1. Lepton Flavour Violation
in SUSY Models
Tomáš Blažek
Theoretical Physics Group
Comenius University Bratislava
LPSC Grenoble, 24 June 2008

2. Contents Intro Construction of Models Beyond MSSM
νMSSM Constraints and Predictions
Results and Conclusions

3. INTRO Big Picture: 1) Standard Model with Exact EW Symmetry
Renormalizable interactions do not allow for Lepton Flavour Violation (LFV)

4. INTRO Big Picture: 2) EW Symmetry Breaking
that we would recommend Nature to take

5. INTRO Big Picture: EW Symmetry Breaking Nature has chosen ...
never asking us

6. „The Flavour Problem“ in particle physics:
Neutrino Masses from Oscillations
atmospheric solar
Valle 2007
Individual Lepton Flavour is violated
in Nature
... specific pattern
... part of the Flavour Problem

7. LFV for charged fermions ?
Intro
LFV for charged fermions ?
B(τ→μγ) < 4.5 × Belle 2007
(Will the B factories find new physics
after all in tau decays ??
T.B. and S.F.King, 2001)
B(μ→eγ) < 1.2 × MEGA 1999,
soon to be pushed down to by MEG at PSI
e→μ conversion in nuclei
μ→3e etc.
So far, LFV seen for neutrinos only
this fits well the SM
in SUSY extensions, the predictions can
be radically different giving excellent
motivation to experimentalists
(Has it been said that there is no SM background?)

8. | | (the last slide of) Intro
See-saw Mechanism, SUSY GUTs and the Origin of LFV
See-saw Mechanism – a GUT/ SO(10) solution to the
smallness of the neutrino masses by introducing
νR with Majorana mass MR>>Mew
GRSY, 1979
Try first the SO(10) guess MR=MGUT and
get the neutrino masses in the right ballpark
everybody
Second guess: find the MR scale for mν=0.1eV
SUSY - already stabilises Higgs against GUT-scale corrections,
can do the same against MR-scale corrections
Origin of LFV in charged fermion decays: LFV in slepton sector
induced by RGE effects
for MR<MGUT | |

9. Construction of Models Beyond MSSM
SUSY SO(10) example:
TB, Raby, Tobe
generate yukawa matrices

10. + Construction of LFV in SO(10) SUSY GUTs Option 1: introduce 126 or
higher dimensional
operators
Option 2:
introduce SO(10) singlets N
and
do the see-saw twice.
Generalised neutrino
mass matrix:
the Nbar states are
candidates for coupled
sterile neutrinos if µ3, µ’≠0 +

11. νMSSM Constraints and Predictions
Different approach: Try a plausible construction of the MSSM
just below MGUT as an effective theory
of some more complete theory above MGUT.
The construction does not have to be the most
economic for the charged femion masses and mixings.
The emphasis is not on the GUT model but
rather on the low energy phenomenology
one obtains after running RGEs down to Mew .
Try to be economic in the neutrino sector and
get constraints and predictions for LFV involving
charged fermions.
Example: TB + S.F.King,
SU(4)×SU(2L)×SU(2R) Pati-Salam model as the underlying GUT

12. heavy or light sequential dominance
Low-Energy Phenomenology: Generic Main Ideas
large atmospheric neutrino mixing from
neutrino mass hierarchy from the dominance
of a single right-handed neutrino in the see-saw
mechanism:
a, b, c, d << e, f X’ < X < Y or Y < X < X’
heavy or light sequential dominance
SO(10)-like regime: f... large 33 yukawa coupling element
common to every yukawa matrix
e... absent in the charged yukawa matrices due to
a suitable choice of Clebsches
a,b,c,d ... related to the charged fermion observables

13. Low-Energy Phenomenology: LFV in charged fermion decays
li→ljγ
mass insertion approximation :
leading log approximation :

14. Low-Energy Phenomenology: Numerical Analysis
top-down global analysis of the constrained MSSM
Initial conditions:
universal soft scalar mass, universal gaugino mass, and universal
trilinear breaking
µ > 0
GUT scale threshold corections included:
Essentially, there are three relevant parameters in the neutrino sector:
X and Y in the MR matrix, and the power of a,b,c in terms of the
CKM parameter λ (for details, check the paper with SFKing).
We also allow for small variations in a,b,c in the neutrino yukawa
matrix.

15. Low-Energy Phenomenology: Table of Low Energy Observables
MSSM analysis only
xiexp
neutrino observables
Global analysis:
evaluate

16. Low-Energy Phenomenology: Results
Quality of the fit: SUSY contribution to aµ :
tanβ=50, a,b,c ~ λ2, c=-b, d=0, case of Heavy Sequential Dominance

17. Low-Energy Phenomenology: LFV Results
Branching ratios
Relative error made
if using just leading
log approximation
As on the previous slide
tanβ=50, a,b,c ~ λ2, c=-b, d=0

18. Low-Energy Phenomenology: Technical Analysis of LFV Results
Variations in the
µ →eγ rate
a,b,c ~ λ4
13 slepton effect:
b,c,d=0
13 yukawa effect:
d >> a,b,c
tanβ variation
of course, we
could have
guessed
this one

19. Low-Energy Phenomenology: LFV Results with Light Sequential Dominance
Branching ratios
Relative error made
if using just leading
log approximation
tanβ=50, a,b,c ~ λ-1, c=-b, d=0

20. Low-Energy Phenomenology: θ13 Best Fit Predictions
r is defined as the
ratio c/b

21. Conclusions
Search for Lepton Flavour Violation involving Charged Fermions
is extremely well motivated
Observations could well be just around the corner
Alas, nothing has been seen yet, ... but that is the normal state of
affairs in Beyond Standard Model Physics
Any measured SUSY signal (e.g. at LHC) would immediately
provide constraints on the LFV charged fermion decays
it is possible to construct a working unified model with all necessary
GUT ingredients, and then find its best fit predictions for LFV
in this talk, we have also presented an alternative approach
focusing on the neutrino sector and allowing for more model
flexibility in other sectors