1. Impact of slepton generation mixing on the search for sneutrinos
K. Hidaka
Tokyo Gakugei University
In collaboration with
A. Bartl, K. Hohenwarter-Sodek,
T. Kernreiter, W. Majerotto and
W. Porod
KEKPH2007, 2 March 2007, KEK

2. Contents 1. Introduction 2. MSSM with Lepton Flavour Violation (LFV)
3. Constraints on the MSSM
4. Scenario with LFV
5. Impact of slepton generation mixing on sneutrino decays
6. Conclusion

3. 1. Introduction (1) Motivation; Why SUSY?;
　　In the Minimal Supersymmetric Standard Model (MSSM)
　　SUSY　partners of all Standard Model (SM) particles with masses less than O(1 TeV) are introduced.
　　This solves the problems of hierarchy, fine-tuning and naturalness of the SM.
Hence discovery of all SUSY partners and study of their properties are essential for testing the MSSM.
Complete study of sneutrino decays including bosonic decays in the MSSM without LFV and　without/with CPV in slepton sector has been performed already.
However, complete study of sneutrino decays including bosonic decays in the MSSM with LFV and without/with CPV has not been performed yet.
Complete study of sneutrino decays in the MSSM with LFV and without CPV will be performed in this work.

4. -> Hisano et. al., Phys.Rev. D60 (1999) 055008 (hep-ph/9808410);
Discovery of neutrino oscillations suggests LFV in slepton sector (i.e. generation mixing in slepton sector).
There are several articles studying effect of the LFV in slepton sector on sneutrino prodution and decays. However, they have not performed complete study of sneutrino decays including both fermionic and bosonic decays .
-> Hisano et. al., Phys.Rev. D60 (1999) (hep-ph/ );
Nomura, Phys.Rev. D64 (2001) (hep-ph/ );
Oshimo, Eur.Phys.J. C39 (2005) 383 (hep-ph/ ).

5. (2)Purpose of this work;
In this article we perform complete study of sneutrino
decays including both fermionic and bosonic decays in the
general MSSM with LFV (and without CPV) in slepton sector.
We show that branching ratios of LFV sneutrino decays
due to slepton generation mixing can be sizable in a
significant part of the MSSM parameter space despite the
recent very strong experimental limits on LFV processes.
This could have an important impact on the search for
sneutrinos and the MSSM parameter determination in the
future colliders, such as LHC, ILC, CLIC and muon collider.

6. 2. MSSM with LFV: { tanb, mH+, M2, m, M2L(a,b), M2E(a,b), AE(a,b) }
Basic parameters of the MSSM with LFV:
{ tanb, mH+, M2, m, M2L(a,b), M2E(a,b), AE(a,b) }
(a,b=1,2,3=e,mu,tau) (at Q=m_Z)
M2L(a,b) : left-slepton soft mass matrix
M2E(a,b) : right-slepton soft mass matrix
AE(a,b) : lepton trilinear coupling matrix
LFV parameters in our study of smu-stau mixing case are:
M2L(2,3)　: smu_L - stau_L mixing term 　(snu_mu - snu_tau mixing term)
M2E(2,3)　: smu_R - stau_R mixing term
AE(2,3) 　 : smu_L - stau_R mixing term
AE(3,2) 　 : smu_R - stau_L mixing term
(note) Here we study smu-stau mixing case.
(note) We assume that all the basic parameters are real.
(note) The basic parameters determine all of the physics here.

7. Charged Slepton Mass Matrix:
The most general charged slepton mass matrix including left-right mixing
as well as flavour mixing in the basis of is
given by:
with
(v1 = <H01>)
(α, β = 1, 2, 3 = e, μ, τ) 　

8. Masses and mixings of the sleptons:
Diagonalizing the slepton mass matrix we get mass eigenvalues and
mass eigenstates:
(Mass eigenstates)

9. Sneutrino Mass Matrix:
The most general sneutrino mass matrix with flavor mixing in the basis of
is given by:
with
(α, β = 1, 2, 3 = e, μ, τ) 　

10. Masses and mixings of the sneutrinos:
Diagonalizing the sneutrino mass matrix we get mass eigenvalues and
mass eigenstates:
(Mass eigenstates)

