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

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

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

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

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

„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

LFV for charged fermions ? Intro LFV for charged fermions ? B(τ→μγ) < 4.5 × 10-8 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 × 10-11 MEGA 1999, soon to be pushed down to 10-13 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?)

| | (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 | |

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

+ 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 +

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

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

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

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.

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

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

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

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

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

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

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