A variety of lepton number violating processes related to

Majorana neutrino masses

(E. Takasugi , M. Yoshimura, C.S.L., a paper in preparation)

C.S. Lim (Kobe University, Japan)

@ NuFact04 (July 28,’04, Osaka)

I. Introduction・ neutrino oscillation → 　 Δmν ≠0, mν ≠0

・ the origin of neutrino masses is an issue

Majorana nature is crucial:

・ See-Saw (Gell-Mann, Ramond, Slansky & Yanagida)

(νR) Majorana mass >> Dirac mass

・ Radiatively induced Majorana mass of νL (A. Zee )

・ neutrino oscillation cannot prove the Majorana nature

, since oscillation with chilarity flip, νL → 　 ν’R , is suppressed by (mν/E)2 <<1

(Majorana) (Dirac)

the difference cannot be seen more precisely, neutrino oscillation is measuring (M: neutrino mass matrix )

→ 　 M M† 　　 rather than M itself

e.g. in 2 generation case of Majorana mass matrix,

Φ ： Majorana phase

the (physical) CP Majorana phase Φ has disappeared

to test the Majorana nature, we need to see M itself

Mαβ

ν α ν β which inevitably leads to L-violating processes. ν –less double β decay: N → 　 N’ + 2 e– : typical example We wish to study systematically a variety of L-violating processes due to an effective (low energy) operator, (ΔL = 2)

induced by

(NB) ・ this operator is a universal as long as neutrinos have Majorana masses, irrespectively of the scenario of the mass generation ・ when there is flavor mixing, by studying various

combination of l α l β , we basically can determine Mαβ

・ ν –less double β decay search may provide negative result, even in the case of inverted hierarchy : may be suppressed by the

presence of 2 Majorana phases

→ 　 the search for various (not (α , β ) = (e,e) alone) L-violating processes is quite important

（ why not l l H H operator ? ）　 l l H H is the gauge invariant operator to produce νL

Majorana masses

however, its contribution is relatively suppressed basically by the additional Yukawa couplings

II. L- violating processes Here we discuss the following typical processes : (eμ) e– + AZ → 　 μ+ + A Z – 2

(μe) μ– + AZ → 　 e+ + A Z – 2 (μ -capture) (ee) e– + e– (atomic) → π – + π –

(eμ) νμ + e– (atomic) → π – + π 0

・　 e– + AZ → 　 μ+ + A Z – 2 　

background : μ+ from π + decay

→ 　 mμ 　≤　 Ee 　 ≤ 　 mπ 　 desirable 　

there is an enhancement due to Z(Z-1) factor 　　　 　　　　

・　 μ – + AZ → 　 e + + A Z-2 　 (μ : captured into atomic orbit )

(E. Takasugi, Nucl.Instr. and Methods. in Phys.Res., A503, 252 (‘200

3) ) cute:

(1) self-focusing of incident μ – into the area of

nuclear size

(2) the same μ – can be used repeatedly as in the case of high luminosity accumulator ring → 　 high event rate is expected

but, the rate of μ – → 　 νμ is huge, and

Br(μ – → e + ) ≈ GF2 |m e μ |2 s (s: (CM energy)2)

: quite small

・　 e– + e– (atomic) → π – + π – , νμ + e– (atomic) → π – + π 0

(high intensity νμ may be available in proposed ν factory)

these are unique: lepton number completely disappears

we discuss e– + e– → π – + π – :

Ee > (2m π2)/ me 　≈ 　 80 GeV needed

　　　　　　　　　　　　　　　　　　　　 (fπ ： π decay constant)

event rate:

• background e– + n → e– + p + π – + π – + π +

may be rejected by imposing a kinematical condition

invariant mass of π – + π – = (2 Eeme)1/2

the cross-section may be enhanced by s2 / f π4

in the corresponding inclusive process in the range

2m π << s ½ << 2 MW :

e– + e– (atomic) → Xh (Xh : hadronic state)

but, 2m π << s ½ will demand a TeV electron linac

III. Summary ・　 The Majorana nature of neutrino mass matrix, which

cannot be proved by the neutrino oscillation, can be fully verified by the L-violating processes, whose typical examples were discussed here ・ Though the rates are genarally very small, the predictio

ns in terms of the mass matrix are definite ones, and if some process is observed by a larger than expected rate, it clearly signals another source of L violation, such as R-parity violating superpotential, l l e+, in SUSY theory.

・ The Majorana CP phases, exploited in the L-violating processes, also play crucial roles in the leptogenesis scenario (Fukugita-Yanagida) for baryogenesis in the uni

verse （ NB) 　 the CP phase of MNS matrix, relevant for neut

rino oscillation, does not play a role: the L asymmetry due to N → 　 l H is handled by Y†Y,

in which UMNS disappears since Y = UMNS Y’. ・　 Suppose the Majorana neutrino mass matrix is real with

6 freedom. Then, there should be a relation among, say, 7 observable

s,

e.g. (neutrino oscillations)

νe → 　 νμ , νμ → 　 ντ , ντ 　→ νe (L-violating)

　 nn → e– e–pp, 　 e– →μ + , 　

　　　　　 νμ 　→ μ – μ + μ + , 　 pp → 　 τ + τ + nn 　　 the violation of the relation → 　 CP violation