arXiv:0809.2047v1 [hep-ph] 11 Sep 2008
Reconstructing SUSY and R-Neutrino Masses in SO(10)
F. Deppisch∗, A. Freitas†,∗∗, W. Porod‡and P.M. Zerwas§,¶
∗School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
†Department of Physics & Astronomy, University of Pittsburgh, PA 15260, USA
∗∗HEP Division, Argonne National Laboratory, Argonne, IL 60439, USA
‡Inst. Theor. Physik und Astrophysik, Universität Würzburg, D-97074 Würzburg, Germany
§Inst. Theor. Physik E, RWTH Aachen U, D-52056 Aachen, Germany
¶Deutsches Elektronen-SynchrotronDESY, D-22603 Hamburg, Germany
Abstract. We report on the extrapolation of scalar mass parameters in the lepton sector to reconstruct SO(10) scenarios close
to the unification scale. The method is demonstrated for an example in which SO(10) is broken directly to the Standard Model,
based on the expected precision from coherent LHC and ILC collider analyses. In addition to the fundamental scalar mass
parameters at the unification scale, the mass of the heaviest right-handed neutrino can be estimated in the seesaw scenario.
Keywords: Supersymmetry, Grand Unified Theories, Neutrinos
PACS: 12.10.Dm, 12.60.Jv, 14.60.Pq
in relation to the electroweak scale is offered by the see-
saw mechanism , which naturally suggests the sym-
metry group SO(10) as the grand unification group .
In this report, which summarizes the results of
Ref. , we focus on a simple model incorporating
one-step symmetry breaking from SO(10) down to the
Standard Model SM gauge group, SO(10) → SM, at
the GUT scale ΛU ≈ 2 · 1016GeV where the gauge
couplings unify in SUSY. We implicitly assume that a
number of fundamental problems  are solved without
interfering strongly with the key points of the present
analysis, i.e. mechanisms leading to doublet-triplet split-
ting and suppressing proton decay. Such solutions may
include extended Higgs sectors or higher-dimensional
Planck-scale suppressed operators.
The SUSY SO(10) model is characterized by the fol-
lowing part of the superpotential which involves matter
The matter superfields of the three generations belong to
16-dimensional representations of SO(10). Two Higgs-
10 fields generate masses separately for up- and down-
type fermions at the electroweak scale. The masses of
the heavy R-neutrino superfields are generated by a 126-
dimensional Higgs, resulting in a seesaw type I mecha-
nism of light neutrino mass generation.
The superpotential is supplemented by soft SUSY
breaking masses for the fermion and Higgs multiplets,
assumed to be universal at the unification scale,
m16= m10= m10′ = m126= M0.
However, the breaking of the SO(10) symmetry group to
the SM group generates GUT D-terms DUsuch that the
boundary conditions at the GUT scale read 
for the slepton L-isodoublet and R-isosinglet fields. The
D-term is of the order of the soft SUSY breaking masses
and we will treat DUas a free parameter.
The neutrino sector
The heavy right-handedneutrino masses are related to
the light neutrino masses by the Yukawa matrix Yν in
the seesaw mechanism. Neglecting higher-order effects
in the calculation of the Majorana neutrino mass matrix,
it follows from the Higgs-10 SO(10) relation
that Yν≈ diag(mu,mc,mt)/vu holds approximately for
the neutrino Yukawa matrix at the GUT scale; vu=
vsinβ, with v and tanβ being the familiar vacuum and
RG runningeffects in the neutrinosector are neglectedin
the numerical analysis.
tions of the lightest neutrino mass mν1. The dashed (blue) lines
assume perfect Yukawa unification, Eq. (3). The solid (black)
lines indicate shifts of the νRmasses if the Yukawa identity
Eq. (3) is violated by an additional contribution ∼ 100 MeV/v.
Masses of right-handed neutrinos MνRias func-
The effectivemass matrixof the light neutrinosis con-
strained by the results of the neutrino oscillation experi-
We will assume the normal hierarchy for the light neu-
trino masses mνi, and for the MNS mixing matrix the
tri-bimaximal form. From the seesaw relation
the heavy Majorana R-neutrino mass matrix MνRcan
now be calculated. Solving Eq. (5) for the eigenvalues
MνRi(i = 1,2,3), the heavy Majorana masses are deter-
mined by the up-quark masses mu,c,t at the GUT scale
and the lightest neutrino mass mν1, assuming best fit
values for the light neutrino squared mass differences.
