LLIGHT STOP DECAYS
RAMONA GR ¨OBER ∗ INFN, Sezione di Roma Tre, Via della Vasca Navale 84,I-00146 Roma, Italy
If the stop is the next-to-lightest supersymmetric particle (NLSP) and the mass difference tothe neutralino is smaller than the top mass, it can decay via flavour-violating decay modes to c ˜ χ /u ˜ χ or a four-body decay to b ˜ χ f ¯ f (cid:48) , which above the W boson threshold corresponds tothe decay to b ˜ χ W . Improving on existing calculations for these decay modes, we analyse thebranching ratios (BRs) for the respective decays and show that they can significantly deviatefrom one. While the limits for squarks of the first and second generations are pushed already above the 1TeV range, lighter stops are not yet completely excluded. In particular, in the mass range wherethe mass difference to the neutralino is below the top mass, experimental searches are very chal-lenging. In this kinematic region, assuming the neutralino ˜ χ to be the lightest supersymmetricparticle (LSP), the stop can decay via flavour violating decays to c ˜ χ /u ˜ χ or via a four-bodydecay to b ˜ χ f ¯ f (cid:48) , or above the W boson threshold to b ˜ χ W . For the latter decays ATLAS andCMS provide limits in searches for one or two leptons and missing energy , for the four-bodydecays in searches with one isolated lepton, jets and missing energy or in monojet searches and for the decays to c ˜ χ in monojet searches and charm-tagged searches .Branching ratios of the stop in the respective decay channels can often differ from one.Only since recently the experimental collaborations account for that . After discussing flavourviolation (FV) in the minimal supersymmetric extension of the Standard Model (MSSM) insec. 2, the computation of the decay widths and BRs of the aforementioned decays are reviewedin sec. 3. In sec. 4 numerical results are shown and compared to experimental exclusion bounds,before concluding in sec. 5. The MSSM provides many new sources of FV. However, these sources are strongly restricted byflavour experiments. This so-called ”new physics flavour puzzle” can e.g. be solved by MinimalFlavour Violation (MFV) . In MFV the Lagrangian is constructed such that it is formallyinvariant under a flavour SU (3) Q L × SU (3) u R × SU (3) d R symmetry, by promoting the Yukawacouplings to spurions. Hence the only source of FV is restricted to the Yukawa couplings. Evenreduced flavour symmetries can still be in accordance with flavour experiments . In particular,to obtain one lighter stop, we will allow for a smaller soft-SUSY breaking mass m ˜ t R . This willhence reduce the flavour symmetry of the right-handed up sector to SU (2) u R . Furthermore, we ∗ Talk given at the 27th Rencontres de Blois on Particle Physics and Cosmology, May 31 - June 05, 2015. a r X i v : . [ h e p - ph ] S e p m ˜ u − m ˜ χ [GeV]1 . . . . . K U (3)
10 20 40 70 m ˜ u m ˜ [GeV]10 ( b o d y ) / ( b o d y ) | m b = m ⌧ = U (3) Figure 1 –
Left: K factor for the decay ˜ u → c ˜ χ . Right:
The four-body decay width in full mass dependence Γ(4-body) divided by the decay width where the third generation fermion masses are set to zero Γ(4-body) | m b =0 ,m τ =0 . distinguish between two cases, namely whether the SU (3) Q L flavour symmetry is reduced to a SU (2) Q L or not (dubbed with U (2) or U (3), respectively). Note that even if at one scale themixing matrix of the squarks is chosen flavour diagonal, this does not hold true at any otherscale. Renormalisation group running induces FV at any other scale. For further reference, weassume that the lightest mass eigenstate ˜ u is mainly stop-like and hence call it stop, but havingin mind that it is an admixture of all flavour eigenstates. For flavour universal couplings at the Planck scale Λ
P lanck the dominant logarithmic termslog Λ
P lanck /m W with m W denoting the W boson mass for the stop decay to c ˜ χ /u ˜ χ have beenfirst computed in . In a full one-loop computation of the decay was done under the assumptionof no FV at tree-level. This computation is hence restricted to the scale at which the couplingsare flavour universal. In (see also ), the SUSY QCD corrections to the decay widths Γ c ˜ χ and Γ u ˜ χ allowing for a FV coupling at tree-level were computed. The result for the K factor,defined as K = Γ NLO / Γ LO , is displayed in Fig. 1 (left panel). ˜ u → d i ˜ χ f ¯ f (cid:48) The four-body decays to b ˜ χ f ¯ f (cid:48) have been computed for the first time in . In this computationwas updated by including the mass dependence of the third generation fermions in the finalstates and by including FV, hence allowing in general for a final state d i ˜ χ f ¯ f (cid:48) , where d i denotesa down-type quark. The effect of including the mass dependence on the final state bottom quarkand τ lepton is depicted in Fig. 1 (right panel). ˜ u → d i ˜ χ W If the mass difference between stop and neutralino m ˜ u − m ˜ χ becomes larger than the W bosonmass, the stop can decay via a three-body decay to d i ˜ χ W . The three-body decay width to b ˜ χ W has been computed in . In this was extended allowing for FV. In addition, off-shelleffects were considered by incorporating a W boson width into the four-body decay width of .In Fig. 2 the impact of these off-shell effects is shown. It can be inferred that for mass differencesbetween stop and neutralino up to m W + 30 GeV the off-shell effects can be quite important. m ˜ u − m ˜ χ [GeV]0 . . . . . . Γ − b o d y / Γ − b o d y
200 250 300 350 400 450 500 550 m ˜ u [GeV]150200250300350400450500550 m ˜ χ [ G e V ] m ˜ u − m ˜ χ < G e V m ˜ u − m ˜ χ > G e V . . . . . . . . . . B R ( − b o d y ) Figure 2 –
Left:
Four-body decay width divided by three-body decay width for the stop decays to d i ˜ χ W ( ∗ ) . Right:
Scan over parameter space around the W boson threshold. The color code indicates the size of the BRinto the FV two-body decays. In order to investigate the viable parameter space for light stops, a scan was performed. TheSUSY spectrum has been generated by
SPHENO . Viability with Higgs data was checked bymeans of the codes HiggsSignals and HiggsBounds , with the Higgs BRs and effectivevertices obtained from HDECAY . With SuperIsoRelic we checked several flavour observablesand that the relic density is not too large. The masses of the sparticles were chosen such thatthey escape the direct bounds of ATLAS and CMS. For m ˜ u − m ˜ χ < m W we scaled down theexclusion limits by the BRs and combined the different decay modes assuming that the BRsadd up to one. Above the W boson threshold we checked the exclusion limits for the decays to b ˜ χ W by means of the code SModelS . Limits for the decays into c ˜ χ above the W thresholddo not exist so far.In Fig. 2 (right panel) a scan for the U (2) flavour assumption is shown for mass differencesbetween stop and neutralino around the W boson threshold. Apparently, even above the W boson threshold the stop can still have a sizeable BR into c ˜ χ .In Fig. 3 a scan restricted to m ˜ u − m ˜ χ < m W is shown. Two different flavour implemen-tations are displayed, see sec. 2. If more FV is allowed the decay into c ˜ χ dominates, whereasfor less FV the four-body decays dominate for mass differences larger than 15 GeV. There arealso points where the stop has sizeable BRs in both decay channels, such that the experimen-tal exclusion limits are reduced. Experimental exclusion bounds in terms of BRs are useful tocompare to theory, a first attempt has been started in . We have improved on the computation of the light stop decays by calculating SQCD correctionsto the decays into c ˜ χ /u ˜ χ , inclusion of the mass dependence of third generation fermions inthe four-body decays d i ˜ χ f ¯ f (cid:48) and the off-shell effects for the three-body decays to d i ˜ χ W . Allof these decays were implemented into SUSYHIT allowing for general FV. A numerical analysisshowed that BRs of the stop can significantly deviate from one, which lowers the experimentalexclusion limits. For stop-neutralino mass differences larger than the W boson mass, it shouldbe considered in the experimental analyses that there can be sizeable BRs to c ˜ χ .
