JHEP06(2015)122 . ˜ u m Springer June 3, 2015 . The most June 17, 2015 , April 20, 2015 : 1 : : − Accepted Received Published c 10.1007/JHEP06(2015)122 doi: Published for SISSA by [email protected] , and Michael Spannowsky b . 3 Alberto Mariotti a 1504.00927 The Authors. c Phenomenology

Supersymmetric extensions of the with highly mixed squark , [email protected] and International Solvay Institutes, PleinlaanInstitute 2, for B-1050 Brussels, PhysicsDurham Belgium Phenomenology, University, Department Durham of DH1 Physics, 3LE,E-mail: U.K. [email protected] Center for Cosmology, ParticleUniversite Physics Catholique and de Phenomenology Louvain, — Louvain-la-neuve, CP3, Theoretische Belgium Natuurkunde and IIHE/ELEM, Vrije Universiteit Brussel, b c a Open Access Article funded by SCOAP be also probed to comparable squark masses at highKeywords: luminosity LHC14. ArXiv ePrint: the flavour physics constraints onthat scenarios such with models. maximal In squarksignatures a flavour at mixing simplified the result model LHC. in950 approach, GeV interesting we in We phenomenological show show the that single-topdistinctive the event signature topology of model at highly can LHC14 mixed be with scenarios, probed as the up little same to sign as masses positive 300 fb of charge di-top, can Abstract: flavours beyond minimalwhich flavour have violation so provide farscenarios interesting received in limited scenarios models attention. of of Wemessengers new gauge and propose mediation the physics, a up augmented type calculable with squark. realization an We compute of extra the such interaction supersymmetric spectrum between and the analyze Mihailo Backovi´c, Signs of tops from highly mixed stops JHEP06(2015)122 = 14 TeV, and s √ 26 14 19 – 1 – 4 19 16 ]. At the dawn of the LHC Run II at 3 22 6 3 – 1 19 14 12 14 11 11 1 24 As an example of scenarios which were previously less studied, one could consider 5.1 Event generation5.2 and reconstruction Single-top channel 5.3 Same sign top channel 3.2 Benchmark points 4.1 Production4.2 modes and cross Constraints sections from LHC8 2.1 Low energy2.2 constraints Extended gauge2.3 mediation Mass spectrum 3.1 Branching ratios relaxing the minimal flavour violation (MFV) assumptionoption on SUSY for models. non-standard One interesting SUSYsquark flavours. beyond The MFV immediate benefit involvesbranching of ratios considerations scenarios of where of squark squark decays mixing mixing into is between final allowed states is predicted that by standard SUSY models are the Standard Model (MSSM). Yet,models the spectrum has of not non-standardstandard supersymmetric been (SUSY) SUSY studied are in weakerwith [ full the prospects detail, for the while futureimposed high the in luminosity studies current LHC, of it the data is MSSMhave important parameter been constraints to space, overlooked revisit on and and/or constraints to non- could explore be if some accessed viable through realizations new types of collider signatures. 1 Introduction Recent results from the Largeof supersymmetry Collider (LHC) and impose considerably stringent limits constrain on the the minimal scale supersymmetric extension of 6 Conclusions A Soft terms from R-symmetric hidden sector 5 Top signatures at LHC14 4 Collider signatures 3 Simplified model Contents 1 Introduction 2 The model formulation JHEP06(2015)122 . 1 ˜ u m ] or in R- 45 ]. Same sign up to – 33 1 43 – − 28 we define a simplified 3 ]. However, in the latter 47 , 46 ], for instance with the purposes 27 – ]. In the context of supersymmetry, we present the model setup and we 11 2 42 , 41 – 2 – ]. 10 – 6 problem, of raising the Higgs mass and/or investigating their µ B − µ ], or in composite models [ 40 – 34 we discuss its main production modes at collider and the constraint on the model 4 The paper is organized as follows: in section We define a simplified model for LHC searches that consists only of the (that We study in detail the reach of LHC14 for the case where the light squark is maximally In this paper we investigate the possibility that the low energy part of the supersym- explore the relevant parameter space, identifying thepossible phenomenologically benchmark viable points. regions and On themodel basis for of collider this studies, analysis, withsection in a section light and maximally mixed sup-stop squark (MMUT). In (mostly Bino).show Considering that benchmark the points not single950 yet top GeV excluded signal in by can the LHC8,stop aforementioned be we channels. mixing, discovered (i.e. at The LHC14 same moremissing energy, distinctive with sign can signature 300 be tops), fb of probed leadinga at sizeable eventually High concrete sup- Luminosity to proposal LHC14. to same Our test sign collider the analysis positive mixing represents property of plus the light squark in the next LHC runs. an initial state of two upof . the In single the top context ofhence signature R-parity be in preserving a MSSM, association the robust with presence hint the of same large sign squark positive mixing. we top fix signature representatively at would 2 TeV), the maximally mixed sup-stop right-type squark and the same-sign top final statesparity can preserving arise theories either throughcase in a we R-parity gluino expect violating decay asign chain models roughly negative [ top equivalent [ pairs. number of Instead,contribution in same at scenarios the sign with LHC positive large will sup-stop top be mixing, dominantly pairs the of and same-sign positive top of charge, since same it is obtained through peculiar to atop scenario production. with maximal Thesescenarios. stop-sup signatures mixing, The have single already i.e. top beentops single signatures have investigated been top have in studied been and in several studiedasymmetry new same new for physics [ sign instance physics models in attempting di- to [ explain the forward backward been recently studied inof several different addressing contexts the [ possibly unusual flavor patterns. mixed between top- and up-type squark. We focus on the collider signatures which are metric spectrum is characterizedflavour by between a stop single and (rightrealization handed) up-squark of light or such squark, stop scenarios highly andwith in mixed an scharm-squark. a in extra simple We interaction extension propose betweenWe of the study an gauge messengers the explicit mediated and constraint thequirement models, imposed of right augmented a up on viable type such Higgs models mass. superfield. by A flavour similar observables extension and of the by gauge the mediation re- scheme has results, particularly from flavourand physics, second give generation strong constraints squarks,remains on while relatively mixing mixing unconstrained. between between first have Several third recently scenarios and been of first/second discussed SUSY generations in models refs. [ with squark mixing lowered, hence weakening the experimental bounds on the stop mass. Current experimental JHEP06(2015)122 12 ) (2.1) RR u δ or the distinctive T / E ]. ! 49 LR RR u u δ δ ]. ]) is one of the most interesting 2 48 LL RL u u δ δ

= u δ ]. However, the EDM processes also . ) – 3 – 51 23 u ) δ + RR u δ 6 × 6 mixing, which bounds the absolute value of the ( I signature. We show the reach of LHC14 for these final or ( 3 matrix which is determined by the soft mass of the up- ( 0 ]. Apart from this bound, low energy observables do not 2 T ¯ 13 × D m ) / E parameterise the deviations from flavour alignment. We are 50 − , = ˜ RR u 0 u we study in detail the LHC14 signals of the simplified model δ 49 δ D is a 3 5 M ij ) . The most relevant constraint on the mass matrix is obtained through RR u ij δ ) ˜ 2 u m The matrix ( Another possibly relevant constraint to keep into account for the 1-3 mixing is given by The up-type squark mass matrix in the superCKM basis can be written as The flavour bounds in the MSSM can be analysed in a model independent way by the neutron electric dipole momentsymmetry (EDM). breaking Even parameters, in a the small case deviationto of of the no the CP identity soft phases terms matrix in fromCKM can the being basis. super- induce proportional some The extraconstraints strict CP on experimental violating the bounds effect allowed on once mass the we spectra rotate neutron [ into EDM the can lead to stringent type squark ( the measurement of the to be smaller thanindependently 0.05 constrain ( [ where the dimensionless interested in flavour mixing showingmatrix, up since in they the are right-right less part constrained of by the flavour up-type physics squark [ mass review the constraints on thewhile up-type squark for mass a matrix more that comprehensive are review relevant in we our refer analysis, the reader to [ way, by modifying the structureframework of for supersymmetric the models soft with terms.with large mixing one Our in purpose light the is squark rightfirst to squark eigenstate. and up provide the sector, a In third and predictive particular generation. we will focusconstraining on the RR mixing structure between of the the supersymmetry breaking parameters. Here we briefly terms and more generally on theto mechanisms the of MSSM. supersymmetry In breaking this andpossibilities, context, its since gauge mediation mediation it (see provides e.g. aing [ for predictive the and constraints computable from flavour frameworkmediation physics. while involving In accommodat- extra this interactions paper we that consider break an the extension of flavour gauge degeneracy in a controllable 2.1 Low energy constraints In the minimal supersymmetric extensionmetry of breaking the parameters Standard Modelviolation. (the (MSSM), Hence, soft the low energy supersym- terms) observables put can strong constraints be on generic the structure sources of the of soft flavour and CP MMUT, i.e. processes withsame a sign single positive top topstates quark with on and some missing representative benchmark energy points of the MMUT model. 2 The model formulation from LHC8. In section JHEP06(2015)122 (2.2) ]. An 27 – In addition, 16 ], where also , 1 11 14 – 11 sets the overall size λ ¯ 5 + 5 that we denote in the framework of extension , ) ij = 1, while ) ,D ˜ 2 u 3 2 ¯ 5 c m 2( ¯ 5 messengers with the same quantum + φ ) 2 2 c ,D ¯ 5 + 1( 1 2 φ c i ]) includes messenger fields charged under the U p i – 4 – c 48 3 =1 i X λ = δW runs here on the flavour index. Hence the interaction is not diagonal i . We take the normalization ). We assume that the component of the } 2 3 ˜ φ , c , 2 1 ˜ φ , c , 1 2 ], since it has a generic flavor pattern. Moreover, contrary to most models considered c The model we consider consists of a pair of messengers in the Here we focus on a specific superpotential interaction involving messenger fields and This class of models has recently been studied in several papers [ In the following we provide a computable model which induces large off diagonal con- { Another interesting aspect of these deformations, which we do not exploit here, is that they could also , φ 11 1 1 = φ where the index in flavor, and can induce non-trivial flavor mixing, depending on the values ofinduce the large A-terms. vector ( numbers of right handed downtial quark couplings interact with the up type quarks via the superpoten- other MSSM-messenger couplings and avoidsdiagonal the A-terms problematic which issue are of genericallyoff-diagonal strongly generating bounded large A-terms by off- low could energy alsoSUSY observables. spectrum, lead Large as to we other will discuss problematic in issues the in following. the evolution of the the right handed type squarks,the since right we up squark aim mass forin matrix. the [ possibility For this of reason inducing ourin large model mixing the differs in from literature, the it one considered also respects a discrete R symmetry. This motivates the absence of automatically diagonal in flavour space,of and flavour hence violation, they which are canthe normally represent set controllable absent of in sources possible standard gauge extraof mediation. interactions unified involving gauge the group) messengersthe and (in complete complete the formulas representation SM for the induced fields soft have masses been have classified been in computed. [ tion of gauge mediation (forSM a gauge review groups. see [ Itcouple is directly to then SM natural matterinteractions to fields. in explore turn Extending the induces gauge possibility mediation extra that with contributions the extra to superpotential the messengers soft could interesting terms. aspect of the above mentioned superpotential deformations is that they are not We proceed to definemediated a supersymmetry class of breaking. modelsmodated with Scenarios by large with extensions squark of largeinteractions mixing among gauge in squark the the mediated mixing messengers context and models can of some augmented be gauge superfield with of accom- the extra MSSM. superpotential The typical realiza- RR mixing and (diagonal or off diagonal) large LRtribution mixing. only to the RRof up-type squark gauge mass mediation, matrix and ( which is compatible with2.2 flavour constraints. Extended gauge mediation involve L-R mixing, hence they can be relevant only in the combined presence of large 1-3 ~c JHEP06(2015)122 , i ) ]) φ ,L 52 ¯ 5 = 4. (2.4) (2.5) (2.3) ( , 2 3 φ ) deforma- ,C 2 ,D 4 . It can be λ ¯ 5 Λ M 1( = 0 A . This implies  2 ,L 1 Qφ d ¯ 5 messengers is Λ M -symmetry under ,C 5 R  ,H 1 / h u sets the energy scale 4 2 Z , λ ) = 2 . The gauge mediation M ij 1 Q, H c 1 ˜ φ F M 2 symmetry under which 2 ) in appendix C π U x φ symmetry of the messengers, 2  ( d 2 Z 48 h + Λ M Z 2 0 = 4, . − ˜ φ  2 1 φ s 1 U, D, E φ f d Λ ( 2  Y 2 r 2 2Λ 2 ˜ g ) is the only one compatible with these φ r  4 ) + r C 2.2 2 g 2 3 ˜ , ˜ 0 f φ r φ = 2 and 2 C =1 X φ . The messenger scale r U – 5 – term. 1 d r 2 ) adds to the usual MSSM superpotential which F + 0 ). ˜ φ X 2 , µ 4 1 − θ j 2 2 ˜ x 2.2 -symmetry charge assignment. φ c 2 ) ( φ i 1 1 2 R = c d Λ 2 φ O )Λ φ π 2 2 4 ( . The soft masses for this model are obtained in the λ Y ij -terms cannot be generated by this sector and by the = Z + ) λ M  .c.y (16 . A 2 2 † ij Y U x c y = d = .c.y 4 5 , consisting of a two loop contribution (which can be positive † 2 ˜ 2 f ij y λ Tr( c ( ij m 2 -pres 4 4 2 c Table 1 λ R π π λ 4 ). The contribution to the soft masses induced by the U 4 π U W d ) = 1 + has charge 2, with the other charges reported in table 1 d x 256 256 3 x ( ( 256 Y − − O h R-symmetry = = = + 4 . 2 j u ij 36 x Z λ U 2 H i Q 2 , here we report simply the results, defining Λ = ) is the usual minimal gauge mediation function for (see e.g. [ 2 U m m x A ( m s are odd, implies that the deformation ( f i ˜ φ The up type right squark gets off diagonal contributions whose flavour structure is The boundary conditions induced at the messenger scale by this SUSY breaking sector The discrete R-symmetry, together with a messenger The supersymmetry breaking superpotential for the two pairs of 5 + ) = 1 + x ( s where we defined theWe matrix give the complete expressionapproximated by for the one loop function determined by the matrix includes gauge mediated contributionsbecause to of the the scalarappendix new masses and interaction the contribution arising and discrete simmetries and with gaugetogether invariance. Indeed with the gauge invariance,which would is allow forbidden only by the for discrete the R-symmetry extra in coupling table where f tion are with the SUSY breakingwhere spurion the soft masseswhich are the generated. spurion Note thatthat there is masses adeformation residual and also contribution is of CP violation. Theincludes superpotential the Yukawa ( couplings and the of the deformation. We take all couplings to be real, in order to not introduce sources JHEP06(2015)122 , 1 M 58 (2.6) , the M . In particular ij y symmetry implies that ]. R 56 . 2 S Λ ] and generated the spectrum and 4 r g ˜ f r 54 , C ]. We also computed the contribution 53 deformation. Indeed, large off diagonal A- r 55 . Besides the up-type squark, the rest of X λ . G of the deformation. In the left plot of figure Λ S 2 M Λ 2 ) ~c 2 2 – 6 – 2 ) and a one-loop negative contribution, which r π π 2 g λ and Λ and varying the messenger mass 16 and Λ (16 ). S G = = 2.6 r ) plane. The points respecting flavour constraints are ,Λ ˜ g 2 f mixing arises through hadronic long-distance physics [ G ), ( M m 0 /M D Λ 2.5 λ, ), ( , that would have implied otherwise strong bounds from flavor ij 2.4 Q m , and the flavour direction λ ] and are summarized in table 57 mixing, which is sensitive to the mixing between the first and second generation 0 In order to establish general low energy physics constraints on the model, we performed As a large contribution to We explored the parameter space of this model and the implication for flavor observ- In summary, the total contribution to the soft masses in the complete model is given In order to induce non vanishing gaugino masses and sizable scalar masses we consider Moreover, the fact that the hidden sector respects a discrete D ], which is plagued by large theoretical uncertainties, for the limit setting we only impose a scan by fixingdeformation size the values ofwe show Λ the resultshown in as the circular ( dots, while the crosses are points violating flavour observables. The red squarks, and the neutron EDM, using the SUSYFLAVOR code59 [ an upper bound, i.e. itsThe measured flavour central observables value, on that the wetaken short-distance checked, from SUSY together [ contributions. with the bounds that we applied, were by adding expressions ( ables. We implementedcompute the the model flavor in observables SARAHto using [ SPheno [ For simplicity we assume that suchas contribution above, is which induced hence at sets the the same range messenger of scale scales of the renormalisation group (RG) flow. sector inducing general gaugeSUSY breaking mediation scales, contribution, respectively with Λ different gaugino and scalar incompatible with the actualabsence of value of A-terms the impliesconsider at that light least in quark one order masses. stop to to be On get quite the the heavy. also correct other in Higgs hand, addition mass the to we the will previous have SUSY to breaking sector another supersymmetry breaking we have not generatedlarge any off-diagonal A-term. contributions induced by This the terms is would a have raised welcome two featurethe problematic first in issues. generation perspective First, can lead large ofde to off possible large facto diagonal neutron A-term excluding EDM, involving above theterms, the model, current together experimental as with bound, we gaugino previously masses, mentioned. induces corrections Second, to large off masses diagonal which A- can be can be relevant forthe not soft too masses contributions smallthe are values contribution determined of to by theobservables, is Yukawa couplings projected along the Yukawa couplings. or negative depending on the value of JHEP06(2015)122 )), which 2.5 5 TeV. The Higgs Tool . SPheno SPheno SPheno SPheno SPheno SPheno SPheno SPheno SPheno SPheno SPheno SPheno (see eq. ( the negative one loop ij SUSYFLAVOR SUSYFLAVOR 2 U /M m ] ] ] ] ] ] ] ] ] ] 60 60 60 60 60 60 60 60 60 60 ] ] ] ] 61 61 62 63 . In particular the final spectrum [ [ [ [ Source /M HFAG [ HFAG [ HFAG [ HFAG [ HFAG [ HFAG [ HFAG [ HFAG [ HFAG [ HFAG [ , as we explain now. ~c at the messenger scale. The allowed region , and the spectrum is rejected. Indeed, the , because it determines how large is the one ij GeV ~c 2 U (e cm) 15 /M m – 7 – − 26 − 10 10 and large ratio Λ × × λ [0.84, 1.16] [0.87, 1.08] [0.90, 1.06] [0.90, 1.17] [0.85, 1.13] [0.95, 1.01] [0.95, 1.03] [0.99, 1.01] [0.12, 1.87] [0.68, 1.34] 82 9 . [0.875, 1.125] [0.997, 1.003] . Imposed limit 8 2 ≤ ≤ | n d | ) ) ) ) ) ) SM SM ) ) SM SM SM SM ) SM γ SM ) ) ) ) ) ) ) s γ µν µµ µµ SM SM µν µν SM s d s ) sµµ ) X D µν µµ µµ ) Kµµ µν K µν SM → → → s B d B sµµ → → X Kµµ ) s → 0 0 K d s K → → → → B B → M → → M  M M D K s → 0 0 d s K → D B B B → B ( M ( B  M ∆ M ( ( ( ( D K ( ∆ ∆ ( D B ∆ B B ( B . Flavour bounds imposed during the scan on the model parameter space. ( ( B ( ( ( ( ( ( (∆ (∆ (∆ BR BR BR BR BR BR BR BR BR BR BR BR BR BR BR BR is determined by the fact that for large values of Λ 1 Neutron EDM Flavour Observable Table 2 . Since we are marginalizing over the flavour direction, there are overlapping points The main effect of the deformation is on the mass squared S is very sensitive to theloop value negative of contribution to the the ratio softin Λ mass figure contribution to the up-typetachionic squark the mass squark (independently eigenstate on aligned the flavour with direction) renders bounds. However the plot isthe useful soft in spectrum, order independently to on understand the the direction effect of the deformationcan on be negative (or veryEW small) scale, in at the the region messenger of moderate scale and hence positive but small at the points are scenarios wheremass the is lightest correct (within up the type errors)of squark on Λ all is the lighter points than shownwhich in 1 have the plot, the due same to size the large of value the deformation but which can or cannot satisfy the flavour JHEP06(2015)122 . , , j u in λ 1.0 ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ æ ´ c ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ æ æ æ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ æ æ ´ ´ ´ ´ ´ ´ ´ ´ æ æ ´ ´ ´ ´ ´ æ ´ æ æ ´ æ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ æ ´ H ´ ´ ´ i æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ æ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ æ æ æ ´ ´ æ ´ ´ ´ æ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ æ æ ´ ´ ´ ´ æ ´ æ æ æ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ~c ´ æ ´ æ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ c æ ´ ´ ´ æ æ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ æ æ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ æ ´ ´ ´ ´ ´ ´ ´ ´ m ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ æ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ 5 TeV, ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ 5 TeV), ´ ´ ´ æ æ = ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ . ´ ´ ´ ) plane. ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ . ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ij ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ æ æ æ ´ ´ ´ æ æ ´ ´ ´ æ ´ ´ ´ ´ ´ ' − ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ æ ´ ´ æ ´ æ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ c 0.8 ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ /M ´ ´ ´ ´ ´ æ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ = 1 and we ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ µ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ Λ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ æ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ æ ´ ´ ´ ´ λ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ 2 ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ æ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ λ, ´ ´ ´ = 1 (2.7) ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ æ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ 2 ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ | ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ , since the gauge ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ 0.6 ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ æ ´ ´ ´ ´ ´ æ ´ ´ 16 ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ æ λ ´ ´ æ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ æ ´ ´ ´ ´ ´ ´ ´ æ È ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ U ´ ´ æ ´ ´ ´ æ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ æ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ | ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ 14 ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ U ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ + ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ È ´ ´ ´ ´ ´ ´ ´ ´ æ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ æ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ 2 ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ | ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ 0.4 ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ æ ´ æ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ is light and much lighter ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ æ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ 15 ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ); we show only points having ). ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ 1 ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ U ´ ´ ´ ´ ´ ´ ´ 3 ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ | ´ ´ ´ ´ ´ ´ R ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ u ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ˜ ´ t ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ , c ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ 2 + ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ↔ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ 2 ´ ´ ´ ´ ´ ´ 0.2 ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ , c ´ ´ ´ ´ æ ´ ´ ´ ´ ´ | ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ 6 ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ 1 ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ , ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ c ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ 14 ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ R ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ U ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ˜ ´ c is also negative, but it is a two loop ´ ´ æ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ | ´ ´ ´ ´ ´ ´ æ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ ´ . The red points have one squark with ) changes sign. ´ æ æ ´ ´ æ ´ æ æ ´ ´ æ æ ´ æ ´ æ ´ ´ æ æ æ ´ æ ´ ´ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ 5 GeV. æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ . æ æ æ æ æ æ æ æ æ 2 Q æ æ æ æ ↔ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ M 2 0.0

