Neutrino Mass and Grand
Unification
R. N. Mohapatra
University of Maryland
LAUNCH, 2007
Heidelberg
Theme Group 2
March 2005
Hypothesis of Grand unification
(i) Grand unification is an interesting hypothesis
which says that all forces and all matter become
one at high energies no matter how different they
look at low energies.
(ii) Two examples of theories where simple
renormalization group analysis of the low energy
couplings do indeed lead to coupling unification at
high energies:
(A). MSSM at TeV scale -> GUC
(B)
GSTD  SU (2) L  SU (2) R  U (1) B  L  GUC
Theme Group 2
March 2005
Unification of Couplings:
Weak scale susy
Non SUSY SO(10) with seesaw
Theme Group 2
March 2005
Other advantages of GUTs
• (i) Higher symmetry could give better
understanding of fermion masses ;
(ii) Explains charge quantization;
(iii) High scale explains proton stability;
(iv) High scale goes well with
cosmological issues such as inflation
and baryogenesis.
Theme Group 2
March 2005
Simplest example: SUSY SU(5)
Theme Group 2
March 2005
Lessons from SU(5): Learning from failure
• Does not mean the idea of GUTs is dead.
• Key to predictivity is to keep the model
renormalizable; e.g. the 10.10.10.5 coupling
in SU(5) has to have a coupling < 10^-7 –
also indicating that non-ren. Couplings have
tiny couplings for whatever reason.
• Neutrino mass has again put new life into the
GUT idea- perhaps best to use theories with
ren. Yukawas (as we do here).
Theme Group 2
March 2005
m
to GUTs via seesaw
• Simplest way to understand small neutrino masses :
why m

 mu ,d ,e?
Add right handed neutrinos to the SM with large
Majorana mass:
2
M  
mD
 mu ,d ,e
MR
M R  mD  vwk
MR is the new physics scale.
[Minkowski; Gell-Mann, Ramond, Slansky; Yanagida; RNM, Senjanovic;Glashow]
Theme Group 2
March 2005
What is the seesaw scale, MR?
• Using Atmospheric mass measured by
Super-K and mD  mt in the seesaw
2
m 2 atm
One gets
mt

MR
M R  10 GeV
14
(i) SEESAW SCALE CLOSE TO GUT SCALE(ii) If mD is suppressed (by symmetries), seesaw
scale could be lower (even TeV).
Case (i) seesaw another indication for SUSY GUT since
16
the GUT scale is 10 GeV ?
Theme Group 2
March 2005
Minimal GUT group for neutrinos
• Seesaw provides the answer:
• The fact that M R  M U is most easily
understood if there is a new symmetry
associated with RH neutrino mass
generation.
• The obvious symmetry is B-L, which is
broken by  0 R  0 which gives RH
neutrino mass.
GUT group must have B-L as the subgroup.
Theme Group 2
March 2005
SO(10) Grand unified theory
• Natural GUT group is SO(10) since its spinor
rep contains all 16 needed fermions
(including RH neutrino) in a single rep.
• Georgi; Fritzsch, Minkowski (74)
• Contains B-L needed to understand why
MR<< M_Planck .
• B-L if properly broken also allows a naturally
stable dark matter in MSSM. (RNM, 1986)
Theme Group 2
March 2005
From SO(10) down to the Std Model
•
SO(10)

• Left-right sym. theory

•
Nu mass
 ( B  L)  0
Standard Model-> seesaw

SU (3)c U (1) em
Theme Group 2
0 0 


0 M 
0 m


m M 
March 2005
How is B-L Broken ? {16} vs {126}
• B-L can either be broken by {16}- Higgs by
its
R component.

