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
###### Abstract

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.

###### pacs:
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 ():

 Wν=−12νcTRMνcR+νcTRYνL⋅H2. (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,

 Mν=mTDM−1mD=YTνM−1Yν(vsinβ)2. (2)

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

 UTMNSMνUMNS=diag(m1,m2,m3). (3)

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,

 (4)

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

 δm2L = −18π2(3m20+A20)(Y†νLYν), (5) δm2LR = −3A0vcosβ16π2(YlY†νLYν), (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),

 Yν=1vsinβdiag(√Mi)⋅R⋅diag(√mi)⋅U†MNS, (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 ():

 pp → ~qα~qβ,~g~qα,~g~g, ~qα(~g) → ~χ02qα(g), ~χ02 → ~lali, ~la → ~χ01lj, (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

 σ(pp→l+αl−β+X)= {∑a,bσ(pp→~qa~qb)×Br(~qa→~χ02qa) +∑aσ(pp→~qa~g)×Br(~qa→~χ02qa) +σ(pp→~g~g)×Br(~g→~χ02g) }×Br(~χ02→l+αl−β~χ01), (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 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.

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

 (~l1~l2)=U⋅(~eL/R~μL/R) (10)

with

 U=(cosθL/RsinθL/R−sinθL/RcosθL/R), (11)

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

 Br(~χ02→μ+e−~χ01) = 2sin2θL/Rcos2θL/R (12) × (Δm)2L/R(Δm)2L/R+Γ2~l × Br(~χ02→e+e−~χ01),

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.

## 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:hep-ph/0103065].
• (2) J. Hisano and D. Nomura, Phys. Rev. D 59, 116005 (1999) [arXiv:hep-ph/9810479].
• (3) K. Agashe and M. Graesser, Phys. Rev. D 61, 075008 (2000) [arXiv:hep-ph/9904422].
• (4) Yu. M. Andreev, S. I. Bityukov, N. V. Krasnikov and A. N. Toropin, arXiv:hep-ph/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:hep-ph/9610490].
• (6) J. Pumplin, D. R. Stump, J. Huston, H. L. Lai, P. Nadolsky and W. K. Tung, JHEP 0207 (2002) 012 [arXiv:hep-ph/0201195].
• (7) A. Bartl, K. Hidaka, K. Hohenwarter-Sodek, T. Kernreiter, W. Majerotto and W. Porod, Eur. Phys. J. C 46, 783 (2006) [arXiv:hep-ph/0510074].
• (8) F. Deppisch, H. Päs, A. Redelbach, R. Rückl and Y. Shimizu, Eur. Phys. J. C 28, 365 (2003) [arXiv:hep-ph/0206122]; F. Deppisch, H. Pas, A. Redelbach, R. Ruckl and Y. Shimizu, Nucl. Phys. Proc. Suppl. 116, 316 (2003) [arXiv:hep-ph/0211138].
• (9) M. Battaglia et al., Eur. Phys. J. C 22 (2001) 535 [arXiv:hep-ph/0106204].
• (10) M. Maltoni, T. Schwetz, M.A. Tortola and J.W.F. Valle, Phys. Rev. D 68, 113010 (2003) [arXiv:hep-ph/0309130].
• (11) F. Deppisch, H. Päs, A. Redelbach and R. Rückl, Phys. Rev. D 73, 033004 (2006) [arXiv:hep-ph/0511062]; F. Deppisch, S. Albino and R. Ruckl, AIP Conf. Proc. 903, 307 (2007) [arXiv:hep-ph/0701014].
You are adding the first comment!
How to quickly get a good reply:
• Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
• Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
• Your comment should inspire ideas to flow and help the author improves the paper.

The better we are at sharing our knowledge with each other, the faster we move forward.
The feedback must be of minimum 40 characters and the title a minimum of 5 characters