2.5 5

1.0 0.8 0.6 0.4 0.2 0.0

is the charm component of the lightest squark m , 15 È È U ± R 15 ˜ and u U 3 with ↔ – 8 – 0.50 = 125 , c GeV (corresponding to gluino mass around 1 ´ 2 ´ ´ ´ , and hence it becomes very large and negative at ´ æ h ´ ´ ´ 5 ´ æ æ ´ , c ´ ´ ´ ´ m 1 ´ M æ 10 . ´ R ´ ´ æ ´ ´ ´ æ ´ 3 ˜ t ´ æ æ 0.45 ´ ] (i.e. 4 ´ æ ´ ´ ´ ´ 2, varying freely on ( ´ c ´ ´ ´ × æ æ æ æ ´ . æ ´ ´ ´ ´ æ λ, c 16 ´ ´ ´ ´ ´ 64 ´ ´ ´ (if we neglect the effects of the CKM mixing). This can æ ´ ´ 0 æ æ ´ 9 ´ ´ ´ æ ´ ´ ´ ´ ´ . ´ ´ ´ æ æ U ´ ´ ´ æ ´ æ æ ´ ´ ´ æ æ ´ ´ æ ´ ´ æ æ ´ æ ´ λ æ ´ ´ ´ æ | ' ' ´ ´ ´ ´ ´ ´ ´ ´ ´æ ´ æ ´ æ æ æ æ ´ 0.40 ´ æ æ ´ ´ ´ ´ ´ æ æ + ´ æ ´ ´ æ æ æ æ ´ ´ ´ ´ ´ æ ´ æ æ æ æ 16 = 1 æ ´ æ æ ´ ´ ´ ´ æ ´ ´ æ ´ ´ ´ ´ sector descending from the deformation ´ æ æ æ ´ ´ æ æ æ ´ æ æ æ æ æ æ æ æ ´ æ ´ ´ æ ´ æ ´ as eigenvector. Hence the lightest right up-type squark will ´ æ ´ æ ´ R æ æ ´ ´ ´ æ ´ ´ ´ ´ æ ´ ´ ´ ´ æ U ´ ´ æ . This is also a welcome feature to alleviate possible sources æ ´ ´ æ ´ ´ ´ æ æ æ æ ´ /M æ æ æ ´ æ æ æ G ´ ´ æ ´ ´ ) can be positive or negative, depending on the value of æ ˜ | æ æ c æ æ ´ æ ´ æ æ æ ´ æ ´ æ ´ ´ ´ æ ´ ´ ´ ´ ´ æ S æ ´ ´ æ ´ ´ ~c ´ ´ ´ æ ´ ´ æ æ æ ´ æ Q ´ æ ´ , ´ ´ ´ ´ æ ´ æ æ æ ´ ´ ´ æ ´ æ ´ ´ æ æ æ æ ´ æ ´ æ ´ æ ´ ´ ´ æ ´ æ æ æ ´ ´ ´ æ 15 ´ æ æ 2 ´ ´ 0.35 ´ ´ æ æ ´ ´ ´ æ ´ ´ ´ æ ´ ´ æ æ æ ´ æ ´ æ æ æ ´ æ ´ æ æ æ æ ´ æ æ ´ ´ ´ æ æ ´ ´ ´ ´ ´ ´ æ 2.5 æ ´ æ æ c æ æ ´´ æ æ æ æ æ ´ ´ æ ´ ´ æ ´ æ æ ´ ´ ´ ´ æ M æ ´ æ æ æ U ´ æ æ æ ´´ æ æ ´ æ ´ æ æ æ æ æ æ ´ ´ æ æ ´ ´ æ ´ æ ´ ´ æ æ æ æ  ´ ´ ´ ´ ´ ´ æ æ æ ææ ´ ´ æ æ æ ´ æ æ ´ ´ æ deformation contributions are proportional to the matrix ´ ´ ´ ´æ æ æ ´ ´ ´ ´ ´ ´ ´ æ æ ´ ´ æ æ æ æ æ ´ æ ´ æ æ ´ ´ æ æ ´ æ æ æ ´ ´ æ æ ´ ´ æ ´ æ ´ æ æ ´ æ ´ æ æ ´ ´ æ æ ´ ´´ ´ æ æ ´ æ æ ´ æ æ æ ´ ´ ´ æ æ æ æ æ + ´ ´ ´æ ´ æ æ æ ´ ´ ´ æ ´ ´ æ is the up component and ´ ´ æ æ æ æ æ ´ ´ æ æ æ L ´ æ ´ ´ ´ ´ æ ´ ´ ´ æ æ æ ´ æ ´ ´ ´ ´ æ æ ´ æ æ ´´ æ æ λ æ ´ æ ´ æ æ ´ ´ ´ | ' ´ æ ´ ´ ´ GeV, Λ ´ æ æ æ ´ ´ ´ ´ ´ ´ æ æ æ æ æ ´ æ æ ´ æ æ æ æ æ ´ æ æ æ æ ´ æ ´ ´ æ ´ æ ´ ´ ´ 0.30 æ æ æ æ æ æ æ æ æ æ ´ ´ ´ æ æ ´ æ ´ æ æ ´ æ æ æ ´ æ ´ æ ´ æ ´ æ ´ ´ æ æ æ æ æ ´ ´ ´ R ´ ´ æ æ æ æ ´ ´ ´´ æ ´ ´ æ ´ ´´ ´ ´ æ æ æ ´ æ æ æ æ 6 ´ æ ææ ´ æ ´ æ ´ ´ æ ´´ æ æ æ æ ´ ´ ´ ´ æ ´ æ ´æ æ ´ æ ´ ´ æ 14 æ ´ ´ ´ æ ´ æ ´ æ ´ æ ´ ´ ´ ´ æ ´ ´ æ æ ´ ´ ´ æ æ æ æ 15 ´ ´ æ æ æ æ æ æ æ æ æ ´ æ ´ æ ´ æ æ æ ´ æ ´ æ ´ ´ ´ æ ´ æ æ ´ ´ æ æ ´ ´ ´ ´ æ æ ´ ´ ˜ ´ ´ ´ ´ ´æ æ æ æ æ æ ´ æ ´ ´ ´ ´ u æ ´ ´ æ æ ´ ´ æ ´ æ ´ ´ ´ ´ æ ´ ´ æ æ ´ æ æ ´ ´ æ æ ´ æ ´ æ ææ æ ´ æ æ ´ ´ ´ æ ´ ´ ´ æ æ æ ´ ´ æ æ ´ ´ æ æ ´ ´ ´ æ æ æ ´ æ æ ´ ´ æ æ ææ ´ ´ ´ ´ æ æ æ ´ ´ ´ ´ ´ æ æ ´ ´ æ æ æ ´ ´ æ ´ æ ´ æ ´ æ ´ æ ´ æ ´ ´ ´ ´ æ ´ ´ æ U ´ ´ ´ æ æ æ ´ ´ ´ æ æ æ æ ´ ´ ´ ´ ´ æ ´ æ æ æ æ ´ æ æ ´ æ ´ æ ´ æ æ ´æ æ ´ æ æ ´ ´ ´ æ ´ ´ æ ´ æ U æ ´ ´ æ ´ æ æ æ 10 æ ´ æ æ ´ æ ´ æ ´ æ ´ æ æ ´ æ æ ´ æ ´ æ æ æ æ æ æ ´ æ æ ´ ´ ´ æ ´ æ ææ ´ ´ ´ æ æ æ æ ´ ´ æ ´ æ ´ ´ æ æ ´ æ ´ æ æ ´ æ æ ´ ´ ´ ´ ´ ´ ´ æ æ æ æ æ ´ ´ æ ´ ´ ´ æ ´ æ ´ æ ´ ´ ´ æ æ æ ´ æ æ æ æ æ ´ ´ æ ´ æ æ æ æ æ æ æ æ æ ´ ´ æ æ æ æ æ æ ´ æ æ æ ´ ´ ´ ´ ´ ´ æ ´ ´ æ ´ æ æ ´ ´ ´ ´ ´ æ ´ æ ´ ´ æ ´ æ ´ æ ´æ æ æ æ ´ ´ æ ´ | æ æ æ ´ æ ´ ´ ´ ´´ ´ ´ æ ´ ´ ´ æ æ æ æ ´ æ ´ æ ´ ´ æ æ æ æ æ ´ æ ´ æ ´ ´ ´ æ ´ 14 ´ æ æ ´ ´ ´ ´ ´ æ æ æ æ ´ æ ´ ´ ´ ´ æ æ ´ ´ æ æ ´ æ æ æ ´ ´ ´ æ æ ´ æ æ æ ´ ´ æ æ ´ æ ´ æ æ æ ´ æ æ ´ æ ´ ´ ´ ´ æ æ æ æ ´ ´ ´ æ æ ´ æ æ ´ ´ ´ æ ´ æ ´ ´ æ ´ ´ æ ´ ´ æ ´ æ æ ´ ´ ´ æ æ ´ ´ æ ´ æ ´ ´ æ æ æ æ ´ æ æ æ ´ æ æ æ ´ ´ æ ´ æ ´ ´ æ ´ ´ æ ´ ´ ´ ´ æ ´ æ ´ æ æ æ æ ´ æ æ ´ ´ æ æ ´ æ æ æ æ ´ æ ´ æ ´ æ ´ ´ æ æ ´ æ ´ ´ æ ´ ´ ´ æ æ ´ ´ ´ æ æ ´æ ´ æ ´ æ ´ æ æ ´ æ æ æ æ ´ ´ æ æ ´ ´ ´ ´ æ æ ´ æ æ ´ ´ ´ ´ ´ ´ æ ´ ´ , æ æ æ ´ ´ ´æ ´ ´ ´ æ æ ´ æ ´ æ ´ æ ææ æ ´ æ æ æ æ ´ æ æ æ ´ æ æ æ æ æ ´ ´ æ æ ´ æ æ ´ ´ æ ´ ´ ´ æ æ æ æ ´ ´ ´ æ ´ ´ æ æ ´ ´ ´ æ æ ´ æ æ ´ ´ æ ´ æ æ ´ ´ ´ æ ´ æ æ ´ ´ ´ æ ´ æ ´ ´ ´ æ ´ æ æ ´ ´ æ ´ æ æ æ ´ æ æ æ ´ ´ æ ´ ´ ´ æ × æ æ ´ ´ æ æ ´ æ ´ æ æ æ ´ ´ æ ææ ´ ´ æ æ ´ ´ ´ æ æ æ æ æ ´ æ æ æ ´ æ æ æ ´ æ ´ æ ´ æ æ ´ æ ´ æ ´ æ ´ ´ æ ´ ´ æ ´ æ ´ æ æ ´ æ ´ æ æ æ ´ æ U ´ ´ ´ æ ´ ´ ´ ´ æ æ æ ´ 0.25 ´ ´ ´ æ ´ ´ ´ ´æ ´ ´ ´ ´ æ æ ´ ´ ´ æ æ ´ æ æ æ ´ ´ æ æ æ æ ´ æ ´ æ ´ æ ´ æ æ ´ æ ´ æ æ æ ´ ´ ´ ´ ´ ´ æ æ æ æ ´ ´ æ æ ´ ´ æ æ æ æ æ æ ´ ´ ´ ´ ææ æ 1 æ æ ´ æ æ æ ´ æ ´ æ ´ æ æ æ ´ æ ´ æ ´ æ æ æ æ æ æ ´ ´ ´ ´ æ æ ´ æ ´ ´ ´ ´ æ æ æ æ ´ ´ ´ ´ æ ´ æ æ æ ´ ´ ´ æ æ ´ æ æ ´ æ æ æ æ ´ æ ´ ´ æ ´ æ ´ æ ´ ´ ´ æ ´ æ æ ´ æ ´ æ æ ´ æ æ æ ´´ æ ´ ´ ´ ææ æ æ ´ æ æ ´ ´ æ ´ æ ´ ´ æ ´ æ æ ´ ´ ´ ´ ´ æ æ æ æ æ æ æ æ ´ æ ´ æ æ ´ ´ ´ æ æ æ æ ´æ ´ æ ´ æ ´ æ æ æ æ æ ´ ´ æ æ ´ æ æ æ æ æ ´ ´ ´ æ ´ æ æ ´ ´ æ æ ´ ´ æ æ æ ´ ´ ´ æ æ ´ æ ´ æ ´ ´ æ ´ æ ´ æ ´ ´ æ æ ´ æ æ ´ æ ´ æ æ ´ æ æ ´ ´ æ æ ´ æ æ æ æ ´ æ æ æ æ æ æ ´ ´ æ ´ ´ æ æ ææ ´ ´ æ ´ ´ ´ ´ ´ æ ´ æ æ æ æ æ æ æ æ ´æ æ ´æ ´ ´ æ æ æ ´ æ æ æ æ ´ ´´ æ ´ æ ´ æ æ æ æ æ æ æ ´ æ ´ ´ æ æ æ ´ æ æ ´ ´ æ æ æ æ æ ´ æ æ æ ´ ´ æ ´ æ ´ æ ´ ´ ´ æ æ ´ æ ´ ´ ´ æ æ c æ ´ ´ æ æ ´ æ æ æ æ æ æ ´ ææ ´ æ ææ æ ´ æ æ ´ æ æ ´ ´ æ æ ´ ´ æ ´ ´ æ ´ æ æ ´ ´ ´ æ ´ ´ æ æ ´ ´ æ ´ ´ ´ ´ æ æ æ ´ æ æ æ æ ´ ´ æ æ ´ ææ ´ ´ ´ ´ ´ æ ´ æ æ ´ ´ ´ æ æ ´ æ æ æ ´ ´ æ æ ´ æ ´ æ ´ ´ ´ æ æææ æ æ ´ æ æ ´ ææ ´ ´æ ´ æ æ æ æ ´ æ ´ ´ ´ æ æ ´ ´ æ ´ æ æ ´ æ ´ æ ´ æ æ ´ æ ´æ æ æ ´ æ æ ´ æ æ æ ´ æ æ ´ æ ´ ´ æ ´´ ´ ´ æ æ ´ æ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ æ æ æ ´ æ ´ æ ´ ´ æ æ æ æ æ æ ´ æ ´ æ æ ´ æ ´ ´ æ ´ æ ´ ´ ´ æ æ æ æ ´ æ ´ ´ æ ´ ´ æ æ æ æ ´ æ æ æ ´ ´ æ ´ ´ æ ´ æ ´ æ ´ æ ´ ´ ´ ´ ´ ´ æ ´ æ æ æ æ ´ æ æ æ æ ´ æ æ æ æ æ ´ ´ æ ´ ´ ´ æ ´ æ ´ ´ ´ æ ´ ´ æ ´ æ æ æ æ æ ´ ´ ´ æ ´ ´ æ ´ æ ´ ´ æ æ æ æ ´ ´ æ ´ æ æ æ ´ ´ æ æ æ æ ´ æ æ æ æ ´ ´ æ æ æ æ æ æ ´ ´ æ æ ´ æ ´ ´ ´ æ æ ´ ´ æ æ æ æ æ æ æ ´ æ æ æ ´ æ æ æ ´ ´ æ ´ ´ æ æ æ ´ ´ ´ ´ æ æ ´ ´ ´ ´ æ ´ æ æ ´ ´ ´ ´ æ æ æ æ ´ ´ ´ æ ´ æ æ ´ ´ æ æ æ ´ ´ æ æ ´ æ æ ´ ´ ´ æ æ æ ´ æ æ ´ ´ ´ ´ æ æ æ æ æ ´ æ æ æ ´ ´ ´ ´ æ æ æ ´ ´ æ ´ ´ ´ ´ æ æ ´ æ ´ ´ ´ ´ ´ ´ æ æ æ ´ ´ æ æ æ ´ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ ´ æ ´ ´ ´ æ æ ææ æ æ æ æ ´ æ æ æ æ æ æ æ æ æ æ æ ´ æ = æ æ æ ´ ´ æ æ ´ æ æ æ ´ ´ ´ æ ´ ´ ´ ´ æ æ ´ æ æ æ æ ´ ´ æ æ æ ´ ´ æ æ ´ æ æ æ æ æ ´ ´ æ æ æ æ ´ æ æ ´ ´ ´ æ ´ ´ ´ æ ´ æ ´ ´ ´ ´ æ æ æ æ ´ ´ æ æ æ ´ ´ æ ´æ æ ´ ´ ´ ´ æ æ ´ æ æ æ ´ æ ´ æ ´ ´ ´ æ ´ ´ ´ ´ ´ æ ´ ´ æ ´ æ ´ æ æ æ æ æ æ ´ æ æ æ æ æ ´ æ æ æ æ æ ´ æ æ æ ´ æ ´ ´ æ ´ ´ ´ æ ´ æ ´ æ æ æ æ ´ æ ´ æ æ ´ ´ æ ´ ´ æ æ æ ´ ´ æ æ ´ æ ´ ´ æ æ æ æ æ æ æ ´ ´ æ æ ´ æ æ ´ æ ´ ´ æ æ æ æ æ æ æ ´ æ æ æ æ æ ´ ´ ´ ´ æ æ æ æ æ ´ æ ´ æ æ æ æ æ æ æ æ ´ æ æ ´ ´ ´ ´ ´ æ æ ´ ´ æ æ ´ ´ æ ææ ´ æ æ æ æ ´ ´ ´ æ ´ æ æ ´æ æ ´ æ æ æ æ æ æ æ æ æ æ ´ ´ ´ ´ æ æ æ æ ´ æ ´ æ æ ´ ´ æ ´ æ æ æ ´ æ ´ æ ´ ´ ´ æ ´ ´ æ ´ æ æ æ æ æ æ ´ ´ æ ´ æ ´ ´ æ æ æ ´ ´ ´ æ æ ´ æ æ ´ ´ æ æ æ æ æ æ ´ ´ æ æ ´ æ æ ´ ´ æ ´ æ æ æ æ ´ ´ æ ´ æ ´ æ ´ æ æ æ æ ´ ´ æ ´ æ ´ ´ ´ ´ ´ æ æ ´ ´ æ ´ æ ´ æ æ æ ´ ´ æ is very small at the scale ´ ´ æ ´ ´ ´ æ æ GeV. We scanned over ´ æ æ æ ´ ´ æ æ æ æ æ æ æ æ æ æ ´ ´ æ æ ´ æ æ ´ ´ ´ ´ ´ æ æ ´ æ ´ ´ æ ´ æ æ æ æ ´ ´ æ æ æ æ ´ æ æ æ æ ´ ´ ´ ´ ´ æ æ æ ´ ´ æ æ ´ æ ´ ´ æ æ ´ æ ´ ´ æ æ ´ ´ ´ ´ ´ æ æ æ æ ´ ´ æ æ ´ æ æ ´ ´ æ ´ ´æ ´ ´ æ æ æ ´ ´ ´ æ æ ´ æ æ æ æ ´ ´ æ æ ´ æ æ æ æ ´ æ æ æ æ æ ´ ´ æ ´ æ ´ ´ ´ æ ´ ´ æ ´ æ æ æ æ æ ´ ´ æ ´ ´ ´ ´ ´ ´ æ æ ´ ´ ´ ææ ´ æ ´ æ æ ´ æ æ æ ´ ´ ´ ´ æ æ to be such that Λ ´ æ ´ æ ´ æ æ æ ´ æ ´æ æ æ æ ´ ´ æ æ æ ´ ´ æ ´ æ æ æ æ æ ´ ´ æ æ æ ´ ´ ´ ´ æ ´ æ ´ ´ ´ ´ æ æ ´ æ æ æ ´ æ æ ´ æ ´ æ ´ ´ ´ ´ æ æ ´ ´ æ ´ æ æ æ ´ ´ ´ æ ´ ´ ´ ´ æ ´ ´ æ æ æ ´ æ æ æ ´ ´ ´ ´ ´ æ ´ ´ ´ æ æ æ æ æ ´ æ æ ´ æ æ æ ´ ´ ´ ´ æ æ ´ æ æ ´ æ æ ´ æ ´ ´ ´ æ æ æ ´ æ ´ ´ ´ æ = 1 æ ´ æ ´ ´ ´ ´ ´ æ æ æ ´ æ æ æ ææ ´ æ æ ´ ´ æ æ ´ æ æ æ æ ´ æ æ ´ æ æ æ æ æ ´ æ ´ ´ ´ ´ æ æ ´ æ æ æ æ ´ æ æ ´ ´ æ æ ´ ´ ´ æ ´ ´ æ æ ´ ´ ´ ´ ´ ´ æ æ æ æ ´ æ æ æ ´ æ ´ ´ æ æ æ ´ ´ æ æ æ æ ´ ´ ´ æ æ æ ´ ´ ´ æ ´ ´ ´ æ ´ ´ æ æ ´ æ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ ´ æ æ æ ´ æ æ ´ ´ æ æ ´ ´ ´ ´æ ´ æ æ ææ æ ´ ´ æ æ æ æ æ æ æ æ ææ ´ ´ æ ´ ´ æ æ ´ æ æ æ ´ ´ æ ´ æ æ æ æ æ ´ æ æ æ ´ æ æ ´ ´ ´ ´ æ ´ ´ ´ æ ´ æ æ æ ´ æ æ æ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ æ æ ´ ´ æ æ æ ´ æ æ ´´ ´ æ æ æ ´ ´ æ ´ ´ ´ ´ æ ææ ´ ´ æ æ æ æ æ ´ ´ æ æ ´ æ ´ ´ æ æ æ ´ ´ æ æ ´ æ æ æ ´ ´ ´ æ æ æ æ ´ ´ æ æ æ ´ ´ æ ´ ´ æ æ æ æ æ æ ´ ´ ´ æ æ æ ´ ´ ´ ´ ´ æ ´ æ æ æ æ ´ ´ ´ æ æ æ ´ ´ ´ ´æ æ æ æ æ æ æ ´ æ ´ ´ æ ´ ´ æ æ æ ´ ´ æ ´ æ æ æ æ æ æ ´ 1 æ ´ æ ´ æ ´ æ ´ æ æ æ æ æ æ ´ æ æ ´ ææ æ æ æ æ ´ ´ æ æ æ æ æ æ æ æ æ æ ´ æ æ æ ´ ´ )). All points displayed have ´ æ æ ´ æ æ æ ´ æ æ ´ ´ ´ ´ æ æ ´ æ ´ æ æ ´ æ æ æ æ ´æ ´ æ æ æ ´ æ ´ æ æ æ æ ´ ´ ´ æ æ æ æ ´ ´ æ æ æ æ æ ´ æ æ ´ æ æ æ æ ´ æ ´ æ ´ æ æ ´ æ æ ´ æ æ æ ´ æ ´ æ ´ ´ ´ æ ´ ´ ´ ´ æ æ æ æ æ æ æ æ æ ´ æ ´ ´ ´ ´ æ æ ´ ´ ´ æ æ ´ ´ ´ æ æ ´ æ ´ ´ ´ ´ æ æ ´ æ æ ´ æ æ ´ æ ´ æ ´ æ ´ æ ´ æ æ æ æ ´ æ æ æ æ æ æ ´ ´ æ æ æ ´ æ æ æ ´ ´ ´ æ ´ ´ æ æ æ æ æ æ ´ ´ æ æ æ æ æ æ ´ æ æ ´ ´ æ æ ´ æ æ æ æ ´ ´ æ ´ æ ´ ææ æ æ æ æ æ ´ ´ æ ´ æ æ æ æ ´ ´ æ æ ´ ´ ´ æ æ ´æ ´ ´ ´ æ ´ ´ ´ æ æ æ æ æ ´ æ ´ 5 æ ´ ´ æ ´ ´ ´ ´ ´ æ æ ´ ´ æ æ ´ ´ ´ ´ æ æ ´ æ ´ æ ´ æ ´ ´ æ ´ æ æ ´ ´ ´ æ æ ´ æ æ æ ´ æ æ ´ ´ æ æ æ æ æ æ æ æ æ ´ ´ ´ æ æ æ ´ ´ æ ´ æ ´ æ æ æ ´ æ ´ ´ æ æ æ æ ´ æ æ ´ æ æ æ ´ æ æ æ ´ æ ´ ´ æ æ æ ´ æ æ ´ æ ´ æ ´ æ æ æ æ ´ ´ æ æ ´ æ ´ æ ´ æ æ æ æ æ æ ´ æ æ æ æ ´ ´ ´ æ æ æ ´ ´ ´´ ´ æ æ ´ ´ ´ æ ´ ´ ´ æ æ æ ´ ´ æ ´ æ æ æ æ æ ´ ´ æ æ ´ æ æ æ æ æ æ æ ´ æ ´ æ æ ´ ´ æ æ æ æ ´ ´ æ æ æ ´ æ æ æ ´ ´ ´ ´ ´ æ ´ æ æ ´ æ ´ ´ æ æ æ æ ´ æ ´ ´ ´ æ ´ æ æ ´ æ æ æ æ æ æ ´ ´ ´ æ ´ æ æ ´æ æ æ æ æ ´ æ æ æ æ æ æ æ æ ææ ´ æ ´ æ ´ ´ ´ æ æ æ æ æ ´ æ æ ´ ´ æ ´ ´ ´ ´ æ æ ´ ´ ´ ´ æ æ ´ æ æ æ æ ´ æ æ ´ ´ ´ ´ æ ´ æ ´ æ ´ æ æ æ æ æ ´ æ æ æ ´ ´ ´ ´ æ ´ æ æ ´ ´ æ æ ´ æ æ ´ æ æ æ æ æ æ ´ æ æ ´ æ æ æ æ ´ æ æ ´ ´ ´ æ æ æ ´ æ ´ æ æ æ æ ´æ æ æ ´ ´ æ ´æ æ ´ ´ æ æ æ ´ æ æ æ æ ´ ´ æ ´ æ æ æ æ ´ ´ ´ æ ´ æ æ ´ æ æ æ æ ´ æ ´ æ ´æ ´ ´ ´ ´ æ æ æ æ ´ ´ æ æ ´ ´ ´ æ æ ´ ´ æ æ æ æ ´ ´ æ æ ´ ´ ´ æ æ æ æ ´ æ æ | ' æ ´ ´ æ æ ´ ´ æ æ æ ´ æ æ æ ´ ´ u ´ ´ ´ ´ æ æ æ ´ ´ ´ æ ´ ´ æ æ ´ ´ æ æ ´ ´ ´ ´ æ æ æ ´ ´ æ æ ´ æ æ ´ ´ æ ´ æ æ æ æ ´ æ ´ ´ ´ ´ ´ ´ ´ ´ æ æ æ æ ´ ´ ´ ´ æ æ æ æ æ ´ æ æ ´ æ æ ´ æ ´ ´ æ æ ´ æ æ æ æ ´ ´ ´ ´ ´ æ ´ æ æ æ ´ æ ´ æ æ æ æ ´ æ æ ´ ´ æ ´ æ æ æ æ æ æ æ æ ´ ´ ´ ´ æ æ æ ´ æ æ æ æ ´ æ æ æ æ æ ´ æ ´ æ æ ´´ æ æ æ ´ æ ´ æ ´ æ æ æ ææ æ æ ´ ´ æ æ ´ ´ æ æ ´ æ æ ´ æ ´ æ ´ ´ æ ´ æ æ æ ´ æ ´ ´ æ ´ æ æ æ ´æ ´ æ æ æ æ æ ´ æ ˜ ´ æ ), where ´ æ ´ ´ ´ æ æ æ æ æ æ æ æ ´ ´ æ æ ´ æ ´ ´ æ æ æ ´ æ æ æ ´ ´ æ ´ ´ æ æ ´ ´ ´æ ´ æ æ æ ´ ´ ´ ´ æ ´ 0.20 ´ æ æ æ æ ´ æ ´ ´ æ æ æ æ æ æ ´ ´ ´ æ æ æ æ æ ´ æ ´ æ æ æ ´ ´ ´ ´ æ æ æ æ æ æ ´ ´ æ æ ´ ´ æ æ æ æ æ ´ ´ æ æ æ u ææ æ æ ´ æ æ ´ æ æ æ ´ æ æ æ æ æ æ æ æ ´ æ ´ æ ´æ ´ æ æ ´ æ æ ´ ´ ´ æ ´ æ æ æ æ æ æ ´ æ æ æ æ ´ ´ æ æ ´ æ æ æ æ ´ æ ´ ´ æ æ æ æ æ ´ æ æ æ ´ ´ ´ æ æ æ æ æ æ ´ æ ´ ´ æ ´ æ æ S ´ æ æ æ ´ ´ ´ æ ´ æ ´ æ ´ æ æ ´ ´ ´ ´ ´ ´ æ ´ æ æ æ ´ æ æ ´ ´ ´ æ æ ´ æ æ æ æ æ æ ´ æ æ ´ æ æ æ æ æ ´ æ æ æ ´ ´ ´ ´ æ æ æ ´ ´ ´ æ æ æ ´ æ ´ ´ ´ ´ æ ´ æ æ æ ´ æ æ æ ´ ´ ´ ´ æ æ ´ ´ ´ æ æ ´ ´ æ æ æ æ ´ æ ´ ´ æ æ ´ ´ ´ ´ æ æ ´ ´ æ ´ æ ææ æ æ æ æ ´ ´ ´ æ ææ ´ ´ æ ´ ´ ´ ´ ´ ææ ´ æ æ æ æ æ æ æ ´ æ æ æ æ æ ´ æ ´ æ æ æ æ æ æ ´ æ æ æ æ ´ æ ´ ´ ´ ´ æ æ ´ æ æ æ ´ æ æ æ æ æ æ ´ ´ æ ´ ´ ´ æ ´ ´ ´ æ ´ ´ æ ´ ´ ææ æ æ ´ ´ æ æ æ æ ´ æ æ ´ ´ æ ´ ´ ´ ´ æ æ æ æ ´ ´ æ æ æ æ æ æ ´ æ æ ´ æ ´ ´ ´ ´ æ æ ´ æ ´ ´ ´ æ ´ ´ ´ æ æ ´ ´ æ | æ æ æ æ æ æ ´ ´ ´ æ ´ ´ æ ´ æ æ æ ´ æ æ æ æ æ æ æ æ æ æ æ ´ ´ æ æ æ æ ´ ´ ´ ´ æ æ æ ´ ´ ´ æ ´ æ æ ´ æ æ ´ ´ ´ ´ æ æ æ æ ´ æ ´ æ æ ´ æ ´ ´ ´ ´ ´ æ æ æ æ æ æ ´ æ æ ´ ´ æ ´ ´ ´ æ æ æ æ ´ ´ æ ´ ´ ´ æ æ ´ æ ´ æ æ æ ´ æ æ æ æ æ æ æ ´ ´ ´ æ æ æ æ ´ æ æ æ ´ æ æ æ æ æ æ ´ ´ æ æ æ ´ ´ ´ ´ ´ æ æ ´ ´ æ æ æ æ æ æ ´ æ ´ æ æ æ æ æ ´æ æ æ æ æ ´ æ ´ æ æ ´ ´ ´ æ æ æ æ ´ æ æ æ ´ æ æ ææ æ æ ´ ´ æ æ æ æ æ æ ´ æ æ æ æ æ æ æ ´ æ ´ ææ æ æ æ ´ æ ´ ´ æ æ ´ ´ æ æ æ æ ´ æ æ æ æ æ ´ æ ´ æ æ ´ æ æ æ æ æ ´ æ ´ ´ ´ ´ æ ´ æ ´ ´ æ æ ´ æ æ ´ æ æ æ ´ æ æ æ æ æ ´ æ ´ æ æ æ æ æ æ æ æ ´ ´ æ æ ´ ´ ´ ´ ´ ´ æ æ æ ´ ´ ´ æ æ ´ ´ ´ æ æ ´ æ ææ æ ´ æ ´ æ ´ æ ´ ´ æ ´ ´æ ´´ æ æ æ æ æ æ æ æ ´ ´ ´ æ æ ´ æ æ ´ æ æ æ æ æ ´ ´ æ æ æ ´ ´ æ æ æ æ æ æ ´ æ æ æ ´ æ æ æ æ ´ æ æ ´ ´ ´ ´ æ æ æ ´ æ æ æ ´ æ æ æ æ æ æ æ æ ´ æ æ æ æ ´ æ ´ æ æ æ æ ´ æ æ æ æ ´ ´ ´´ æ æ ´ æ æ æ æ æ æ æ ´ æ æ æ æ æ ææ æ ´ æ æ ´ æ æ ´ æ æ ´ æ æ ´ ´ æ æ æ ´ æ æ æ æ æ ´ æ æ æ æ æ æ æ æ æ æ ææ M ´ æ æ æ æ ´ æ ´ æ ´ æ æ æ æ æ æ ´ æ ´ æ æ æ ´ ´ æ æ æ ´ æ ´ æ æ ´ æ æ æ æ ´ æ æ ´ ´ æ æ ´ ´ æ æ ´ æ æ æ æ ´ æ æ æ æ æ æ ´ æ ´ ´ æ æ æ ´ æ ´ ´ ´ ´ æ æ æ ´ ´ æ æ æ æ æ ´ ´ æ ´ æ æ æ æ ´ æ æ æ æ ´ H æ ´ æ æ æ ´ ´ æ æ æ æ æ ´ ´ ´ æ ´ ´ æ ´ ´ ´ ´ æ æ æ æ ´ ´ ´ æ æ æ æ æ æ ´ ´ æ æ ´ ´ æ æ æ æ æ æ æ ´ æ ´ æ 10 æ æ ´ æ ´ æ ´ ´ æ æ æ ´ ´ æ æ æ ´ ´ ´ æ æ æ ´ ´ æ æ æ æ æ ´ æ ´ ´ æ æ æ æ ´ æ æ æ ´ æ æ æ æ æ ´ ´ æ æ æ æ æ æ ´ ´ æ æ æ æ æ æ æ æ ´ æ æ ´ ´ ´ æ æ ´´ ´ æ æ æ æ æ ææ ´ ´ ´ æ æ æ æ æ ´ æ æ ´ ´ æ æ æ ´ ´ ´ ´ æ æ æ æ æ æ æ ´ ´ æ ´ æ æ æ æ ´ ´ æ æ æ æ æ æ æ ´ ææ ´ æ æ æ æ ´ æ æ æ æ æ æ ´ æ ´ ´ ´ æ æ æ æ ´ æ æ æ æ ´ æ æ ´ æ æ ´ æ æ ´ æ ´æ ´ æ ´ æ æ ´ æ ´ æ æ æ æ æ æ æ ´ æ ´ ´ æ ´ æ æ æ æ ´ æ ´ æ æ ´ ´ æ ´ ´ æ æ ´ æ æ æ æ æ æ æ ´ æ æ æ ææ æ æ ´ ´ æ æ æ æ ´ æ æ æ æ ´ æ ´ . Left: results of the scan on the parameter space of the model on the ( ´ ´ æ æ æ æ æ æ ´ æ æ ´ 2.7 ´ æ æ æ æ æ æ æ ´ æ ´ æ æ ´ æ ´ æ æ æ æ æ æ ´ ´ æ æ æ æ ´ ´ æ ´ æ ´ æ æ ´æ ´ æ æ æ æ æ ´ æ æ ´ æ æ ´ æ ´ æ æ æ ´ ´ æ æ æ æ æ ´ æ ´ ´ ´ ´ æ ´ ´ ´ ´ ´ æ æ æ æ ´ æ æ 14 ´ æ ææ æ æ ´ ´ ´ æ æ ´ æ æ æ ´ æ æ ´ æ æ æ æ æ ´ ´ æ æ æ æ æ æ æ ´´ ´ ´ æ æ æ æ æ æ ´ ´ ´ ´ æ æ æ æ æ æ æ æ æ ´ ´ ´ æ æ æ æ æ æ æ æ æ ´ ´ æ æ æ æ ´ ´ ´ æ æ æ ´ ´ æ æ æ ´ ´ ´ ´ æ æ æ æ æ æ æ ´ æ æ æ æ ´ æ æ æ æ æ ´ ´ ´ ´ æ æ æ æ ´ æ ´ æ æ æ æ æ æ æ ´ æ æ æ ´ æ æ ´ ´ æ æ æ æ ´ æ æ æ æ æ ´ æ æ æ æ æ ´ æ æ æ æ ´ ´ ´ ´ æ æ æ ´ ´ ´ æ æ æ ´ æ æ ´ ´ æ æ æ ´ ´ æ ´ ´ æ æ æ æ æ æ æ æ ´ æ æ æ æ æ æ æ æ æ æ ´ æ ´ æ ´ æ æ æ æ ´ ´ ´ ´ æ æ ´ ´ æ ´ ´ æ æ æ æ æ æ æ ´ æ ´ æ æ ´ æ ´ æ æ ´ æ ´ æ æ æ æ æ ´ æ æ æ æ ´ æ ´ ´ æ æ æ æ ´ ´ æ æ ´ ´ ´ æ æ æ æ ´ ´ æ ´ ´ æ ´ æ ´ ´ æ æ æ æ æ æ ´ æ æ ´ ´ ´ æ æ æ æ æ ´ æ æ æ ´ æ æ ´ æ ´ ´ ´ æ æ æ ´ æ æ æ ´ æ ´ æ ´ æ æ æ ´ æ ´ ´ æ æ æ æ æ æ ´ æ ´ æ æ æ ´ æ æ æ æ æ ´ ´ ´ æ æ æ æ æ ´ æ æ ´ æ ´ æ ´ æ æ æ æ æ æ æ æ ´ æ æ ´ æ æ æ ´ æ æ ´ ´ ´ ´ ´ ´ ´ æ æ æ æ ´ æ æ æ æ ´ æ æ ´ æ æ æ æ ´ æ æ æ ææ ´ æ æ æ æ æ ´ æ æ æ æ æ ´ æ ´ ´ æ ´ ´ ´ ´ æ ´ ´ æ æ æ æ æ æ æ ´ æ æ æ æ æ ´ ´ æ æ æ æ æ æ æ ´ æ æ æ ´ æ æ ´ æ æ æ ´ ´ æ æ ´ ´ ´æ ´ æ æ æ ´ æ ´ æ ´ æ æ æ æ ´ æ ´ ´ ´ æ æ æ æ æ æ æ æ æ æ ´ æ ´ ´ æ æ ´ æ æ æ æ æ æ ´ ´ æ ´ ´ æ æ æ æ ´ ´ æ ´ ´ æ æ ´ æ æ ´ æ ´ æ æ æ æ æ æ ´ æ ´ ´ æ ´ æ æ æ ´ æ æ æ æ ´ ´ ´ ´ æ ´ ´ æ æ æ æ æ ´ ´ ´ æ æ ´ ´ ´ æ æ æ ´ æ æ æ ´ æ æ æ æ ´ ´ æ æ æ ´ æ æ ´ æ æ æ æ æ æ æ ´ ´ æ æ æ æ ´ æ æ ´ ´ ´ ´ æ æ ´ ´ ´ æ æ æ ´ æ æ ´ æ æ ´ ´ æ ´ æ æ æ æ ´ æ æ ´ ´æ æ æ æ æ æ æ ´ æ æ æ æ æ æ æ ´ ´ ´´ ´ æ æ æ æ ´ æ æ ´ ´ ´ æ æ æ ´ æ æ æ ´ æ æ æ ´ æ æ æ æ æ æ æ æ ´ ´ ´ æ æ æ æ æ æ æ æ æ æ ´ æ ´ æ ´ æ æ æ æ 15 æ æ ´ æ æ æ æ æ æ ´ æ æ æ æ æ æ ´ æ æ ´ ´ ´ æ æ æ æ ´ æ ´ ´ æ ´ æ ´ æ æ æ ´ ´ æ ´ æ ´ æ æ æ æ æ ´ æ æ ´ æ æ æ æ æ ´ æ æ æ æ æ ´ ´ æ æ ´ æ æ æ æ æ æ æ æ æ ´ æ æ æ æ ´´ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ ´ æ ´ ´ ´ ´ ´ æ æ æ æ ´ ´ ´ æ æ æ æ æ ´ æ ´ æ æ æ æ æ æ æ æ æ æ æ ´ æ æ æ æ ´ æ æ æ æ æ æ æ ´ æ æ ´ æ æ ´ æ ´ æ æ æ æ ´ æ æ æ æ ´ æ æ æ æ ´ æ ´ æ ´ æ æ ´ ´ æ æ æ æ ´ æ ´ ´ æ æ æ ´ ´ ´ æ ´ ´ ´ ´ æ æ æ æ æ æ æ ´ ´ ´ ´ æ æ æ ææ æ æ æ ´ æ æ æ æ ´ æ æ æ æ æ ´ ææ æ ´ æ æ ´ æ ´ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ ´ ´ æ ææ æ æ æ æ ´ æ æ ´ æ æ æ ´ ´ æ æ ´ æ æ æ æ ´ æ æ æ æ æ æ æ ´ æ æ æ æ æ æ æ ´ ´ æ æ æ ´ æ ´ ´ æ ´ æ æ æ æ æ æ ´ æ ´ æ æ æ ´ æ æ æ æ æ ´ æ æ æ æ æ æ æ æ æ ´ æ æ æ ´ ´ ´ ´ ´ æ æ ´ ´ æ æ æ æ æ æ æ æ æ ´ æ æ æ æ æ æ ´ æ æ æ æ ´ æ æ æ ´ æ ´ ´ æ æ æ æ æ æ ´ æ æ ´ æ æ æ æ æ æ æ æ æ æ ´ ´ æ æ æ æ æ æ æ æ æ ´ æ æ æ æ æ æ ´ æ ´ ´ æ æ æ æ æ æ ´ æ æ æ æ ´ æ ´ ´ æ ææ ´ ´ æ æ æ æ æ æ æ ´æ ´ ´ ´ æ æ ´ ´ æ ´ ´ ´ æ æ æ æ æ æ ´ æ æ æ æ æ ´ ´ æ æ ´ æ æ æ æ æ ´ æ æ æ æ æ æ ´ æ ´ æ æ ´ ´ æ ´ ´ æ ´ æ æ ´ ´ æ æ æ ´ æ æ æ æ æ æ ´ ´ ´æ æ æ æ æ ´ æ ´ ´ ´ ´ æ æ ´ æ æ ´ æ æ æ æ æ æ æ ´ æ æ æ æ ´ æ æ æ æ ´ æ æ ´ æ æ æ ´ æ æ æ ´ æ æ æ æ ´ ´ æ ´ æ æ æ æ æ æ æ æ ´ æ æ æ æ æ ´ æ ´ ´ æ æ æ æ æ æ ´æ æ æ æ ´ æ æ æ ´ æ æ ´ æ æ æ æ æ æ ´ æ æ æ æ æ ´ ´ æ æ æ æ ´ ´ ´ ´ æ ´ æ æ æ ´ ´ ´ æ æ æ æ æ æ æ æ æ ææ ´ æ æ æ ´ æ æ æ æ æ ´ æ æ æ ´ ´ æ æ æ æ æ æ ´ æ ææ æ ´ æ æ æ æ æ æ æ ´ æ æ ´ æ ´ æ æ ´ ´ æ æ æ æ æ ´ ´ æ ´ æ æ ´ æ ´ ´ æ æ æ æ æ ´ æ ´ æ æ æ æ æ ´ æ æ æ ´ æ æ æ ´ æ æ ´ æ æ æ æ ´ æ æ æ æ ´ æ ´ ´ ´ æ ´ æ æ ´ æ ´ ´ ´ ´ æ æ æ æ ´ ´ ´ æ ´ ´ ´ æ æ æ æ ´ æ ´ æ æ æ æ æ æ æ ´ æ æ ´ æ æ ´ ´ ´ æ æ æ ´ æ æ æ ´ ´ æ æ æ æ æ ´ æ æ æ æ æ æ ´ æ æ æ æ æ æ æ æ æ æ æ ´ æ ´ æ æ æ æ ´ ´ æ æ æ æ æ ´ æ æ ´ æ æ ´ æ æ æ æ æ ´ æ æ æ ´ ´ æ æ æ ´ ´ æ æ æ æ æ ´ æ æ ´ ´ æ æ æ ´ ´ ´ ´ ´ æ æ æ æ ´ æ æ æ æ æ æ æ ´ æ ´ æ æ æ U æ æ æ æ ´ æ ´ æ ´ æ æ æ æ æ ´ æ æ æ æ æ æ æ ´ æ æ æ æ ´ æ ´ ´ æ æ ´ æ ´ ææ æ æ ´ ´ æ æ ´ ´ ´ ´æ æ æ m æ æ æ ´ æ æ æ æ æ æ ´ ´ ´ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ ´ æ æ ´ ´æ ´ æ æ æ ææ æ æ æ æ æ ´ ´ æ æ ´ æ æ æ ´ æ æ æ æ æ æ æ ´ æ æ ´ æ ´ ´ æ æ æ æ ´ ´ æ æ æ æ æ æ æ ´ æ æ æ ´ ´ æ æ ´ ´ ´ æ æ æ æ æ ´ æ æ æ æ ´ æ ´ ´ ´ ´ æ æ æ ´ ´ æ æ ´ æ æ æ æ æ æ æ æ ´ æ ææ æ ´ æ ´ æ æ æ ´ æ ´ æ æ æ æ æ æ æ ´ æ æ ´ æ æ æ æ æ ´ æ ´ æ ´ æ ´ æ æ æ ´ æ æ ´ æ æ æ æ æ æ ´ ´ æ ææ æ æ ææ æ æ æ æ ´ æ æ æ æ ´ æ æ ´ ´ æ æ ´ æ æ æ æ æ ´ æ 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| 0.8 0.6 1.4 1.2 1.0