The mass spectrum of the R-neutrinos is strongly hi-
erarchical in this scenario, MνR3: MνR2: MνR1∼ m2
like RG running effects, is displayed in Fig. 1 for a
wide range of mν1values. Modifying the relation be-
tween the neutrinoand up-typequarkYukawacouplings,
Eqs. (3), ad-hoc by a small additional term, Yν= Yu+
O(100 MeV)/v, associated potentiallywith a morecom-
plex Higgs scenario, Planck-scale suppressed contribu-
tions or non-perturbative effects, the first generation R-
u. The numericalevaluation,includingrefinements
The scalar sector
To leading order,the solutions of the RG equations for
the masses of the scalar selectrons, can be expressed in
neutrino parameters in an example scenario point
(µ > 0).
Reconstruction of SO(10), SUSY and
terms of the universal scalar mass M0, the gaugino mass
M1/2, and the GUT and electroweak D-terms, DU and
Z/2 cos2β, respectively1,
˜ eR= M2
˜ eL= M2
The coefficients αLand αRare determined by the gaug-
ino/gauge boson loops in the RG evolution from the
˜ M  to the unification scale, and the
numerical evaluation yields αR≈ 0.15 and αL≈ 0.5.
The universal gaugino mass parameter M1/2can be pre-
determined in the chargino/neutralino sector. The non-
universal initial conditions in the evolution due to the D-
terms generate the small generation-independentcorrec-
tions S′, cf. Ref. .
The masses of the staus are shifted relative to the
masses of the first two generationsby two terms [3, 7, 8]:
The shifts ∆τ and ∆ντ, generated by loops involving
chargedlepton and neutrino superfields, respectively, are
given to leading order by
with the universal trilinear coupling A0defined at the
Anticipating high-precision measurements at future
colliders, such an SO(10) model can be investigated in
1In the following we omit the discussion of sneutrino and Higgs
masses and their role in reconstructing GUT scale parameters, but
their effect is included in the numerical results. For further details see
slepton and Higgs mass parameters [DU= 0].
Evolution of the first and third generation L,R
central facets. As a concrete example, we study a sce-
nario with SUSY parameters close to SPS1a/a′[6, 9] de-
Themeasurementofthe sleptonmasses ofthefirst two
generations allows us to extract the common sfermion
parameter m16= M0 as well as the D-term DU, cf.
Eqs. (6/7).Includingthe completeone-loopand the lead-
ingtwo-loopcorrections,theevolutionofthe scalar mass
parameters is displayed in Fig. 2 with the D-term set to
zero for illustration. By extrapolating the measurements
of slepton, Higgs and gauginomasses with the estimated
experimental errors from the results of Refs. [6, 8, 10],
the high-scale parameters can be reconstructed with the
precision shown in Tab. 1. The RG evolution equations
are evaluated to 2-loop order by means of the SPheno
program. The results indicate that the high-scale pa-
rameters M0and DU, driven by the slepton analysis, can
be reconstructed at per-mill to per-cent accuracy.
The right-handedneutrino affects the logarithmicevo-
lution of the mass parameter m2
tion in the most direct form.Thecharacteristic difference
in the evolution between m2
Fig. 2. The position of the kink at MνR3can be derived
from the intersection of the parameter ∆ντas a function
of MνR3, Eq. (11), with its measuredvalue extracted from
the slepton masses. Based on this estimate of MνR3, the
value of the lightest neutrino mass is then determined
via the seesaw mechanism, cf. Fig. 1. The reconstructed
values of MνR3and mν1in the SUSY scenario defined
above,are shown in Tab. 1, along with their uncertainties
from propagating expected experimental errors.
L3of the third genera-
L1is exemplified in
If the roots of physics are located near the Planck
scale, experimental methods must be devised to explore
the high-scalephysicsscenarioincludingthe grandunifi-
cation of the Standard Model interactions. In this report,
we have demonstratedhow this goal can be achievedin a
simplified SO(10) model with direct breaking to the SM
gauge group.As naturally expected,the analysis of more
complicated models will require a larger set of assump-
tions before the analysis can be performed, constrained
however by additional observables like charged lepton
masses, etc. Such an extended scheme is exemplified in
a two-step breaking scenario SO(10) → SU(5) → SM
analyzed in Ref. . The example described in this re-
port has proved nevertheless that renormalization-group
extrapolations based on high-precision results expected
from Terascale experiments can provide essential ele-
ments for the reconstruction of the physics scenario near
the GUT scale.
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