11. 3. Constraints on the MSSM
The following constraints are imposed in our plots in order to
respect experimental and theoretical constraints::
(a) The LEP limits on sparticle masses.
(ex) m_chargino_1 > 103GeV
(b) The vacuum stability conditions.
(ex) A_E(2,3)**2 < h_tau**2*(M^2_L(2,2)+M^2_E(3,3)+m_12)
(c) The lepton (g-2) limits.
(ex) limit on SUSY contribution to muon (g-2)
(d) The limits on LFV lepton decay branching ratios.
(ex) B(tau -> mu gamma) < 4.5*10^(-8)

12. B(B_u -> tau nu) from ICHEP2006 (BELLE exp.).
(e) The constraint on m_H+ and tanb from the experimental data on
B(B_u -> tau nu) from ICHEP2006 (BELLE exp.).
(ex) *0.51 < R_Btaunu(SUSY) < *0.51 (95% CL).
with
R_Btaunu(SUSY) = B^(SUSY)(B_u -> tau nu) / B^(SM)(B_u -> tau nu)
= (1 - (m_B+/m_H+)**2*(tanb**2))**2
(-> hep-ph/ )
(Note) We find that experimental constraints from B(tau -> mu gamma),
B(B_u -> tau nu) and muon g-2 data are very important:
B(tau -> mu gamma) data -> strong constraints on the LFV slepton parameters
B(B_u -> tau nu) data > strong constraint on (tanb, m_H+)
muon g-2 data > excludes negative m region

13. 4. Scenario with LFV
We take the following scenario with LFV (and without CPV)
in slepton sector (i.e. smu-stau mixing scenario):
tanb=20, mH+=150GeV, M2 =650GeV, m =150GeV,
M2 L(1,1)= (440GeV)2 , M2 L(2,2)= (410GeV)2 , M2 L(3,3)= (400GeV)2 ,
M2 L(2,1)= (1GeV)2 , M2 L(3,1)= (1GeV)2 , M2 L(3,2)= (61GeV)2 ,
M2 E(1,1)= (240GeV)2 , M2 E(2,2)= (210GeV)2 , M2 E(3,3)= (200GeV)2 ,
M2 E(2,1)= (1GeV)2 , M2 E(3,1)= (1GeV)2 , M2 E(3,2)= (22GeV)2 ,
AE(1,1) = AE(2,2) = 0 , AE(3,3) = 150GeV,
AE(2,3) = 25GeV, all the other AE(a,b) = 0

14. Our scenario is within reach of LHC and ILC.
m_(snu_1) = 393GeV, m_(snu_2) = 407GeV, m_(snu_3) = 435GeV
m_(sl_1) = 204GeV, m_(sl_2) = 215GeV, m_(sl_3) = 244GeV,
m_(sl_4) = 401GeV, m_(sl_5) = 415GeV, m_(sl_6) = 443GeV
m_(chargino_1) = 147GeV, m_(chargino_2) = 661GeV
m_(neutralino_1) = 138GeV , m_(neutralino_2) = 155GeV,
m_(neutralino_3) = 331GeV , m_(neutralino_4) = 661GeV
Our scenario is within reach of LHC and ILC.

15. 5. Impact of slepton generation mixing on sneutrino decays
Possible important sneutrino decays are:
snu_i -> nu neutralino_j (fermionic mode)
snu_i -> l_a chargino_k (fermionic mode)
snu_i -> sl_j W (bosonic mode)
snu_i -> sl_j H (bosonic mode)
We study the effect of slepton generation mixing on
these sneutrino decays.

16. Sneutrino decay branching ratios in our scenario:
In our scenario we have:
B(snu_1 -> mu + chargino_1)= ~1.4% (LFV)
B(snu_1 -> tau + chargino_1)= ~36% (LFC).
B(snu_2 -> sl_1 + H+) = ~38% (LFV)
B(snu_2 -> sl_1 + W+) = ~0.3% (LFV)
B(snu_2 -> tau + chargino_1)= ~12% (LFV)
B(snu_2 -> mu + chargino_1)= ~20% (LFC)
(note) snu_2 ~ snu_mu , sl_1 ~ stau_R
We have large LFV decay branching ratios!

17. Contour plots of LFV BR’s in our scenario
(note) snu_2 ~ snu_mu , sl_1 ~ stau_R
LFV BR’s are large in a significant region of M_2 – mu plane
in our scenario!

