In this paper we review our main results for Lepton Flavour Violating (LFV)
semileptonic tau decays and muon-electron conversion in nuclei within the
context of two Constrained SUSY-Seesaw Models, the CMSSM and the NUHM. The
relevant spectrum is that of the Minimal Supersymmetric Standard Model extended
by three right handed neutrinos, $\nu_{R_i}$ and their corresponding SUSY
partners, ${\tilde \nu}_{R_i}$, ($i=1,2,3$). We use the seesaw mechanism for
neutrino mass generation and choose a parameterisation of this mechanism that
allows us to incorporate the neutrino data in our analysis of LFV processes. In
addition to the full one-loop results for the rates of these processes, we will
also review the set of simple formulas, valid at large $\tan \beta$, which are
very useful to compare with present experimental bounds. The sensitivity to
SUSY and Higgs sectors in these processes will also be discussed. This is a
very short summary of the works in Refs. \cite{Arganda:2008jj} and
\cite{Arganda:2007jw} to which we refer the reader for more details.Comment: 6 pages, 6 figures. To be published in the proceedings of the Tau08
  Conference, Novosibirsk, Russia, 22-25 September 200

A. Rodriguez-Sanchez

A. Teixeira

Arganda

Casas

E. Arganda

Ecker

Gasser

J. Portolés

Kuno

M. Herrero

Weinberg

Nuclear Physics B - Proceedings Supplements

English

arXiv

Crossref

Lepton Flavour Violation in charged leptons within SUSY-seesaw

6 pages, 6 figures.-- Pre-print archive.In this paper we review our main results for Lepton Flavour Violating (LFV) semileptonic tau decays and muonelectron
conversion in nuclei within the context of two Constrained SUSY-Seesaw Models, the CMSSM and the
NUHM. The relevant spectrum is that of the Minimal Supersymmetric Standard Model extended by three right
handed neutrinos, νRi and their corresponding SUSY partners, ˜νRi, (i = 1, 2, 3). We use the seesaw mechanism
for neutrino mass generation and choose a parameterisation of this mechanism that allows us to incorporate the
neutrino data in our analysis of LFV processes. In addition to the full one-loop results for the rates of these
processes, we will also review the set of simple formulas, valid at large tan β, which are very useful to compare
with present experimental bounds. The sensitivity to SUSY and Higgs sectors in these processes will also be
discussed. This is a very short summary of the works in Refs. [1] and [2] to which we refer the reader for more
details.Project FPA2006-05423 of
Spanish MEC for finantial support.Peer reviewe

Arganda, Ernesto

Herrero, María José

Portolés, Jorge

Rodríguez-Sánchez, Ana M.

Teixeira, A. M.