In which case M_R arises from nonrenormalizable terms;
Leads to R-parity breaking and hence no
stable dark matter without extra
assumptions.
Theme Group 2
March 2005
Alternatively Break B-L by 126-Higgs
• SM singlet in 126 is  RR which has B-L=2;
• Leaves R parity unbroken in MSSM and gives
stable dark matter.
• Also 16 X 16 = 10 + 126 + 120
Matter
Higgs
Minimal model: one each of 10+126+ 120.
126 gives mass to charged fermions as well as
RH neutrinos relating RH neutrino spectrum
to charged fermion spectrum.
Also uses only renormalizable couplings.
(not true for 16- Higgs models.)
Theme Group 2
March 2005
Large neutrino mixings in minimal SO(10)
• How large mixings arise naturally in the
minimal models:
Simple Example: Model with only one {10}
and {126} Higgs:
• Has only 12 parameters (for CP conserving
case)- all determined by quark masses and
mixings and charged leptons; all neutrino
mixings are predicted.
• Babu, RNM (92); Bajc, Senjanovic, Vissani (2003); Goh,
Ng, RNM (2003).
Theme Group 2
March 2005
Details of minimal SO(10)
• Yukawa: h16.16 10+f 16 .16.126-bar
• Leads to fermion mass formulae
Theme Group 2
March 2005
Neutrino mass and seesaw in SO(10)
• SO(10) model (and all LRS) models modify
seesaw as follows:
M  fvL  M
Type II
T
D
1
MD
fvR
2
vwk
Type I with vL 
M triplet
[Magg, Wetterich; Lazaridis, Shafi, Wetterich; RNM, Senjanovic; 80]
For first term to be significant, triplet mass
must be around 10^14 GeV.
Does it affect unification ?
Theme Group 2
March 2005
A New sumrule for neutrino mass:
• Dominant Type II
Theme Group 2
March 2005
Including CP violation:
• In the 10+126 model, CP violation can arise
from complex Yukawas- (but works only for a
narrow range of parameters)
• In the full minimal 10+126+120 model, CP is
more natural.
Grimus, Kuhbock; Aulakh, G arg
Grimus, Kuhbock
•
Grimus and Kuhbock, 2006
Theme Group 2
March 2005
Restrictions from P-decay for all tan 
Theme Group 2
March 2005
Some predictions of the 120 model:
• Prediction for U_e3:
Theme Group 2
March 2005
Predictions for the MNSP Phase
Dirac phase can be predicted
Sin MNSP 
= 0.5-0.7
U e3  0.08
Theme Group 2
March 2005
Predictions for lepton flavor violation
Theme Group 2
March 2005
Beyond Flavor Issues
• Realization of type II seesaw
dominance in the models:
2
1
T
vwk
M  fvL  M D
MD
vL 
fvR
M triplet
(i) Higher B-L scale
(ii) together with lower triplet mass
• Coupling Unification and avoiding
early non-perturbativity;
• Proton decay
Theme Group 2
March 2005
What happens in the truly minimal
model:
• {10}+{126}+{210}: Implies
M T  MU
• Needs modification: Two possibilities:
• (i) Add extra {54} to lower Triplet mass by a
mini-seesaw; also overcomes large
thershold effect objection.
• (ii) Use mini-warping- Physics above GUT
scale strongly coupled.
Theme Group 2
March 2005
Coupling Unification with type II seesaw
Usual allegation of large threshold effects
FALSE !! Could have higher unif. scale with SO(10)->
SU(5) and Triplet, {15 } of SU(5) at 10^13 GeV; Goh,
RNM, Nasri,04
Theme Group 2
March 2005
Another way to achieve Type II dominance
• Use mini-warped 5-D model:
• Idea: (Fukuyama, Kikuchi, Okada(2007);
Okada, Yu, RNM-in prep.)
• Consider warped 5-D model with warping from
Planck to GUT:
• Locate Higgs in the Bulk so that their effect on the 4D brane depends on location and U(1) charge. That
way one can ensure lighter {15} and also unification.
• No large Threshold effect since theory nonperturbative after M_U.
Theme Group 2
March 2005
Type II seesaw and Higgs Profiles
•
Theme Group 2
March 2005
True test of GUT hypothesis
m m
• Coupling unification,
often
b

cited as evidence for GUTs are not really so.
True test of GUTs is proton decay;
In particular no proton decay to the
level of 10^36-37 years will be
evidence against GUTs.
Theme Group 2
March 2005
Nucleon Decay in SUSY GUTs
• Gauge Boson exchange:
Theme Group 2
March 2005
SUSY changes GUT scale dependence
O p  decay
1
~~

