Do Neutrons Oscillate R N Mohapatra University of

Do Neutrons Oscillate ? R. N. Mohapatra University of Maryland Beijing Colloqium, June, 2007 Theme Group 2 March 2005

Particle oscillations • Oscillations of quantum mechanical states is a familiar phenomenon in Nature. • In the domain of particle physics, electrically neutral particles such as Kaons and neutrinos have been observed to oscillate, teaching us a great deal about the fundamental forces and matter. • Neutron is another neutral particle- could it possibly be having any oscillation ? Theme Group 2 March 2005

What can neutrons Oscillate to ? • Conservation of electric charge allows: (i) Neutron to anti-neutron (requires violation of baryon number) (ii) Neutron to mirror neutron; (requires the existence of a mirror universe. ) Both involve untested ideas and will reveal new physics. Here I discuss case (i) since there are reasons to suspect baryon number violation. Theme Group 2 March 2005

Why Baryon number non-conservation ? • Standard model has it. • Understanding the origin of matter in the universe requires it. • Most interesting new physics scenarios beyond the SM predict it. Theme Group 2 March 2005

Modes of interest Two modes of interest are: (i)Proton decay (ii)Neutron-anti-neutron oscillation Theme Group 2 March 2005

Phenomenology of N-N-bar Osc Theme Group 2 March 2005

Present expt situation in N-N-bar Osc. Range accessible to current reactor fluxes: Present limit: ILL experiment: Baldoceolin et al. (1994) New proposal by Y. Kamyshkov, M. Snow et al for an expt. DUSEL GOAL: Figure of merit ~ Theme Group 2 March 2005

De-gaussing of Earth B necessary • In free N-N-bar osc. , in the presence of Earth Mag. Field • Effect will be suppressed. • Needed de-gaussing to the level of Nano. Tesla. • Mu-metal shielding can do it. Known technology. Theme Group 2 March 2005

Oscillation inside Nuclei Theme Group 2 March 2005

Searches in Nucleon decay • Inside a nucleus e. g. Oxygen, • giving For This leads to nucleon lifetime Limits from Super-K, Soudan, IMB, SNO are of this order. Theme Group 2 March 2005

Comparision P-decay vs N-N-bar Theme Group 2 March 2005

Free vs Bound N-N-bar • Nuclear Physics uncertain: Uncertainty in R -need to do free neutron osc. Search. Theme Group 2 March 2005

A Proposal for N-Nbar search experiment 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, Snow et al. Theme Group 2 March 2005

Present collaboration: • Seeking collaborators: new site for expt. Theme Group 2 March 2005

Physics reason for N-N-bar • Different baryon nonconserving processes probe different physics: • Need both proton decay and N-N-bar for complete understanding of physics beyond SM Theme Group 2 March 2005

Modes and new physics scales • P->e+ , P->K mediated by the operator: Obeys Present lower limit on Implies This probes very high scales close to GUT scale. Theme Group 2 March 2005

B-L=2 Processes • Neutron-anti-neutron oscillations : PROBES INTERMEDIATE SCALES; Leads to Or for M= Theme Group 2 March 2005

Power counting: model dependent • Depends on : (i) low energy symmetry (ii) Te. V scale particle spectrum: • Te. V scale SUSY: sparticles < Te. V scale • Dominant P-decay operator Severely constrains SUSY GUTs : N-N-bar operator Allows N-N-bar to probe scales upto Ge. V. Much weaker suppressions also possible allowing probes till 10^11 -10^12 Ge. V. Theme Group 2 March 2005

Key symmetry is B-L • Proton decay does not search for B-L breaking whereas Neutron antineutron oscillation does. • B-L connected to neutrino mass-N-N-bar can clarify the origin of nu mass. Theme Group 2 March 2005

Plan for the rest of the talk 1. Why B-L symmetry ? 2. Two classes of local B-L models 3. Proton Decay, and N-N-bar Oscillations as tests of these models. Theme Group 2 March 2005

Why B-L Symmetry ? • Standard model has global B-L symmetry. • Immediate questions therefore are: • What is the nature of this symmetry ? Is it a global or local symmetry ? • Is it broken or exact ? If broken, what is the breaking scale and what new physics is associated with it ? Theme Group 2 March 2005

Any Hint of B-L symmetry beyond SM? • Neutrino Mass points towards a BL symmetry beyond the standard model. • As does SUSY dark matter. • One popular way to understand the origin of matter also involves B-L breaking. Theme Group 2 March 2005

Neutrino mass and • -standard model Starting point: add RH neutrino to SM for nu mass: Theme Group 2 March 2005

Seesaw paradigm for neutrino masses Add right handed neutrinos to the standard model and give them a large Majorana mass: Minko wski (77); Gell-Mann, Ramond, Slansky; Yanagida; Glashow; RNM, Senjanovic (79) Theme Group 2 March 2005