Digital.CSIC

arXiv:0812.2692v1  [hep-ph]  14 Dec 2008 Lepton Flavour Violation in charged leptons within SUSY-seesawE. Argandaa, M. Herrerob ∗, J. Portole´sc, A. Rodriguez-Sanchezb and A.Teixeirada Departamento de F´ısica Ato´mica, Molecular y Nuclear, Facultad de Ciencias F´ı sicas,Universidad Complutense de Madrid, Avda. Complutense s/n, E-28040 Madrid, SpainbDepartamento de F´ısica Teo´rica C-XI and Instituto de F´ısica Teo´rica C-XVI,Universidad Auto´noma de Madrid, Cantoblanco, E-28049 Madrid, SpaincIFIC, Universitat de Valencia-CSIC, Apt. Correus 22085, E-46071, Valencia,SpaindLaboratoire de Physique Theorique, UMR 8627, Pris-Sud XI, Bat.210, F-91405 Orsay Cedex,FranceIn this paper we review our main results for Lepton Flavour Violating (LFV) semileptonic tau decays and muon-electron conversion in nuclei within the context of two Constrained SUSY-Seesaw Models, the CMSSM and theNUHM. The relevant spectrum is that of the Minimal Supersymmetric Standard Model extended by three righthanded neutrinos, νRi and their corresponding SUSY partners, ν˜Ri , (i = 1, 2, 3). We use the seesaw mechanismfor neutrino mass generation and choose a parameterisation of this mechanism that allows us to incorporate theneutrino data in our analysis of LFV processes. In addition to the full one-loop results for the rates of theseprocesses, we will also review the set of simple formulas, valid at large tan β, which are very useful to comparewith present experimental bounds. The sensitivity to SUSY and Higgs sectors in these processes will also bediscussed. This is a very short summary of the works in Refs. [1] and [2] to which we refer the reader for moredetails.1. Framework for LFV in charged leptonsFrom the present neutrino data on neutrino os-cillations, we know that Lepton Flavour Viola-tion (LFV) occurs in the neutral lepton sector.However, we do not know yet if this LFV oc-curs in the charged lepton as well. Even if itoccurs, we do not know either if these two vi-olations are related or not. Within the Stan-dard Model with mass less neutrinos there is notLFV. Futhermore, it is extremely suppressed evenwith massive neutrinos. In contrast, in supersym-metric (SUSY) models with Majorana neutrinosLFV can be sizeable. In particular, we considerhere the spectrum of the Minimal Supersymmet-ric Standard Model (MSSM) extended with threerigth handed neutrinos, νRi , and their SUSYpartners, ν˜Ri (i = 1, 2, 3), and with the seesawmechanism implemented to generate the neutrino∗Talk given at the 10th International Workshop on Tau-Lepton Physics, Tau08, 22-25 September 2008, Novosi-birsk (Russia)masses, where it is known that large LFV ratesoccur. These are induced by the soft SUSY break-ing slepton masses and are transmitted to thelepton sector by means of the Yukawa neutrinocouplings, which can be large if the neutrinos areof Majorana type, and via loops of SUSY parti-cles. Therefore, in the context we work within ofSUSY-seesaw models the LFV in both the neutraland the charged lepton are closely related.Regarding the seesaw mechanism we use theparameterisation proposed in [3], which isvery useful to implement the neutrino data intoour analysis of LFV. With this parameterisa-tion, the 3 × 3 Yukawa coupling and Diracmass matrices are set by mD = Yν v2 =√mdiagN R√mdiagν U†MNS, with the 3 × 3 orthog-onal matrix R defined by three complex anglesθi (i = 1, 2, 3) which represent the additionalmixing introduced by the right handed