Supersymmetric Lepton Flavour Violation at the LHC and LC

0.51 MB·English

by  F. Deppisch

WUE-ITP-2004-004
IFT-06/04
January2004
Supersymmetric Lepton Flavour Violation
at the LHC and LC
F. DEPPISCH1, J. KALINOWSKI2, H. PA¨S1, A. REDELBACH1, R. RU¨CKL1
4
0
0
2
1Institutfu¨rTheoretischePhysikundAstrophysik,Universita¨tWu¨rzburg,D-97074

n
Wu¨rzburg,Germany
a
J
0 2InstituteofTheoreticalPhysics,WarsawUniversity,Warsaw,Poland
3

1
v
3
4
2 Abstract
1
0 In supersymmetric extensions of the Standard Model, the Yukawa and/or mass
4
termsoftheheavyneutrinoscangenerateleptonflavourviolatingsleptonmassterms.
0
Thesenewsupersymmetricsourcesofleptonflavourviolationmaybothenhancethe
/
h
rates of charged lepton flavour violating processes, l l γ, and generate distinct
p α → β
- finalstates,likelβlα+jets+E/T,atfuturecolliders. First,wediscussthesensitivityof
p futuree+e colliderstotheSLFVindependentlyoftheleptonflavourviolatingmech-
e −
h anism. Second,westudyleptonflavour violating sleptonpair productionanddecay
v: at a future e+e− linear collider in the context of the seesaw mechanism in mSUGRA
i post-LEPbenchmark scenarios. We investigate the correlations of these signals with
X
thecorrespondingleptonflavourviolatingraredecaysl l γ,andshowthatthese
r α → β
a correlationsareparticularlysuitedforprobingtheoriginofleptonflavourviolation.
1
1 Introduction
Neutrinooscillationsimplytheviolationofindividualleptonflavoursandraisetheinter-
estingpossibilityofobservingleptonflavourviolationinprocesseswithchargedleptons,
suchasµ eγ orτ µγ. IntheStandardModeltheseprocessesarestronglysuppressed
→ →
due to small neutrino masses. In the supersymmetric extension of the Standard Model,
however, the situation may be quite different. For example, the slepton mass matrices
need not simultaneously be diagonalized with the lepton mass matrices. When sleptons
are rotated to the mass eigenstate basis, the slepton mass diagonalization matrices W
iα
enterthe chargino and neutralino couplings
e˜(W ) e¯ χ˜0 +ν˜(W ) e¯ χ˜ +... (1)
i ˜l∗ iα α i ν˜∗ iα α −
and mix lepton flavour (Latin and Greek subscripts refer to the mass-eigenstate and
flavour basis, respectively). Contributions from virtual slepton exchanges can therefore
enhancetheratesofraredecayslikeµ eγ. Furthermore,oncesuperpartnersarediscov-
→
ered,thesupersymmetricleptonflavourviolation(SLFV)canalsobesearchedfordirectly
atfuture colliderswhere thesignal willcome from theproduction ofreal sleptons(either
directly or from chain decays of other sparticles), followed by their subsequent decays.
Searches for SLFV at colliders have a number of advantages: superpartners can be pro-
ducedwithlargecross-sections, flavourviolationintheproductionanddecayofsleptons
occursattreelevelandthereforeissuppresedonlybypowersof∆m /Γ [1]incontrastto
˜l ˜l
the ∆m /m suppression in radiative lepton decays, where SLFV occurs at one-loop ( [2]
˜l ˜l
and references therein). Generally, respecting the present bounds on rare lepton decays,
large SLFV signals are possible both at the LHC [3] and at e+e colliders [1,4–8]. This
−
suggests that in some cases the LHC and future e+e colliders may provide competitive
−
tools to search forand explore supersymmetric lepton flavour violation.