Seesaw scale and B-L symmetry • Seesaw formula applied to atmospheric neutrino data tells us that • Simple way to understand this inequality is to have a new symmetry that protects M_R. B-L is the appropriate symmetry since Majorana mass of RH neutrino breaks B-L by 2 units. Theme Group 2 March 2005

Another reason to suspect a B-L sym. • Common belief: SUSY at Te. V scale for various reasons: (i) Gauge hierarchy (ii) EWSB: origin of W, Z mass (iii) Dark matter: requires R-parity exact. Note that if B-L is a good symmetry beyond MSSM and breaks by two units (as in the RH neutrino mass), R-parity is exact in MSSM, dark matter is stable: otherwise not !! (RNM, 86; Font, Ibanez, Quevedo, 89; Martin, 92) Theme Group 2 March 2005

Origin of matter and B-L • If matter-anti-matter symmetry originated from early universe above the Te. V scale, then, it must break B-L. If it did not, Sphalerons would erase it !! • Proof: Suppose such that it has generated in the early Universe is B- L=0; Then = ; But B+L is violated by sphalerons which are in equilibrium down to the electroweak phase transition temp and will therefore wipe out B+L and hence all baryon asymmetry. Theme Group 2 March 2005

B-L: Local or Global ? • SM or MSSM: • But • So B-L is not a local symmetry. • Add the RH neutrino: • (B-L) becomes a gauge-able symmetry. • We will consider B-L to be a local symmetry. Theme Group 2 March 2005

New electroweak symmetry with B-L • Gauge group: • Fermion assignment • Higgs fields: Theme Group 2 March 2005

Symmetry breaking Theme Group 2 March 2005

Electric Charge Formula • New Improved Formula for electric charge Standard model: Y has no physical meaning. The formula In LR models: Theme Group 2 March 2005

Parity Violation leads to B-L violation • Electric charge formula of LR models imply: • Connects the origin of parity violation to B-L violation. Understanding B-L violation will elucidate the origin of parity violation. implies: or Majorana neutrinos or neutron-anti-N oscill. (RNM, Marshak, 80) Theme Group 2 March 2005

Minimal Models with B-L and N-N-bar • Need to unify quarks and leptons to transmit the BL=2 information to generate N-N-bar oscillations. • Two simple models with local B-L: (A): SO(10) : the minimal GUT theory with B-L (Georgi; Fritzsch and Minkowski (75)) (B) Partial Unif. Th. In both cases, fermions fit into the basic representation: • (Pati, Salam, 73) Theme Group 2 March 2005

B-L scale in SO(10) Grand unification Note that SUSY at TEV SCALE + no new physics till Ge. V implies that coupling constants unify: This suggests that perhaps local B-L is part of a grand unifying symmetry and it breaks at GUT scale. Related physics is GUT physics. Theme Group 2 March 2005

Does seesaw favor GUT scale B-L breaking ? • Atmospheric mass measured by Super-K can be related to B-L scale using the seesaw formula: assuming GUT relation for the 3 rd generation that This gives for the seesaw scale IN THIS CASE, SEESAW SCALE IS GUT SCALE and B-L PHYSICS IS GUT PHYSICS: Theme Group 2 March 2005

LOWER B-L SCALE POSSIBLE ? However, Experiments do not tell us the value of. if is suppressed by some symmetries (e. g. family sym. ), seesaw scale could be lower. In case of lower B-L scale, possible unification theory is the Model. Minimal B-L scale in this case is: Could also be at the Te. V scale. Theme Group 2 March 2005

So two key questions are: • What is the physics associated with B-L symmetry in this case ? • What is the scale of B-L symmetry ? Theme Group 2 March 2005

Message of this talk: P-decay, N-N-bar osc. probe the scale of local B-L sym. P-decay if it is GUT scale and N-N-bar if it is intermediate!! HOW SO ? Theme Group 2 March 2005

Digression on GUTs and Proton decay SU(5) as a Warm-up example: Theme Group 2 March 2005

Nucleon Decay in Generic SUSY GUTs • Gauge Boson exchange: Theme Group 2 March 2005

SUSY changes GUT scale dependence • Sakai, Yanagida, Weinberg (1982) • Murayama, Pierce; Bajc, Perez, Senjanovic (02); Perez, Dorsner, Rodrigo(06) 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: highly model dependent: in one class of models (Babu, Pati and Wilczek (2000)) Theme Group 2 March 2005

Predictions for proton decay in SO(10)-126 • Minimal SO(10) model with 10+126 which predict neutrino mixings: • 4 parameter model: predicts • (Goh, R. N. M, Nasri, Ng (2004)) Decay model highly suppressed. So again proton decay modes like these are highly model dependent. Theme Group 2 March 2005

