Neutrinoless double beta decay and lepton flavor 2008-10-16آ Neutrinoless double beta decay. and...
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Transcript of Neutrinoless double beta decay and lepton flavor 2008-10-16آ Neutrinoless double beta decay. and...
double beta decay and lepton flavor violation
Petr Vogel Caltech
INT, Seattle, 10/17/08
Thanks to the fundamental discoveries of the last decade 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 superpositions of states with definite mass,
> = Σi
> . The mass squared differences Δm2solar
, and Δm2atmospheric have been measured quite accurately, and two out of three mixing angles (θ12
) are known as well. The status of the present knowledge is schematically depicted in the following slide.
The status of the present knowledge of the neutrino oscillation phenomena. These quantities are unknown at present: a)
The mass m1 b)
The angle θ13 c)
Whether the normal or inverted hierarchy is realized.
d) Most importantly,we do not know whether neutrinos are Dirac or Majorana
fermions. Need 0νββ decay to decide this question.
masses are much smaller than the masses of other fermions
Is that a possible “Hint of”
a new mass-generating mechanism?
D E S E R T
Mass hierarchies of quarks and leptons In this plot the mass of the heaviest particle is taken as unity While the patterns of up quarks, down quarks, and charged leptons are not really identical, the neutrino masses are noticeably more squeezed together.
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.
= LTC, where C is charge conjugation and ε
. This operator clearly violates the lepton number by two units and represents neutrino Majorana
L(M) = C(5)/Λ v2/2 (νLc
) + h.c.
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is more or less the energy above which the effective operator expressions above are no longer valid.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
It is remarkable, but perhaps a coincidence, that this scale Λ is quite near the scale at which the running gauge coupling constants meet, MGUT ~ 1015-16
The most popular theory of why neutrinos are so light is the —
NRVery heavy neutrino
Familiar light neutrino
(Gell-Mann, Ramond, Slansky
(1979), Yanagida(1979), Mohapatra, Senjanovic(1980) and even earlier Minkowski
It assumes that the very heavy neutrinos NR
exist. Their mass plays an analogous role as the scale Λ of Weinberg, i.e., mν
. Both the light and heavy neutrinos are Majorana
Or equivalently, is the total lepton number conserved?
• Measure mixing parameters (esp. unknowns θ13
) • 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
How can we tell whether total lepton number is conserved?
A partial list of processes where the lepton number would be violated:
decay: (Z,A) -> (Z±2,A) + 2e(±), T1/2
charge changing conversion: μ-
+ (Z,A) -> e+
+ (Z-2,A), BR < 10-12 Anomalous kaon
-> 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 lepton number is not conserved, and that neutrinos are massive Majorana particles.
It turns out that the study of the 0νββ decay is by far the most sensitive test of the total lepton number conservation, so we restrict further discussion to this process.
0νββe – e–
u d d u
Whatever processes cause 0νββ, its observation would imply the existence
Schechter and Valle,82
By adding only Standard model interactions we obtain
Hence observing the
decay guaranties that ν
are massive Majorana
(⎯ν)R → (ν)L Majorana mass term
If (or when) the 0νββ decay is observed two problems must be resolved:
a)What is the mechanism of the decay, i.e., what kind of virtual particle is exchanged between the affected nucleons (or quarks)?
b) How to relate the observed decay rate to the fundamental parameters, i.e., what is the value of the corresponding nuclear 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
neutrino, only Standard Model
neutrino interacting with WR
. Model extended to include
right-handed current interactions.
Light or heavy Majorana neutrino. Model extended
to include right-handed WR
. Mixing extended between the left and right-handed
Supersymmetry with R-parity violation. Many new particles invoked. Light Majorana
neutrinos exist also.
The relative size of the heavy (AH
) vs. light particle (AL
) exchange to the decay amplitude is
(a crude estimate, due originaly
AL ~ GF2
/, AH ~ GF2 MW4/Λ5
where Λ is the heavy scale and k ~ 100 MeV
is the virtual neutrino momentum.
For Λ ~ 1 TeV
~ 0.1 –
~ 1, hence both mechanisms contribute equally.
It is well known that the amplitude for the light neutrino exchange scales as . On the other hand, if heavy particles of scale Λ are involved the amplitude scales as 1/Λ5
(dimension 9 operator) .
/AH ~ mββ
Thus for mββ
= 0.2 eV, = 1002 MeV2, and AL
~ 1 Λ5
~ 502x1012x804x1036/0.2 eV
eV Λ ~ 1012 eV
= 1 TeV
Clearly, the heavy particle mechanism could compete with the light Majorana
neutrino exchange only if the heavy
is between about 1 -
5 TeV. Smaller Λ
are already excluded and larger ones will be unobservable due to the fast Λ5
Observing the 0νββ decay will not (in general) make it possible to draw conclusion about the `mechanism’
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) 075007 V. 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.
) < 1.2x10-11
+(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 and should reach sensitivity ~ 2 orders of magnitude better.