The contribution to the other squark mass Note that in the red region only one mass eigenstate ˜ µ We used here the SLHA2 notations [ Λ 14 2 U | mediation contributions are flavour diagonal.is that The other genericthe effect EW scale. of As the a deformation the consequence, since the EWSB condition sets approximately where effect and it iswe compensated have by considered the large largeof Λ value flavour of violation the in gauge mediation the contribution since flavor space while the which has by construction be a mixture of right handed stop, scharm and up-squark in the combination approximately where the two loop correction in ( than all theflavor other space, squarks. as the deformation Thisbe easily mass understood eigenstate by will observing be that the aligned gauge along mediation contributions the are vector diagonal in points where there is athe single light red right-handed up points, squark withthe are mass up at smaller than squark the 1 This mass border determines in of the ( the shape allowed of the region. allowed region, The and two the loop location of contribution the to throat, which is mass smaller than 1.5 TeV.restricted Right: we focusone on light a squark region with with( light mass squark: smaller than we(see fixed 1.2 TeV, eqn and ( we plot in the physical mixing angle plane Figure 1 We fixed Λ Λ = 5 JHEP06(2015)122 1 2. c . = 0 2 c mixing | we show 15 . However 3 U S | , | 14 U | , where we fix 2 in the range around 0 /M mixing. The plot shows that off 0 ¯ is in the RR up squark mass matrix, D λ ). There is no off diagonal contribution − 0 2.5 D = 1 and set Λ ]. to a representative value, at the border of the λ 65 – 9 – G = 1). For a recent treatment of the Higgs mass we focus on points with one light up-type squark 2 3 c 1 are negligible compared to the flavour diagonal gauge = 1). + λ i 2 2 2 1 c U i + 1 2 2 TeV. We fix P . c . The plot shows the result of the scan on the ~c is actually coming from 1 it is evident that we can easily get viable points with a correct Higgs ) for all the scanned points. As a consequence the only relevant flavour 2 2.6 = 1 and that λ -terms, hence no LR mixing, and the two loop contributions to the LL squark A , where the deformation is mainly aligned along the direction 3 in flavour (note, we 2 c Summarizing, the deformation presented in this section provides a model realization of From figure This effect can be qualitatively estimated by considering figure In the plots, all points have a viable Higgs mass, which is a consequence of the fact The red crosses are points which are not allowed because they do not respect flavour In the plot on the right of figure one light squark state. squark eigenstate, maximally mixed between stop and sup gaugescenarios eigenstates. with a light squarkof with this a model large stop-supspectrum is or to that stop-scharm be the mixing. heavy, Higgs implying The drawback mass a certain is unavoidable obtained amount by of requiring tuning in the order other to squarks have in the mass, satisfying flavor constraints, andup having squark. a In very the lightLHC8 and scatter exclusion highly plots mixed we reach fixed right-handed for Λ spectrum the does gluino mass; not however, changetwo the by prototypical benchmark qualitative raising points, feature further with of different the gluino the gaugino mass, typical both mass presenting scale. one lightest In table and we plot thevalues) contours as for a the function value ofviable of the Higgs the lightest mass Higgs squark is denoted mass mass inalong and (now red. the of allowed The direction the to lighter 1 mixing the take in angle. squarkto also flavour is, have The small space, the a region more and large with it hence enough should less be Higgs in aligned mass. the direction 3 in flavour, in order aligned along the thirdand family. This explainshave the fixed hole of pointsformula in in a the fully region flavored of MSSM small see e.g. [ that at least onethe of Higgs the mass two stops constraintof implies is the very that lightest heavy, the with eigenstate, deformationspace. a if cannot Hence mass this lower very set too has low mainly much mass a by the values significant Λ for mass component the in lightest squark the are direction allowed 3 only in if they flavor are not diagonal contributions to RR upcontraints squark if masses the can mixing be betweenthis compatible the model with first low we and can energy the realize flavour flavor second scenarios basis, generation where is the either not lightest sup-stop squark large.two or is axes). Hence a scharm-stop in highly (essentially mixed the state circular in the red points along the flavour violating effect induced byprecisely the the deformation one loop negativeto contribution the in ( masses induced by the deformation mediated one ( constraint in figure with a mass smallerEventually we than vary 1 over angle plane (remember that observables, while the circular dots are viable points. As mentioned above, the main JHEP06(2015)122 and 1 ˜ u 5 GeV, . 2 m ± = 120 h is set to zero, hence m 2 c 2 2 / / 612 eV 614 eV 3 3 0.8 × × m m /k /k 1 1 0.7 GeV), and where we furthermore 1 5 c 1 0.75 c 10 0.75 × h h 0.6 λ m m 1.0 | λ 1.0 GeV. The parameter 124 GeV 124 GeV 14 5 GeV, the yellow region . 5 0.5 2 U | | | 10 ± 16 16 GeV × GeV, Λ = 5 GeV ˜ ˜ 6 U U B B | | 0.707 0.707 5 6 – 10 – 0.4 0). 10 m m = 125 10 M 10 ' M | | × h 260 GeV 345 GeV 0 0 × × 15 15 15 9 m . U U ∼ 0.3 ∼ U | | 31 315 . . 2 2 = 1 ˜ ˜ W W | | G . The mass of the lightest squark mass is denoted with m m 14 14 0.2 GeV and Λ = 5 h U U

