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

March 2005Theme Group 2

Do Neutrons Oscillate ?Do Neutrons Oscillate ?

R. N. Mohapatra

University of Maryland

Beijing Colloqium, June, 2007


Particle oscillationsParticle 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 ?


What can neutrons Oscillate to ?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.


Why Baryon number non-conservationWhy 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.


Modes of interestModes of interest0B

Two modes of interest are:

(i)Proton decay

(ii)Neutron-anti-neutron oscillation

Kpep ,0


Phenomenology of N-N-bar OscPhenomenology of N-N-bar Osc

n

n

Vm

Vm

n

n

ti

2

1

tVVSinVV

P nn )( 212

2

21

Two :cases:1))(( 21 tVVi

2

nnnn

tP

1))(( 21 VVii2

21

VVP nn

nnDef ~.


Present expt situation in N-N-bar OscPresent 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 ~

.sec108 nn

.sec1010 1110 2

nn

tFlux

.sec1010~ 118 nn


De-gaussing of Earth B necessaryDe-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.

BVV 221


Oscillation inside NucleiOscillation inside Nuclei


Searches in Nucleon decaySearches 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.

MeViWVVV 10021 2

21

VVP nn

.sec108nn

6410

yrs3210


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

2. freeNuc R

freeNuc R 2 123 sec103.0 R


Free vs Bound N-N-barFree vs Bound N-N-bar

• Nuclear Physics uncertain: Uncertainty in R

-need to do free neutron osc. Search.


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.


Present collaboration:Present collaboration:

• Seeking collaborators: new site for expt.


Physics reason for N-N-barPhysics reason for N-N-bar

• Different baryon non-conserving processes probe different physics:

• Need both proton decay and N-N-bar for complete understanding of physics beyond SM


Modes andModes and new 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.

0

QQQLM

O B 20

1

yrsep

331050

GeVM 1510

0B

0)( LB


B-L=2 ProcessesB-L=2 Processes

• Neutron-anti-neutron oscillations :

PROBES INTERMEDIATE SCALES;

Leads to

Or

for M=

2BO cccccc ddudduM 5

1

62 QCDBnn Om

5~/ Mm nnnn 6/

giving .sec10~ 8nn GeV5.510


Power countingPower counting: : model dependentmodel dependent• Depends on : (i) low energy symmetry (ii) TeV scale

particle spectrum:

• TeV scale SUSY: sparticles < TeV scale

• Dominant P-decay operator

Severely constrains SUSY GUTs : N-N-bar operator

Allows N-N-bar to probe scales upto GeV. Much weaker suppressions also possible allowing probes till 10^11-10^12 GeV.