neutri-nos. The other quantities in this formula arev1(2) = v cos(sin)β, v = 174 GeV; mdiagν =12 E. Arganda, M. Herrero, J. Portoles, A. Rodriguez-Sanchez and A.M. Teixeiradiag (mν1 ,mν2 ,mν3) denotes the three light neu-trino masses, andmdiagN = diag (mN1 ,mN2 ,mN3)the three heavy ones. UMNS is given by the three(light) neutrino mixing angles θ12, θ23 and θ13,and three phases, δ, φ1 and φ2. With this param-eterisation it is easy to accommodate the neutrinodata, while leaving room for extra neutrino mix-ings (from the right handed sector). It furtherallows for large Yukawa couplings Yν ∼ O(1) bychoosing large entries in mdiagN and/or θi.Here we focus in the particular LFV proc-cesses: 1) semileptonic τ → µPP (PP =pi+pi−, pi0pi0,K+K−,K0K¯0), τ → µP (P =pi, η, η′), τ → µV (V = ρ, φ) decays and 2)µ − e conversion in heavy nuclei. The predic-tions in the following are for two different con-strained MSSM-seesaw scenarios, with universaland non-universal Higgs soft masses. The re-spective parameters (in addition to the previ-ous neutrino sector parameters) are: 1) CMSSM-seesaw: M0, M1/2, A0 tanβ, and sign(µ), and2) NUHM-seesaw: M0, M1/2, A0 tanβ, sign(µ),MH1 =M0(1 + δ1)1/2 and MH2 =M0(1 + δ2)1/2.The predictions presented here include a fullone-loop computation of the SUSY diagrams con-tributing to these LFV processes and do not usethe Leading Logarithmic (LLog) nor the mass in-sertion approximations. In the case of semilep-tonic tau decays we have not included the boxeswhich are clearly subdominant, but we have in-cluded correspondingly: the γ, Z and Higgsbosons, h0 and H0, mediated diagrams in τ →µPP , and the Z boson and A0 Higgs boson medi-ated diagrams in τ → µP . The hadronisation ofquark bilinears in all these semileptonic channelsis performed within the chiral framework, usingChiral Perturbation Theory [4] to order and Reso-nance Chiral Theory [5] whenever the resonanceslike the ρ, etc., play a relevant role. The predic-tions for the µ − e conversion rates include thefull set of SUSY one-loop contributing diagrams,mediated by γ, Z and Higgs bosons, as well asboxes. In this case we have followed very closelythe general parameterisation and approximationsof ref. [6].2. Results and discussionHere we present the predictions for BR(τ →µPP ) (PP = pi+pi−, pi0pi0,K+K−,K0K¯0),BR(τ → µP ) (P = pi, η, η′), BR(τ → µV )(V = ρ, φ) and CR(µ− e, Nuclei) within the pre-viously described framework and compare themwith the following experimental bounds: BR(τ →µpi+pi−) < 4.8 × 10−7, BR(τ → µK+K−) <8 × 10−7, BR(τ → µpi) < 5.8 × 10−8, BR(τ →µη) < 5.1 × 10−8, BR(τ → µη′) < 5.3 × 10−8,BR(τ → µρ) < 2 × 10−7, BR(τ → µφ) <1.3 × 10−7, CR(µ − e,Au) < 7 × 10−13 andCR(µ − e,Ti) < 4.3 × 10−12. As a general re- 200 400 600 800 1000 1200 300  400  500  600  700  800  900  1000mH0  (GeV)M0 = M1/2 (GeV)mN = (1010, 1011, 1014 ) GeVA0 = 0, tan β = 50θ13 = 5°, θi = 0δ2 = 0δ1 = -1.8δ1 = -1.6δ1 = -1.  δ1 = 0.    200 300 400 500 600 700 800 300  400  500  600  700mA0 (GeV)       (also mH0 )M0 = M1/2 (GeV)mN = (1010,1011,1014 ) GeVA0 = 0, tan β = 50θ2 = 2.9eipi/4, θ1 = θ3 = 0δ1 = δ2 = 0δ1 = -1, δ2 = 0.2δ1 = -2, δ2 = 0.2δ1 = -2.35, δ2 = 0.2δ1 = -2.4, δ2 = 0.2δ1 = -2.45, δ2 = 0.2Figure 1. Predictions of the Higgs boson massesas a function ofMSUSY in the CMSSM (δ1 = δ2 =0) and NUHM (δ1 6= 0 and/or δ2 6= 0) scenarios.sult in LFV processes that can be mediated by3Higgs bosons we have found that the H0 andA0 contributions are relevant at large