Neutrino mass and grand unification
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Neutrino Mass and Grand Unification. R. N. Mohapatra University of Maryland LAUNCH, 2007 Heidelberg. Hypothesis of Grand unification.

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Neutrino mass and grand unification

Neutrino Mass and Grand Unification

R. N. Mohapatra

University of Maryland

LAUNCH, 2007

Heidelberg

Theme Group 2


Hypothesis of grand unification
Hypothesis of Grand unification

  • 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.

  • 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)

Theme Group 2


Unification of couplings
Unification of Couplings:

Weak scale susy

Non SUSY SO(10) with seesaw

Theme Group 2


Other advantages of guts
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



Lessons from su 5 learning from failure
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


To guts via seesaw
to 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]

Theme Group 2


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 ?

Theme Group 2


Minimal gut group for neutrinos
Minimal 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.

Theme Group 2


So 10 grand unified theory
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


From so 10 down to the std model
From SO(10) down to the Std Model

  • SO(10) Nu mass

  • Left-right sym. theory

  • Standard Model-> seesaw

Theme Group 2


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

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

    itscomponent.

    In which case M_R arises from non-renormalizable terms;

    Leads to R-parity breaking and hence no

    stable dark matter without extra assumptions.

Theme Group 2


Alternatively break b l by 126 higgs
Alternatively 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 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


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).

Theme Group 2


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

  • Yukawa: h16.16 10+f 16 .16.126-bar

  • Leads to fermion mass formulae

Theme Group 2


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 ?

Theme Group 2


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

  • Dominant Type II

Theme Group 2


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

Theme Group 2



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

  • Prediction for U_e3:

Theme Group 2


Predictions for the mnsp phase
Predictions for the MNSP Phase

Dirac phase can be predicted

= 0.5-0.7

Theme Group 2



Beyond flavor issues
Beyond 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

Theme Group 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.

Theme Group 2


Coupling unification with type ii seesaw
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


Another way to achieve type ii dominance
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 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.

Theme Group 2


True test of gut hypothesis
True 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.

Theme Group 2


Nucleon decay in susy guts
Nucleon Decay in SUSY GUTs

  • Gauge Boson exchange:

Theme Group 2



Predictions for proton decay in so 10 16
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


Proton decay in so 10 126
Proton 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))

Theme Group 2


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 ?

Theme Group 2


Yes since new operators can appear
YES 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

Weaker

suppression

Even weaker

suppression

Theme Group 2


224 models do lead to such operators
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



Proposal to search for n n bar at dusel
Proposal 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)

Theme Group 2



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

Theme Group 2


Unification scenario with s 4 sym
Unification scenario with S_4 sym.

Y

Parida,RNM,07

B-L

2L

3c

Theme Group 2




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