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Eur. Phys. J. C (2014) 74:2809

DOI 10.1140/epjc/s10052-014-2809-3

Regular Article - Theoretical Physics

Implications of improved Higgs mass calculations

for supersymmetric models

O. Buchmueller

,M.J.Dolan

, J. Ellis

3,4

, T. Hahn

, S. Heinemeyer

6,a

, W. Hollik

, J. Marrouche

,K.A.Olive

H. Rzehak

,K.J.deVries

, G. Weiglein

High Energy Physics Group, Blackett Lab., Imperial College, Prince Consort Road, London SW7 2AZ, UK

Theory Group, SLAC National Accelerator Lab., 2575 Sand Hill Road, Menlo Park, CA 94025-7090, USA

Theoretical Particle Physics and Cosmology Group, Department of Physics, King’s College London, London WC2R 2LS, UK

Theory Division, CERN, 1211 Geneva 23, Switzerland

Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 Munich, Germany

Instituto de Física de Cantabria (CSIC-UC), 39005 Santander, Spain

William I. Fine Theoretical Physics Institute, School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA

Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, 79104 Freiburg, Germany

DESY, Notkestrasse 85, 22607 Hamburg, Germany

Received: 9 January 2014 / Accepted: 4 March 2014 / Published online: 18 March 2014

Abstract We discuss the allowed parameter spaces of

supersymmetric scenarios in light of improved Higgs mass

predictions provided by FeynHiggs 2.10.0. The Higgs

mass predictions combine Feynman-diagrammatic results

with a resummation of leading and subleading logarithmic

corrections from the stop/top sector, which yield a signiﬁ-

cant improvement in the region of large stop masses. Scans

in the pMSSM parameter space show that, for given val-

ues of the soft supersymmetry-breaking parameters, the new

logarithmic contributions beyond the two-loop order imple-

mented in FeynHiggs tend to give larger values of the

light CP-even Higgs mass, M

, in the region of large stop

masses than previous predictions that were based on a ﬁxed-

order Feynman-diagrammatic result, though the differences

are generally consistent with the previous estimates of the-

oretical uncertainties. We re-analyse the parameter spaces

of the CMSSM, NUHM1 and NUHM2, taking into account

also the constraints from CMS and LHCb measurements of

BR(B

→ μ

−

)and ATLAS searches for /E

events using

20/fb of LHC data at 8 TeV. Within the CMSSM, the Higgs

mass constraint disfavours tan β  10, though not in the

NUHM1 or NUHM2.

1 Introduction

The ATLAS and CMS experiments did not discover s uper-

symmetry (SUSY) during the ﬁrst, low-energy LHC run at 7

e-mail: Sven.Heinemeyer@cern.ch

and 8 TeV. However, an optimist may consider that the head-

line discovery of a Higgs boson weighing ∼126 GeV [1,2]

has provided two additional pieces of indirect, circumstan-

tial evidence for SUSY, beyond the many previous motiva-

tions. One piece of circumstantial evidence is provided by the

Higgs mass, which falls within the range 135 GeV calcu-

lated in the minimal SUSY extension of the Standard Model

(MSSM) for masses of the SUSY particles around 1 TeV [3–

15]. The other piece of circumstantial evidence is provided by

measurements of Higgs couplings, which do not display any

signiﬁcant deviations from Standard Model (SM) predictions

at the present level of experimental accuracy. This disfavours

some composite models but is consistent with the predictions

of simpliﬁed SUSY models such as the constrained MSSM

(CMSSM) [ 16–25] with universal input soft SUSY-breaking

masses m

for scalars, m

1/2

for fermions as well as A

,the

soft SUSY-breaking trilinear coupling and NUHM models

that have non-universal soft SUSY-breaking contributions

to Higgs supermultiplet masses: see [26–30] and [31]for

areview.