tanβ if theHiggs masses are light enough. It is in this aspectwhere the main difference between the two con-sidered scenarios lies. Within the CMSSM, lightHiggs H0 and A0 bosons are only possible forlow MSUSY (here we take MSUSY = M0 = M1/2to reduce the number of input parameters). Incontrast, within the NUHM, light Higgs bosonscan be obtained even at large MSUSY. In Fig. 1it is shown that some specific choices of δ1 andδ2 lead to values of mH0 and mA0 as low as 110-120 GeV, even for heavyMSUSY values above 600GeV. Therefore, the sensitivity to the Higgs sec-tor is higher in the NUHM.We start by presenting 10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 300  350  400  450  500  550  600  650BR (τ → µ P P)M0 = M1/2 (GeV)mN = (1010, 1011, 1014) GeVA0 = 0, tan β = 50, θ2 = 2.9eipi/4δ1 = -2.4, δ2 = 0.2 -τ → µ pi+ pi-τ → µ K+ K-τ → µ K0 K0τ → µ  pi0 pi0 10-12 10-11 10-10 10-9 10-8 10-7 10-6 250  300  350  400  450  500  550  600  650BR (τ → µ P)M0 = M1/2 (GeV)mN = (1010, 1011, 1014) GeVA0 = 0, tan β = 50, θ2 = 2.9eipi/4δ1 = -2.4, δ2 = 0.2τ → µ ρτ → µ piτ → µ ητ → µ η’τ → µ φFigure 2. Present sensitivity to LFV in semilep-tonic τ decays within the NUHM scenario. Thehorizontal lines denote experimental bounds. 10-13 10-12 10-11 10-10 300  400  500  600  700  800  900BR (τ → µ K+ K-)M0 = M1/2 (GeV)mN = (1010, 1011, 1014) GeVA0 = 0, tan β = 50, θi = 0δ1 = -1.8, δ2 = 0TotalPhotonHiggs 10-18 10-16 10-14 10-12 10-10 10-8 10  20  30  40  50BR(τ→ µη)tan βmN = (1010, 1011, 1014) GeVM0 = M1/2 = 250 GeV, A0 = 0θ2    = 2.9eipi/4, θ1 = θ3 = 0δ1 = -2.4, δ2 = 0FullApprox.Higgs.Z bosonFigure 3. Comparison between the various contri-butions to the semileptonic LFV tau decays in theNUHM scenario: BR(τ → µK+K−) plot above,BR(τ → µη) plot below. In this later case, theaproximate result is also shown for comparison.the results for the semileptonic tau decays. Thementioned sensitivity to the Higgs sector withinthe NUHM scenario can be seen in Fig. 2. Con-cretely, the BRs of the channels τ → µK+K−,τ → µK0K¯0, τ → µpi0pi0, τ → µpi, τ → µηand τ → µη′ present a growing behaviour withMSUSY, in the large MSUSY region, due to thecontribution of light Higgs bosons, which is non-decoupling. The decays involving Kaons and ηmesons are particularly sensitive to the Higgscontributions because of their strange quark con-tent, which has a stronger coupling to the Higgsbosons. On the other hand, the largest predictedrates are for τ → µpi+pi− and τ → µρ, dominated4 E. Arganda, M. Herrero, J. Portoles, A. Rodriguez-Sanchez and A.M. Teixeira 10-11 10-10 10-9 10-8 10-7 10-6 120  140  160  180  200  220  240BR (τ → µ η)mA0 (GeV)mN1 = 1010 GeV, mN2 = 1011 GeV250 GeV < MSUSY < 750 GeVθ2 = 2.9eipi/4, δ1 = -2.4, δ2 = 0Approx. (60, 1015)Approx. (50, 3x1014)Approx. (60, 1014)Approx. (50, 1014)Full (tanβ, mN3(GeV)) = (50, 1014)3Figure 4. Sensitivity to Higgs sector in τ → µηdecays.by the photon contribution, which are indeed atthe present experimental reach in the lowMSUSYregion.The comparison between the various contri-butions to the semileptonic LFV tau decays inthe NUHM scenario for BR(τ → µK+K−) andBR(τ → µη) can be seen in Fig. 3. It is clearfrom this figure, that τ → µK+K− is dominatedby the photon contribution, except in the largeMSUSY region , sayMSUSY > 750 GeV, and largetanβ region, say tanβ ≥ 50, where the Higgs bo-son contribution plays an important role. Similarresults are found for τ → µK0K¯0. In contrast, inτ → µpi+pi−, the photon