In this note we first discuss the sensitivity at future e+e colliders to SLFV inde-
−
pendently of the lepton flavour violating mechanism. The simulation has been per-
formed assuming a simplified situation with a pure 2-3 intergeneration mixing between
˜
ν˜ and ν˜ , and ignoring any mixings with ν˜ . In the analysis the mixing angle θ and
µ τ e 23
∆m˜ = m m have beentaken asfree, independentparameters [6].
23 | ν˜2 − ν˜3|
In the second part, SLFV generated by the seesaw mechanism is considered. The
heavy right-handed Majorana neutrinos give rise not only to light neutrino masses but
also to mixing of different slepton flavours due to the effects of the heavy neutrinos on
therenormalization-grouprunningofthesleptonmasses. Theimplicationsofrecentneu-
trino measurements on this mixing are investigated. Moreover we emphasize the com-
plementarity of the radiative decays l l γ and the specific lepton flavour violating
α β
→
processes e e l l χ˜0χ˜0 involving slepton pairproduction andsubsequent decay[8].
± − → β± α− b a
2 Sensitivity at future e+e colliders to SLFV
−
IndiscussingtheSLFVcollidersignalsatfuturecolliders,onehastodistinguishtwocases
inwhichanoscillationofleptonflavourcanoccur: inprocesseswithsleptonpairproduc-
tion and in processes with single slepton production, which differ in the interference of
theintermediatesleptons[1]. Sleptonpairproduction isthedominantmechanismatlep-
ton colliders, but it may also occur at hadron colliders via the Drell-Yan process. Single
2
sleptonsmaybeproducedincascadedecaysofheaviernon-leptonicsuperparticles. Such
processes are particularly important for hadron colliders, but they may also be relevant
forlepton colliderswhereasingle slepton canbethedecayproduct ofachargino orneu-
tralino.
The amplitudes for pair production, f¯f ˜l+˜l l+Xl Y, and single production,
→ i i− → α β−
f f l+X˜l l+Xl Y, read, e.g.,
′ → α i− → α β−
i i
pair = pair W + W (s-channel) (2)
Mαβ MP q2 m˜2 +im˜ Γ iαMDp2 m˜2 +im˜ Γ i∗βM−D
i − i i i − i i i
X
i
sin = sinW W (3)
Mαβ MP iαq2 m˜2 +im˜ Γ i∗βM−D
i − i i i
X
where and are the respective production and decay amplitudes for sleptons in
P D
M M
the absence ofSLFV, andW standsfor the lepton flavour mixing matrixelement.
iα
For nearly degenerate in mass and narrow sleptons, ∆m˜ m˜ and m˜Γ (m˜ Γ +
ij ij i i
≪ ≃
m˜ Γ )/2 m˜2, the products ofslepton propagators can be simplified asfollows
j j
≪
i i 1 π
− δ(q2 m˜2). (4)
q2 m˜2 +im˜ Γ q2 m˜2 im˜ Γ ∼ 1+i∆m˜ /Γ m˜Γ −
− i i i − j − j j ij ij ij
Then,inthe caseof2-3 intergeneration mixing, thecross-sections forthe aboveprocesses
(2, 3),take a particularly simpleform [9]:
σpair = χ (3 4χ )sin22θ˜ σ(f¯f ˜l+˜l )Br(˜l+ l+X)Br(˜l l Y) (5)
αβ 23 − 23 23 → α α− α → α α− → α−
σsin = χ sin22θ˜ σ(f f l+X˜l )Br(˜l l Y) (6)
αβ 23 23 ′ → α α− α− → α−
where σ(f f l+X˜l ), σ(f¯f ˜l+˜l ) and Br(˜l l X) are the corresponding cross-
′ → α α− → α α− α± → α±
sections and branching ratios in the absence of flavour violation. The slepton flavour
violating mixing effects are encodedin
x2
χ = 23 and sin22θ˜ (7)
23 2(1+x2 ) 23
23
where x = ∆m˜ /Γ . In the limit x 1, χ approaches 1/2, the interference can
23 23 23 23 23
≫
be neglected and the cross-sections behave as σ sin22θ˜ . In the opposite case, the
23
∼
interference suppresses the flavour changingprocesses, and σ (∆m˜ sin2θ˜ )2.