6

526 GeV 688 GeV | | m 0.706 0.706 800 600 400

1200 1000 1400 1

u ] [ 10 GeV GeV m GeV ~ 5 5 GeV, Λ × G G 6 10 10 Λ Λ 1 1 ˜ ˜ g g ˜ ˜ 10 u u = 1 × × m m × m m S 9 5 . . 446 GeV 1 1.56 TeV 2 657 GeV 1.99 TeV = 1 = 0. The red region has S 2 c . Concerning the rest of the spectrum, for both benchmarks: the sleptons are at least 2 1 . Higgs mass constrains on the supersymmetric spectrum, assuming parameter as in c . Two example of viable spectra. The supersymmetry breaking scales for the scalar , (i.e. Λ − 1 = 1 and is the sup-stop mixing angle (here λ = 1 14 2 3 the black region evenU smaller Figure 2 figure set c heavier than 1 TeV;than the few other TeV’s. squarks and the are further heavier, with masses larger Table 3 sector are fixed to Λ JHEP06(2015)122 (2.8) ], effectively 67 , 66 we show also the . This implies that 3 G ) . . However, we expect that this 2 S 2 1 2 Pl Λ g , : M 2 G 2 2 2 ˜ / 5 X g 2 3 Pl : m 2 3 πm g kM 3 48 = + Max(Λ √ ' 2 1 ) Λ – 11 – M the gaugino masses respect the following relation ˜ G : q 3 X 2 M M → = : ˜ 2 3 X / 3 M Γ( is a one loop suppression. In the table m ]. ) is typically large in order to have the other squarks in the few k 6 S are generated at one loop in some model of dynamical supersym- S . Λ , 2.2 G Λ . We have shown in the previous section that the complementary case , 2 is a factor which is smaller than 1, taking into account that the fact that the k The LSP is always the , whose mass is given by Hence the and the gravitino are the only other supersymmetric that The supersymmetry breaking scale determining the gauge mediation contribution as- We are interested in regions of the parameter space where there is a very light right- , the decay of the NLSP can be displaced or longlived. In the following we assume the k simplified spectra that we investigate in the phenomenological study of the rest of the of second case, such that the Bino decay does not3 play any role in Simplified collider model signals. Based on the previous analysis of the parameter space of the model, we here define the supersymmetry breaking parameters couplingsupersymmetry to breaking the scale messengers of can thebreaking scales complete be Λ model. smaller For thanmetry instance, the if breaking, the the supersymmetry factor value of the gravitino mass for the prototypical benchmark point. Depending on the value and all the sparticles have universal decay to it with the formula Here hence could modify quantitatively but not qualitatively the results we obtained above. in the benchmark points showninvolving in table the gauge couplings relation can be relaxeddisentangling considering the a Bino complete from GGM thegaugino parameter Wino mass space and at from [ the the gluino messenger mass. scale Note will that affect modifying the the running of the masses, and TeV range. As afrom consequence, collider also physics. the The sleptons higgsinosexplained are are in also very section heavy heavy and and decoupled, essentially following decoupled the argument can play a rolewe in made the the collider assumption phenomenology that of we these have models. only one In gaugino the mass model scale formulation, Λ shown in figure of scharm/stop mixing can bebeen also recently easily discussed in generated. [ The phenomenology of suchsociated case with has the scalars (Λ In this section we discussthe the previous typical section. spectra that are generated by the modelhanded presented up in squark, which islarge highly sup/stop mixed in mixing, flavor. assuming In a the small following scharm we focus component, on consistently the with case the of points 2.3 Mass spectrum JHEP06(2015)122 and and 1 1 u u )) is always 2.8 3 . 0 , with masses varying 1 ) tχ u R ˜ t → 1 . + , with mass varying between 1 u with a branching ratio which 0 R u χ 0 . In this case its signature will u 1 (˜ χ and ˜ u 2 1 + √ 0 . ) u R , which can then decay only to the gravitino. uχ = ˜ t 1 0 1 u + → ˜ ˜ u χ g 1 R u u (˜ 2 1 – 12 – √ ]. 7 = We focus on this parameter region in the following will decay to ∗ component inside ˜ 1 is heavier than ˜ 1 4 ˜ u /u u 0 u ∗ χ t + 1 ˜ t/u u to the gravitino (given also by the universal formula ( 1 u , and is motivated by the spectrum structure that we described in the 200). The gluino, which is relevant since it participates in the production 3 − 1 ˜ u m . Maximally Mixed Sup-Stop (MMUT) scenario: the simplified model considered in the is larger than the top mass. 0 A more unusual scenario can be realized when the mass difference between the ˜ The decay of ˜ χ Actually EW production via Wino and also BinoAnother exchange interesting can possibility increase is the if cross section at LHC of a is smaller than the top mass, ˜ 3 4 0 the sections. Here the two competing decays are ˜ few % level, but we do not consider it in the following. suppressed compared to decays viaχ gauge couplings. If theis mass difference almost between 1, ˜ asresemble soon the as one of thereregions a is of light a the up-type squark-neutralino squark. plane [ This can lead to interesting bounds in some 3.1 Branching ratios We are interested inchain. production Hence of here the we lightest study squark the eigenstate possible and decay the channel resulting for decay ˜ The simplified model, thatshown we in dub figure asprevious Maximally sections. Mixed In general, Sup-Stop theeither (MMUT) Wino in is scenario, the considered is squark to be production heavy processes enough or not in to participate possible squark decays. mechanism of the lightfocus squark, on and the can case alsomixture of be with sup directly maximal and produced, stop-sup stop is mixing, right-handed squarks fixed i.e. to the 2 light TeV. We squark state is a perfect paper, and wehighly set mixed our right benchmark handedbetween up-type points. 400 squark, and that The 1000 we200 GeV, only denote and and light with ( a supersymmetric ˜ pure states Bino are neutralino a Figure 3 collider analysis. JHEP06(2015)122 3 (3.1) . 2 t , 2 m .  0 1 0 2 χ 2 χ u m ], and in the case m 2 − − 69  , 1 , at the LHC also the 2 t 2 t ˜ 2 u 68 3 m m m 1 ) mass plane. Note that 1000 ˜ 2 u 0 − 0.3 χ 0 m , 2 χ 1 2 ) + u mass and of the neutralino mass. 2 t m (and the conjugate processes), 900 − 1 m 0.45 0 − ∗ u t 2 χ 1 − 1 ˜ 2 u 0.47 m ˜ u 0 = 200 GeV the branching ratio into 1 2 χ m 800 ˜ 2 u 0 D 0 χ m → ] m ) on the (˜ Χ 2 t 2 m g − t is large (at least larger than 1 TeV on our 1 1 3.1 Ž − u 1 , m ˜ ® 2 u 700 , and 50% to top-quark and ˜ 0 4 t u 1 M 1 2 χ Ž u m @ u m or as ˜ ]( – 13 – 2 t , m + ∗ BR 1 0.4 u ˜ 0 2 u 600 1 , m 4 χ 0 ˜ ) as a function of the ˜ m u [ 0 2 χ m ρ tχ → + , m 500 1 = 450 GeV and 1 g → ˜ 4 u ˜ 2 u 1 1 ˜ u m m u [ (˜ m ρ q 0.01 400