QQQL
MU
Theme Group 2
March 2005
Predictions for proton decay in SO(10)-16
• B-L could be broken either by {16}-H or
{126}-H.
• SU(5) type problem avoided due to
cancellation between diagrams.
• Proton decay in {16} models: model
dependent: in one class of models
(Babu, Pati and Wilczek (2000))
Theme Group 2
March 2005
Proton decay in SO(10)-126
• Minimal SO(10) model with 10+126 which predict
neutrino mixings:
• 4 parameter model: predicts
 (n   )  13 10
32 yrs
 (n  K  )  3 10 yrs
0
33
• For large tan the model is incompatible with
proton decay
(Goh, R.N. M, Nasri, Ng (2004))
Theme Group 2
March 2005
Are GUTs the only choice for seesaw ?
• It could be that B-L scale is lower : How to test for
that possibility ?
• Searching for neutron-anti-neutron
oscillation is one way.
• Few questions: N-N-bar operator:
1 c c c c c c
 5u d d u d d
M
5
Leads to Osc. Time
 nn
M 5  M  10
 6 
 10 sec .

 100TeV 
Since seesaw scale is >10^11 GeV, any chance to see it
?
Theme Group 2
March 2005
YES SINCE NEW OPERATORS CAN APPEAR
• New operators appear with SUSY as well as
unexplored TeV scale spectrum!!
• Examples:

With SUSY:
u cu c
If there is SUSY + diquark fields:
Weaker
suppression
SUSY+  u d
c
c
 ucd c u d d c d c
/M
c
c
Theme Group 2
Even weaker
suppression
March 2005
224 models do lead to such operators
• New Feynman diagrams lead to observable
N-N-bar transition time with high seesaw
scale of 10^11 GeV:
Theme Group 2
March 2005
Comparision P-decay vs N-N-bar
Theme Group 2
March 2005
Scheme
of neutron-antineutron
search
Proposal to search for
N-N-bar
at
DUSEL
experiment with vertical layout
•
Dedicated small-power TRIGA
research reactor with cold
neutron
moderator  vn ~ 1000 m/s
•
 Vertical shaft ~1000 m deep
with
diameter ~ 6 m at DUSEL
•
•
•
 Large vacuum tube, focusing
reflector, Earth magnetic field
compensation system
•
•
 Detector (similar to ILL N-Nbar
detector) at the bottom of the
shaft
(no new technologies)
Kamyshkov et al. (2005)
•
•
•
Annular Core
TRIGA Reactor
3.4 MW with
convective
cooling.
3E+13 n/cm2/s
central thermal flux
LD2 CM
Focusing
Reflector
L~150 m
Vacuum
tube
L~1000 m
dia ~ 4 m
Transition
point
Neutron
trajectory
X
•
•
Annihilation
target
dia ~ 2 m
Annihilation
detector
10 m
1m
Beam dump
Approximate
scales
Theme Group 2
March 2005
Proton decay vs N-N-bar oscillation
Theme Group 2
March 2005
SUMMARY
• Neutrino mass introduces B-L as a symmetry
of Nature. What is its scale ?
• Very interesting possibility is that B-L scale
is GUT scale: Minimal SO(10) realizations
with 10+120+126 Higgs are realistic and
predictive. Can be tested by forthcoming
neutrino experiments !
• Lower B-L scales can be tested by neutronanti-neutron oscillation using current reactor
fluxes. Urge a renewed effort to search for
this process.
Theme Group 2
March 2005
Unification scenario with S_4 sym.
Y
 1
Parida
Parida,RNM,07
 1
B-L
2L
3c
U (1)Y
Theme Group 2
March 2005
Theme Group 2
March 2005
Predictions for long baseline experiments:
Theme Group 2
March 2005