23 23
∼
To assess the sensitivity of a 500 GeV e+e linear collider to the SLFV, the following
−
processes have beenanalysed
e+e ν˜ν˜c τ µ χ˜+χ˜ (8)
− → i j → ± ∓ 1 −1
e+e χ˜+χ˜ τ µ χ˜+χ˜ (9)
− → 2 −1 → ± ∓ 1 −1
e+e χ˜0χ˜0 τ µ χ˜0χ˜0 (10)
− → 2 1 → ± ∓ 1 1
Here χ˜ χ˜0ff¯, and χ˜0 escapes detection. The signature of SLFV would be τ µ +
±1 → 1 ′ 1 ± ∓
4 jets+E/ , τ µ +ℓ+2jets+E/ , orτ µ +E/ , dependingon the hadronicor leptonic
T ± ∓ T ± ∓ T
χ˜ decay mode. The purely leptonic decay modes are overwhelmed by background.
±1
In particular, the neutralino pair production process (10), which could still be open if
3
∆m˜ /GeV
23
˜
sin2θ
23
˜
Figure 1: Various 3σ significance contours in the ∆m˜ sin2θ plane, for the SUSY
23 23
−
point mentioned in the text. The contours A and B show the integrated signals (8–9) at
√s =500 GeV and for 500 fb 1 and 1000 fb 1, respectively. The contour C shows the ν˜ν˜c
− −
contribution separately for 500 fb 1 [6]. The dotted lines indicate contours for Br(τ
−
→
µγ)=10 7, 10 8 and10 9 [11].
− − −
the second chargino and sleptons were too heavy for (8) and (9), is difficult to extract
from background. On the other hand, with charginos decaying hadronically, the signal
τ µ +4jets+E/ comesfrom bothprocesses(8)and(9)andisSM-background free. The
± ∓ T
flavour-conserving processes analogous to (8) and (9), but with two τ’s in the final state
where one ofthe τ’s decaysleptonically to µ, contribute to the background. On the other
hand, if jets are allowed to overlap, an important SM background to the final states with
τ µ + 3 jets+E/ comes from e+e tt¯g.
± ∓ ≥ T − →
ThesimulationofthesignalandbackgroundhasbeenperformedforoneoftheMSSM
representative points chosen fordetailedcasestudiesatthe ECFA/DESYWorkshop [10]:
a mSUGRA scenario defined by m = 100 GeV, M = 200 GeV, A = 0 GeV, tanβ = 3
0 1/2 0
and sgn(µ) = +. A simple parton level simulation has been performed with a number of
kinematic cuts listed in [6]. For the processes (8) and (9) we find after cuts the following
cross-sections, χ (3 4χ )sin22θ˜ 0.51fbandχ sin22θ˜ 0.13fb,respectively,while
23 23 23 23 23
− × ×
the background amounts to0.28 fb.
In Fig. 1 the significance is given by σ = S where S and B are the numbers of
d √S+B
signal and background events, respectively, for a given luminosity. Shown is the region
˜
(totherightofthecurves)inthe∆m˜ sin2θ planethatcanbeexploredorruledoutat
23 23
−
a 3σ level at a linear collider of energy 500 GeV for the given integrated luminosity. The
contour Aisfor 500 fb 1 and B for 1000fb 1. For comparison, the boundary Cshows the
− −
reachintheprocessν˜ν˜c alone(previouslystudiedin[1,5])usingourcutsandassuminga
i i
luminosityof500fb 1. Thecharginocontributionincreasesthesensitivityrangetosin2θ˜
− 23
by10-20%,while the sensitivity to∆m˜ doesnot change appreciably.