contribution dominanteslargely the rates in all the studied region of theparameter space and therefor it is not sensitive atall to the Higgs sector. In the τ → µpi0pi0 chan-nel, only the Higgs boson contributes, but therates are extremely small. They are indeed muchsmaller that decays into kaons due to the fact thatthe Higgs couplings to the pions are proportionalto m2pi whereas the the Higgs couplings to the pi-ons are proportional to m2K . On the other hand,the τ → µη channel is dominated by the A0 Higgsboson contribution for all MSUSY values, and formoderate and large tanβ, say tanβ > 22. No-tice that for smaller values of tanβ it is, however,dominated by the Z boson contribution.A set of useful formulae for all these channels,within the mass insertion approximation whichare valid at large tanβ, have also being derivedby us in [1]. We include the most relevant of theseaproximate formulas here, for completeness. Theapproximate results for the H0-mediated con-tributions and the γ-mediated contributions areshown separately for comparison,BR(τ → µη)Happrox =1.2× 10−7 |δ32|2(100mA0(GeV))4(tanβ60)6BR(τ → µη′)Happrox =1.5× 10−7 |δ32|2(100mA0(GeV))4(tanβ60)6BR(τ → µpi)Happrox =3.6× 10−10 |δ32|2(100mA0(GeV))4(tanβ60)6BR(τ → µpi0pi0)Happrox =1.3× 10−10 |δ32|2(100mH0(GeV))4(tanβ60)6BR(τ → µpi+pi−)Happrox =2.6× 10−10 |δ32|2(100mH0(GeV))4(tanβ60)6BR(τ → µK+K−)Happrox =2.8× 10−8 |δ32|2(100mH0(GeV))4(tanβ60)6BR(τ → µK0K¯0)Happrox =3.0× 10−8 |δ32|2(100mH0(GeV))4(tanβ60)6BR(τ → µpi+pi−)γapprox =3.7× 10−5 |δ32|2(100MSUSY(GeV))4(tanβ60)2BR(τ → µK+K−)γapprox =3.0× 10−6 |δ32|2(100MSUSY(GeV))4(tanβ60)2BR(τ → µK0K¯0)γapprox =1.8× 10−6 |δ32|2(100MSUSY(GeV))4(tanβ60)2(1)5We have shown that the predictions with theseformulae agree with the full results within a factorof about 2. In the case of τ → µη this compar-ison is shown in Figs. 3 and 4. It is also clear,from Fig. 3 that the approximation works muchbetter in the large tanβ region, tanβ > 22 wherethe H0 boson dominates. Similar conclusions arefound for τ → µη′. The next relevant channel insensitivity to the Higgs sector is τ → µK+K−,but it is still below the present experimentalbound. To our knowledge, there are not experi-mental bounds yet available for τ → µK0K¯0 andτ → µpi0pi0.Finally, the maximum sensitivity to the Higgssector is found for τ → µη and τ → µη′ channels,largely dominated by the A0 boson exchange.Fig. 4 shows that BR(τ → µη) reaches the exper-imental bound for large heaviest neutrino mass,large tanβ, large θi angles and low mA0 . For thechoice of input parameters in this figure, it occursat mN3 = 1015 GeV, tanβ = 60, θ2 = 2.9eipi/4and mA0 = 180 GeV.Next we comment on the results for µ− e con-version in nuclei. Fig. 5 shows our predictions ofthe conversion rates for Titanium as a functionof MSUSY in both CMSSM and NUHM scenar-ios. As in the case of semileptonic tau decays,the sensitivity to the Higgs contribution is onlymanifest in the NUHM scenario. The predictionsfor CR(µ−e, Ti) within the CMSSM scenario arelargely dominated by the photon contribution andpresent a decoupling behaviour at large MSUSY.In this case the present experimental bound isonly reached at lowMSUSY. The perspectives forthe future are much more promising. If the an-nounced sensitivity by PRISM/PRIME of 10−18is finally attained, the full studied range ofMSUSYwill be covered.Fig. 5 also illustrates that within the NUHMscenario the Higgs contribution dominates atlarge MSUSY for