Thanks to the fundamental discoveries of the lastdecade we know that neutrino flavor is not conserved.From that it follows that neutrinos are massive and mixed,i.e. the flavor (observable) neutrinos are superpositionsof states with definite mass,
|
νl
> = Σi
Ul
i
|
νi
> .The mass squared differences Δm2
solar
, and Δm2atmospheric
have been measured quite accurately, and two out ofthree mixing angles (θ12
and θ23
) are known as well.The status of the present knowledge is schematicallydepicted in the following slide.
The status of the present knowledge of the neutrinooscillation phenomena.These quantities areunknown at present:a)
The mass m1b)
The angle θ13c)
Whether the normal or inverted hierarchy is realized.
d) Most importantly,wedo not know whetherneutrinos are Diracor Majorana
fermions.Need 0νββ decay todecide this question.
However,
ν
masses are much smaller than the masses of other fermions
Is that a possible “Hint of”
a new mass-generating mechanism?
DESERT
Mass hierarchies of quarks and leptonsIn this plot the mass of the heaviest particle is taken as unityWhile the patterns of up quarks, down quarks, and chargedleptons are not really identical, the neutrino masses are noticeably more squeezed together.
neutrinos
charged leptons
down quarks
up quarks
10-5 10-4 10-3 10-2 10-1 1
Weinberg already in 1979 (PLR 43, 1566) showed that there is only one
dimension d=5 gauge-invariant operator given the particle content of the standard model:
L(5) = C(5)/Λ (LcεH)(HTεL) +h.c.
Here Lc
= LTC, where C is charge conjugation and ε
= -iτ2
. Thisoperator clearly violates the lepton number by two units and represents neutrino Majorana
mass
L(M) = C(5)/Λ v2/2 (νLc
νL
) + h.c.
If Λ
is larger than v, the Higgs vacuum expectation value, the neutrinos will be `naturally’
lighter than the charged fermions.
To solve the dilemma of `unnaturally’
small neutrino mass we can give up on renormalizability
and add operators of dimension d > 4 that are suppressed by inverse powers of some scale Λ but are consistent with the SM symmetries.
The energy scale Λ
is more or less the energy above which theeffective operator expressions above are no longer valid.
In order to estimate the magnitude of Λ
suppose that C(5) ~ O(1) and neutrino mass ~ 0.1 eV. Then
Λ~ v2/mν
~ 1015
GeV
It is remarkable, but perhaps a coincidence, that this scale Λis quite near the scale at which the running gauge couplingconstants meet, MGUT ~ 1015-16
GeV.
The most popular theory of why neutrinos are so light is the —
See-Saw Mechanism
ν
NRVery heavy neutrino
Familiar light neutrino
}{
(Gell-Mann, Ramond, Slansky
(1979), Yanagida(1979), Mohapatra, Senjanovic(1980)and even earlier Minkowski
(1977))
It assumes that the very heavy neutrinos NR
exist. Their massplays an analogous role as the scale Λ of Weinberg, i.e.,mν
~ v2/MN
. Both the light and heavy neutrinos are Majorana
fermions.
• Measure mixing parameters (esp. unknowns θ13
and δCP
)• Resolve the mass `hierarchy’• Determine magnitude of at least one mν• Demonstrate Majorana
or Dirac hypothesis
• Use neutrinos as astrophysical probes• Look for the unknown
Current experimental goals in neutrino physics
This talk
How can we tell whether total lepton number is conserved?
A partial list of processes where the lepton number would be violated:
Neutrinoless
ββ
decay: (Z,A) -> (Z±2,A) + 2e(±), T1/2
> ~1025
yMuon
charge changing conversion: μ-
+ (Z,A) -> e+
+ (Z-2,A), BR < 10-12
Anomalous kaon
decays: K+
-> π-μ+μ+ , BR
< 10−9
Flux of νe
from the Sun: BR < 10-4
Flux of νe
from a nuclear reactor: BR < ?Production of same charge leptons (and no ν) at LHC: σ
= ?
Observing any of these processes would mean that the leptonnumber is not conserved, and that neutrinos are massive Majorana particles.
It turns out that the study of the 0νββ decay is by far the mostsensitive test of the total lepton number conservation, so werestrict further discussion to this process.
0νββe– e–
u d d u
(ν)R νL
W W
Whatever processes cause 0νββ, its observation would imply the existence
of a
Majorana
mass term:
Schechter and Valle,82
By adding only Standard model interactions we obtain
Hence observing the
0νββ
decay guaranties that ν
are massive Majorana
particles.
(⎯ν)R → (ν)L Majorana mass term
If (or when) the 0νββ decay is observed twoproblems must be resolved:
a)What is the mechanism of the decay,i.e., what kind of virtual particle isexchanged between the affectednucleons (or quarks)?
b) How to relate the observed decay rateto the fundamental parameters, i.e.,what is the value of the correspondingnuclear matrix element?
