Lepton Flavour & CP Violations in Charged Lepton Transitions Carlos A. Savoy Neutrino 2004, Paris SACLAY • Leptonic physical observables and limits on New Physics scales • Limits on LFV & CPV in SUSY scalar masses* • Impact on Seesaw and GUT models* n * Thanks to I. Masina for collaboration and for all the plots herein.
INTRODUCTION ! Neutrino oscillations require LFV in the effective neutrino mass matrix ! Seesaw Leptogenesis requires phases in the Yukawa couplings of the leptons to the Higgsses ! The impact of these important LFV&CPV in the charged lepton sector is experimentally irrelevant in the minimal framework: SM ⊕ Seesaw, 2 / M W 2 ) because of GIM - like factors . ( Δ m ν ! The observation of LFV in , or CPV in lepton electric µ → e γ , τ → µ γ dipole moments would be signals of New Physics beyond SM ⊕ Seesaw. ! Conversely, the present experiments constrain and will strongly constrain New Physics around and above the TeV region to introduce LFV&CPV inhibition mechanisms. E.g., SUSY. ! Some tests provide already relevant constraints on radiative corrections involving new LFV&CPV couplings.
Planned improvements in experimental limits on L epton F lavour V iolating Decay and Lepton E lectric D ipole M oments constrain the Yukawa couplings and masses of heavy states of the Seesaw Model and/or GUT s from their quantum corrections to the Slepton mass matrix ∝ ln (MPLANCK / MHEAVY) LFV & CP patterns of Seesaw and GUTS are constrained! N.B. - These constraints are complementary to those from neutrino oscillations and leptogenesis (seesaw) and proton decays
OBSERVABLE PRESENT LIMITS PROSPECTS S.M.PREDICTION B.R . CLFV τ→ µ γ 10-6 10-8(?) < 10-48 µ → e γ 10-11 10-14 PSI < 10-48 EDM e.cm < 10-38 10-27 de 10-29 d μ 10-18 10-24 BNL <10-35 10-26 KEK Experimental limits on LFV & CPV (See the talk by M. Aoki for a more complete list of processes and for the references. )
⇔ MAGNETIC MOMENTS, LFV & CPV chirality flip effective lepton ⇒ Δ I = 1/2 coupling mass ⇒ <H> insertion Γ NP e m � L σ µ ν � j � i R F µ ν ij ¯ M 2 16 π 2 NP effective loop NP scale factor Γ NP ( g − 2) µ ( g − 2) e f lavour diagonal: i=j ii Γ NP μ ➙ e γ τ ➙ μΥ flavour violating: i ≠ j i � = j Γ NP d µ d e CP violating: i=j Im ii
LIMITS ON NP CONTRIBUTIONS TO LFV AND CPV Naive Scaling Experiment Prospects 2 M 2 NP (TeV ) (g-2) > Γ ⁄ 1000 e NP e ee m / m 2 2 e μ > Γ ⁄ 20 NP (g-2) μ μ μμ > Γ × 20 NP × 30 μ ➙ e γ μ e m / m τ μ NP > Γ ⁄ 40 × 10 (?) τ ➙ μ Υ τμ d NP >Im Γ × 70 d × 100 ee e ee m / m e μ -5 6 NP >Im Γ × 10 d × 10 (!) μ μμ
New Physics across the TeV barrier ⇒ new flavour and CP violations Present (future) experiments constrain (will strongly constrain) contributions from NP around the TEV scale: LFV & CPV ones are much more restricted than the flavour and CP conserving ones. ⇒ A generic NP flavour and CP problem to be controlled both at tree and quantum levels SUSY is (one of) the best candidate(s) for a NP framework but it has many effective sources of low energy LFV & CPV, in particular in the slepton/squark mass matrices ⇒ contributions to LFV and EDM ⇒ strong constraints on SUSY breaking parameters (masses). SEESAW theories and GUT ’s contain LFV & CPV in their couplings that radiatively correct the low energy effective SUSY breaking parameters and are potentially measureable in LFV decays and EDMs.