That said, the absence of SUSY in the ﬁrst LHC run

and the fact that the Higgs mass is in the upper part of the

MSSM range both suggest, within simple models such as the

CMSSM and NUHM (see, e.g., [32,33]) as well as in the

pMSSM, that the SUSY particle mass scale may be larger

than had been suggested prior to the LHC, on the basis of

ﬁne-tuning arguments and in order to explain the discrep-

ancy between calculations of (g − 2)

within the SM and the

experimental measurement [34]. A relatively large SUSY

particle mass scale also makes it easier to reconcile SUSY

123

2809 Page 2 of 14 Eur. Phys. J. C (2014) 74:2809

with the experimental measurement of BR(B

→ μ

−

)

[35–37], particularly if tan β (the ratio of SUSY Higgs vac-

uum expectation values, v.e.v.s) is large.

The mathematical connection between the Higgs mass and

the SUSY particle spectrum is provided by calculations of

the lightest SUSY Higgs mass M

in terms of the SUSY

particle spectrum [3–11,14,15]: see [38–40] for reviews. As

is well known, one-loop radiative corrections allow M

exceed M

by an amount that is logarithmically sensitive

to such input parameters as the top squark masses m

in the

pMSSM, or the universal m

1/2

and m

masses in the CMSSM

and NUHM. Inverting this calculation, the inferred values of

,orm

1/2

, m

and A

are exponentially sensitive to the

measured value of M

. For this reason, it is essential to make

available and use the most accurate calculations of M

within

the MSSM, and to keep track of the unavoidable theoretical

uncertainties in these calculations due to unknown higher-

order corrections, which are now larger than the experimental

measurement error.

Several codes to calculate M

are available [41–48]. In

terms of low-energy parameters, the most advanced calcula-

tion is provided by FeynHiggs [14,49–52]. The differences

between the codes are in the few GeV range for relatively

light SUSY spectra, but they may become larger for higher

third family squark masses and values of m

1/2

, m

and A

This is particularly evident in the phenomenological MSSM

(pMSSM), where the soft supersymmetry-breaking inputs to

the SUSY spectrum codes are speciﬁed at a low scale, close

to the physical masses of the supersymmetric particles.

In this paper we revisit the constraints on the CMSSM

and NUHM parameter spaces imposed by the Higgs mass

measurement using the signiﬁcantly improved 2.10.0 ver-

sion of the FeynHiggs code [49–53] that has recently been

released. We situate our discussion in the context of a com-

parison between this and the earlier version FeynHiggs

2.8.6, which has often been used in phenomenological

studies of SUSY parameter spaces (e.g., in [54]), as well as

with SOFTSUSY 3.3.9 [41]. We also discuss the implica-

tions for constraints on SUSY model parameters. Updating

previous related analyses [32,33], we also take into account

the complementary constraint on the CMSSM and NUHM

parameter spaces imposed by the recent experimental mea-

surement of BR(B

→ μ

−

), and we incorporate the 95 %

CL limit on m

1/2

and m

established within the CMSSM by

ATLAS following searches for missing transverse energy,

, events using 20/fb of LHC data at 8 TeV [55].

The layout of this paper is as follows. In Sect. 2 we

ﬁrst summarise the main improvements between the results

implemented in FeynHiggs 2.8.6 and 2.10.0, and

then we present some illustrative results in the pMSSM, dis-

cussing the numerical differences between calculations made

using FeynHiggs versions 2.8.6 and 2.10.0. We then

display in Sect. 3 some representative parameter planes in

the CMSSM, NUHM1 and NUHM2, discussing the inter-

play between the different experimental constraints including

BR(B

→ μ

−

)as well as M

. Section 4 contains a discus-

sion of the variations between the predictions of M

made in

global ﬁts to CMSSM and NUHM1 model parameters using

different versions of FeynHiggs and SOFTSUSY. Finally,

Sect. 5 summarises our conclusions.

