Split SUSY and the LHC

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1 Split SUSY and the LHC Pietro Slavich LAPTH Annecy IFAE 2006, Pavia, April 19-21

2 Why Split Supersymmetry SUSY with light (scalar and fermionic) superpartners provides a technical solution to the electroweak hierarchy problem (why is m 2 H M 2 P???) Two bonuses come with light fermionic superpartners: + Improved gauge coupling unification; + The lightest neutralino is a natural candidate for dark matter;...but light scalar superpartners bring along several problems: Quite light Higgs boson mass (tension with LEP searches); New sources of flavour and CP violation; New contributions to SM precision observables; Fast proton decay from dimension-five operators. Also, hierarchy and fine tuning don t want to go away: the cosmological constant problem still has to be solved (why is Λ M 4 P???)

3 Why Split Supersymmetry (II) An approach to the cosmological constant problem comes in the string landscape: in theories with a large ( ) number of metastable vacua, we must find ourselves in those where Λ has the right (small) value to allow for structure formation Maybe the electroweak hierarchy problem too is solved by a similar selection principle, and we do not need to worry about the fine tuning in the Higgs mass Scalar superpartners are needed to be light only to avoid fine tuning. If we accept them to be heavy, we can retain the advantages of weak-scale SUSY and get rid of all its disadvantages In Split SUSY all the scalars but the SM Higgs are much heavier than the weak scale ( em = GeV), while gaugino and higgsino masses are protected by symmetries and are of O( GeV)

4 The Effective Lagrangian of Split SUSY L m 2 H H λ 2» 2 H H h u ij q ju i ɛh + h d ij q jd i H + h e l ij j e i H + M 3 2 ga g A + M 2 2 W a W a + M 1 2 B B + µ H T u ɛ H d + H g u σ a W a + g B u Hu + HT ɛ g d σ a W B a + g d Hd + h.c. 2 2 «1 + O em 2 Finely tuned SM like Higgs doublet: H = cos βɛh d + sin βh u Boundary conditions at the scale em: λ( em) = 1 4 ˆg2 ( em) + g 2 ( em) cos 2 2β h u ij ( em) = λu ij ( em) sin β, hd,e ij ( em) = λd,e ij ( em) cos β g u ( em) = g( em) sin β, g d ( em) = g( em) cos β, g u ( em) = g ( em) sin β, g d ( em) = g ( em) cos β

5 Prediction for the light Higgs boson mass M t = 178 ± 4.3 GeV, tan β = 1.5, 50 [picture from Giudice and Romanino, NPB699 (2004) 65]

6 Unification of gauge couplings MSSM Split SUSY ( em = 10 9 GeV) Coming in complete SU(5) multiplets, the sfermions do not affect unification [pictures from Arkani-Hamed and Dimopoulos, JHEP06 (2005) 073]

7 Charginos and Neutralinos in Split SUSY The mass matrices depend on the effective Higgs higgsino gaugino couplings: M 1 0 g M + M d v/ 2 g u v/ 2 2 g u v A 0 M 2 g d v/ 2 g u v/ 2 M 0 = g d v µ g d v/ 2 g d v/ 2 0 µ C g u v/ 2 g u v/ A 2 µ 0 The lightest neutralino remains a viable candidate for Dark Matter Light charginos and neutralinos may improve the precision EW fit (Martin et al.) They might also give sizeable two-loop contributions to electron and neutron dipole moments, visible at the next generation experiments (Giudice and Romanino) With heavy sfermions, charginos and neutralinos are difficult to detect at the LHC The chargino loop contribution to H γγ is also below the sensitivity of LHC

8 Gluino decays in Split SUSY The LHC may be a gluino factory: gluinos/fb 1 for m g = GeV Gluinos decay only through the exchange of the heavy virtual squarks, thus they can be extremely long lived ( displaced vertices, heavy muons, delayed decays) Since τ g em 4 /m5 g, a measurement of the gluino lifetime would provide us with a direct determination of the large SUSY breaking scale em The allowed gluino decay modes are g χ 0 q q, g χ ± q q and g χ 0 g The radiative corrections to the gluino decay processes are enhanced by powers of the potentially large log( em/m g ) For a precise theoretical prediction of the gluino lifetime and branching ratios the large logarithms must be resummed to all orders with the usual RG techniques

9 Effective Lagrangian for Gluino decays We integrate out the squarks and get a set of effective operators: g g q g q q χ q χ χ g g g χ The effective Lagrangian of Split SUSY contains: L 1 em 2 7X i=1 C e B i Q e B i + 1 em 2 2X i=1 C f W i Q f W i + 1 em 2 5X i=1 C e H i Q e H i + h.c.! Now we need to compute [see Gambino, Giudice and Slavich, NPB726 (2005) 35]: High energy matching conditions: C χ i ( em) =... Anomalous dimensions: γ χ ij =... Low-energy Wilson coefficients: C χ i (m g) =... Partial decay widths: Γ xy =...

