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C.S. Lim (Kobe University, Japan) @ NuFact04 (July 28,’04, Osaka)

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 → Δm ν ≠0, m ν ≠0

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C.S. Lim (Kobe University, Japan) @ NuFact04 (July 28,’04, Osaka)

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  1. 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)

  2. 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

  3. (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

  4. 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

  5. (NB) ・this operator is a universalas 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

  6. （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 • 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

  7. ・　e– + AZ→μ+ + A Z – 2 background : μ+ from π + decay →mμ≤Ee≤mπdesirable there is an enhancement due to Z(Z-1) factor

  8. ・　 μ– + AZ→e + + A Z-2(μ : captured into atomic orbit ) (E. Takasugi, Nucl.Instr. and Methods. in Phys.Res., A503, 252 (‘2003)) 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

  9. ・　e– + e– (atomic) → π – + π – , νμ + e– (atomic) → π – + π 0 (high intensity νμ may beavailable 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:

  10. 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 2mπ << s ½ << 2 MW : e– + e– (atomic) → Xh (Xh : hadronic state) but, 2mπ << s ½ will demand a TeV electron linac

  11. 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 predictions 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.

  12. ・ The Majorana CP phases, exploited in the L-violating processes, also play crucial roles in the leptogenesis scenario (Fukugita-Yanagida) for baryogenesis in the universe （NB)the CP phase of MNS matrix, relevant for neutrino 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 observables,

  13. 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

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