23
Inthesamefigure,thecontourlinesforconstantbranchingratiosofτ µγ areshown
→
for comparison [11]. In the limit of small mass splitting, Br(τ µγ) can be calculated
→
4
in the flavour basis using the mass insertion technique [12]. In our 2-3 intergeneration
mixing scenariothe radiative process τ µγ constrains the combination ofparameters
→
˜
δ = sin2θ ∆m˜ /m˜. (11)
µτ 23 23
The contours in Fig. 1 have been obtained from the approximate formula of Ref. [13],
normalized tothe current experimental limit,
2 4
δ 100GeV
Br(τ µγ) 1.1 10 6 µτ . (12)
−
→ ∼ × 1.4 m˜
(cid:18) (cid:19) (cid:18) (cid:19)
This approximation only provides an order of magnitude estimate of the upper limit for
the supersymmetric contribution to the radiative lepton decay. The exact result, which
is sensitive to the details of mass spectra and mixings, can in fact be much smaller due
to cancellations among different contributions [2]. Fig. 1 demonstrates that information
from slepton production and decay could be competitive to the radiative lepton decays.
In particular a LC can help to explore the small ∆m˜ region. It should be stressed,
23
though,thatinagivenmodelforleptonflavourviolationalsothecorrelationwithµ eγ
→
hastobeconsidered[8],whichinmanycasescanyieldamoreseverebound,asdiscussed
in the nextsection.
3 Case study for the supersymmetric seesaw model
Asadefinite andrealisticexampleforSLFV weconsiderthe seesawmechanismin mSU-
GRA models. In supersymmetric theories with heavy right-handed Majorana neutrinos,
the seesaw mechanism [14] can give rise to light neutrino masses at or below the sub-eV
scale. Furthermore,themassiveneutrinosaffecttherenormalizationgrouprunningofthe
slepton masses, generating flavour off-diagonal terms in the mass matrix. These in turn
leadtoSLFVinscatteringprocessesathighenergiesandinraredecays. Forillustrationof
the potential and complementarity of such SLFV searches we focus on the LC processes
e e l l χ˜0χ˜0 involving slepton pair production and subsequent decay, and on the
± − → β± α− b a
correspondingradiativedecayl l γ. Inparticular,inanearlyATLASnote[15]τ µγ
α β
→ →
is estimated to be observable at the LHC for a branching ratio of order 10 7. However,
−
the limitone can reasonably expectmay bean order ofmagnitude better [16].
For our study we use the mSUGRA benchmark scenarios proposed in [17] for LC
studies, concentrating on those which predict charged left-handed sleptons that are light
enoughtobepair-producedatthecenter-of-massenergy√s = 500GeV.Furthermore, we
implement the seesaw mechanism assuming degenerate Majorana masses for the right-
handedneutrinos andconstrain theneutrinoYukawa couplingsbythemeasuredmasses
and mixings of the light neutrinos. Further sources of SLFV exist in other models such
as GUTs [18]. However, no realistic three generation case study of effects for collider
processes has been performed so far, so that we restrict the discussion to the minimal
seesawmodel,here.
5
3.1 Supersymmetric seesaw mechanism
If three right-handed neutrino singlet fields ν are added to the MSSM particle content,
R
one hasthe additional terms [19]
1
W = νcTMνc +νcTY L H (13)
ν −2 R R R ν · 2
inthesuperpotential. Here,Y isthematrixofneutrinoYukawacouplings,M istheright-
ν
handedneutrinoMajoranamassmatrix, andLandH denotetheleft-handedleptonand
2
hypercharge +1/2 Higgs doublets, respectively. At energies much below the mass scale
M of the right-handed neutrinos, W leads to the following mass matrix for the light
R ν
neutrinos:
M = YTM 1Y (vsinβ)2. (14)
ν ν − ν
From that the light neutrino masses m , m , m are obtained after diagonalization by the
1 2 3
unitary MNS matrix U. The basis is chosen such that the matrices of the charged lepton
Yukawa couplings andMajorana massesare diagonal, which isalways possible.
