Two-loop corrections to the triple Higgs boson production cross section
Received: October
Two-loop corrections to the triple Higgs boson production cross section
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0 25 de Mayo y Francia , (1650) Buenos Aires , Argentina
1 Physik-Institut, Universitat Zurich
2 International Center for Advanced Studies (ICAS) , ECyT-UNSAM, Campus Miguelete
In this paper we compute the QCD corrections for the triple Higgs boson production cross section via gluon fusion, within the heavy-top approximation. We present, for the rst time, analytical results for the next-to-leading order corrections, and also compute the soft and virtual contributions of the next-to-next-to-leading order cross section. We provide predictions for the total cross section and the triple Higgs invariant mass distribution. We nd that the QCD corrections are large at both perturbative orders, and that the scale uncertainty is substantially reduced when the second order perturbative corrections are included.
QCD Phenomenology; NLO Computations
1 Introduction 2 3 4
Virtual corrections up to NNLO
NLO and NNLOSV partonic cross sections
Phenomenological results
to study its properties in order to determine whether it is indeed the particle predicted
which are so far compatible with the SM expectations, it is of great interest to determine
therefore the electroweak symmetry breaking mechanism.
The Higgs boson trilinear and quartic self-couplings 3 and 4 can be studied in hadron
method based on single Higgs production). The SM expectations for these processes,
corresponding to 3 =
value and mH its mass, are very low. For a collider energy of 14 TeV, the leading order
(LO) predictions for the double and triple Higgs production cross sections are of O(20 fb)
and O(0:05 fb). As a consequence, in a SM-like scenario, a determination of the trilinear
via triple Higgs boson production will be at best relegated to a future collider [4, 5]. Of
course, the situation can be largely modi ed in the presence of new physics scenarios for
the Higgs sector.
As it also happens for single and double Higgs production, the triple-Higgs nal state
is mainly produced in the SM via gluon fusion, mediated by a heavy quark (mainly top)
predictions were obtained in ref. [7], where only the exact real corrections were included.
In this paper, we present the rst calculation of the QCD perturbative corrections
for triple Higgs production within the Higgs e ective
eld theory (HEFT). Within this
framework, which formally corresponds to the large top quark mass limit of the SM, the
leading order (NNLO) soft and virtual contributions for the total cross section and the
triple Higgs system invariant mass distribution.
This work is organized as follows: in section 2 we present the virtual corrections up
in section 5 we present our conclusions.
Virtual corrections up to NNLO
duction cross section in hadronic collisions via gluon fusion. As was stated before, we
work within the HEFT were the Higgs bosons couple directly to gluons via the e ective
Le =
CHH 2v2 + CHHH 3v3 + : : : ;
and where the matching coe cients can be expanded in powers of the strong coupling S as
CX =
with D = 4
2 dimensions.
squared matrix element as
The three coe cients needed for our calculation are known up to fourth order in their
perturbative expansion [8{14].
For the generation of the relevant Feynman diagrams we employed qgraf [15], while
The virtual corrections to the partonic cross section can be written in terms of the
^v =
2s 3!2282(1
d^v dPS3
three particle phase space. Expanding in powers of the strong coupling, we have
d^v =
Exploiting the well known one and two-loop infrared behaviour of QCD
amplitudes [17{19], we can write the renormalized NLO and NNLO virtual corrections as
d^(2) =
d^(0)+ 2 Re hI(1)i d^(1n) + d^(2n) ;
g
where I(1) and I(2) represent the one and two-loop insertion operators de ned, for instance,
in ref. [17].
The D dimensional LO cross section can be written as
d^(0) = FLDOjCL3HO j2(1
FLDO =
1728v6(1
and where the coe cient CL3HO is de ned as
CL3HO = 2 +
Here sij:::k = (pi + pj +
due to the Higgs width is negligible), in which case the CL3HO coe cient is a real number.
The one and two-loop infrared-regulated parts can be organized in the following way:
The contributions labelled F arise from diagrams with only one HEFT operator insertion.
The ones in R originate from the interference between amplitudes with two HEFT operator
insertions and amplitudes with only one insertion. On the other hand, contributions in
T arise from the interference between diagrams with three operator insertions and the
LO, and the ones in V come from the square of amplitudes with two insertions. Finally,
contributions to S have their origin on the di erence between the NNLO QCD corrections
to the e ective vertices Hgg, HHgg and HHHgg. In gure 1 we show illustrative examples
already mentioned, since we adopted the Higgs zero-width approximation, both CL3HO and
CL2HO are real numbers. Beyond that limit, there is also a numerically negligible co (...truncated)