18. Exclusion by B(tau -> mu gamma) limit
BR(τ → μγ) < 4.5 × 10-8

19. (note) snu_2 ~ snu_mu , sl_1 ~ stau_R
RL23=M2L(2,3)/<M2L> (<M2L>=(M2L(1,1)+M2L(2,2)+M2L (3,3))/3)
RAE23=AE(2,3)/<|AE|> (<|AE|>=(|AE (1,1)|+|AE (2,2)|+|AE (3,3)|)/3)
LFV BR’s are large in a significant region of RL23 – RAE23 plane
in our scenario!
B(snu_2 -> tau + chargino_1) is sensitive to LFV param. M2L(2,3)!
B(snu_2 -> sl_1 + H+) is sensitive to LFV param. M2L(2,3) and AE(2,3)!

20. Exclusion by B(tau -> mu gamma) limit
BR(τ → μγ) < 4.5 × 10-8

21. Scatter Plots of LFV BR’s in our scenario
There are strong correlations among the LFV sneutrino decays and the LFV tau decay (i.e. tau -> mu gamma);
(ex) B(snu_2 -> sl_1 + H+) v.s. B(tau -> mu gamma)
Scatter plot with scatter parameters of
RL23, RE23, RAE23, RAE32, M2 and MU

22. Scatter Plot for our scenario
with the LFV scatter parameters of RL23, RE23, RAE23 and RAE32
and the LFC scatter parameters of M2 and MU:
(10 < M2 < M2MAX+10), M2MAX=1200GeV
(-MUMAX< MU < MUMAX), MUMAX=1000GeV
(-RL23MAX < RL23 < RL23MAX), RL23MAX=0.035
(-RE23MAX < RE23 < RE23MAX), RE23MAX=0.2
(-RAE23MAX < RAE23 < RAE23MAX), RAE23MAX=2.5
(-RAE32MAX < RAE32 < RAE32MAX), RAE32MAX=2.5

23. Experimental search for LFV in slepton sector
In experimental search for LFV it is important to have both
significant tau and mu flavor modes in decay of a sneutrino; e.g.
both sizable B(snu_2 -> mu + chargino_1) and sizable
B(snu_2 -> tau + chargino_1).
In this case we could have the following LFV signals
e+ e- -> snu_2 snu_2* -> mu- tau+ chargino_1+ chargino_1-
-> mu- tau+ 4jets + missing E ,
whereas we can never have such signals in case of LFC.
Study of LFV signals and BG in sneutrino production and decays for
our scenario is now under way.

24. 6. Conclusion
In this article we have performed complete study of sneutrino decays including both fermionic and bosonic decays in the general MSSM with LFV (and without CPV) in slepton sector.
We have shown that branching ratios of LFV sneutrino decays can be sizable due to slepton generation mixing in a significant part of the MSSM parameter space despite the recent very strong experimental limits on LFV processes.
This could have an important impact on the search for sneutrinos and the MSSM parameter determination in the future colliders, such as LHC, ILC, CLIC and muon collider.

25. Backup

26. 2. MSSM with LFV The basic parameters of the MSSM with LFV:
{tanb, mH+ , M2 , m , M2L,ab , M2E,ab , Aab } (at weak scale)
tanb: 　　　ratio of VEV of the two Higgs doublets <H0 2>/<H01>
M2: 　　　 SU(2) gaugino mass
m : 　　　　 higgsino mass parameter
M2L,ab : left slepton soft mass matrix
M2E,ab : right slepton soft mass matrix
Aab : 　 trilinear coupling matrix of sleptons and a Higgs boson
(a,b = 1,2,3 = e,m,t )

27. (Note) There are stringent constraints on these LFV
parameters from the experiment al limits on the
rare LFV processes:
BR(μ → e γ) < 1.2 × 10-11
BR(τ → e γ) < 1.1 × 10-7
BR(τ → μγ) < 4.5 × 10-8
BR(μ- → e- e+ e- ) < 10-12
BR(τ- →μ- μ+ μ- ) < 1.9 × 10-7
R(μ- N → e- N) < 7.8 × (μ- - e- conversion rate)
We take into account these constraints in our analysis.