march 2005 theme group 2 do neutrons oscillate ? do neutrons oscillate ? r. n. mohapatra university...
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March 2005Theme Group 2
Do Neutrons Oscillate ?Do Neutrons Oscillate ?
R. N. Mohapatra
University of Maryland
Beijing Colloqium, June, 2007
March 2005Theme Group 2
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 ?
March 2005Theme Group 2
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.
March 2005Theme Group 2
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.
March 2005Theme Group 2
Modes of interestModes of interest0B
Two modes of interest are:
(i)Proton decay
(ii)Neutron-anti-neutron oscillation
Kpep ,0
March 2005Theme Group 2
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 ~.
March 2005Theme Group 2
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
March 2005Theme Group 2
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
March 2005Theme Group 2
Oscillation inside NucleiOscillation inside Nuclei
March 2005Theme Group 2
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
March 2005Theme Group 2
Comparision P-decay vs N-N-barComparision P-decay vs N-N-bar
2. freeNuc R
freeNuc R 2 123 sec103.0 R
March 2005Theme Group 2
Free vs Bound N-N-barFree vs Bound N-N-bar
• Nuclear Physics uncertain: Uncertainty in R
-need to do free neutron osc. Search.
March 2005Theme Group 2
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.
March 2005Theme Group 2
Present collaboration:Present collaboration:
• Seeking collaborators: new site for expt.
March 2005Theme Group 2
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
March 2005Theme Group 2
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
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O B 20
1
yrsep
331050
GeVM 1510
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0)( LB
March 2005Theme Group 2
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
March 2005Theme Group 2
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
March 2005Theme Group 2
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.
March 2005Theme Group 2
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.
March 2005Theme Group 2
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 ?
March 2005Theme Group 2
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.
March 2005Theme Group 2
Neutrino mass and -standard modelNeutrino mass and -standard model
• Starting point: add RH neutrino to SM for nu mass:
March 2005Theme Group 2
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
March 2005Theme Group 2
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
March 2005Theme Group 2
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(
March 2005Theme Group 2
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
March 2005Theme Group 2
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
March 2005Theme Group 2
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
March 2005Theme Group 2
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
March 2005Theme Group 2
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
March 2005Theme Group 2
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
March 2005Theme Group 2
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(
March 2005Theme Group 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
March 2005Theme Group 2
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
March 2005Theme Group 2
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
March 2005Theme Group 2
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 ?
March 2005Theme Group 2
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 ?
March 2005Theme Group 2
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:
March 2005Theme Group 2
Nucleon Decay in Generic SUSY GUTsNucleon Decay in Generic SUSY GUTs
• Gauge Boson exchange:
March 2005Theme Group 2
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
March 2005Theme Group 2
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))
March 2005Theme Group 2
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)(
March 2005Theme Group 2
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
March 2005Theme Group 2
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”.
March 2005Theme Group 2
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
March 2005Theme Group 2
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
March 2005Theme Group 2
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.............
March 2005Theme Group 2
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)
March 2005Theme Group 2
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
March 2005Theme Group 2
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
March 2005Theme Group 2
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)
March 2005Theme Group 2
Baryogenesis Diagrams in the second modelBaryogenesis Diagrams in the second model
Possible to obtain right n_B/N_gamma
March 2005Theme Group 2
Proton decay vs N-N-bar oscillationProton decay vs N-N-bar oscillation
March 2005Theme Group 2
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.
March 2005Theme Group 2
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
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WM
meB
March 2005Theme Group 2
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
March 2005Theme Group 2
Generic predictions forGeneric predictions for e
e
GeVV LB1410
VempatiVivesMasiero ,,
March 2005Theme Group 2
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.
March 2005Theme Group 2
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.