massless result for quark FFs when applied to physics in the low energy region, both for the non-decoupling mass logarithms and for an appropriate renormalization scale dependence. In this work, we have numerically computed the so-called singlet contribution to quark FFs with the exact top quark mass dependence over the full kinematic range. We discuss in detail the renormalization formulae of the individual subsets of the singlet contribution to an axial quark FF with a particular flavor, as well as the renormalization group equations that govern their individual scale dependence. Finally we have extracted the 3-loop Wilson coefficient in the low energy effective Lagrangian, renormalized in a mathrm{non}hbox{-} overline{mathrm{MS}} scheme and constructed to encode the leading large mass approximation of our exact results for singlet quark FFs. We have also examined the accuracy of the approximation in the low energy region.

Three-loop form factors for Higgs boson pair production in the large top mass limit

We consider the virtual corrections to Higgs boson pair production at next-to- next-to-leading order, in the large top quark mass limit. We compute five expansion terms for the box-type form factors and eight expansion terms for the triangle form factor, which serve as useful input for the construction of approximations. We present analytic results for the form factors in the soft-virtual approximation.From a technical point of view the calculation is quite challenging since huge intermediate expressions are produced. We describe our methods and optimizations to overcome these difficulties, which might be useful for other calculations.

Tr(F3) supersymmetric form factors and maximal transcendentality. Part I. mathcal{N} = 4 super Yang-Mills

In the large top-mass limit, Higgs plus multi-gluon amplitudes in QCD can be computed using an effective field theory. This approach turns the computation of such amplitudes into that of form factors of operators of increasing classical dimension. In this paper we focus on the first finite top-mass correction, arising from the operator Tr(F3), up to two loops and three gluons. Setting up the calculation in the maximally supersymmetric theory requires identification of an appropriate supersymmetric completion of Tr(F3), which we recognise as a descendant of the Konishi operator. We provide detailed computations for both this operator and the component operator Tr(F3), preparing the ground for the calculation in mathcal{N} < 4, to be detailed in a companion paper. Our results for both operators are expressed in terms of a few universal functions of transcendental degree four and below, some of which have appeared in other contexts, hinting at universality of such quantities. An important feature of the result is a delicate cancellation of unphysical poles appearing in soft/collinear limits of the remainders which links terms of different transcendentality. Our calculation provides another example of the principle of maximal transcendentality for observables with non-trivial kinematic dependence.

Universality of next-to-leading power threshold effects for colourless final states in hadronic collisions

We consider the production of an arbitrary number of colour-singlet particles near partonic threshold, and show that next-to-leading order cross sections for this class of processes have a simple universal form at next-to-leading power (NLP) in the energy of the emitted gluon radiation. Our analysis relies on a recently derived factorisation formula for NLP threshold effects at amplitude level, and therefore applies both if the leading-order process is tree-level and if it is loop-induced. It holds for differential distributions as well. The results can furthermore be seen as applications of recently derived next-to-soft theorems for gauge theory amplitudes. We use our universal expression to re-derive known results for the production of up to three Higgs bosons at NLO in the large top mass limit, and for the hadro-production of a pair of electroweak gauge bosons. Finally, we present new analytic results for Higgs boson pair production at NLO and NLP, with exact top-mass dependence.

Higgs boson gluon-fusion production in QCD at three loops.

We present the cross section for the production of a Higgs boson at hadron colliders at next-to-next-to-next-to-leading order (N^{3}LO) in perturbative QCD. The calculation is based on a method to perform a series expansion of the partonic cross section around the threshold limit to an arbitrary order. We perform this expansion to sufficiently high order to obtain the value of the hadronic cross at N^{3}LO in the large top-mass limit. For renormalization and factorization scales equal to half the Higgs boson mass, the N^{3}LO corrections are of the order of +2.2%. The total scale variation at N^{3}LO is 3%, reducing the uncertainty due to missing higher order QCD corrections by a factor of 3.

QCD corrections to [Formula: see text] in FDR.