BR

500 400 300 200 800 700 600

0 Χ ] = ] = M 0 2 t tχ , m 0 2 χ → 1 u , m [˜ 1 ˜ 2 u m we plot the branching ratio of eq. ( BR [ ρ . Branching ratio 4 Given the spectrum of the simplified MMUT scenario in figure The branching ratio for decays into top quarks is slightly suppressed even in the case of the gluino (at 2 TeV) andparameter space), the the lightest phase squark space suppression ˜ Indeed induced we by checked the that top mass thequarks is branching always is negligible. ratio always of proportional the tothe gluino the gluino decay mixing will into angle. decay squark 50% Hence and to in up up-quark the or and MMUT top model ˜ of figure top is still between 30%into and tops 40%. drops For an abruptly. even more compressed region the branchingassociated ratio production of gluinoThe and gluino the can lightest decayhence squark either giving state as extra can ˜ jets play or a extra tops significant in role. the final state. Since the mass difference between In figure the branching ratio intospectrum. top is For still instance sizable for even in region of moderate compression of the where maximal mixing due to thefor phase the space branching suppression ratio from canof the be maximal large extracted mixing top by reads mass. the The analytic formula results of [ Figure 4 JHEP06(2015)122 (4.1) 1100 2 2 2 2 2 1 1 1 1 1 √ √ √ √ √ 1000 = = = = = ]. | | | | | 14 15 15 15 15 15 70 900 [ U U U U U | | | | | ˜ g 1 = = = = = ˜ 800 u , at the LHC we expect | | | | | mixing angles → 14 14 14 14 14 3 1 ˜ 700 u U U U U U | | | | | 2.0 TeV 600 MadGraph 5 0 , pp χ 500 m 200 GeV 200 GeV 400 GeV 200 GeV 400 GeV 1 4 3 2 1 0 400 ˜ u 10 10 10 10 10 1 ˜ u 1 ˜ u → m – 14 – 450 GeV 700 GeV 700 GeV 950 GeV 950 GeV 1100 ˜ g 1000 , pp 8 , computed at LO using m 2 TeV 2 TeV 2 TeV 2 TeV 2 TeV 5 900 ∗ 1 ˜ u 1 800 ˜ u → 700 2.0 TeV pp . The first one has very light squark but quite compressed spectra, with 600 4 500 = 250 GeV. The others have larger squark masses and light or moderately heavy . Benchmark points considered in the collider study of the simplified MMUT model. Benchmark Point 1 Benchmark Point 2 Benchmark Point 3 Benchmark Point 4 Benchmark Point 5 0 1 2 2 1 0 3 400 . Cross sections in the MMUT model for squark-antisquark, squark-squark and gluino- − − χ 10 10 10 10 10 10 m − 1 Table 4 ˜ u the following production modes: Cross sections for squark-antisquark, squark-squark andand gluino-squark LHC14 production are at LHC8 shown in figure 4 Collider signatures 4.1 Production modesGiven and the cross simplified sections spectrum of the MMUT scenario in figure gluino mass fixed atreported 2 in TeV, table and withm different squark andneutralino. neutralino In masses. the next TheyLHC8 sections and are we their will distinctive discuss signatures the for exclusion LHC14, limits characterized on by such tops benchmark in at the final state. to 2 TeV. 3.2 Benchmark points We define five benchmark points on which we concentrate in the collider analysis, all with Figure 5 squark production at LHC8 and LHC14 as a function of the squark mass. The gluino mass is fixed JHEP06(2015)122 7 fb . 0 , which 0 0 4 ∼ ∗ | χ χ σ /u 14 ∗ t/u t U | = 400 GeV and fb and ˜ u 3 m − 10 1 ∗ 1 ˜ ˜ u u ∼ ∗ σ 0 /u 0 χ ∗ χ t t/u t/u p p ∗ 1 ˜ u 1 – 15 – ˜ g ˜ u 0 0 χ χ t/u t/u p p we evaluate these cross section with 5 1 fb. For the anti-squark pair production cross section we find ∼ 1 1 6 fb at 8 TeV and 14 TeV respectively. Hence they are negligible and . ˜ ˜ u u σ 1 ∼ σ p . Depending on the decay of the gluino and of the lightest squark, the final 02 fb and p . Top left: squark pair production (note that this process is produced through t-channel . 6 0 2 fb and . ∼ 4 in our maximally mixed scenario. This production mode vanishes in the scenario 0 Including the possible decay modes, the relevant production mechanisms are depicted We stress that the production modes of squark-squark and gluino-squark are sizeable Note that gluino pair production, gluino-antisquark production and antisquark pair = 2 TeV. The cross section for gluino pair production is / σ ˜ ∼ g in figure state can be composedthe of neutralino up to quarks orenergy be of signatures. stable top in quarks terms and . of collider Since we time consider scales, it will give rise to missing only because of the upmixing component in angle. the lightest For squark, instanceis and the thus 1 they squark-squark are production weighted by iswhere the proportional the lightest to squark isa purely pure stop-like, up and squark. is maximized when the lightest squark is m at 8 TeV and 14 TeVis respectively, while the cross sectionσ for gluino anti-squark production we will not consider them in our analysis. production do not contribute significantlyPDF to suppressions. the To SUSY give productionsections an modes, estimate depicted because of in of these the figure contribution and compare with the cross Figure 6 exchange of gluino). Top right:tion squark (also antisquark the pair conjugate production. decay Bottom: process for squark the gluino produc- gluino decay should be included). JHEP06(2015)122 ] ], ) 71 71 [ 6 T / E ]. ]. We find ) (4.4) 74 0 7 is the largest 73 . χ 0 ) χ ∗ 6 ], and process them , ttt 0 are not excluded by 75 χ [ searches of ATLAS [ in the final states, they 4 ] and CMS [ 0 T T 7, the CheckMate analysis 73 ) (4.3) ) (4.2) / . or of top-antitop pair plus / E 0 0 E 1 χ χ , jttχ T 5 0 0 0 / χ E χ ∗ 0 Herwig++ , ttχ χ 4 suppression, as mentioned above 0 , tt ∗ / 0 χ 0 χ 0 , jtt 0 χ 0 , jtχ , , jtχ 0 0 χ ∗ χ χ 0 0 factor as large as – 16 – are still not excluded by LHC8 searches. The , jjt ]. K ], and single- stop searches [ jjχ jjχ 0 4 ( ( χ 71 77 0 → → , shower them with ∗ 1 1 ˜ ˜ u u 1 1 , jjtχ ˜ ˜ 0 u u search [ χ 0 T → → variables [ / E ]. pp pp T jjjχ α ( MadGraph 5 79 , ], using all the available LHC searches, including jets plus 78 → ˜ g 76 [ 1 ˜ u . However, with an overall → ] at 8 TeV. Analogously, presenting top pair and ). Second, the different decay modes of the light squark eigenstate, including 4 72 pp 5 ) CheckMate 6 This result could be surprising given that the SUSY cross section is enlarged by the We thus have to verify that our benchmark points in table One can generate the following signals from squark-antisquark pair production (right Considering the relevant production modes involved in our process, a K-factor of 1 , among the possible final state we can find the single top (hence single lepton) and 5 T / squark channel is only mild,angle given to that the this fourth production(see power; mode figure this is results suppressed in by a the factor mixing of 1 possible value at 8 TeV [ contribution of the squark-squarkscenario, production where the mode only relevant with contribution(the is respect coming gluino-squark from to squark-antisquark associated production the productionregion). unmixed is squark However, negligible there at areMMUT 8 two TeV model effects in difficult which to the both exclude. small contribute First, in squark the making mass cross the section signal enhancement due of to the the squark- that all five benchmarkbenchmark points points in which table areone at in table the borderconcludes of that these the two benchmark exclusion pointsfrom are are the still the allowed. ATLAS jets first The plus stronger and constraints the come second existing LHC8 searches.produce In samples order with tousing ascertain the viability ofsearches our exploting benchmark the points we The supersymmetric processes described above contributeing to transverse final energy, states and with are jetsand and possibly miss- CMS probed [ by the jetscould plus be also probed by the standard stop searches of ATLAS [ E same sign tops (hencei.e. two same positive sign same tops, sign isscenario, and leptons). a can unique be Especially consequence considered of this as the second a maximal probe signature, flavour4.2 of mixing the in mixing our angle Constraints of MMUT from the lightest LHC8 squark state. and the following signatures from squark-gluino associated production (bottom figure Besides the usual supersymmetric signatures of jets plus figure the following final states from squark-squark pair production (left figure JHEP06(2015)122 1 and ), but . 4 = 1 1 ˜ u 1 ˜ u ] in the case of K 74 we plot the total 6, 7 . = 200 GeV). In this 0 1100 ) χ = 1 r r m ∗ 1 to to ˜ u 1 ˜ u 1000 topologies. This is particular K 1502.04358 T / - no K-fac - w/ K-fac E 2.0 TeV 900 (from CMS pure r. h. up-squark (MMUT) (MMUT) tot tot exc tot = 450 GeV and σ σ σ σ 800 1 ˜ u m [ GeV ] -factors; we used ˜ u – 17 – K m 700 600 = 200 GeV and the gluino mass to 2 TeV. The dashed, blue curve is ]. The solid, dark red curve is the exclusion cross section extracted 0 500 χ 79 , m ] for neutralino mass at 200 GeV. The dotted, red curve, for comparison ). The solid, blue curve is the same total cross section for the MMUT 78 74 ˜ g 1 1 0 3 2 ˜ 400 u