What is the nature of the `black box’? In other words, what is the mechanism of the 0νββ
decay?All these diagrams can in principle contribute to the 0νββ
decay amplitude
Light Majorana
neutrino,only Standard Model
weak interactions
Heavy Majorana
neutrinointeracting with WR
.Model extended to include
right-handed currentinteractions.
Light or heavy Majorananeutrino. Model extended
to include right-handed WR
.Mixing extended betweenthe left and right-handed
neutrinos.
Supersymmetrywith R-parity violation. Many new particlesinvoked. LightMajorana
neutrinos exist also.
d u
e-
e-
WL
WL
ν
ud
d u
WR
WR
νheavy
ud
e-
e-
d u
WR
WL
ν
ud
d u
e (selectron)
χ
(neutralino)
ud
e (selectron)
e-
e-
e-
e-
The relative size of the heavy (AH
) vs. light particle (AL
)exchange to the decay amplitude is
(a crude estimate, due originaly
toMohapatra)
AL ~ GF2
mββ
/<k2>, AH ~ GF2 MW
4/Λ5
,
where Λ is the heavy scale and k ~ 100 MeV
is the virtualneutrino momentum.
For Λ ~ 1 TeV
and mββ
~ 0.1 –
0.5 eV
AL
/AH
~ 1, hence bothmechanisms contribute equally.
It is well known that the amplitude for the light neutrino exchange scales as <mββ
>. On the other hand, if heavyparticles of scale Λ are involved the amplitude scales as 1/Λ5
(dimension 9 operator).
AL
/AH ~ mββ
Λ5/ <k2> MW4
Thus for mββ
= 0.2 eV, <k2> = 1002 MeV2, and AL
/AH
~ 1Λ5
~ 502x1012x804x1036/0.2 eV
~ 2x1060
eVΛ ~ 1012 eV
= 1 TeV
Clearly, the heavy particle mechanism could compete with the light Majorana
neutrino exchange only if the heavy
scale Λ
is between about 1 -
5 TeV. Smaller Λ
are alreadyexcluded and larger ones will be unobservable due to the fast Λ5
scale dependence.
Observing the 0νββ decay will not (in general) make it possible to draw conclusion about the `mechanism’
of
the process. We need additional information.
⇒
I will discuss how the study of lepton flavor violation (LFV) can help us to decide what mechanism is responsible for the 0νββ
decay if it is observed in a foreseeable future.
This is based on “Lepton number violation without supersymmetry”Phys.Rev.D 70 (2004) 075007V. Cirigliano, A. Kurylov, M.J.Ramsey-Musolf, and P.V.and on “Neutrinoless
double beta decay and lepton flavor violation”
Phys. Rev. Lett. 93 (2004) 231802
V. Cirigliano, A. Kurylov, M.J.Ramsey-Musolf, and P.V.
Bμ→eγ
= Γ(μ→eγ)/Γ(μ→eνμ
νe
) < 1.2x10-11
Γ(μ−
+(Z,A) →
e-
+ (Z,A))
Γ(μ−
+(Z,A) → νμ
+ (Z-1,A))Bμ→e
=
Lepton flavor violation (LFV) involving charged leptons has not been observed as yet. The most sensitive limits are for the decay
New experiment, MEG at PSI, started data taking in June andshould reach sensitivity ~ 2 orders of magnitude better.
The “muon
conversion”
is constrained by
< 8x10-13
Several proposals extending the sensitivity to ~10-17
have been proposed.
The fact that neutrinos have finite mass and that they mix willnot make these LFV processes observable, they are suppressedby (Δm2/Mw
2)2 ≤
10-50. Hence observation of them would imply “new physics”
unrelated (or only indirectly related) to neutrino mass.
So, why are people even looking for LFV?
Because most particle physics models of `physics beyond the Standard Model’
contain LFV originating at
some high mass scale. Most of them also contain LNV and,naturally, all realistic models should include light and mixed neutrinos, known to exist.
If the scales of both
LFV and LNV are well above the weak scale, then Γ0νββ
~ <mββ
>2 and <mββ
> can be derived from the 0νββ
decay rate. However, the ``dangerous”
case is when both
LFV and LNV scales are low (~ TeV). In that case there might be an ambiguity in interpreting the results of 0νββ
decay experiments.
An example of the possible scenario is based on the SUSY SU(5) model.(Barbieri, Hall and Strumia, Nucl. Phys.B 445, 219 (1995))
here is an extra factor of α
Thus a) MEG and MECO should see an effect, andb) μ
-> e
+ γ
is enhanced by a factor ~1/α
compared to μ
->
e conversion. The feature b) is generic for theories with high
scale LNV
arXiv:0707.2955
Ratio of the branching ratiosfor μ
conversionto μ→e+γas a functionof the Higgsmass. Note thetypical valueof ~1/200.
From Arganda
and Herrero
arXiv
0810.0160,
again a factor ~200 between
μ-> e
+ γ and μ→e conversionand again suggesting thatboth processes should beseen in the next generationof experiments.