2 Comparisons of Higgs mass calculations

within the general MSSM

2.1 The improved Higgs mass calculation in FeynHiggs

2.10.0

The evaluation of Higgs boson masses in the MSSM, in par-

ticular of the mass of the lightest Higgs boson, M

, has

recently been improved for larger values of the scalar top

mass scale. This new evaluation has been implemented in the

code FeynHiggs 2.10.0, whose details can be found in

[53]. Here we just summarise some salient points.

The code FeynHiggs provides predictions for the

masses, couplings and decay properties of the MSSM Higgs

bosons at the highest currently available level of accuracy

as well as approximations for LHC production cross sec-

tions (for MSSM Higgs decays see also [56] and refer-

ences therein). The evaluation of Higgs boson masses within

FeynHiggs is based on a Feynman-diagrammatic calcula-

tion of the Higgs boson self-energies. By ﬁnding the higher-

order corrected poles of the propagator matrix, the loop-

corrected Higgs boson masses are obtained.

The principal focus of the improvements in FeynHiggs

2.10.0 has been to attain greater accuracy for large stop

masses. The versions of FeynHiggs as used, e.g., previ-

ously in [54] included the full one-loop and the leading and

subleading two-loop corrections to the Higgs boson self-

energies (and thus to M

). The new version, FeynHiggs

2.10.0 [53], which is used for the evaluations here, con-

tains in addition a resummation of the leading and next-to-

leading logarithms of type log(m

) in all orders of per-

turbation theory, which yields reliable results for m

, M



. To this end the two-loop Renormalisation-Group Equa-

tions (RGEs) [57,58 ] have been solved, taking into account

the one-loop threshold corrections to the quartic coupling at

the SUSY scale: see [59] and references therein. In this way

at n-loop order the terms

∼ log

), ∼ log

n−1

) (1)

are taken into account. The resummed logarithms, which are

calculated in the

MS scheme for the scalar top sector, are

matched to the one- and two-loop corrections, where the on-

shell scheme had been used for the scalar top sector. The

123

Eur. Phys. J. C (2014) 74:2809 Page 3 of 14 2809

ﬁrst main difference between FeynHiggs 2.10.0 and

previous versions occurs at three-loop order. As we shall

see, FeynHiggs 2.10.0 yields a larger estimate of M

for stop masses in the multi-TeV range and a correspondingly

improved estimate of the theoretical uncertainty, as discussed

in [53]. The improved estimate of the uncertainties arising

from corrections beyond two-loop order in the top/stop sector

is adjusted such that the impact of replacing the running top-

quark mass by the pole mass (see [14]) is evaluated only

for the non-logarithmic corrections rather than for the full

two-loop contributions implemented in FeynHiggs.

Other codes such as SoftSusy [41], SPheno [42,43]

and SuSpect [44] implement a calculation of the Higgs

masses based on a

DR renormalisation of the scalar quark

sector

. These codes contain the full one-loop corrections

to the MSSM Higgs masses and implement the most impor-

tant two-loop corrections. In particular, SoftSusy contains

the O(α

), O(α

) and

O(α

) corrections of [11–13,15] evaluated at zero external

momentum for the neutral Higgs masses. These codes do not

contain the additional resummed higher-order terms included

in FeynHiggs 2.10.0. We return in Sect. 4 to a compari-

son between SoftSusy3.3.9 and FeynHiggs2.10.0.

More recently a calculation of M

taking into account

leading three-loop corrections of O(α

) has became avail-

able, based on a

DR or a “hybrid” renormalisation scheme

for the scalar top sector, where the numerical evaluation

depends on the various SUSY mass hierarchies, resulting

in the code H3m [46–48], which adds the three-loop correc-

tions to the FeynHiggs result. A brief comparison between

FeynHiggs and H3m can be found in [53,60].

