Lepton Flavor Violation at the LHC
Abstract
In supersymmetric scenarios, the seesaw mechanism involving heavy righthanded 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 righthanded slepton sector. The results are compared with the sensitivity of rare LFV decay experiments.
pacs:
11.30.HvFlavor symmetries and 12.60.JvSupersymmetric models and 14.60.StNonstandardmodel neutrinos, righthanded 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 ():
(1) 
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,
(2) 
The matrix is diagonalized by the unitary matrix , yielding the three light neutrino masses:
(3) 
The other three neutrino mass eigenstates are too heavy to be observed directly, but, through virtual corrections, induce small offdiagonal terms in the evolved MSSM slepton mass matrix,
(4) 
leading to observable LFV processes. These corrections in leading log approximation are Hisano:1999fj ()
(5)  
(6) 
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),
(7) 
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 ():
(8) 
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
(9) 
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 modelindependent 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.
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 lefthanded slepton sector only. However, it is instructive to analyze general mixing in the left and righthanded 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/righthanded slepton mixing, respectively^{1}^{1}1This is different to the approach in Bartl:2005yy (), where the slepton mass matrix elements are scattered randomly.. In particular, the left/righthanded selectron and smuon sector is then diagonalized by
(10) 
with
(11) 
and a mass difference between the slepton mass eigenvalues^{2}^{2}2For lefthanded 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
(12)  
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 righthanded 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.
Acknowledgments
The author would like to thank S. Albino, D. Ghosh and R. Rückl for the collaboration on which the presentation is based.
References
 (1) J. A. Casas and A. Ibarra, Nucl. Phys. B 618, 171 (2001) [arXiv:hepph/0103065].
 (2) J. Hisano and D. Nomura, Phys. Rev. D 59, 116005 (1999) [arXiv:hepph/9810479].
 (3) K. Agashe and M. Graesser, Phys. Rev. D 61, 075008 (2000) [arXiv:hepph/9904422].
 (4) Yu. M. Andreev, S. I. Bityukov, N. V. Krasnikov and A. N. Toropin, arXiv:hepph/0608176.
 (5) S. Dawson, E. Eichten and C. Quigg, Phys. Rev. D 31 (1985) 1581; H. Baer and X. Tata, Phys. Lett. B 160 (1985) 159; W. Beenakker, R. Hopker, M. Spira and P. M. Zerwas, Nucl. Phys. B 492 (1997) 51 [arXiv:hepph/9610490].
 (6) J. Pumplin, D. R. Stump, J. Huston, H. L. Lai, P. Nadolsky and W. K. Tung, JHEP 0207 (2002) 012 [arXiv:hepph/0201195].
 (7) A. Bartl, K. Hidaka, K. HohenwarterSodek, T. Kernreiter, W. Majerotto and W. Porod, Eur. Phys. J. C 46, 783 (2006) [arXiv:hepph/0510074].
 (8) F. Deppisch, H. Päs, A. Redelbach, R. Rückl and Y. Shimizu, Eur. Phys. J. C 28, 365 (2003) [arXiv:hepph/0206122]; F. Deppisch, H. Pas, A. Redelbach, R. Ruckl and Y. Shimizu, Nucl. Phys. Proc. Suppl. 116, 316 (2003) [arXiv:hepph/0211138].
 (9) M. Battaglia et al., Eur. Phys. J. C 22 (2001) 535 [arXiv:hepph/0106204].
 (10) M. Maltoni, T. Schwetz, M.A. Tortola and J.W.F. Valle, Phys. Rev. D 68, 113010 (2003) [arXiv:hepph/0309130].
 (11) F. Deppisch, H. Päs, A. Redelbach and R. Rückl, Phys. Rev. D 73, 033004 (2006) [arXiv:hepph/0511062]; F. Deppisch, S. Albino and R. Ruckl, AIP Conf. Proc. 903, 307 (2007) [arXiv:hepph/0701014].