Lepton Flavour & CP Violations in Charged Lepton Transitions - - PowerPoint PPT Presentation

Carlos A. Savoy

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.

Neutrino 2004, Paris

Lepton Flavour & CP Violations in Charged Lepton Transitions

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, because of GIM - like factors .

! The observation of LFV in , or CPV in lepton electric

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.

(Δmν

2 / MW 2 )

µ → eγ , τ → µγ

Planned improvements in experimental limits on Lepton Flavour Violating Decay and Lepton Electric Dipole Moments constrain the Yukawa couplings and masses of heavy states of the Seesaw Model and/or GUTs

from their quantum corrections to the Slepton mass matrix

∝ ln (MPLANCK / MHEAVY)

N.B. - These constraints are complementary to those from neutrino

• scillations and leptogenesis (seesaw) and proton decays

LFV & CP patterns

• f Seesaw and GUTS

are constrained!

Experimental limits on LFV & CPV

OBSERVABLE PRESENT LIMITS PROSPECTS S.M.PREDICTION

CLFV

τ→µ γ µ→e γ B.R.

10-6 10-11 10-8(?) 10-14 PSI

< 10-48

< 10-48

EDM

de dμ

e.cm 10-27

10-18 10-29 10-24 BNL 10-26 KEK < 10-38 <10-35

(See the talk by M. Aoki for a more complete list of processes and for the references. )

MAGNETIC MOMENTS, LFV & CPV

¯ i

L σµν j R F µν

ΓNP

ij

M 2

NP

e m 16π2

effective coupling effective NP scale lepton mass loop factor

chirality flip ⇒ ΔI = 1/2 ⇒ <H> insertion

⇔

flavour diagonal: i=j

flavour violating: i≠j CP violating: i=j Im

ΓNP

i=j

ΓNP

ii

ΓNP

ii

(g − 2)e (g − 2)µ

μ ➙e γ τ➙μΥ

dµ

de

LIMITS ON NP CONTRIBUTIONS TO LFV AND CPV

d

μ

e

ee

Experiment Prospects

Naive Scaling

(g-2)

m / m

(g-2)

μ ➙ e γ

× 30

m / m

τ ➙ μ Υ

>Γ ⁄ 40 × 10 (?)

d

>ImΓ × 70

× 100

m / m

d

>ImΓ ×10

×10 (!)

e

μ

M 2

NP (TeV )

2

e

2 2

μ

e

μ μ

τ

NP NP

ee μμ μe

NP

τμ μμ

NP NP NP

• 5

6

ee

e μ

>Γ ⁄ 1000 >Γ ⁄ 20 >Γ × 20

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.

ΔI=0

m0

2

µ tan β + Ai

( )mi

ΔI=1/2

SCALAR LEPTON MASS MATRICES

• m0

2 × δ LR

m0

2 × δ LL,RR

☹ ☹

FLAVOUR CONSERVING (phases in μ and A)

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 + Ai) mi + (δRR)ik (µ tan β + Ak) mk(δLL)ki + . . . ]

lepton flavour

conserving CP violation lepton flavour violating CP violation (standard notation)

SUSY (MDM + “i”EDM) - flavour conserving

φµ = ph[µ]

δaµ ≤ 20 × 10−10 de <10−29e.cm

×1/100 for

de <10−27e.cm

Kosower, Krauss, Sakai (83) Carena, et al. ph/9610236 Everett, et al. ph/0102145 Feng, Matchev ph/0102146 Chatopadhyay, Nath ph/0102157 Ellis, et al. ph/0102331 . . . . . . . . . . . . . Ibrahim, Nath ph/9807501 Falk, Olive ph/9806236 Brhlik, Good, Kane ph/9810457 Abel, et al. ph/0103320 Masina, et al ph/0211283 . . . . . . . . . . . . . . . . .

Text

REFERENCES

( Figures from ph/0211283)

limits on LFV slepton masses

Planned experiments are expected to improve these limits by a factor of 30

from B.R.( μ→eΥ)

Gabbiani, et al. ph/9604387 Hisano, et al. ph/9510309 Hisano, Nomura ph/9810479 Masina, et al. ph/0211283

REFERENCES

( Figures from ph/0211283)

flavour violating CP violation

Therefore:

the LFV & CPV contributions from SUSY loops must be reduced by several orders of magnitude w.r.t. analogous radiative corrections to flavour & CP conserving processes = SUSY FCNC & CP problems

e-EDM

(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:

GUT COLOUR TRIPETS decouple @M T

U = Y †

u ln

MP l MT

• Yu

( in SO(10) GUT: N ≈ U )

LFV e.m. decays:

δ i≠ j

LL ∝Nij ⊕...

δ i≠ j

RR ∝ Uij ⊕...

Im

• δLLmδRR

ii ∼ O(1)Im(U ∗mN)ii

E.D.M (flavour conserving A-term) ≠ 0 iff strong hierarchy in M R E.D.M (flavour violating): N = Y †

ν ln

MP l MR

• Yν

SEESAW HEAVY NEUTRINOS decouple @ M R

LFV from SEESAW: Borzumati, Masiero, 1987 Buchmuller, et al. hep/9904219 Feng, et al. ph/9911370 Ellis, et al. ph/9911459 Hisano, Tobe ph/0102315 Casas, Ibarra ph/0103065 Carvalho, et al. ph/0103256 Blazek, King ph/0105005 Lavignac, et al. ph/0202086 Masiero, et al. ph/0209303 Pascoli, et al. ph/0301095 LFV from GUTs: Hall, et al (86) Barbieri, Hall ph/9408406 Dimopoulos, Hall ph/911273 Romanino, Strumia ph/0108275 Masiero, et al. ph/0209303 EDM from SEESAW: Ellis, et al. ph/0109125, ph/0111324, 0206110 Masina ph/0304299 Farzan, Peskin ph/0405214 EDM from GUTs: Barbieri, et al. ph/9501334, ph/9511305 Romanino, Strumia ph/9610485 ph/0108275 Lebedev ph/0209023 Masina, ph/0304299 Ciuchini, et al. ph/0307191 Masina, Savoy ph/0309067

limits on seesaw couplings in SU(5)

Im

• i

ti t3 Y ∗

νi1Yνi3e−iβ

ti = 1 16π2 ln MP l Mi

• β = phase(Vtd) ≈ .42

How relevant are these limits for GUT’s?

These limits will be multiplied by a 1/100 with the future limit:

de <10−29e.cm

(Masina, ph/0304299)

Model I: SU(5) (minimal) with Model II: SO(10) (minimal) with Model III: SO(10) (pseudoDirac) with

MT 1 = MT2

Y

ν = Y u

MT

1 MT2

= (r −1) (r +1)

III III II II It I

τ p (yrs)

de (e.cm)

r r

expt. expt.

limits on colour triplet masses: proton decay vs. electron EDM

˜ M1 = 200 GeV meR = 400 GeV MT = 1017 GeV

tan β = 3

(Masina, S. ph/0309067)

• Conclusion -

de , dμ, μ➙eγ 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

dμ > (mμ/me)de IS AN INTERESTING THEORETICAL CHALLENGE

AND dμ EXPERIMENTS ARE IMPROVING A LOT.