10 Effect of resummation on the partial decay widths χ 0 g χ 0 q q χ ± q q 1.5 Γ / Γ m ~ (GeV)

11 Gluino lifetime vs squark mass τ g (sec) m g = 0.5 TeV m g = 1 TeV m g = 2 TeV m g = 5 TeV m ~ (GeV)

12 4 5 factoring out the leading dependence on em: τ g = 4 sec N em 10 9 GeV 1 TeV m g 5 4 with resummation without resummation 3 N m ~ (GeV) m g = (500, 1000, 2000) GeV

13 10 18 Limit on the SUSY scale from gluino cosmology SUSY Breaking Scale GeV Collider Run II Heavy Hydrogen Diffuse Γ ray CMBR BBN LHC Gluino Mass GeV [picture from Arvanitaki et al., PRD72 (2005) ]

14 Gluino signatures at the LHC Gluinos will be produced in pairs through quark-quark or gluon-gluon fusion As long as τ g 1/Λ QCD s, which roughly happens for em 10 3 GeV, gluinos hadronize in the detector before decaying For s τ g 10 7 s, which roughly happens for 10 6 GeV em 10 7 GeV, gluinos decay inside the detector but give rise to displaced vertices For τ g 10 7 s gluinos either escape the detector or are stopped and decay later A gluino pair produced near threshold might form a bound g g state (gluinonium), which may annihilate in a t t pair with large p T (however, large backgrounds) Otherwise, stable R hadrons containing gluinos come in different varieties: R g = g g, R mesons = g q q, R baryons = g q q q

15 Signatures of R-hadrons in ATLAS (Kraan et al., hep-ex/ ) Charged R hadron Neutral R hadron Inner detector High pt track Hits in TRT (possibly HT! ) No track (unless charge changing nuclear interaction) Energy deposit Calorimeters Repeated charge exchange Conversion meson to baryon Punch through Stopped Absorbed in Calo.!! Muon Chambers Charged R hadron Neutral R hadron Track in muon chambers Possibly β 1 No track

16 iscovery reach for R-hadrons with ATLAS (Kraan et al., hep-ex/ ) Mass Selected background (1 fb 1 ) (GeV) QCD b b t t W Z WW/ WZ/ZZ Selected signal (1 fb 1 ) S/ B (1 fb 1 ) S/ B (30 fb 1 )

17 Stopped gluinos In one year of high-luminosity (100 fb 1 ) running, gluinos stop in both ATLAS and CMS for 300 GeV < m g < 1300 GeV [Arvanitaki et al., hep-ph/ ] Late gluino decays will induce events out of place with respect to the interaction region and out of time with respect to the bunch crossings They may produce jets in the hadronic calorimeter without accompanying signals in the electromagnetic calorimeter or in the tracking chambers In events where both gluinos produced in pair are stopped in the detector, the average time between the two decays can be used to measure the gluino lifetime If the gluino lifetime is longer than a few years, exotic heavy nuclei might even be found in the detector or in the surrounding material when the LHC is dismantled

18 Conclusions At the price of giving up the solution to the electroweak hierarchy problem, Split SUSY gets rid of the nuisances of the MSSM and retains its advantages In Split SUSY charginos and neutralinos can give contributions to precision observables, but their direct detection at the LHC is difficult In Split SUSY gluinos are the only new particles copiously produced at the LHC. They are long lived and can give rise to spectacular signatures Gluino decays provide direct information on the SUSY scale em, and their theoretical prediction must take into account large radiative corrections Long-lived gluinos are the trademark for Split SUSY. Their discovery at the LHC, in the absence of sfermions, would lead us to rethink our current understanding of fine tuning and the hierarchy problem