However, SM extensions with low (~
TeV) scale LNV fl**
Left-right symmetric model,R-parity violating SUSY, etc.possibly Γ0νββ unrelated to
mββ2 R = Bμ→e
/Bμ→eγ
» 10-2
** In absence of fine-tuning or hierarchies in flavor couplings. Important caveat!
See: V. Cirigliano
et al., PRL93,231802(2004)
Thus we found a diagnostic tool: Link between LNV and LFV
Also, if LFV is not found in the next round of experiments, the TeVscale of LFV and LNV becomes even less probable.
In such case R = Bμ→e
/Bμ→eγ
~ 10-2
and LNV is associatedwith GUT scale hence Γ0νββ
∼ mββ2
as usually assumed.
Effective theory description
- arises at loop level
- , may arise at tree level
- Leading pieces in ci are nominally of order (Yukawa)2
Operators (omitting L ¨ R)
dimension 9 operator
dimension 6 operator
The ratio R can be expressed in terms
of the constants ci
as follows
• Phase space + overlap integrals:
• ηn are coefficients of O(1)
• Origin of large logs:one loop operator mixing
for light nuclei
[Raidal-Santamaria ’97]
Thus from the expression for R it follows:
(i) No tree level , fl
(ii) Tree level , fl
log enhancement and
(iii) Tree level fl
We need to show that in models with low scale LNV Ol
and/or Olq
are generated at tree level. We offer no general proof, but two illustrations.
Low scale LNV and LFV: Left-Right Symmetric Model (LRSM)SU(2)L ≈
SU(2)R ≈
U(1)B-L fl
SU(2)L ≈
U(1)Y fl
U(1)EM
fl
Neutrino mass matrix 6x6 of see-saw type
yM
is 3x3 Yukawa coupling matrix, we expect yM
~ O(1)
When Mν
is diagonalized
there are 3 small eigenvalues
mν
∼ MD2/MR
Note that if MR
~ O(TeV) we need MD
~ O(MeV) to accommodatethe correct order of magnitude of mν
this requires fine tuning.
Also note that in our case ΔL
is assumed to be vanishingly small.
hij are coupling constants of leptons and the doubly charged Higgs
They are related to the mixing matrix KR of the heavy neutrinos
Note that glfv vanishes for degenerate heavy neutrinos, but hij need not.
Within LRSM the LFV branching ratios depend only on thesame combination of parameters denoted here as glfv :
Thus the present limits suggest that either the scale is >> 1 TeV,or that glfv is very small, i.e. that he heavy neutrino spectrumis degenerate or has very little mixing. Note that the extra αin the muon conversion is compensated by the large log2 factorin this case. The two branching ratios could be of similar magnitude.
KR is the heavy neutrinomixing matrix
Clearly, the way to avoid the connection between LFV and LNV is if λ’
111 >> λ’211
, etc. That is if λ’
is nearly flavor diagonal. Note thatempirically both λijk
and λ’ijk
are small << 1.
For the discussion of neutrino masses in the R-parity violatingsupersymmetric
models see Y. Grossman and S. Rakshit, hep-ph/0311310
Generally, a hierarchical neutrino spectrum is predicted,but small neutrino masses require some fine tuning. Notealso that R-parity violation excludes LSP as a dark mattercandidate. Discovering it would exclude R-parity violation.
As long as only a limit on the 0νββ
decay rate exists,we can constrain all parameters entering the decayamplitudes (light and heavy neutrino masses, strengthof the right-handed current, SUSY R-parity violatingamplitude, etc.).However, once the decay rate is convincingly measured,we need to determine which of the possible mechanismis responsible for the observation.To see the actual experimental situation let us in the following assume that the three light activeneutrinos, ν1
,ν2
,ν3
, are Majorana
particles. The 0νββdecay exists then for sure (excluding the fine tuningthat would make <mββ
> vanishing small), and concentrate on the corresponding rate.
There is a steady progressin the sensitivity of thesearches for 0νββ
decay.Several experiments thatare funded and almostready to go will reachsensitivity to ~0.1 eV.There is one (so farunconfirmed) claim thatthe 0νββ
decay of 76Gewas actually observed.The deduced mass <mββ
>would be then 0.3-0.7 eV.
Moore’s law of 0νββ
decay:
What should happen next?1)
In a number of new experiments ( CUORE, EXO,Majorana, MOON, SuperNEMO, GERDA, SNO+, etc) the amount of source will be increased from the present ~10 kg to ~100 kg, and the sensitivity from the ~1025
y to ~ 1026-27
y, covering the `degenerate’
mass region.2)
This should open, if needed, the door for ~ton 0νββ
decay
experiments that will reach into the `inverted hierarchy’
.3) Next generation of experiments on LFV will extend
the sensitivity considerably. In parallel, running ofLHC will shed light on the existence of particles with~TeV
masses.
4) Hopefully, progress in the nuclear structure calculationwill remove some or most of the uncertainty in the0νββ nuclear matrix elements.