I apply FDR—a recently introduced four-dimensional approach to quantum field theories (QFTs)—to the computation of the NLO QCD corrections to H rightarrow gg in the large top mass limit. The calculation involves all key ingredients of QCD—namely ultraviolet, infrared, and collinear divergences, besides alpha _S renormalization—and paves the way for successful use of FDR in massless one-loop QFT computations. I show in detail how the correct result emerges in FDR, and discuss the translation rules to dimensional regularization.

On Higgs-exchange DIS, physical evolution kernels and fourth-order splitting functions at large x

We present the coefficient functions for deep-inelastic scattering (DIS) via the exchange of a scalar ϕ directly coupling only to gluons, such as the Higgs boson in the limit of a very heavy top quark and n f effectively massless light flavours, to the third order in perturbative QCD. The two-loop results are employed to construct the next-to-next-to-leading order physical evolution kernels for the system ( F 2 , F ϕ ) of flavour-singlet structure functions. The practical relevance of these kernels as an alternative to MS ¯ factorization is bedevilled by artificial double logarithms at small values of the scaling variable x, where the large top-mass limit ceases to be appropriate. However, they show an only single-logarithmic enhancement at large x. Conjecturing that this feature persists to the next order also in the present singlet case, the three-loop coefficient functions facilitate exact predictions (backed up by their particular colour structure) of the double-logarithmic contributions to the fourth-order singlet splitting functions, i.e., of the terms ( 1 − x ) a ln k ( 1 − x ) with k = 4 , 5 , 6 and k = 3 , 4 , 5 , respectively, for the off-diagonal and diagonal quantities to all powers a in ( 1 − x ) .

Analytic one-loop amplitudes for a Higgs boson plus four partons

We compute the one-loop QCD amplitudes for the processes H{anti q}q{anti Q}Q and H{anti q}qgg, the latter restricted to the case of opposite-helicity gluons. Analytic expressions are presented for the color- and helicity-decomposed amplitudes. The coupling of the Higgs boson to gluons is treated by an effective interaction in the limit of large top quark mass. The Higgs field is split into a complex field {phi} and its complex conjugate {phi}{sup {dagger}}. The split is useful because amplitudes involving {phi} have different analytic structure from those involving {phi}{sup {dagger}}. We compute the cut-containing pieces of the amplitudes using generalized unitarity. The remaining rational parts are obtained by on-shell recursion. Our results for H{anti q}q{anti Q}Q agree with previous semi-numerical computations. We also show how to convert existing semi-numerical results for the production of a scalar Higgs boson into analogous results for a pseudoscalar Higgs boson.

Next-to-leading order Higgs + 2 jet production via gluon fusion

We present phenomenological results for the production of a Higgs boson in association with two jets at the LHC. The calculation is performed in the limit of large top mass and is accurate to next-to-leading order in the strong coupling, i.e. ${\cal O}(\alpha_s^6)$

One-loop helicity amplitudes for H → gluons: the all-minus configuration

We use twistor inspired rules to compute the one-loop amplitude for a Higgs boson coupling to any number of negative helicity gluons in the large top mass limit.

Three loop top quark contributions to the ρ parameter

We present results for the three-loop top quark contributions to the ρ parameter in the limit of large top quark mass. The simultaneous dependence on the mass of the Higgs boson M H and the mass of the top quark m t is obtained from expansions in the range of M H around m t and in the limit M H ⪢ m t . In combination with the previous result for M H =0 the dependence of the ρ parameter on the leading Yukawa contributions, i.e., on m t and M H , is well under control for all mass values of practical importance. The effects lead to a shift in the W mass in the order of 5 MeV and are relevant for precision measurements at TESLA.

