Neutrino Mass and Grand Unification

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Neutrino Mass and Grand Unification

• R. N. Mohapatra
• University of Maryland
• LAUNCH, 2007
• Heidelberg

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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 -gt GUC
• (B)

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Unification of Couplings
Weak scale susy
Non SUSY SO(10) with seesaw
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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.

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Simplest example SUSY SU(5)
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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 lt 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).

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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, SenjanovicGlashow

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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 ?

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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.

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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 MRltlt
  M_Planck .
• B-L if properly broken also allows a naturally
  stable dark matter in MSSM. (RNM, 1986)

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From SO(10) down to the Std Model

• SO(10)
  Nu mass
• Left-right sym. theory
• Standard Model-gt seesaw

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How is B-L Broken ? 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.

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Alternatively Break B-L by 126-Higgs

• SM singlet in 126 is which has
  B-L2
• 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 10126 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.)

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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).

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Details of minimal SO(10)

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

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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 1014 GeV.
• Does it affect unification ?

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A New sumrule for neutrino mass

• Dominant Type II

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Including CP violation

• In the 10126 model, CP violation can arise from
  complex Yukawas- (but works only for a narrow
  range of parameters)
• In the full minimal 10126120 model, CP is more
  natural.
• 
  Grimus and Kuhbock, 2006

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Restrictions from P-decay for all tan
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Some predictions of the 120 model

• Prediction for U_e3

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Predictions for the MNSP Phase
Dirac phase can be predicted
0.5-0.7
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Predictions for lepton flavor violation
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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

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What happens in the truly minimal model

• 10126210 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.

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Coupling Unification with type II seesaw
Usual allegation of large threshold effects FALSE
!! Could have higher unif. scale with SO(10)-gt
SU(5) and Triplet, 15 of SU(5) at 1013 GeV
Goh, RNM, Nasri,04
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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.

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Type II seesaw and Higgs Profiles

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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
  1036-37 years will be evidence against GUTs.

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Nucleon Decay in SUSY GUTs

• Gauge Boson exchange

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SUSY changes GUT scale dependence
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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))
• 
  
  

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Proton decay in SO(10)-126

• Minimal SO(10) model with 10126 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))

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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 gt1011 GeV, any chance to
  see it ?

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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
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224 models do lead to such operators

• New Feynman diagrams lead to observable N-N-bar
  transition time with high seesaw scale of 1011
  GeV

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Comparision P-decay vs N-N-bar
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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)

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Proton decay vs N-N-bar oscillation
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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
  10120126 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.

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Unification scenario with S_4 sym.
Parida,RNM,07
Y
B-L
2L
3c
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(No Transcript)
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Predictions for long baseline experiments