Furthermore, the heavy neutrino mass eigenstates give rise to virtual corrections to
the slepton mass matrix that are responsible for lepton flavour violating processes. More
specifically, in the mSUGRAmodels considered, the mass matrix of the charged sleptons
isgiven by
m2 (m2 )
m2 = ˜lL ˜lLR † (15)
˜l m2 m2
˜lLR ˜lR !
with
1
(m2 ) = (m2) +δ m2 +m2 cos2β +sin2θ
˜lL ij L ij ij li Z −2 W
(cid:18) (cid:18) (cid:19)(cid:19)
(m2 ) = (m2) +δ (m2 m2 cos2βsin2θ )
˜lR ij R ij ij li − Z W
(m2 ) = A vcosβ δ m µtanβ.
˜lLR ij ij − ij li
Whenm2 isevolvedfromtheGUTscaleM totheelectroweakscalecharacteristicforthe
˜l X
experiments, one obtains
m2 = m21+(δm2) +δm2 (16)
L 0 L MSSM L
m2 = m21+(δm2) +δm2 (17)
R 0 R MSSM R
A = A Y +δA +δA, (18)
0 l MSSM
where m is the common soft SUSY-breaking scalar mass and A the common trilin-
0 0
ear coupling. The terms (δm2 ) and δA are well-known flavour-diagonal MSSM
L,R MSSM MSSM
corrections. In addition, the evolution generates the off-diagonal terms δm2 and δA
L,R
which, in leading-log approximation and for degenerate right-handed Majorana masses
M = M ,i = 1,2,3,are given by[20]
i R
1 M
δm2 = (3m2 +A2)(Y Y )ln X (19)
L −8π2 0 0 ν† ν M
(cid:18) R(cid:19)
δm2 = 0 (20)
R
6
3A M
0 X
δA = (Y Y Y )ln . (21)
−16π2 l ν† ν M
(cid:18) R(cid:19)
In order to determine the product Y Y of the neutrino Yukawa coupling matrix en-
ν† ν
tering these corrections, one usesthe expression
√M
R
Y = R diag(√m ,√m ,√m ) U , (22)
ν 1 2 3 †
vsinβ · ·
which follows from UTM U = diag(m ,m ,m ) and (14) [19]. Here, R is an unknown
ν 1 2 3
complex orthogonal matrix parametrizing the ambiguity in the relation of Yukawa cou-
pling and mass matrices. In the following we will assume R to be real which suffices for
the presentpurpose. Inthis case, R dropsout from the product Y Y ,
ν† ν
M
R
Y Y = U diag(m ,m ,m ) U . (23)
ν† ν v2sin2β · 1 2 3 · †
Using existing neutrino data on the mass squared differences and the mixing matrix U
togetherwithboundsandassumptionsontheabsolutemassscaleonecancalculateY Y .
ν† ν
The only free parameter is the Majorana mass scale M . The result is then evolved to
R
the unification scale M and used as an input in the renormalization group corrections
X
(19) to the slepton mass matrix. Finally, diagonalization of (15) yields the slepton mass
˜
eigenvaluesm˜ and eigenstatesl (i = 1,2,...6).
i i
3.2 Lepton flavour violating processes
The flavour off-diagonal elements (19) in m2 (δA = 0 in the mSUGRA scenarios of [17])
˜l
induce, among other SLFV effects, the processes e+e ˜l+˜l l+l χ˜0χ˜0, where SLFV
− → j i− → β α− b a
can occur in the production and decay vertices. The helicity amplitudes for the pair pro-
duction of ˜l+ and ˜l , and the corresponding decay amplitudes are given explicitly in [8].
j i−
pair
Inthe approximation (5)for σ one finds
αβ
(δm )2 2
σpair α4| L αβ| σ(f¯f ˜l+˜l )Br(˜l+ l+χ˜ )Br(˜l l χ˜ ) (24)
αβ ∝ m˜2Γ2 → α α− α → α 0 α− → α− 0
In the numerical evaluation no slepton degeneracy has been assumed as in (4), and the
amplitude for the complete 2 4 processes is summed coherently over the intermediate
→
slepton mass eigenstates.