SCALAR LEPTON MASS MATRICES (standard notation) Δ I=0 Δ I=1/2 � FLAVOUR CONSERVING � 2 ( ) m i m 0 µ tan β + A i (phases in μ and A) 2 × δ LL , RR 2 × δ LR m 0 m 0 FLAVOUR VIOLATING ☹ ☹ (complex flavour non-diagonal) The limits on the δ matrix elements are obtained (not necessarily) by expanding the amplitudes in their products. E.g.: EDM ∈ Im [( µ tan β + A i ) m i + ( δ RR ) ik ( µ tan β + A k ) m k ( δ LL ) ki + . . . ] lepton flavour lepton flavour violating CP violation conserving CP violation
SUSY (MDM + “i”EDM) - flavour conserving d e < 10 − 27 e.cm φ µ = ph [ µ ] δ a µ ≤ 20 × 10 − 10 d e < 10 − 29 e.cm × 1/100 for
REFERENCES Kosower, Krauss, Sakai (83) Ibrahim, Nath ph/9807501 Text Carena, et al. ph/9610236 Falk, Olive ph/9806236 Everett, et al. ph/0102145 Brhlik, Good, Kane ph/9810457 Feng, Matchev ph/0102146 Abel, et al. ph/0103320 Chatopadhyay, Nath ph/0102157 Masina, et al ph/0211283 Ellis, et al. ph/0102331 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( Figures from ph/0211283)
limits on LFV slepton masses from B.R.( μ→ e Υ ) Planned experiments are expected to improve these limits by a factor of 30
REFERENCES Gabbiani, et al. ph/9604387 Hisano, et al. ph/9510309 Hisano, Nomura ph/9810479 Masina, et al. ph/0211283 ( Figures from ph/0211283)
flavour violating CP violation Therefore: the LFV & CPV contributions from SUSY loops e-EDM must be reduced by several orders of magnitude w.r.t. analogous radiative corrections to flavour & CP conserving processes = SUSY FCNC & CP problems (I. Masina, CAS ph/0211283)
LOOKING FOR FOOTPRINTS OF VERY HEAVY (DECOUPLED) STATES: GUT COLOUR TRIPLETS SEESAW MAJORANA NEUTRINOS PATTERN OF FLAVOUR AND CP VIOLATIONS IN THE SLEPTON MASS MATRIX INDUCING LFV AND CPV THRU SUSY RADIATIVE CORRECTIONS: SUSY mediated LFV & CP
FOOTPRINTS OF SEESAW & GUT HEAVY STATES IN THE SLEPTON MASS MATRICES LFV & CP phases are radiatively generated from heavy state contributions to the RGE running until their decoupling . In 1st. order these loop contributions are like: SEESAW HEAVY NEUTRINOS GUT COLOUR TRIPETS decouple @ M decouple @M R T � M P l � � M P l � N = Y † U = Y † ν ln Y ν u ln Y u M R M T ( in SO(10) GUT: N ≈ U ) RR ∝ U ij ⊕ ... LL ∝ N ij ⊕ ... δ i ≠ j δ i ≠ j LFV e.m. decays: E.D.M (flavour conserving A -term) ≠ 0 iff strong hierarchy in M R δ LL m � δ RR � E.D.M (flavour violating): � Im ii ∼ O(1)Im( U ∗ m � N ) ii
LFV from SEESAW: LFV from GUTs: Borzumati, Masiero, 1987 Hall, et al (86) Buchmuller, et al. hep/9904219 Barbieri, Hall ph/9408406 Feng, et al. ph/9911370 Dimopoulos, Hall ph/911273 Ellis, et al. ph/9911459 Romanino, Strumia ph/0108275 Hisano, Tobe ph/0102315 Masiero, et al. ph/0209303 Casas, Ibarra ph/0103065 Carvalho, et al. ph/0103256 Blazek, King ph/0105005 EDM from GUTs: Lavignac, et al. ph/0202086 Barbieri, et al. ph/9501334, Masiero, et al. ph/0209303 ph/9511305 Pascoli, et al. ph/0301095 Romanino, Strumia ph/9610485 ph/0108275 Lebedev ph/0209023 EDM from SEESAW: Masina, ph/0304299 Ellis, et al. ph/0109125, Ciuchini, et al. ph/0307191 ph/0111324, 0206110 Masina, Savoy ph/0309067 Masina ph/0304299 Farzan, Peskin ph/0405214
limits on seesaw couplings in SU(5) t i � M P l � � 1 ν i 1 Y ν i 3 e − i β Y ∗ Im t i = 16 π 2 ln t 3 M i i β = phase( V td ) ≈ . 42 These limits will be multiplied by a 1/100 with the future limit: d e < 10 − 29 e.cm How relevant are (Masina, ph/0304299) these limits for GUT’s?
limits on colour triplet masses: proton decay vs. electron EDM τ p ( yrs ) (Masina, S. ph/0309067) Model I: SU(5) (minimal) Y ν = Y with u III expt. Model II: SO(10) (minimal) with I t II MT = MT 2 r 1 d e (e.cm) Model III: SO(10) (pseudoDirac) II with M T = ( r − 1) III 1 M T 2 ( r + 1) expt. ˜ m e R = 400 GeV M 1 = 200 GeV I M T = 10 17 GeV tan β = 3 r
- Conclusion - d e , d μ , μ ➙ e γ experiments STRONGLY CONSTRAIN NEW LFV & CPV AT O(TeV) SCALE • • LFV & CPV IN THE SCALAR LEPTON MASS MATRICES • • WILL SEVERELY CONSTRAIN SUSY GUT’s and SEESAW’ • (ALTHOUGH ONE CANNOT EXCLUDE CANCELATIONS BETWEEN DIFFERENT PHASES) LEPTON EDM WILL PROVIDE RELEVANT BOUNDS ON HEAVY TRIPLET MASSES IN GUT’S d μ > (m μ /m e )d e IS AN INTERESTING THEORETICAL CHALLENGE AND d μ EXPERIMENTS ARE IMPROVING A LOT.
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