MQLQQ

1~~

cccccc ddudduM

~~~~13

910


Key symmetry is B-LKey symmetry is B-L

• Proton decay does not search for B-L breaking whereas Neutron anti-neutron oscillation does.

• B-L connected to neutrino mass-N-N-bar can clarify the origin of nu mass.


Plan for the rest of the talkPlan 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.


Why B-L Symmetry ?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 ?


Any Hint of B-L symmetry beyond SMAny Hint of B-L symmetry beyond SM??

• Neutrino Mass points towards a B-L symmetry beyond the standard model.

• As does SUSY dark matter.

• One popular way to understand the origin of matter also involves B-L breaking.


Neutrino mass and -standard modelNeutrino mass and -standard model

• Starting point: add RH neutrino to SM for nu mass:


Seesaw paradigm for neutrino masses Seesaw paradigm for neutrino masses

Add right handed neutrinos to the standard model and give them a large Majorana mass:

Minkowski (77); Gell-Mann, Ramond, Slansky; Yanagida; Glashow; RNM, Senjanovic (79)

edum ,,DRT

D mMmm 1

Dm Dm

1RM


Seesaw scale and B-L symmetrySeesaw 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.

PlR MM


Another reason to suspect a B-L Another reason to suspect a B-L sym.sym.

• Common belief: SUSY at TeV 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)

SLBR 2)(3)1(


Origin of matter and B-LOrigin of matter and B-L

• If matter-anti-matter symmetry originated from early universe above the TeV scale, then, it must break B-L. If it did not, Sphalerons would erase it !!

• Proof: Suppose generated in the early Universe is

such that it has 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.

B

B )( LB


B-L: Local or Global ?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.

0

LBJ

0)( 3 LBTr

0)( 3 LBTr


New electroweak symmetry with B-LNew electroweak symmetry with B-L

• Gauge group:

• Fermion assignment

• Higgs fields:

LBRL USUSU )1()2()2(

L

L

d

u

R

R

d

u

L

L

e

R

R

e

P

P

)0,2,2( )2,1,3()2,3,1(; LR


Symmetry breakingSymmetry breaking

LBRL USUSU )1()2()2(

YL USU )1()2(

0 R0, ' ZW MM

R

'0

0

emU )1(0;0, , lqZW mMM

L


Electric Charge FormulaElectric Charge Formula

• New Improved Formula for electric charge

Standard model:

Y has no physical meaning.

The formula In LR models:

23

YIQ L

233

LBIIQ RL


Parity Violation leads to B-L violationParity 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)

2

)(3

LBI R

13 RI2L

2B


Minimal Models with B-L and N-N-barMinimal Models with B-L and N-N-bar

• Need to unify quarks and leptons to transmit the B-L=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)

cRL SUSUSU )4()2()2(


B-L scale in SO(10) Grand unificationB-L scale in SO(10) Grand unification

Note that SUSY at TEV SCALE + no new physics till GeV 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.

1610


Does seesaw favor GUT scale Does seesaw favor GUT scale B-L breakingB-L breaking ? ?

• Atmospheric mass measured by Super-K can be related to B-L scale using the seesaw formula:

assuming GUT relation for the 3rd generation that

This gives for the seesaw scale

IN THIS CASE, SEESAW SCALE IS GUT SCALE and B-L PHYSICS IS GUT PHYSICS:

R

tatm

M

mm

22

GeVM R1410tD mm


LOWER B-L SCALE POSSIBLE ?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 TeV scale.

DmDm

cRL SUSUSU )4()2()2(

GeVGeVM 1611224 1010


So two key questions are: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 ?


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 ?


Digression on GUTs and Proton decayDigression on GUTs and Proton decay

SU(5) as a Warm-up example:SU(5) as a Warm-up example:


Nucleon Decay in Generic SUSY GUTsNucleon Decay in Generic SUSY GUTs

• Gauge Boson exchange:


SUSY changes GUT scale dependenceSUSY changes GUT scale dependence

• Sakai, Yanagida, Weinberg (1982)

• Murayama, Pierce; Bajc, Perez, Senjanovic (02); Perez,Dorsner,Rodrigo(06)

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: highly model dependent: in one class of models

(Babu, Pati and Wilczek (2000))


Predictions for proton decay in SO(10)-126Predictions 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.

yrsn 321013)( yrsKn 330 103)(


Truly “model independent” predictionTruly “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.

0


Now to N-N-BAR OSCILLATIONNow 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”.


Testing Sub-GUT B-L with N-N-barTesting Sub-GUT B-L with N-N-bar

• Recall with SM spectrum in the TeV range, NN operator is•

O

• Feynman diagram for N-N-bar Feynman noSUSY• RNM and Marshak,80

• Tiny n-n-bar for M >100 TeV. Can n-n-bar test higher B-L scales ?

cccccc ddudduM 5

1

LB


Things change with SUSY and new particlesThings change with SUSY and new particles

A. Dominant operator with SUSY:

B.SUSY + diquark Higgs field , at TeV scale

C.If the TeV scale has fields, effective op. is

/M

ccuu

ccdu

ccddccduccdu

Note weakerSeesaw

suppression

Supression Still weaker !

WeakestSuppression


A G(224) theory for case A G(224) theory for case BB and N-N-bar and N-N-bar

)1,3,1(

:tialSuperpoten

cccc MMW 2'

)1,3,1(

eLarg weakscaleLeavesSymGlobal cc uu.............


Estimate of N-N-bar in Minimal 224 model: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)


Other examples-Other examples-Babu,RNM,Nasri-PRL (2007)Babu,RNM,Nasri-PRL (2007)

• 3x2 seesaw model with the third RH neutrino in the TeV 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 !!

XddXNuW lc

kc

klic

i NNM N XXM X


N-N-bar PredictionN-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.

NXB MM

G4

1212


Baryogenesis in N-N-bar modelsBaryogenesis 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 GeV. 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)


Baryogenesis Diagrams in the second modelBaryogenesis Diagrams in the second model

Possible to obtain right n_B/N_gamma


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


ConclusionConclusion• With the discovery of neutrino mass the case

for N-N-bar oscillation is a lot stronger now than it was in the 1980s. Urge new search at the level of 10^10 sec to test for B-L seesaw scale around 10^11 GeV as against GUT scale seesaw.

• N-N-bar discovery will completely change the 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 P-decay as a test of GUT idea is the 10^36 yrs level search and should be the ultimate goal.

Thank you for your attention.


Role of Lepton Flavor ViolationRole of Lepton Flavor Violation

• Standard model with Majorana neutrino mass

without supersymmetry and high scale seesaw:

Very tiny:

With SUSY, things are different.

4

32

3)(

WM

meB


SUSY seesaw and FCNC effectsSUSY 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.

DRT

D mMmm 1 wkD vYm


Generic predictions forGeneric predictions for e

e

GeVV LB1410

VempatiVivesMasiero ,,


Lower V_BLLower 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 TeV range:

In this case even without SUSY, mu-> e +gamma Br. Can be observable.


ConclusionConclusion• With the discovery of neutrino mass the case

for N-N-bar oscillation is a lot stronger now than it was in the 1980s. Urge new search at the level of 10^10 sec to test for B-L seesaw scale around 10^11 GeV as against GUT scale seesaw.

• N-N-bar discovery will completely change the 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 P-decay as a test of GUT idea is the 10^36 yrs level search and should be the ultimate goal.

Thank you for your attention.

Documents

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