Similary,theterms(19)areresponsibleforSLFVradiativedecaysl l γ inducedby
α β
→
photon-penguin type diagrams with charginos/sneutrinos or neutralinos/charged slep-
tons in the loop. Again schematically, the decayratesare given by [19,20]
(δm )2 2
Γ(l l γ) α3m5 | L αβ| tan2β, (25)
α → β ∝ lα m˜8
where m˜ stands forthe relevantsparticle massesin the loop.
7
101
100
10-1
b
σ / f
10-2
10-3
10-4
1011 1012 1013 1014 1015
M / GeV
R
Figure 2: Cross-sections at √s = 500 GeV for e+e µ+e + 2χ˜0 (circles) and e+e
− → − 1 − →
τ+µ +2χ˜0 (triangles) in scenarioB.
− 1
Scenario m1/2/GeV m0/GeV tanβ m˜6/GeV Γ˜6/GeV mχ˜01/GeV
B 250 100 10 208 0.32 98
C 400 90 10 292 0.22 164
G 375 120 20 292 0.41 154
I 350 180 35 313 1.03 143
Table1: ParametersofselectedmSUGRAbenchmarkscenarios(from [17]). Thesign ofµ
is chosen to be positive and A is set to zero. Given are also the mass and total width of
0
the heaviestcharged slepton and the massofthe lightest neutralino.
3.3 Signals and background
Among the mSUGRA benchmark scenarios proposed in [17] for LC studies, the models
B,C,G,andI(seeTab.1)predictleft-handedsleptonswhichcanbepair-producedate+e
−
colliders√s = 500 800GeVcms energies. Inthe following we willconfine ourselves to
÷
these models.
Most likely, at the time when a linear collider will be in operation, more precise mea-
surements of the neutrino parameters will be available than today. In order to simulate
the expected improvement, we take the central values of the mass squared differences
∆m2 = m2 m2 and mixing angles θ from a global fit to existing data [21] with errors
ij | i − j| ij
that indicate the anticipated 90 % C.L. intervals ofrunning and proposed experimentsas
further explainedin [2]:
tan2θ = 1.40+1.37, tan2θ = 0.005+0.001, tan2θ = 0.36+0.35, (26)
23 0.66 13 0.005 12 0.16
− − −
∆m2 = 3.30+0.3 10 5 eV2, ∆m2 = 3.10+1.0 10 3 eV2. (27)
12 0.3 · − 23 1.0 · −
− −
Furthermore, forthelightestneutrinoweassumethemassrangem 0 0.03eV,which
1
≈ −
8
10-6
10-8
10-10
γ)
→lj10-12
Br(li
10-14
10-16
10-18
1011 1012 1013 1014 1015
M /GeV
R
Figure 3: Branching ratios Br(τ µγ) (upper)andBr(µ eγ) (lower) inscenario B.
→ →
at the lower end corresponds to the case of a hierarchical spectrum. Towards the upper
end,it approachesthe degenerate case.
InFig.2,thecross-sections fore+e µ+e +2χ˜0 ande+e τ+µ +2χ˜0 areplotted
− → − 1 − → − 1
for model B. The channel τ+e + 2χ˜0 is not shown since it is strongly suppressed by the
− 1
small mixing angle θ , and therefore more difficult to observe. As can be seen, for a
13
sufficiently large Majorana mass scale the SLFV cross-sections can reach several fb. The
spread ofthe predictions reflectsthe uncertainties in the neutrino data.
The Standard Model background mainly comes from W-pair production, W produc-
tion with t-channel photon exchange, and τ-pair production. A 10 degree beam pipe
cut and cuts on the lepton energy and missing energy reduce the SM background cross-
sections to less than 30 fb for (µe) final states and less than 10 fb for (τµ) final states. If
one requires a signal to background ratio, S/√S +B = 3, and assumes a typical signal
cross-section of 0.1 fb, one can afford a background of about 1 fb. Here an integrated
luminosity of 1000 fb 1 has been assumed. Whether or not the background process esti-
−
mate above can be further suppressed to this level by applying selectron selection cuts,
for example, on the acoplanarity, lepton polar angle and missing transverse momentum
hastobestudiedindedicatedsimulations. Forleptonflavourconservingprocessesithas
been shown that the SM background to slepton pair production can be reduced to about
2-3 fbat√s = 500GeV [22].