A numerical analysis in the CMSSM including leading

three-loop corrections to M

(with the code H3m) was pre-

sented in [60]. It was shown that the leading three-loop terms

can have a strong impact on the interpretation of the measured

Higgs mass value in the CMSSM. Here, with the new ver-

sion of FeynHiggs, we go beyond this analysis by includ-

ing (formally) subleading three-loop corrections as well as a

resummation to all orders of the leading and next-to-leading

logarithmic contributions to M

; see above.

2.2 Comparing the improved Higgs mass calculation in

FeynHiggs 2.10.0 with FeynHiggs 2.8.6

In the following we examine the effect of including the

resummation of leading and subleading logarithmic correc-

tions from the (scalar) top sector in the pMSSM. We com-

pare the new FeynHiggs version 2.10.0 withaprevi-

Since the differences between the on-shell and DR renormalisation

in the scalar quark sector are formally of higher order, comparisons can

be used to assess the uncertainties in the predictions of the Higgs mass.

ous one, 2.8.6, where the only relevant difference in the

Higgs mass calculation between the two codes consists of the

aforementioned resummation effects. (A comparison includ-

ing SOFTSUSY can be found in Sect. 4.) These corrections

are most sensitive to the soft SUSY-breaking parameters in

the stop sector, m

q

in the diagonal entry (which we assume

here to be equal for left- and right-handed stops) and the

trilinear coupling A

. To have direct control over these two

parameters, we consider a 10-parameter incarnation of the

MSSM, denoted as the pMSSM10. In the pMSSM10 we set

the squark masses of the ﬁrst two generations to a common

value m

q

, the third-generation squark mass parameters to a

different value m

q

, the slepton masses to m



and the trilinear

couplings A

= A

= A. The remaining parameters of

the pMSSM10 are the soft SUSY-breaking parameters in the

gaugino sectors, M

, M

, the Higgs mixing parameter

μ, the CP-odd Higgs mass scale M

as well as tan β.

We generate 1000 random sets of the eight parameters

q



, M

, tan β,μ and M

, without regard to

the experimental constraints. For each of these sets we

vary m

q

= 0.5, 1, 2, 3, 4 and 5 TeV and A/m

q

0, ±1.0, ±2.0, ±2.4, and we calculate the corresponding

spectra using SOFTSUSY-3.3.9. Using these spectra, we

calculate M

with FeynHiggs 2.8.6 and FeynHiggs

2.10.0. We stress that the pMSSM10 spectra are only

meant to illustrate the size of the corrections as a function

of m

q

and the trilinear coupling A, and we do not necessar-

ily correspond to phenomenologically interesting regions of

parameter space.

The sizes of the corrections from the (scalar) top sector are

given by the differences (M

FH2.10.0

− M

FH2.8.6

) shown

in Fig. 1 as functions of M

FH2.8.6

. The different panels in

this ﬁgure correspond to the different third-generation squark

masses m

q

= 0.5 TeV (upper left), 1 TeV (upper right),

2 TeV (middle left), 3 TeV (middle right), 4 TeV (lower left)

and 5 TeV (lower right), whereas the colours dark blue, blue,

light blue, light green, orange, red and dark red correspond to

A/m

q

=−2.4, −2.0 , −1.0, 0.0 , 1.0, 2.0 , 2.4, respectively.

At low stop masses of around 500 GeV we see that the resum-

mation corrections are O(0.5) GeV, whereas with increasing

stop masses they may become as large as 5 GeV. The depen-

dence on A/m

q

is less signiﬁcant. We also note that, for

similar values of m

q

, the resummation corrections tend to

be smaller for models yielding M

∼ 125 GeV than for mod-

els yielding smaller values of M

The latter effect is related to the (random) choice of M

and tan β, with lower M

values corresponding to lower

and smaller tan β.IftheM

value without resummed

corrections, i.e., from FeynHiggs 2.8.6, is smaller, the

newly added correction, which is independent of M

and

tan β has a larger effect. We should furthermore mention

that the size of the resummed correction stays (mostly)

within the previously predicted estimate for the theoretical

123

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