March 2005 Theme Group 2 Neutrino Mass and Grand Unification R. N. Mohapatra University of Maryland LAUNCH, 2007 Heidelberg.

March 2005Theme Group 2

Neutrino Mass and Grand Neutrino Mass and Grand UnificationUnification

R. N. MohapatraUniversity of Maryland

LAUNCH, 2007Heidelberg


Hypothesis of Grand Hypothesis of Grand unificationunification

(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)

GUCUSUSUG LBRLSTD )1()2()2(


Unification of Couplings:Unification of Couplings:

Weak scale susyWeak scale susy Non SUSY SO(10) with seesawNon SUSY SO(10) with seesaw


Other advantages of GUTsOther 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.


Simplest example: SUSY SU(5)Simplest example: SUSY SU(5)


Lessons from SU(5): Lessons from SU(5): Learning from failureLearning 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).


to GUTs via seesawto GUTs via seesaw

• Simplest way to understand small neutrino masses : why ?

Add right handed neutrinos to the SM with large Majorana mass:

MR is the new physics scale.[Minkowski; Gell-Mann, Ramond, Slansky; Yanagida; RNM, Senjanovic;Glashow]

R

D

M

mM

2

m

edumm ,,

edum ,, wkDR vmM


What is the seesaw scale, MR?What is the seesaw scale, MR?

• Using Atmospheric mass measured by Super-K and in the seesaw

One gets

(i) SEESAW SCALE CLOSE TO GUT SCALE-

(ii) If is suppressed (by symmetries), seesaw scale could be lower (even TeV).

Case (i) seesaw another indication for SUSY GUT since the GUT scale is GeV ?

R

tatm

M

mm

22

tD mm

GeVM R1410

Dm

1610


Minimal GUT group for neutrinosMinimal GUT group for neutrinos

• Seesaw provides the answer:• The fact that 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 which gives RH neutrino mass.

GUT group must have B-L as the subgroup.

UR MM

00 R


SO(10) Grand unified theorySO(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)


From SO(10) down to the Std ModelFrom SO(10) down to the Std Model

• SO(10) Nu mass

• Left-right sym. theory

• Standard Model-> seesaw

M

0

0

0

M

m

m

0

0)( LB

emc USU )1()3(


How is B-L Broken ?How is B-L Broken ? {16} vs {126}{16} vs {126}

• B-L can either be broken by {16}- Higgs by

its component.

In which case M_R arises from non-renormalizable terms;

Leads to R-parity breaking and hence no

stable dark matter without extra assumptions.

R


Alternatively Break B-L by 126-HiggsAlternatively Break B-L by 126-Higgs

• SM singlet in 126 is which has B-L=2;• Leaves R parity unbroken in MSSM and gives

stable dark matter.

• Also 16 X 16 = 10 + 126 + 120 Matter HiggsMinimal 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.)

RR


Large neutrino mixings in minimal SO(10)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).


Details of minimal SO(10)Details of minimal SO(10)

• Yukawa: h16.16 10+f 16 .16.126-bar• Leads to fermion mass formulae


Neutrino mass and seesaw in SO(10)Neutrino mass and seesaw in SO(10)

• SO(10) model (and all LRS) models modify seesaw as follows:

Type II Type I with

[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 ?

DR

DT

L Mfv

MfvM1

triplet

wkL M

vv

2


A New sumrule for neutrino mass:A New sumrule for neutrino mass:

• Dominant Type II


Including CP violation: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 and Kuhbock, 2006

KuhbockGrimus, arg,;, GAulakhKuhbockGrimus


Restrictions from P-decay for all tanRestrictions from P-decay for all tan


Some predictions of the 120 model:Some predictions of the 120 model:

• Prediction for U_e3:


Predictions for the MNSP PhasePredictions for the MNSP Phase

08.03 eU

MNSPSin = 0.5-0.7

Dirac phase can be predicted


Predictions for lepton flavor violationPredictions for lepton flavor violation


Beyond Flavor IssuesBeyond Flavor Issues

• Realization of type II seesaw dominance in the models:

(i) Higher B-L scale

(ii) together with lower triplet mass

• Coupling Unification and avoiding early non-perturbativity;

• Proton decay

DR

DT

L Mfv

MfvM1

triplet

wkL M

vv

2


What happens in the truly minimal model:What happens in the truly minimal model:

• {10}+{126}+{210}: Implies

• 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.

UT MM


Coupling Unification with type II seesawCoupling Unification with type II seesaw

Usual allegation of large threshold effects Usual allegation of large threshold effects FALSE !!FALSE !! Could have higher unif. scale with SO(10)- Could have higher unif. scale with SO(10)-> SU(5) and Triplet, > SU(5) and Triplet, {15 } of SU(5){15 } of SU(5) at 10^13 GeV; at 10^13 GeV; Goh, Goh, RNM, Nasri,04RNM, Nasri,04


Another way to achieve Type II dominanceAnother 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 4-D brane depends on location and U(1) charge. That way one can ensure lighter {15} and also unification.

• No large Threshold effect since theory non-perturbative after M_U.


Type II seesaw and Higgs Profiles Type II seesaw and Higgs Profiles

•


True test of GUT hypothesisTrue test of GUT hypothesis

• Coupling unification, often

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.

mmb


Nucleon Decay in SUSY GUTsNucleon Decay in SUSY GUTs

• Gauge Boson exchange:


SUSY changes GUT scale dependenceSUSY changes GUT scale dependence

LQQQM

OU

decayp

~~1


Predictions for proton decay in SO(10)-16Predictions 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))


Proton decay in SO(10)-126Proton decay in SO(10)-126

• Minimal SO(10) model with 10+126 which predict neutrino mixings:

• 4 parameter model: predicts

• For large tan the model is incompatible with proton decay

(Goh, R.N. M, Nasri, Ng (2004))

yrsn 321013)(

yrsKn 330 103)(


Are GUTs the only choice for seesaw ?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:

Leads to Osc. Time

Since seesaw scale is >10^11 GeV, any chance to see it ?

cccccc ddudduM 5

1

.sec10100

105

6

5

TeV

MMnn


YES SINCE NEW OPERATORS CAN APPEARYES SINCE NEW OPERATORS CAN APPEAR

• New operators appear with SUSY as well as unexplored TeV scale spectrum!!

• Examples:

With SUSY:

If there is SUSY + diquark fields:

SUSY+

/M

ccuu

Weakersuppression

ccdu

ccddccduccdu

Even weakersuppression


224 models do lead to such operators224 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:


Comparision P-decay vs N-N-barComparision P-decay vs N-N-bar


Proposal to search for N-N-bar at DUSELProposal to search for N-N-bar at DUSEL• 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)


Proton decay vs N-N-bar oscillationProton decay vs N-N-bar oscillation


SUMMARYSUMMARY

• 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 neutron-anti-neutron oscillation using current reactor fluxes. Urge a renewed effort to search for this process.


Unification scenario with S_4 sym.Unification scenario with S_4 sym.

Parida 1

YU )1(

Parida,RNM,07

1

Y

B-L2L

3c



Predictions for long baseline experiments:Predictions for long baseline experiments:

March 2005 Theme Group 2 Neutrino Mass and Grand Unification R. N. Mohapatra University of Maryland LAUNCH, 2007 Heidelberg.

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