The MSSM background is dominated by chargino/slepton production with a total
cross-section of 0.2-5 fb and 2-7 fb for (µe) and (τµ) final states, respectively, depending
on the SUSYscenario andthe colliderenergy. TheMSSM background in the (τe) channel
can also contribute to the µe channel via the decay τ µν ν . If τ˜ and χ˜+ are very
µ τ 1 1
→
light, like in scenarios B and I, this background can be as large as 20 fb. However, such
eventstypicallycontaintwoneutrinosinadditiontothetwoLSPswhicharealsopresent
in the signal events. Thus, after τ decay one has altogether six invisible particles instead
oftwo, whichmayallowtodiscriminatethesignalinµ+e + E/ alsofrom thispotentially
−
dangerous MSSM background by cutting on various distributions. But also here one
9
101
100
b
0χ) / f
+ 2 10-1
-µ
+
τ
→
+-e10-2
e
σ(
d
n
u
10-3 bo
nt
e
s
e
pr
10-4
10-14 10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5
Br(τ → µγ)
Figure 4: Correlation of σ(e+e τ+µ + 2χ˜0) at √s = 800 GeV with Br(τ µγ) in
− − 1
→ →
scenario (from leftto right) C,G(open circles), B and I.
needsa dedicated simulation study, in order to makemore definite statements.
Thecorrespondingbranchingratios, Br(µ eγ)andBr(τ µγ),inmodelBaredis-
→ →
playedin Fig. 3[2]. One seesthata positive signal forµ eγ atthe minimum branching
→
ratioobservableinthenewPSIexperiment,Br(µ eγ) 10 13[23]wouldimplyavalue
−
→ ≃
ofM between2 1012GeVand2 1013GeV.Incomparisontoµ eγ thechannelτ µγ is
R
· · → →
less affected by the neutrino uncertainties. If the sensitivity goal Br(τ µγ) = 10 8 [16]
−
→
atthe LHCis reachedone could probe M = 1015 GeV.
R
Particularly interesting and useful are the correlations between SLFV in radiative de-
cays and slepton pair production. Such a correlation is illustrated in Fig. 4 for e+e
−
→
τ+µ + 2χ˜0 and Br(τ µγ). One sees that the neutrino uncertainties drop out, while
− 1 →
the sensitivity to the mSUGRA parameters remains. An observation of τ µγ with the
→
branching ratio 10 8 at the LHC would be compatible with a cross-section of order 10 fb
−
for e+e ˜l+˜l τ+µ + 2χ˜0, at least in model C. However, there are also corre-
− → i,j j i− → − 1
lations of different flavor channels. This is illustrated in Fig. 5, where the correlation of
P
e+e τ+µ + 2χ˜0 and µ eγ is shown. Despite of the uncertainties from the neu-
− → − 1 →
trino sector, already the present experimental bound Br(µ eγ) < 1.2 10 11 yields a
−
→ ·
stronger constraint on σ(e+e τ+µ +2χ˜0) than the one obtained from Fig. 4, making
− → − 1
cross-sections larger than a few 10 1 fb at √s = 800 GeV very unlikely in model B. If this
−
scenario is correct, non-observation of µ eγ at the new PSI experiment will exclude
→
the observability of this channel at a LC. As a final remark we stress that in the channel
e+e µ+e +2χ˜0 cross-sections of 1 fb are compatible with the present bounds, while
− − 1
→
no signal at the future PSI sensitivity would constrain this channel to less than 0.1 fb.
However we want to emphasize again that these statements are very model dependent,
andmuch biggercross-sections are possible in general, asshown in section 2.
10