Impact of slepton generation mixing on the search for sneutrinos

We perform a systematic study of sneutrino production and decays in the Minimal Supersymmetric Standard Model (MSSM) with lepton flavour violation (LFV). We study bosonic decays of sneutrinos as well as fermionic ones. We show that the effect of slepton generation mixing on the sneutrino production and decays can be quite large in a significant part of the MSSM parameter space despite the very strong experimental limits on LFV processes. This could have an important impact on the search for sneutrinos and the determination of the MSSM parameters at LHC and future colliders, such as ILC, CLIC and muon collider.


Introduction
Systematic studies of decays of sneutrinos, the supersymmetric (SUSY) partners of neutrinos, in the Minimal Supersymmetric Standard Model (MSSM) have been performed already [1].In these studies it is assumed that there is no generation mixing in the slepton sector.In this article based on [2] we study the effect of slepton generation mixing on the production and decays of the sneutrinos in the MSSM.Lepton flavour violating (LFV) productions and decays of SUSY particles have been studied for the case of slepton generation mixing [3].Some of the studies are rather model dependent.Furthermore, so far no systematic study of LFV in sneutrino decays including bosonic decays has been performed.The aim of this article is to perform a systematic study of sneutrino production and decays including the bosonic decay modes in the general MSSM with LFV in slepton sector.

The model
First we summarize the MSSM parameters in our analysis.The most general charged slepton mass matrix including left-right mixing as well as flavour mixing in the basis of l0α = (ẽ L , μL , τL , ẽR , μR , τR ), α = 1, ..., 6, is given by [2]: RL,αβ = v 1 A βα − m ℓα µ * tan βδ αβ .The indices α, β = 1, 2, 3 characterize the flavours e, µ, τ , respectively.M 2 L and M 2 E are the hermitean soft SUSY breaking mass matrices for left and right sleptons, respectively.A αβ are the trilinear soft SUSY breaking couplings of the sleptons and the Higgs boson: µ is the higgsino mass parameter.v 1 and v 2 are the vacuum expectation values of the Higgs fields with ), where m li < m lj for i < j.Similarly, the mass matrix for the sneutrinos, in the basis ν0α = (ν eL , νµL , ντL ) ≡ (ν e , νµ , ντ ), reads where the physical mass eigenstates are given by νi
It has been shown that in general the limit on the µ − − e − conversion rate is respected if the limit on µ → e γ is fulfilled [13].Condition (i) strongly constrains the trilinear couplings A αβ , especially for small tan β where the lepton Yukawa couplings Y E,αα are small.(ii) strongly constrains the lepton flavour mixing parameters; e.g. in case of μ − τ mixing the limit on B(τ − → µ − γ) strongly constrains the μ − τ mixing parameters M 2 L,23 , M 2 E,23 , A 23 and A 32 .The limit on ∆a SUSY µ in (iii) is also important, e.g. it disfavours negative µ especially for large tan β.

Numerical results
We take tan β, m H + , M 2 , µ, M 2 L,αβ , M 2 E,αβ , and A αβ as the basic MSSM parameters at the weak scale.We assume them to be real.The LFV parameters are M 2 L,αβ , M 2 E,αβ , and A αβ with α = β.We take the following μ− τ mixing scenario as a reference scenario with LFV within reach of LHC and ILC: 1 For the limit on SUSY contributions to anomalous magnetic moment of muon ∆a SU SY µ , we allow for an error at 95% CL for the difference between the experimental measurement and the SM prediction [11].
, and all the other A αβ = 0.In this scenario satisfying all the conditions (i)-(v) above we have: 1 H + are essentially LFV decays.Note that the branching ratios of these LFV decays are sizable in this scenario.The reason is as follows: The lighter neutralinos χ0 1,2 and the lighter chargino χ± 1 are dominantly higgsinos as M 1,2 ≫ |µ| in this scenario.Hence the fermionic decays into χ0 1,2 and χ+ 1 are suppressed by the small lepton Yukawa couplings except for the decay into τ − χ+ 1 which does not receive such a suppression because of the sizable τ Yukawa coupling Y E,33 for large tan β.This leads to an enhancement of the bosonic decays into the Higgs boson H + .Moreover the decay ν2 (∼ νµ L,23 the ν2 has a significant ντ component, which results in a further enhancement of this decay due to the large trilinear ντ

