In the minimal supersymmetric extension of the SM (MSSM) the Higgs sector con-
sists of two SU(2) doublets, H
1
and H
2
, whose relative contribution to electroweak (EW)
symmetry breaking is determined by the ratio of vacuum expectation values (VEVs) of
their neutral components, tan β ≡ v
2
/v
1
. The spectrum of physical Higgs bosons is richer
than in the SM, consisting of two neutral scalars, h and H, one neutral pseudoscalar, A,
and two charged scalars, H
±
. The couplings of the scalars to matter fermions and gauge
bosons, as well as their self-couplings, differ in general from the SM ones. However, in
the so-called decoupling limit of the MSSM Higgs sector, m
A
m
Z
, the lightest scalar h
has SM-like couplings and can be identified with the particle discovered at the LHC, with
m
h
≈ 125 GeV [25].
The dominant mechanism for Higgs pair production in the MSSM is gluon fusion,
1
mediated by loops involving the top and bottom quarks and their superpartners, the stop
and sbottom squarks. Only for relatively light squarks, with masses below the TeV scale,
do the squark contributions lead to sizeable effects on the cross section for the production of
SM-like Higgs pairs [28]. Direct searches leave several corners of parameter space for light
stops open, e.g. for reduced branching ratios or difficult kinematic configurations [29–31].
However, the measured value of m
h
implies either stop masses in the multi-TeV range or
a large and somewhat tuned left-right mixing in the stop mass matrix. Scenarios allowing
for light stops are thus restricted to the latter possibility.
Due to the extended Higgs spectrum of the MSSM, a pair of light scalars can also
be produced resonantly through the s-channel exchange of a heavy scalar, leading to a
sizeable increase in the cross section [32–35]. In addition, mixed scalar/pseudoscalar pairs,
and pairs of pseudoscalars, can as well be produced in gluon fusion. In this paper, however,
we will restrict our attention to the production of scalar pairs.
In the SM, the leading-order (LO) cross section for Higgs pair production via gluon
fusion, fully known since the late eighties [36], is subject to large radiative corrections.
The next-to-leading order (NLO) QCD contributions of diagrams involving top quarks
were computed in the late nineties in the limit of infinite top mass m
t
, or, equivalently, of
vanishing external momenta [33]. Whereas this approximation was shown to work quite well
for single Higgs production [37], it can be expected to be less effective for pair production,
due to the larger energy scale that characterizes the latter process. Unfortunately, an exact
two-loop calculation of the “box” form factor that contributes to Higgs pair production at
the NLO in QCD is currently not available. In contrast, the “triangle” form factor entering
diagrams where a single (s-channel) Higgs boson splits into a Higgs pair can be borrowed
from the the calculation of single Higgs production [37–40].
In order to improve the NLO result for Higgs pair production in the SM, ref. [33]
factored out the LO cross section with the full top-mass dependence. The uncertainties of
this approach were estimated to be of O(10%) in refs. [41–44]. The next-to-next-to leading
order (NNLO) contributions in the heavy-top limit were computed in refs. [45–47]. Soft
gluon resummation at next-to-next-leading logarithmic (NNLL) order was performed in
1
For the single production of neutral Higgs bosons with enhanced couplings to down-type fermions, the
bb annihilation process dominates over gluon fusion for intermediate to large values of tan β. In contrast,
for Higgs pair production this is only the case in very limited regions of the MSSM parameter space [26, 27].
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