Truly “model independent” prediction • Gauge exchange mode P-> e+ , which is predicted in minimal GUT models to be around 10^36 years. • “The true holy grail of grand unification” • N-N-BAR IN SO(10) HIGHLY SUPPRESSED. Theme Group 2 March 2005

Now to N-N-BAR OSCILLATION • Can observable N-N-bar emerge in realistic seesaw models with sub-GUT B-L scale ? • Second question is: since high dim N-N-bar operators go out of equilibrium only around the electroweak scale, are they not going to erase any preexisting baryon asymmetry • So can one understand the origin of matter if N-N-bar is visible in expts. ? • The answers to both questions -“YES”. Theme Group 2 March 2005

Testing Sub-GUT B-L with N-N-bar • Recall with SM spectrum in the Te. V range, NN operator is • O • Feynman diagram for N-N-bar Feynman no. SUSY • RNM and Marshak, 80 • Tiny n-n-bar for M L scales ? >100 Te. V. Can Theme Group 2 n-n-bar test higher BMarch 2005

Things change with SUSY and new particles A. Dominant operator with SUSY: B. SUSY + diquark Higgs field Note weaker Seesaw suppression , at Te. V scale Supression Still weaker ! C. If the Te. V scale has fields, effective op. is /M Theme Group 2 Weakest Suppression March 2005

A G(224) theory for case B and N-N-bar Theme Group 2 March 2005

Estimate of N-N-bar in Minimal 224 model: • New Feynman diagram for N-N-bar osc. Observable N-N-bar osc (Dutta, Mimura, RNM; PRL (2006) Theme Group 2 March 2005

Other examples-Babu, RNM, Nasri-PRL (2007) • 3 x 2 seesaw model with the third RH neutrino in the Te. V scale and decoupled from the neutrino sector: • Plus a pair of color triplets: X and X-bar with couplings: + Impose R-parity symmetry as in MSSM. This simple extension provides a remarkably natural model for dark matter, neutrinos and baryogenesis and has testable predictions !! Theme Group 2 March 2005

N-N-bar Prediction • N-N-bar oscillation: Diagram involves Majorana N exchange • Effective strength: • Will lead to N-N-bar osc via the s-content in neutron. • Transition time expected to be around 10^8 sec. Theme Group 2 March 2005

Baryogenesis in N-N-bar models • Usual argument : Any early universe baryon asymmetry will be erased by fast N-N-bar transitions being in equilibrium: Typical out of Equilibrium T is around 100 Ge. V. Need a mechanism for baryogenesis below the electroweak breaking scale. Recent work which resolves this issue by post-sphaleron baryogenesis: Babu, RNM, Nasri PRL, (2006, 2007) Theme Group 2 March 2005

Baryogenesis Diagrams in the second model Possible to obtain right n_B/N_gamma Theme Group 2 March 2005

Proton decay vs N-N-bar oscillation Theme Group 2 March 2005

Conclusion • With the discovery of neutrino mass the case for N-N-bar oscillation is a lot stronger now than it was in the 1980 s. Urge new search at the level of 10^10 sec to test for B-L seesaw scale around 10^11 Ge. V as against GUT scale seesaw. • N-N-bar discovery will completely change thinking on grand unification. • As far as Proton decay goes, predictions below 10^36 yrs are model dependent; while they should be done, the true value of Pdecay as a test of GUT idea is the 10^36 yrs level search and should be the ultimate goal. Theme Group 2 Thank you for your attention. March 2005

Role of Lepton Flavor Violation • Standard model with Majorana neutrino mass without supersymmetry and high scale seesaw: Very tiny: With SUSY, things are different. Theme Group 2 March 2005

SUSY seesaw and FCNC effects • Neutrino mixings induce slepton mixings at low scale via radiative corrections and hence FCNC effects. • Slepton mixings are proportional to Yukawa mixings that go into the seesaw formula: • Since neutrino masses are known, if M_R= fv_R (the B-L breaking scale) is lower , Y_nu will be smaller and hence will be the slepton mixing effects. Theme Group 2 March 2005

Generic predictions for Theme Group 2 March 2005

Lower V_BL • Branching ratio lower by v_BL square. So non-observation of any effect at MEG expt along with a positive signal for N-N-bar oscillation will indicate lower B-L scales. Only exception is if B-L scale is the Te. V range: In this case even without SUSY, mu-> e +gamma Br. Can be observable. Theme Group 2 March 2005

Conclusion • With the discovery of neutrino mass the case for N-N-bar oscillation is a lot stronger now than it was in the 1980 s. Urge new search at the level of 10^10 sec to test for B-L seesaw scale around 10^11 Ge. V as against GUT scale seesaw. • N-N-bar discovery will completely change thinking on grand unification. • As far as Proton decay goes, predictions below 10^36 yrs are model dependent; while they should be done, the true value of Pdecay as a test of GUT idea is the 10^36 yrs level search and should be the ultimate goal. Theme Group 2 Thank you for your attention. March 2005