ν decay branching ratios
We study the basic MSSM parameter dependences of the LFV sneutrino decay branching ratios for the reference scenario specified above.In Fig. 1 we show contours of the LFV ν2 decay branching ratios in the µ − M 2 plane.All basic parameters other than µ and M 2 are fixed as in the reference scenario specified above.We see that the LFV decay branching ratios B(ν 2 → τ − χ+ 1 ) and B(ν 2 → l− 1 H + ) can be sizable in a significant part of the µ − M 2 plane.The main reason for the increase of B(ν 2 → l− 1 H + ) in the region M 2 ≫ µ is that the partial widths for the decays into µ − χ+ chargino/neutralino states become more and more higgsino like.The τ − χ+ 1 decay mode has a different behaviour due to the sizable τ Yukawa coupling for large tan β.We remark that the limit on ∆a SUSY µ excludes the region with B(ν 2 → l− 1 H + ) > ∼ 0.5.In the following we use the quantities ) as a measure of LFV.In Fig. 2 we present the R L23 dependence of ν2 decay branching ratios, where all basic parameters other than M 2 L,23 are fixed as in the reference scenario specified above.We see that the LFV decay branching ratios B(ν 2 → τ − χ+ 1 ) and B(ν 2 → l− 1 H + ) can be large and very sensitive to R L23 .Note that l− 1 ∼ τ − R and that the ντ component in ν2 (∼ νµ ) increases with the increase of the νµ − ντ mixing parameter M 2 L,23 , which explains the behaviour of the branching ratios.Similarly we have found that B(ν 2 → l− 1 H + ) can be very sensitive to R A23 ; this decay can be enhanced also by a sizable A 23 as explained above.To exemplify this behaviour further, in Fig. 3 we show the contours of these decay branching ratios in the R L23 − R A23 plane, where all basic parameters other than M 2 L,23 and A 23 are fixed as in the reference scenario specified above.As can be seen, these LFV decay branching ratios can be large in a sizable region of the R L23 − R A23 plane and their dependences on R L23 and R A23 are quite remarkable and very different from each other.Hence, a simultaneous measurement of these two branching ratios could RL23 dependence of ν2 decay branching ratios for our μ − τ mixing scenario.The shown range of RL23 is the whole range allowed by the conditions (i) to (v) given in the text.
-  play an important role in determination of the LFV parameters M 2 L,23 and A 23 .In Fig. 4 we show a scatter plot of the LFV decay branching ratios B(ν ilar to that for B(ν 2 → l− 1 H + ) versus B(τ − → µ − γ), with the upper limits of the ν1,2 decay branching ratios B(ν We have also studied sneutrino decay branching ratios in the case of ẽ− τ mixing, where we have obtained similar results to those in the case of μ− τ mixing.This is due to the fact that Y E,11 ∼ Y E,22 (∼ 0), that the experimental limits on B(τ − → e − γ) and B(τ − → µ − γ) are comparable, and that the theoretical limits of the condition (i) on the LFV parameters A 13 and A 31 are also similar to those on A 23 and A 32 .

LFV contributions to collider signatures
It is to be noted that in ẽ − τ mixing scenario the tchannel chargino exchanges contribute significantly to the cross sections σ(e + e − → νi νj ) ≡ σ ij for i, j =1,3, enhancing the cross sections (including the LFV production cross section σ 13 ) strongly, where ν1 ∼ ντ and ν3 ∼ νe [2].We have studied the LFV contributions to signatures of sneutrino production and decay at the ILC [2].We have shown that the LFV processes (including the LFV νi productions and the LFV bosonic νi decays also) can contribute significantly to signal event rates.For example, in the ẽ − τ mixing scenario described in [2], assuming ILC with √ s = 1 TeV and a longidutinal polarization of -90% and 60% for the electron and positron beam, respectively, the dominant LFV contributions (steming from e + e − → νi νj → e ± τ ∓ χ+ 1 χ− 1 ) to the rate of the signal event e ± τ ∓ +4jets+/ E is calculated to be σ LF V = 6.6fb,where / E is the missing energy.Lepton flavour conserving (LFC) processes in ν production and decay can also contribute to the rate of the signal event above.The dominant LFC contributions to the signal rate is calculated to be σ LF C = 0.033fb which is two orders of magnitude smaller than σ LF V .This strongly suggests that one should take into account the possibility of the significant contributions of both the LFV fermionic and bosonic decays in the sneutrino search and should also include the LFV parameters in the determination of the basic SUSY parameters at colliders.It is clear that detailed Monte Carlo studies taking into account background and detector simulations are necessary.However, this is beyond the scope of the present article.

Summary
We have performed a systematic study of sneutrino production and decays including both fermionic and bosonic decays in the general MSSM with slepton generation mixings.We have shown that LFV sneutrino production cross sections and LFV sneutrino decay branching ratios can be quite large due to slepton generation mixing in a significant part of the MSSM parameter space despite the very strong experimental limits on LFV processes.This could have an important impact on the search for sneutrinos and the MSSM parameter determination at future colliders, such as LHC, ILC, CLIC and muon collider.