,

10 10 10 10

1 b] fb [ σ ˜ -factors. u 1 K ˜ u , ∗ 1 ], and the cross section exclusion limit extracted from CMS [ ˜ u 1 u . Simplified exclusion plots based only on the SUSY production cross section. The 7, taken from [ 79 . , 78 = 1 In order to give an intuitive explanation of these features, in figure ˜ g 1 ˜ u from CheckMate. Tomixing provide angle a suppression, further ina quantitative the right estimate plot handed of we up also thesuppressed squark, show effectiveness by not the the of mixed. total mixing the Inpotentially production angle to this and cross very case the section strong the bounds. total for same cross In sign our section plot, production is the mode considerably exclusion larger, is limit for leading not scenarios with a pure neutralino mass at 200 GeV.account This the plot different is decay an modesallows oversimplification, to and since get efficiencies some it in insight does the onmixing not various angle the channels. plays LHC8 take a reach into Nevertheless crucial for it roleregion the in MMUT of reducing simplified squark the model masses experimental and between bounds.the how 500 the GeV We 700 observe GeV and that 680 benchmarks the GeV just is excluded, above with the the experimental 450 GeV reach, and consistent with our results the spectrum is moderately compressedreducing and the the efficiencies. resulting tops will be quite soft, effectively cross section offrom our [ supersymmetric production modes, weighted with K-factors taken the appropriate top quarks, make the signaleffective less in clean than the pure first jetscase benchmark plus the point branching (with ratio of the lightest squark into top is still sizeable (see figure channels (˜ model, but re-weightedK by the appropriate from the CMS analysis [ purposes, is the cross section for the case of a pure (right handed) up squark, also re-weigthed with Figure 7 neutralino mass is fixed to the LO total SUSY production cross section for the MMUT model, including all relevant production JHEP06(2015)122 ). 4 4 ) ), in order to re- 0 4.4 tχ ), ( → 1 4.3 u (˜ ), ( BR 4.2 = 200 GeV) this implies that the cross 0 χ m – 18 – ]. ) 80 4.4 ]. However, note that the total production cross section in = 450 GeV and 74 , 1 ˜ u 73 ) and ( m 4.3 duction modes ( The new signature of the sup-stop mixing, i.e. same sign-tops, arising from the pro- Single-top signal arising from all production modes ( The collider signatures distinctive of our simplified models are: The above discussion is valid for a neutralino mass of 200 GeV. ForTo lower summarize, neutralino the five benchmark points for the MMUT model we defined in table For squark masses smaller than 450 GeV, the branching ratio into tops drops signif- Other searches that could potentially constraint the model are the standard supersym- 2. 1. the five benchmark points of the MMUT simplified model. In the next section we will study the prospects for these two new channels at LHC14 for strategy to test the mixing property of the light squark. are still allowed by actualrun at LHC8 higher searches. energy the Nevertheless, standardprobe SUSY we them. searches expect for light that In squarks in theflavour or mixing, stops the following could and we next eventually access concentrate LHC the onchannels LHC14 the to reach look for new such for signatures signatures. supersymmetric associated These scenarios, with are and large new at interesting the same time represent a powerful discuss its phenomenology at LHC14. masses, the bound onleads the to squark weaker mass bounds. is stronger. Conversely, a heavier neutralino mass Moreover, the spectrum is considerablysearches. compressed and hence Hence weakly in constrained450 GeV by the LHC which MMUT is model stillthanks allowed there to by the LHC8 is peculiar searches a properties andwe associated small which find with present therefore window maximal tops interesting flavour for to in mixing. include the squark In this final the mass blind-spot state, following, benchmark around point in our analysis and the same mass. Hence,is these consistent simplified with estimates the already robust providethan result an obtained 700 GeV through understanding we Checkmate. which do For not squark masses expect larger existing stop searchesicantly, to to be get relevant. completely negligible already at a squark mass of 420 GeV (see figure the squark-antisquark production mode wethe have entire also cross the section squark-squarkquire should production at be mode, least multiplied one by topbenchmark a in factor point the of (with final state.section One times the can branching easily ratio checklower for that than a for the single instance single top on top in the production the first in MMUT a model model would be with eventually a light pure (right handed) stop with is a consequence ofevaluation of the the oversimplification LHC of reach this see [ estimate, for ametry complete searches for recasting stops and [ our scenario is smaller than in the case of a pure light stop. Indeed, even if in addition to up-type right handed squark seems to reach very large values for the squark mass; this JHEP06(2015)122 ) ¯ t b 0 ¯ ˜ g t b χ u 5.2 + ]. This W ] set for 10 85 [ , 1.4 for ˜ and ˜ u ¯ t t u xqcut = 20 GeV . The transverse 7 -tagging efficiencies ) channel, requiring b T and NNPDF 2.3 / E for production of weak contribute to this final 3 for rare SM processes. . + u ], while we assume a con- + l 89 + l events matched to one extra jet ] with the b ¯ ) is inspired by previous work of -jet, and the other decays into ˜ b 70 b QCUT=30 GeV [ u + + W T xqcut = 10 GeV / E ], with and a + 0 and 87 l χ . ¯ and t ) t T MadGraph 5 – 19 – / l E φ . Here we require at least one positive lepton in the cos(∆ and single top production and 1 ]. b ¯ − b 79 WZ (1 QCUT=15 GeV , + ]. We match the background event samples, where relevant, T 78 / 86 E W [ and l T p 2 − q W ≡ + T W Pythia 6 m Analogously, the gluino squark associated production generates single top production [ + events, where we require at least one lepton of unspecified charge at hard ] with the default CMS settings for event reconstruction, ∗ 6 ˜ u shows examples of interesting kinematic distributions for signal and back- 88 u [ 8 tW ) channel as well as the same sign positive top (i.e. b quark. . The pair production of either same or opposite sign ˜ ]. We include modifications to optimise the analysis for the high luminosity LHC. + t ¯ 6 tZ, ZZ, W T 82 Figure In order to improve our estimates of background event yields, we normalise the Our SM background samples for the same sign lepton analysis consist of In the following sections we consider signatures of our model in the single top (i.e. / Here we define We note that mixing between sup and stop can give rise to loop-induced direct top production [ E 7 6 + ¯ tW, t ground events. Signal eventsenergy in compared the to single SM top backgrounds, channel are as characterized well by as largecontribution large missing could transverse potential mass increasedirect our top signal production rate, is however, irrelevant. after applying the analysis cuts of eq. ( figure state when one ofand the a squarks decays intotopology a when ˜ either the gluino or the squark present at least one top in its decay chain. 5.2 Single-top channel Our analysis of theref. [ single top channelThe (i.e. single top event topology of signal events results from all the processes depicted in production cross sections toservative the K-factor of NNLO+NNLL 1.4 value for ofFor ref. the [ purpose of signaland generation, 1.5 we for always assume ˜ a K-factor of 1.1 for ˜ events matched to one extra jet, wherelevel. we require one In positively charged addition, leptont at we generator also considerfinal state. rare SM processes where we include production of l us to consider a rangereach of in SM background the channels. single For topas the channel, purpose well we of consider as studying theprocess collider generation level. to extra jets using the MLMin matching scheme case [ of topbosons. production and Our analysisDelphes includes 3 detector effectsand on lepton event isolation. reconstruction, where we utilise 5.1 Event generation andWe generate reconstruction all events using leadingthe order parton distribution functions.the Upon events using hard level process generation, we further shower 5 Top signatures at LHC14 JHEP06(2015)122 , 0 = = χ and 0 (5.1) ˜ χ min T ˜ u . u m m mass, as W 400 800 channel. All , W b 350 700 illustrate the + (700, 200) (700, 400) 8 T 300 600 / E 5) = 1 . 2 + 250 500 l = 200 GeV in ˜ 0 ˜ χ [ GeV ] [ GeV ] 200 400 , η < T T m , m m 150 300 min T ¯ production. The effect suggests bb 100 200 + * 20 GeV ˜˜ ˜ g ¯ t ˜ ˜ ug ˜ ˜ uu uu t W tW > m u = 200 GeV. In the bottom panels, the > 50 100 0 T ˜ χ T p m 0 0 2 3 4 5 6 1 5 2 3 4 ( − − − − − − − − − − b

10 10 10 10 10 10 10 10 10 10 its un Arbitrary its un Arbitrary spectra compared to – 20 – ,N , m T = 700 GeV. The benchmark point with 400 800 m 950 GeV respectively. , ˜ u = 450 GeV and ). m 350 700 5) = 1 0 . and 700 ˜ u ˜ (700, 200) (700, 400) χ 2 , T m 250 GeV 300 600 / , m E ˜ u > m 250 500 T , η < = 450 / E ˜ u [ GeV ] which would be appropriate to isolate the signal in the compressed 200 400 [ GeV ] m T T -tagged jets and isolated leptons respectively, and we choose / T E / b E / 150 300 E 20 GeV ¯ > bb or + 100 200 * ˜˜ ¯ t T ˜ ˜ T ˜ ˜ ug uu uu t W tW p refer to ( m 50 l 100 l N leads to much softer 410) GeV for 0 0 6 2 3 4 5 1 4 5 2 3 . Kinematic distributions of signal and background events in the , , − − − − − − − − − −

and

10 10 10 10 10 10 10 10 10 10

its un Arbitrary its un Arbitrary b 310 production, while the effect is much milder in the ˜ , In order to improve the purity of the event sample, we impose the following set of The degree of squark-neutralino mass degeneracy has a large effect on the shape of ∗ ˜ u ˜ (210 kinematic cuts: where that a cut on mass region, might notillustration, be here optimal we in willuncompressed the focus mass non-compressed spectrum only spectrum. scenario. on For cut the selection purpose criteria of which can better probe the allowing the transverse mass distribution to extend to muchtransverse larger mass values. and missingpoint energy for distributions. the Lower400 benchmark panels GeV of mass figure of u values in the labels represent ( mass distributions of thethe SM only source backgrounds of display significant aConversely, missing a energy suppression significant and contribution around hard to the leptons missing energy is in the the decay signal of events the comes from ˜ Figure 8 distributions are normalized to unitpanels area shows a and benchmark assume point no of cuts. The signal distribution in the upper JHEP06(2015)122 , T ) ) 6 m 1 1 − − 950 GeV improves , 80 GeV in for lighter 3.6 3.4 (300 fb (300 fb 10.0 20.0 0.10 0.96 T > 3 B B m T -tagged jet is − √ √ b / E = 450 10 S/ S/ ˜ u ∼ m 3 5 3 − − − 10 10 10 037 . × × × 0.32 0.11 S/B S/B 0 0 9 4 . . . 1 2 3 t t 1 1 1 TeV. A cut on missing energy . . = 2 TeV = 2 TeV + + 0 0 ) to levels of ˜ ˜ g g ∼ < < channel would give indirect evidence , m , m S/B of integrated luminosity at LHC Run b b W b W ¯ ¯ b b 1 1 . + − 0 + + T , while the additional cut on 420.0 405.0 420.0 405.0 < / E + = 200 GeV = 400 GeV S/B l 4 4 channel. The entries show cross sections in fb after 0 0 – 21 – ˜ ˜ χ χ 10 10 b = 300 fb — (0.11, 5.3) (0.11,3.4) = 2 TeV. ¯ ¯ t W t W 450 700 950 t t × × + 3.1 , m , m L ˜ g 12.0 0.15 238.0 16.0 9.3 238.0 16.0 9.3 1 1 T . . m = 200 GeV benchmark point is discoverable with the 4 4 (0.32, 20.0) (0.24, 11.0) (0.12,3.8) channels includes a generation level cut of / E if the squark mass is 0 ˜ χ 5 + ∗ ∗ l tW − ˜ ˜ u u respectively which can be achieved at LHC Run II in the single 5 with ˜ ˜ u u mixing, of which we find that the channel with two positively , m 1 10 ˜ t = 450 GeV = 950 GeV −  8 ˜ ˜ u u ∼ − ˜ ˜ g g B ( GeV ) u m m ˜ ˜ u u ˜ u √ 400 200 100 improvement in +jets and S/ /m 1 TeV. ∼ at 300 fb 0 W ˜ ˜ u u ˜ χ ˜ ˜ u u mixing, as even then minimal flavor-conserving SUSY models predict = 450 GeV 2.6 39.0 1.1 . B 0.67 0.82 8.3 0.27 0.40 3.4 0.37 0.36 0.48 0.26 0.30 0.34 0.093 0.12 0.13 400 GeV. Requiring exactly one lepton and at least one m ˜ ˜ t u √ , m − S/ b b u = 1 = 1 shows an example cutflow for a benchmark signal points of b b + + and = 200 5 T T ,N ,N 210 GeV 410 GeV 250 GeV 250 GeV . Summary of reach for benchmark points in the single top channel. The table entries . Example cutflow in the 0 / / E E cuts at lower integrated luminosities is also likely to be more efficient in signal regions with smaller ˜ χ > > > > + + = 1 = 1 S/B T by an additional factor of 10 at a 50% signal loss. Our results, summarised in table m l l A potential discovery of a signal in the Table T T l l T T E The cuts we chose for this analysis are somewhat optimised for high luminosity LHC. Relaxing the / / 8 E E N N m m determine the presence of ˜ charged leptons is an excellent candidate. and cross sections. masses of roughly for the existence ofany) supersymmetry, of but the would not ˜ signals provide in information the on single-lepton the channel. degree Measuring (if additional channels would be required to squark masses, but only to results in a factor of S/B show that the signal significance of II, while with the same amount of data we should be able to rule out our model for squark and sufficient to bring the signal to background ratio ( Table 6 show top channel. The massescolumn of respectively. squarks All and results neutralinos assume are listed on in the topmost row and leftmost Table 5 each consecutive cut. order to improve the statistics in the signal region. JHEP06(2015)122 ∗ T + ˜ u / E ∗ W u + model + and the positive l process, u and in a non- + 0 T ˜ u l ¯ t mixing, as ˜ u p t ˜ u ˜ t tχ m u 400) GeV, for → , uu 300 decays which yield , , , b illustrate the point. decay to (10) fb level rare SM 9 min T u O to leptons, the = (200 > m ), as well as SM mixing. Production of ˜ ) 120 GeV W Z ˜ t + 1 min T + l > refers to the highest ( − m T W T u + 1 ]. l / 45 [ and + process, where ˜ − l ,E, m + ˜ g l ], while RPV models which also includes W ˜ 1 u + 43 parameter space it is beneficial to relax the [ > 400) GeV displays a much softer spectrum → , W 0 − ˜ + 5) = 2 5) 5) = 0 (5.2) χ l . . . , Composite Top and extra-dimensional models can also – 22 – ug 0 ]. Furthermore typical RPV models with 2 2 2 − l Z , m 46 ˜ u was somewhat optimised to probe high m T , η < , η < , η < ) = (700 0 m ˜ χ the “smoking gun” signal of the maximally mixed ˜ ¯ tZ, ZZ, W events [ 9 , or of the , m 0 and − ˜ u l ¯ tW, t 20 GeV 30 GeV 20 GeV T tχ − t m l / E > > > T T T p p p and ( ( ( j + + − l l l channel. SM backgrounds consist mainly of N + N N l T 950) GeV respectively. / E , shows the characteristic kinematic distributions of the signal and background + 700 9 refer to isolated positive/negative leptons and , + . l which would yield two negative sign leptons in the final state, contributes only mixing angle, as well as the small branching ratios of − 9 + ˜ t l + ∗ l ˜ u − g Our choice of cuts on In order to maximise the signal significance in the same-sign positive lepton channel, Figure The same-sign positive lepton final states are a consequence of the u = (450 Other non-supersymmetric models such as 9 ˜ u , where the same sign lepton background comes mainly from leptonic b ¯ cuts on missing energy andThe transverse mass. benchmark Bottom point panelsof of of figure missing ( energy and transverse mass than theproduce corresponding, final non-compressed states with point two of positive leptons. lepton in the event. Form the purpose of illustration, we set compressed mass spectrum scenario.of probing Again, the it compressed is region important of to note that for the purpose where the signal events are muchof larger figure than in the SM backgrounds, as shown in thehere right we panel employ a set of cuts: in the processes (here we consider b isolated leptons. With thecontain exception two of positive rare isolated processes,cross leptons sections. the probability is In that addition, tiny, SM both yet processes the significant amount due of missing to energy the and large the production transverse mass of other RP conserving supersymmetric modelssame can amounts predict of same-sign leptonviolation signals with lead the to signalslepton with number dominant violation could lead to dominant the ˜ channel offers a very cleanand probe ˜ of the presencefew of large % ˜ to theSUSY, total the strong signal PDF cross suppression section, is a due valuable to feature of the signals PDF with suppressions. large ˜ In the context of Within the framework of SUSY, at the LHC is the final state containing twowith positive consecutive leptons decays and to largedecay missing chain energy. of the gluino present one positive top. Though suppressed by two powers of 5.3 Same sign top channel JHEP06(2015)122 15 − back- space. 10 b ¯ channel. 0 b ˜ χ 400 800 ∼ T b ¯ + b / E + , m ˜ u ¯ t 350 ˜ 700 ˜ ˜ u ˜ u ug t W rare proc. + W (450, 200) (700, 200) (700, 400) m can be achieved + l 300 600 σ 1 TeV at the high + and l ∼ ¯ t 250 500 with masses of up to t lower than the one we u [ GeV ] [ GeV ] T 200 400 T T 400 GeV, suggesting that m m m for ˜ . 150 300 σ and 100 200 ) results in a factor of T / E is comparable to the reach of the 5.2 50 100 1 − 0 0 1 2 3 4 5 3 4 2 − − − − − − − −

10 10 10 10 10 10 10 10 its un Arbitrary its un Arbitrary . In case a signal is observed in the single 1 − – 23 – 400 800 b ¯ b 50% in signal efficiency. + ˜ u ¯ t 350 700 ˜ ˜ ˜ 400 GeV. A significance higher than 3 u ug t W rare proc. ∼ (450, 200) (700, 200) (700, 400) . . In the top panels, we are showing only the benchmark point 300 600 WZ 250 500 and shows an example cutflow for two benchmark parameter points. , the high luminosity LHC should be able to probe and measure [ GeV ] 200 [ GeV ] 400 cut efficiently suppresses the rare-process contribution to the total 1 T T 7 − / 200) GeV. In the bottom panels, the values in the legend represent different / − T , at a cost of , E E 150 300 / 1 TeV, assuming the neutralino masses of W E 200) GeV, suggesting that a cut on ) could be more optimal in the compressed spectrum scenarios. + , ∼ S/B 100 200 W 5.2 + ) = (450 50 0 100 shows a summary of results on five benchmark points in the ˜ χ 8 . Kinematic distributions relevant for the signal search in the ) = (700 0 0 3 4 5 1 2 ) benchmark points. 4 2 3 , m 0 − − − − − − − − 0 ˜