Kinematical limits on Higgs boson production via gluon fusion in association with jets

In this paper, we analyze the high-energy limits for Higgs boson plus two jet production. We consider two high-energy limits, corresponding to two different kinematic regions: a) the Higgs boson is centrally located in rapidity between the two jets, and very far from either jet; b) the Higgs boson is close to one jet in rapidity, and both of these are very far from the other jet. In both cases the amplitudes factorize into impact factors or coefficient functions connected by gluons exchanged in the t channel. Accordingly, we compute the coefficient function for the production of a Higgs boson from two off-shell gluons, and the impact factors for the production of a Higgs boson in association with a gluon or a quark jet. We include the full top quark mass dependence and compare this with the result obtained in the large top-mass limit.

Neutral current in the heavy top quark limit and the renormalization of the singlet axial current

We use a simple renormalization group argument to demonstrate that the large top mass limit of the axial neutral current in QCD is unambiguously determined by the renormalization of the singlet axial current which suggests a natural scheme independent normalization condition for the latter. By calculating the anomalous dimension of the singlet axial current at three-loop level in the\(\overline {MS}\) scheme we derive the result for the top quark decoupling from the axial neutral current valid up to (and including) the terms of order αs2.

Complete QCD corrections of order α2S to the Z decay rate

The axial part of the Z decay rate into hadrons ( Γ A Z ) gets extra singlet contributions due to the huge splitting between top and bottom quark masses. By treating the axial neutral current in the large top-mass limit we partially re-derive in a systematic manner the known results on the contribution of the α 2 S order anomalous “double triangle” diagrams to Γ A Z and resolve an ambiguity concerning the scale at which the strong coupling constant α S is to be taken in these diagrams. We evaluate and sum all leading log and next-to-leading log QCD corrections of orders α 1+n S[ ln( M Z 4m 2 t )] n and α 2+n S[ ln( M Z 4m 2 t )] n respectively. We examine the sensitivity of our results to a change of the renormalization scales to estimate the size of yet unknown corrections of order α 3 S to Γ A Z . The analysis implies that the corrections might change the magnitude of the singlet term by up to 30% while they hardly might be of noticeable numerical significance in comparison with the total contribution from non-singlet terms.

Complete mass corrections of order αs2m b2/M Z2 to the axial Z-boson decay rate in the large top-mass limit

We analytically compute the QCD mass corrections of order α s 2 m b 2/ M Z 2 to the decay rate of the Z-boson coming from anomalous “double triangle” diagrams which comprise single γ 5 matrices inside both of two closed fermion triangles. Coupled with our previous results, the present calculation determines the complete next to leading α s 2 corrections to the leading power suppressed term of order m b 2/ M z 2 in the axial part of the decay rate of the Z-boson. Numerically, the anomalous diagrams lead to a further decrease of the (already quite small) corrections.

Non-linear realizations of SU (2) × U (1) in the MSSM. Model independent analysis and g−2 of W bosons

We perform a model-independent analysis of the spontaneously broken phase of an SU (2) × U (1) supersymmetric gauge theory, by using a non-linear parametrization of the Goldstone sector of the theory. The non-linear variables correspond to an SL(2, C ) superfield matrix in terms of which a non-linear lagrangian can be constructed, and the pattern of supersymmetry breaking investigated. The supersymmetric order parameter is the VEV of the neutral pseudo-Goldstone boson. Some applications of this technique are considered, in relation to the minimal supersymmetric standard model, and to determine the g−2 of the W-bosons in the limit of large top mass.

Two-loop O( αsGμmt2) corrections to the partial decay width of the Z 0 into [formula omitted] final states in the large top-mass limit

The QCD correction to the one-loop electroweak radiative correction of the partial Z-decay width into b-quarks is calculated analytically in the limit of large top mass. The calculation is performed in the 't Hooft gauge with an arbitrary gauge parameter and QCD gauge-invariance is explicitly verified on-shell. Gluon bremsstrahlung is taken into account by integrating over the whole gluon phase space. All calculations, including the bremsstrahlung, are performed in the dimensional regularization scheme. We find a screening of the leading one-loop top mass effects by m t 2→m t 2 [1− 1 3 (π 2−3)α s π ] which is of the same magnitude as the one known for the ϱ-parameter.