Lepton Flavor Violation at the LHC

Lepton Flavor Violation at the LHC

Frank Deppisch Email: frank.deppisch@manchester.ac.ukDeutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany
School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom

In supersymmetric scenarios, the seesaw mechanism involving heavy right-handed neutrinos implies sizable lepton flavor violation (LFV) in the slepton sector. We discuss the potential of detecting LFV processes at the LHC in mSUGRA+seesaw scenarios and for general mixing in either the left- or right-handed slepton sector. The results are compared with the sensitivity of rare LFV decay experiments.

11.30.HvFlavor symmetries and 12.60.JvSupersymmetric models and 14.60.StNon-standard-model neutrinos, right-handed neutrinos

] ] ] ] ] ]

1 SUSY Seesaw Type I and Slepton Mass Matrix

The observed neutrino oscillations imply the existence of neutrino masses and flavor mixing, giving a hint towards physics beyond the Standard Model. For example, the seesaw mechanism involving heavy right handed Majorana neutrinos, which explains well the smallness of the neutrino masses, allows for leptogenesis and induces sizeable lepton flavor violation (LFV) in a supersymmetric extension of the Standard Model.

If three right handed neutrino singlet fields are added to the MSSM particle content, one gets additional terms in the superpotential Casas:2001sr ():


Here, is the matrix of neutrino Yukawa couplings, is the right handed neutrino Majorana mass matrix, and and denote the left handed lepton and hypercharge +1/2 Higgs doublets, respectively. If the mass scale of the matrix is much greater than the electroweak scale, and consequently much greater than the scale of the Dirac mass matrix (where is the appropriate Higgs v.e.v., with  GeV and ), the effective left handed neutrino mass matrix will be naturally obtained,


The matrix is diagonalized by the unitary matrix , yielding the three light neutrino masses:


The other three neutrino mass eigenstates are too heavy to be observed directly, but, through virtual corrections, induce small off-diagonal terms in the evolved MSSM slepton mass matrix,


leading to observable LFV processes. These corrections in leading log approximation are Hisano:1999fj ()


where , and and are the common scalar mass and trilinear coupling, respectively, of the minimal supergravity (mSUGRA) scheme. The product of the neutrino Yukawa couplings entering these corrections can be determined by inverting (2),


using neutrino data as input for the masses and , and evolving the result to the unification scale . The unknown complex orthogonal matrix may be parametrized in terms of 3 complex angles .

2 LFV Rare Decays and LHC Processes

At the LHC, a feasible test of LFV is provided by production of squarks and gluinos, followed by cascade decays via neutralinos and sleptons Agashe:1999bm (); Andreev:2006sd ():


where run over all sparticle mass eigenstates including antiparticles. LFV can occur in the decay of the second lightest neutralino and/or the slepton, resulting in different lepton flavors, . The total cross section for the signature can then be written as


where can involve jets, leptons and LSPs produced by lepton flavor conserving decays of squarks and gluinos, as well as low energy proton remnants. The cross section is calculated at the LO level Dawson:1983fw () with 5 active quark flavors, using CTEQ6M PDFs Pumplin:2002vw (). Possible signatures of this inclusive process are:

  • ,

with at least two leptons of unequal flavor.

The LFV branching ratio is for example calculated in Bartl:2005yy () in the framework of model-independent MSSM slepton mixing. In general, it involves a coherent summation over all intermediate slepton states.

As a sensitivity comparison it is useful to correlate the expected LFV event rates at the LHC with LFV rare decays (see Deppisch:RareDecays () and references therein for a discussion of LFV rare decays in SUSY Seesaw Type I scenarios). This is shown in Figures 1 and 2 for the event rates and , respectively, originating from the cascade reactions (2). Both are correlated with , yielding maximum rates of around per year for an integrated luminosity of in the mSUGRA scenario C’ Battaglia:2001zp (), consistent with the current limit . The MEG experiment at PSI is expected to reach a sensitivity of .

The correlation is approximately independent of the neutrino parameters, but highly dependent on the mSUGRA parameters. This is contemplated further in Figure 3, comparing the sensitivity of the signature at the LHC with in the mSUGRA parameter plane. LHC searches can be competitive to the rare decay experiments for small  GeV. Tests in the large- region are severely limited by collider kinematics.

Figure 1: Correlation of the number of events per year at the LHC and in mSUGRA scenario C’ ( GeV,  GeV,  GeV,  GeV, ) for the case of hier.  (blue stars), deg. /hier.  (red boxes) and deg.  (green triangles). The neutrino parameters are scattered within their experimentally allowed ranges Maltoni:2003sr (). For degenerate heavy neutrino masses, both hierarchical (green diamonds) and degenerate (blue stars) light neutrino masses are considered with real and . In the case of hierarchical heavy and light neutrino masses (red triangles), is scattered over while and are scattered in the ranges allowed by leptogenesis and perturbativity Deppisch:2005rv (). An integrated LHC luminosity of is assumed. The current limit on is displayed by the vertical line.
Figure 2: Same as Figure 1, but correlating with .
Figure 3: Contours of the number of events at the LHC with an integrated luminosity of (solid) and of in the plane . The remaining mSUGRA parameters are as in Figure 1. The neutrino parameters are at their best fit values Maltoni:2003sr (), with and a degenerate r.h. neutrino mass  GeV. The shaded (red) areas are already excluded by mass bounds from various experimental sparticle searches.

Up to now we have considered LFV in the class of type I SUSY seesaw model described in Section 1, which is representative of models of flavor mixing in the left-handed slepton sector only. However, it is instructive to analyze general mixing in the left- and right-handed slepton sector, independent of any underlying model for slepton flavor violation. The easiest way to achieve this is by assuming mixing between two flavors only, which can be parametrized by a mixing angle and a mass difference between the sleptons, in the case of left-/right-handed slepton mixing, respectively111This is different to the approach in Bartl:2005yy (), where the slepton mass matrix elements are scattered randomly.. In particular, the left-/right-handed selectron and smuon sector is then diagonalized by




and a mass difference between the slepton mass eigenvalues222For left-handed slepton mixing, and are also used to describe the sneutrino sector.. The LFV branching ratio can then be written in terms of the mixing parameters and the flavor conserving branching ratio as


with the average width of the two sleptons involved. Maximal LFV is thus achieved by choosing and . For definiteness, we use  GeV. The results of this calculation can be seen in Figures 4 and 5, which show contour plots of in the plane for maximal left- and right-handed slepton mixing, respectively. Also displayed are the corresponding contours of . We see that the present bound still permits sizeable LFV signal rates at the LHC. However, would largely exclude the observation of such an LFV signal at the LHC.

Figure 4: Contours of the events per year for maximal mixing at the LHC with an integrated luminosity of in the plane (solid lines). The remaining mSUGRA parameters are:  GeV, , . Contours of are shown by dashed lines. The shaded (red) areas are forbidden by mass bounds from various experimental sparticle searches.
Figure 5: As in Figure 4 but for maximal mixing.


The author would like to thank S. Albino, D. Ghosh and R. Rückl for the collaboration on which the presentation is based.


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