light Higgs bosons. The pre-dicted rates are close to the present experimen-tal bound not only in the low MSUSY region butalso for heavy SUSY spectra. As in the previ-ous semileptonic tau decays, we have also founda simple formula for the conversion rates, withinthe mass insertion approximation, which is validat large tanβ [2] and can be used for further anal-ysis. This is dominated by the Higgs H0 contri-bution and is given by,CR(µ− e,Nucleus)|Happrox ≃m5µG2F α3 Z4eff F2p8pi2 Z(Z +N)2∣∣∣g(0)LS∣∣∣2 1Γcapt,g(0)LS =g248pi2G(s,p)Smµmsm2H0δ21(tanβ)3(2)It shows clearly the relevant features: the tan6 βenhacement of the rates, the Higgs mass depen-dence, ∝ 1/m4H0 , and the strange quark mass de-pendence, ∝ m2s. 10-20 10-18 10-16 10-14 10-12 10-10 300  400  500  600  700  800  900  1000CR (µ - e, Ti)M0 = M1/2  (GeV)tan β = 30 ,   A0 = 0mN = (1010, 1011, 1014 ) GeVθi = 0 θ13 = 5 °CRtotalCRγCRZCRHCRbox 10-18 10-16 10-14 10-12 10-10 10-8 300  400  500  600  700  800  900CR (µ - e, Ti)M0 = M1/2 (GeV)mN = (1010, 1011, 1014) GeVA0 = 0, tan β = 50θ13 = 5°, θi = 0δ1 = -1.8, δ2 = 0CRtotalCRγCRZCRHCRboxFigure 5. Predictions of CR(µ − e, Ti) as afunction of MSUSY in the CMSSM (above) andNUHM (below) scenarios.The predictions of the µ − e conversion rates6 E. Arganda, M. Herrero, J. Portoles, A. Rodriguez-Sanchez and A.M. Teixeirafor several nuclei are collected in Fig. 6. We cansee again the growing behaviour with MSUSY inthe largeMSUSY region due to the non-decouplingof the Higgs contributions. At present, themost competitive nucleus for LFV searches is Auwhere, for the choice of input parameters in thisfigure, all the predicted rates are above the exper-imental bound. We have also shown in [2] thatµ−e conversion in nuclei is extremely sensitive toθ13, similarly to µ → eγ and µ → 3e and, there-fore, a future measurement of this mixing anglecan help in the searches of LFV in the µ−e sector. 1e-13 1e-12 1e-11 1e-10 300  400  500  600  700  800  900CR (µ - e, Nuclei)M0 = M1/2  (GeV)mN = (1010, 1011, 1014 ) GeVA0 = 0, tan β = 50θ13 = 5°, θi = 0δ1 = -1.8, δ2 = 0CRexp(Au)CRexp(Ti)SbSrTiAuPbAlFigure 6. Present sensitivity to LFV in µ − econversion for several nuclei within NUHM.In conclusion, we have shown that semileptonictau decays nicely complement the searches forLFV in the τ − µ sector, in addition to τ → µγ.The future prospects for µ − e conversion in Tiare the most promising for LFV searches. Bothprocesses, semileptonic tau decays and µ− e con-version in nuclei are indeed more sensitive to theHiggs sector than τ → 3µ.AcknowledgementsM.J. Herrero would like to thank the organiz-ers of this tau-08 conference for the invitation toparticipate in this interesting and fruitful event.She also acknowledges project FPA2006-05423 ofSpanish MEC for finantial support.REFERENCES1. E. Arganda, M. J. Herrero and J. Portoles,JHEP0806 (2008) 079 [arXiv:0803.2039 [hep-ph]].2. E. Arganda, M. J. Herrero and A. M. Teix-eira, JHEP 0710 (2007) 104 [arXiv:0707.2955[hep-ph]].3. J. A. Casas and A. Ibarra, Nucl. Phys. B 618(2001) 171 [arXiv:hep-ph/0103065].4. S. Weinberg, PhysicaA 96 (1979) 327;J. Gasser and H. Leutwyler, Annals Phys.158 (1984) 142.5. G. Ecker, J. Gasser, A. Pich and E. de Rafael,Nucl. Phys. B 321 (1989) 311;6. Y. Kuno and Y. Okada, Rev. Mod. Phys. 73(2001) 151 [arXiv:hep-ph/9909265].

Lepton Flavour Violation in charged leptons within SUSY-seesaw

Abstract

Similar works

Full text

Available Versions

Crossref

Digital.CSIC