50 200 250 300 350 400 450 500 550 m ˜ u [GeV]150200250300350400450500550 m ˜ χ [ G e V ] m ˜ u < m ˜ χ + m c m ˜ u > m ˜ χ + m W + m b U (2) 0 . . . . . . . . . . . B R ( − b o d y )
150 200 250 300 350 400 450 500 550 m ˜ u [GeV]150200250300350400450500550 m ˜ χ [ G e V ] m ˜ u < m ˜ χ + m c m ˜ u > m ˜ χ + m W + m b U (3) 0 . . . . . . . . . . . B R ( − b o d y ) Figure 3 – Scan over the parameter space for different flavour assumptions. The color code indicates the BR intothe FV decay modes.
I am grateful to M. M¨uhlleitner, E. Popenda and A.Wlotzka for the fruitful collaboration andthe organisers for a pleasant and stimulating atmosphere during the 27th Rencontres de Blois.1. G. Aad et al. [ATLAS Collaboration], JHEP (2014) 124 [arXiv:1403.4853]; S. Cha-trchyan et al. [CMS Collaboration], Eur. Phys. J. C (2013) 12, 2677 [arXiv:1308.1586].2. G. Aad et al. [ATLAS Collaboration], JHEP (2014) 118 [arXiv:1407.0583].3. G. Aad et al. [ATLAS Collaboration], Phys. Rev. D (2014) 5, 052008 [arXiv:1407.0608].4. G. Aad et al. [ATLAS Collaboration], [arXiv:1506.08616].5. G. D’Ambrosio, G. F. Giudice, G. Isidori and A. Strumia, Nucl. Phys. B (2002) 155[hep-ph/0207036].6. R. Barbieri, D. Buttazzo, F. Sala and D. M. Straub, JHEP (2012) 040[arXiv:1206.1327].7. K. i. Hikasa and M. Kobayashi, Phys. Rev. D (1987) 724.8. M. Muhlleitner and E. Popenda, JHEP (2011) 095 [arXiv:1102.5712].9. R. Grober, M. Muhlleitner, E. Popenda and A. Wlotzka, Eur. Phys. J. C (2015) 9, 420[arXiv:1408.4662].10. J. Aebischer, A. Crivellin and C. Greub, Phys. Rev. D (2015) 3, 35010 [arXiv:1410.8459].11. C. Boehm, A. Djouadi and Y. Mambrini, Phys. Rev. D (2000) 095006 [hep-ph/9907428].12. W. Porod and T. Wohrmann, Phys. Rev. D (1997) 2907 [Phys. Rev. D (2003)059902] [hep-ph/9608472]; W. Porod, Phys. Rev. D (1999) 095009 [hep-ph/9812230];A. Djouadi and Y. Mambrini, Phys. Rev. D (2001) 115005 [hep-ph/0011364].13. R. Grober, M. Muhlleitner, E. Popenda and A. Wlotzka, Phys. Lett. B (2015) 144[arXiv:1502.05935].14. W. Porod, Comput. Phys. Commun. (2003) 275 [hep-ph/0301101]; W. Porod andF. Staub, Comput. Phys. Commun. (2012) 2458 [arXiv:1104.1573].15. P. Bechtle et al. Eur. Phys. J. C (2014) 2, 2711 [arXiv:1305.1933].16. P. Bechtle et al. Comput. Phys. Commun. (2010) 138 [arXiv:0811.4169]; P. Bechtle et al.
Eur. Phys. J. C (2014) 3, 2693 [arXiv:1311.0055].17. A. Djouadi, J. Kalinowski and M. Spira, Comput. Phys. Commun. (1998) 56 [hep-ph/9704448]; J. M. Butterworth et al. , [arXiv:1003.1643].18. S. Kraml et al. Eur. Phys. J. C (2014) 2868 [arXiv:1312.4175].19. A. Arbey and F. Mahmoudi, Comput. Phys. Commun. (2010) 1277 [arXiv:0906.0369].20. A. Djouadi, M. M. Muhlleitner and M. Spira, Acta Phys. Polon. B38