˜ u

χ

˜

10 10 10 10 10 χ 10 10 10 its un Arbitrary its un Arbitrary m ¯ tZ, ZZ, W The reach of the single top channel at 300 fb Table Continuing, table , m , m ˜ u ˜ u 700 GeV for a neutralino mass m m ¯ tW, t luminosity LHC. same-sign positive leptons searchtop at channel 3000 fb at 300 fb possible large squark mixings. Conversely, in case no signal is observed in the single top We find that the∼ LHC can achieve afor signal masses significance up of to 5 the same sign positive lepton channel could rule out the model up to The requirement on thegrounds, while lepton the multiplicity efficientlyevent yield. reduces We the find thatimprovement a in minimal set of cuts in eq. ( with ( ( ( suggest in eq. ( Figure 9 All histograms aret normalised to unit area. The label “rare proc.” includes SM production of JHEP06(2015)122 − ) ) W 1 1 + − − W + 4.0 2.0 7.9 7.6 3.4 3.1 0.64 0.56 (3000 fb (3000 fb B B . √ √ T / ¯ tZ, ZZ, W S/ E S/ = 2 TeV. ¯ tW, t t ˜ g m 0.26 0.21 0.12 S/B S/B 0.033 0.017 0.013 0.0031 0.0023 = 2 TeV = 2 TeV ˜ ˜ g g , m , m 01 0.081 01 1.2 01 0.45 01 1.2 . . . . 0 0 0 0 respectively which can be achieved at LHC Run +jets rare proc. +jets rare proc. 1 < < < < = 400 GeV = 200 GeV channel. The entries show cross sections in fb after − – 24 – 0 0 ˜ ˜ χ χ T — (0.22 , 5.3) (0.26, 4.0) 450 700 950 / E 01 01 . . , m , m ¯ ¯ t W t W 0 0 t t + (0.21, 7.9) (0.31, 7.5) (0.26, 4.1) 0.033 0.033 0.022 14.0 0.067 0.022 19.0 0.033 0.033 0.022 14.0 0.067 0.022 19.0 < < + . A more distinctive feature of the MMUT model, the l 1 at 3000 fb + − l B ˜ ˜ g g ˜ ˜ u u √ = 950 GeV = 450 GeV ˜ ˜ u u S/ ( GeV ) using the hardest positive lepton in the event and m m ˜ u T 400 200 ˜ ˜ u u and m ˜ ˜ u u /m 0.12 0.034 0.20 0.037 0.21 0.037 0.014 0.0068 0.026 0.014 0.030 0.014 0.031 0.014 0.080 0.019 0 , the parameter region giving raise to measurable same-sign positive ˜ χ 1 − S/B m = 0 = 0 jj jj − − + + l l T T ,N ,N / / E E 400 GeV 200 GeV 120 GeV 120 GeV . We compute . Example cutflow in the . Summary of reach for benchmark points in the same sign positive lepton channel. The 1 1 + + = 2 = 2 > > > > > > + + + + l l T T In this paper we studied an example model of supersymmetry with large mixing in j l j l T T WZ + + / / m E N N l m E N N l the right-handed up-type squark massOur matrix analysis in includes the detailed consideration contextby of of constraints flavour extended imposed observables, gauge on as mediation. the wellsquark parameter as space mixings. prospects We for find that LHCaccessible the Run at single-top II final LHC14 to signatures with discover predicted 300 models by fb our with model large can be The canonical paradigm of supersymmetrya typically flavour assumes symmetry, ultra-violet thereby completions leading with toof aligned large or off diagonal diagonal soft entries masses.the represents context Yet, a the of viable possibility the and MSSM. interesting option to be investigated in channel at 300 fb leptons yield at High Luminosity LHC will already be6 ruled out. Conclusions Table 8 table entries show II in the same-signthe positive topmost lepton row channel. and The leftmost masses column of respectively. squarks All and results neutralinos assume are listed on in each consecutive cut. Theand label “rare proc.” includes SM production of Table 7 JHEP06(2015)122 ], we define a 3) entries. 10) TeV scale. , 6 3) entry in our , − (5 , we should specify , O ξ ..., 2 2 + m 1 2  2 0 u + A 2. Hence we find that in the m . 2 1 † u we assumed that the next to 1 A m ; see also the cross section plot 3 700 GeV, and the tuning of the 1 2 ' 6 + ]. In analogy with [ ≥ ξ u = 2 y 73 ˜ u 2 2 U m m m 2 † u | ∼ 6 y , 1 2 ˜ u + U | m u 650 GeV [ 2 0 y + m – 25 – Q ≈ 2 1 = 450 GeV which is a peculiar very compressed 0 m we considered only one of the lightest eigenstates. m † u 1 2 m y ˜ 3 u | , we can consider it to be at the 6  , the lightest and next to lightest up-squark eigenstate, m 1 2 U 2.2 | m = = 6 Tr 3 , and u 2 0 3 2 H 2 U 1 m m m m d dt ≡ 2 ξ π ). In order to provide a quantitative estimate of 16 7 100. In the most optimal scenario, instead, we can assume that the same we apply a common bound of − 10 30 ). We conclude that generically the MMUT model will be at least slightly more ], where the lightest right handed squark is a pure stop, not mixed in flavor. ' 7 90 ξ In the simplified model of section The reference scenario to which we compare the degree of fine tuning is natural As models with large squark mixings typically suffer from an increased degree of fine Note that here one should rely on some extra mechanism (such as the NMSSM) to obtain the correct 10 extra production modes (inof particular figure process 1 intuned figure than natural SUSY. Higgs mass. LHC bound on the lightestIn squark this eigenstate applies case also toMMUT the model next with to respect lightest eigenstate. tooptimal natural case, SUSY the reduces MMUT to modelThe also reason represents a is slightly that morehigher the un-natural than SUSY LHC the scenario. bound LHC on bound the on lightest a squark pure state stop in eigenstate, the since in MMUT the model former is case we have also the value of thelightest other squark up-squark eigenstate eigenstate. is decoupled Ingauge from section mediation LHC model physics, of and section In taking this inspiration case from the the MMUTfactor model would be considerably more tuned than natural SUSY by a respectively. We found that the lower(neglecting bound on here such the state from possibilitypoint; LHC of 8 see TeV searches figure is around 700 GeV parameter measuring the departure fromMMUT natural scenario SUSY with by the dividing minimal the one (3 of natural SUSY: where we labelled with tuning are the ones projected onto the Yukawa directions,SUSY essentially the [ (3 The tuning in natural SUSYcase of is 200 set GeV by neutralino, the is LHC around bound on right handed stop which, in the of the up type higgs soft mass: eventually leading to aconcludes fine that tuning the in relevant the entries EWSB of correction. the squark From this mass expression, matrix one in the evaluation of the the high luminosity LHC.into A the combination flavor of mixing the properties two of searches the could light provide squarktuning, useful state. we insight take a moment todetermining discuss the the tuning naturalness in of the the MSSM MMUT are model. the dimensionful The terms parameters entering in the corrections same sign positive lepton final state which signals a large squark mixing, can be probed at JHEP06(2015)122 (A.1) 2 4 Λ M  Λ M  h 2 λ ij c 2 π U d 48 − 2 Λ ) (A.2) ) coupled via superpotential in- 2  2 r φ 2.3 g 2 2 r ˜ φ φ C 1 + 3 ]. The coupling with the same structure , φ 1 i 11 =1 φ X U r i 1 c ˜ φ 2 ( 3 − =1 X i 13 in their classification, and it consists of the X – 26 – U I R-symmetry ( λ = d 2 4 = λ Z + W φ SUSYbr d 2 W λ  (A.3) U Λ d ij 2 c λ 2 ij λ c 2 4 . π U π d F 1 16 2 θ 256 − ) to the up type quark. + = = 2.2 j j M U U i F = i U 2 U ] and results X A δm In this case the contribution to the soft masses can be extracted from the formulas The cases of non-R symmetric hidden sectors coupled via messenger matter coupling On the model building side, we note that we did not address the issue about the Future studies of models with large squark mixings would benefit from including the 11 of [ where the messenger are assumedto to a be spurion part as of a supersymmetry breaking sector coupling with to the MSSM have been completelywe classified are in considering [ hasmessenger-matter been coupling denoted as In this section wei.e. obtain an the hidden soft sector termteraction with ( contribution a for discrete the model studied in this paper, Policy Office through the Interuniversitypostdoctoral Attraction Fellowship. Pole A. P7/37. M. is A. alsoHigh M. supported Energy is in Physics a part and Pegasus by the FWO the Strategic Research Research Program Council of the VrijeA Universiteit Brussel. Soft terms from R-symmetric hidden sector version of this paper.the We also draft. thank A.M. David ShihDedes, would and like Didar Jared to Dobur Evans thank for andthank also useful the Diego Riccardo comments University Redigolo on of Argurio, for Kansas Lorenzostages phenomenology interesting of Calibbi, group discussions. the Athanasios for project. their M.B. hospitality M.B. during and would the A.M. like final are to supported in part by the Belgian Federal Science pect at greater depth,UV as perspective. well as to evaluate the model’s effectiveAcknowledgments level of tuning from a We are grateful to Gilad Perez for discussions and insightful comments on a preliminary possible scenario where the neutralinoextra is displaced not to stable the on signaturesat collider we the scales, discussed, LHC adding which Run could typically potentially II. two be accessed dynamical origin of supersymmetry breaking. It would be interesting to explore this as- JHEP06(2015)122 ) j u i u and A.3 Z (A.7) (A.4) 1 X  . ) (A.8) c . 4 ˜ φ 4 . This is analogous + h φ (A.6) 2 ) j and we used that j X + U u i 3 j k † u c ˜ u φ i  and F 3 Z c ) ) 1 ∗ φ j x ]. ( u X X 2 = i ∂ 91 u X )( Z ij ) (A.9) k c | ] splitted the contributions to ) is the same. X u | 2 i ) + ∂ 2 11 u ( 2 X | ˜ X φ Z F ( | 2  j ( X = 4, + 2) ln(1 + j φ u ∂ i u + x ( 11 3 i u + ( 2 u j | Z 1 Z U ,C − ˜ F φ † i | ) 1 to make it explicit. In the formulas ( U ) + x φ | ) 2 ( = 0 )), we adopt the following strategy. Consider 1 j | ) + 1 − u j ) and i A X 2 | | | u X 2.3 u i – 27 – 1 ( u j Z ,C + X u ∗ 5 Z | i ) + ( ∗ / X u 4 (A.5) j 2) ln(1 ∂ X ) Z φ u ) is coming from one-loop correction to the soft mass, 2 soft j i ∂ 3 2 X − u u m 2 = 2 = φ i ∂ X but plays a crucial role in lowering the squark mass. The x Z ( u A.3 ∂ Λ j ( )Λ 2 1 + ( = ˆ u Z |  i 2 ij 2 . C | u X 4 F ) in ( x 3 φ .c.y ∂ x F Z function is 1 † ( j F/M 2 soft ⊃ | φ y U , and another one coming from the square of the first derivative h .c.y −| F ( i m ∗ j † i 2 U = 4, ) = y U U Tr( = = X ( x i † i 2 ( φ 4 4 c j j δm 2 d U λ h π π U U λ ) i i | U 3 =1 and U 2 U U i d X d X 256 256 3 A | m λ X ( ) arise from the correction in the Kahler potential − − j = u i = = = 1. A.3 u = 2 and W 2 3 u ij c θZ 2 H 2 Q 4 U , i.e. the A-term squared. Indeed the authors of [ + d d j schematically into u 2 2 δm δm i c Z Now, in order to obtain the complete set of soft terms induced in our model by the R- The last term in These results have been obtained by studying the threshold corrections to the wave u The two sectors are coupled only via the up type quarks and the correction of one sector to the other , but with the same coupling to the MSSM matter field Z + 2 soft 2 11 2 1 are loop suppressed andto negligible, the unless situation there for is a two SUSY huge breaking hierarchy between hidden sector in gauge mediation [ which receive in this case two additive contributions Note that the functional form of As in the case above,to the the one soft loop masses corrections are to encoded the into A-terms the and the wave function two loop renormalization corrections for the MSSM field and it is an even function of symmetric SUSY breaking sector (seea eq. double ( copy ofX the above non R-symmetric model, with two different spurions the A-term contribution to the soft masses is the secondit term is in not the at big leading roundprecise order parenthesis. expression in for the MSSM field. From thistwo procedure loop) it can is be clearwith divided that respect into the to a contributions to contributionof the coming soft from masses the (at m second derivative of leading to where the second term in the mass squared arises from integrating out the F term of the function renormalization of thesengers. MSSM matter Precisely, fields in induced thethe by case results integrating ( of out the the up mes- type quark (the other sfermions are analogous), where c JHEP06(2015)122 j U † i (A.10) (A.11) U  ) (A.12) ) c | ˜ 2 φ d X | φ i ( . j c + u . i d u ˜ φ ). Moreover we also ). We stress that no Z c + h ∗ 2 2 φ j X 2.5 Λ ) to the soft masses in U + ∂ i A.11 ), the induced soft terms ! 2 † u a 2 r ) X ˜ φ F g d ∂ b r  ˜ F/M ( φ φ ) A.10 2 F d C | | 2 2 3 φ 2 + , θ F X b | + | =1 ˜ − X ). φ ( r c j a ˜ φ 2 u cancel out and we are left only with φ i c M ) + ( A.3 | u j are given by ( φ − 1 2 u Y = Z i 2 φ 2 X + u 2 | in ( d Λ + X b )Λ ( Z 2 j j ˜ ∂ φ λ ij F/M u U 2 b i i )

.c.y F φ u 2 U † U Z y + d .c.y ∗ – 28 – 1 δm † 2 ) + FX a X | ). We hence conclude that the soft terms induced 2 y λ ˜ φ Tr( 1 ∂ ( θ a ij 1 2 4 4 X 2 c 2.2 φ term is not present in the two loop corrections to the | λ X π + ), is indeed the one quoted in ( π ( λ 4 ( ∂ U 2 j π ( U | d u M 2 M 1 2.2 d i 256 | 256 3 A u | ), which permits any use, distribution and reproduction in 1 256 = − − Z F ) and ( ) + | 1 1 d  = = = X φ X , which is exactly two copies of the R-symmetric model consid- 2.3 ), we can rotate the messenger fields in a new basis such that ∂ c + ) and ( j u 1 ij F φ U 2 H i 2 Q F 2 2.3 2 U θ + A.10 h δm b δm CC-BY 4.0 = δm φ ⊃ a Y This article is distributed under the terms of the Creative Commons φ j ( i U ) is equivalent to the following model † i U i U c j A.8 u i 3 =1 u i X λ θZ 4 = d Hence the total contribution to the soft terms for the model discussed in the main The correction induced by the Kahler potential are then Z W expression. Hence for this model,are with twice the the particular following choice contributions ( we have that the termsthe with second first derivatives derivatives contribution of to the soft masses, which are two copies of the same Now, in the special case in which soft masses. Open Access. Attribution License ( any medium, provided the original author(s) and source are credited. computed explicitly the onethe loop R-symmetric model, corrections and (suppressed foundR-symmetric in that model, they i.e. are the equivalent to last the term one in induced by thebody non of the paper, i.e.A-terms ( are generated, and the where we denoted ered in the paper,by see the eq. R-symmetric ( model at leading order in the theory ( In the special choice ( JHEP06(2015)122 D , , , , 08 ]. B JHEP (2009) , ]. ]. SPIRE 06 JHEP (2009) 087 Phys. Rev. IN , (2002) 095004 , ]. ][ ]. ]. 08 SPIRE Nucl. Phys. SPIRE GeV IN JHEP , IN D 66 , ][ SPIRE ][ SPIRE SPIRE IN ]. 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