Supersafe Supersymmetry with a Dirac Gluino

Supersafe Supersymmetry with a Dirac gluino

Graham Kribs University of Oregon

mainly: 1203.4821 with Adam Martin (CERN/Notre Dame); plus 1208.2784 with Adam Martin, Ricky Fok (York), Yuhsin Tsai (UC Davis) and work-to-appear with Nirmal Raj (Oregon) Outline

1. Brief Intro

2. Dirac Gluino and “Supersoft Supersymmetry”

3. Colored Superpartner Production @ LHC

4. Simpiﬁed Models

5. Jets + missing searches for supersymmetry @ LHC

a) ATLAS; CMS αT; (CMS MHT; CMS “razor”) b) Comparisons

6. Generalizations (“mixed gauginos”)

7. Summary Introduction

Weak Scale Supersymmetry @ LHC Many Searches!

In this talk, focus on “jets + MET” that arise from squark and gluino production. ATLAS jets + MET August 2012

Squark-gluino-neutralino model, m(χ∼0) = 0 GeV 2000 1 ATLAS Preliminary Combined

1800 CLs observed 95% C.L. limit

CLs median expected limit Expected limit ±1 σ 1600 ATLAS EPS 2011 ∫ L dt = 4.71 fb-1, s=7 TeV

squark mass [GeV] σ = 1 fb ATLAS SUSY 1400 1st+2nd jets + MET 1200 = 10 fb generation σSUSY March 2011 squark mass 1000

800 σSUSY = 100 fb

600 600 800 1000 1200 1400 1600 1800 2000 gluino mass [GeV] Supersymmetry @ LHC

Squark-gluino-neutralino model, m(χ∼0) = 0 GeV MSUGRA/CMSSM: tanβ = 10, A = 0, µ>0 2000 1 0 ATLAS Preliminary ATLAS Preliminary 700 Combined L dt = 4.71 fb-1, s=7 TeV [GeV] ∫ 1800 CLs observed 95% C.L. limit 1/2 Combined

CLs median expected limit m CLs observed 95% C.L. limit Expected limit ±1 σ 600 q ~ CLs median expected limit 1600 ATLAS EPS 2011 (1800) -1 ∫ L dt = 4.71 fb , s=7 TeV ATLAS EPS 2011

squark mass [GeV] σ = 1 fb SUSY ∼ 500 τ LSP 1400 ~ q (1400) LEP Chargino ~ No EWSBg (1200) 1st+2nd 1200 400 q ~ σSUSY = 10 fb (1000) generation ~g (1000) squark mass 1000 300 ~g (800)

q~ 800 σSUSY = 100 fb (600)

200 ~g (600) 600 600 800 1000 1200 1400 1600 1800 2000 500 1000 1500 2000 2500 3000 3500 4000 gluino mass [GeV] m0 [GeV] ATLAS-CONF-2012-033 Figure 7: 95% CLs exclusion limits obtained by using the signal region with the best expected sensitivity at each point in a simpliﬁed MSSM scenario with only strong production of gluinos and ﬁrst- and second-generation squarks, and direct decays to jets and neutralinos (left); and in the (m0 ; m1/2) plane of MSUGRA/CMSSM for tan = 10, A0 = 0 and µ>0 (right). The red lines show the observed limits, the dashed-blue lines the median expected limits, and the dotted blue lines the 1⇥ variation on the expected ± limits. ATLAS EPS 2011 limits are from [17] and LEP results from [59].

7 Summary

This note reports a search for new physics in final states containing high-pT jets, missing transverse 1 momentum and no electrons or muons, based on the full dataset (4.7 fb ) recorded by the ATLAS experiment at the LHC in 2011. Good agreement is seen between the numbers of events observed in the data and the numbers of events expected from SM processes. The results are interpreted in both a simplified model containing only squarks of the first two generations, a gluino octet and a massless neutralino, as well as in MSUGRA/CMSSM models with tan = 10, A0 = 0 and µ>0. In the simplified model, gluino masses below 940 GeV and squark masses below 1380 GeV are excluded at the 95% confidence level. In the MSUGRA/CMSSM models, values of m1/2 < 300 GeV are excluded for all values of m0, and m1/2 < 680 GeV for low m0. Equal mass squarks and gluinos are excluded below 1400 GeV in both scenarios.

References

[1] L. Evans and P. Bryant, LHC Machine, JINST 3 (2008) S08001.

[2] H. Miyazawa, Baryon Number Changing Currents, Prog. Theor. Phys. 36 (6) (1966) 1266–1276.

[3] P. Ramond, Dual Theory for Free Fermions, Phys. Rev. D3 (1971) 2415–2418.

[4] Y. A. Golfand and E. P. Likhtman, Extension of the Algebra of Poincare Group Generators and Violation of p Invariance, JETP Lett. 13 (1971) 323–326. [Pisma Zh.Eksp.Teor.Fiz.13:452-455,1971].

[5] A. Neveu and J. H. Schwarz, Factorizable dual model of pions, Nucl. Phys. B31 (1971) 86–112.

14 Squark-gluino-neutralino model, m(χ∼0) = 0 GeV MSUGRA/CMSSM: tanβ = 10, A = 0, µ>0 2000 1 0 ATLAS Preliminary ATLAS Preliminary 700 Combined L dt = 4.71 fb-1, s=7 TeV [GeV] ∫ 1800 CLs observed 95% C.L. limit 1/2 Combined

If weak scale CLs median expected limit m CLs observed 95% C.L. limit Expected limit ±1 σ 600 q ~ CLs median expected limit 1600 ATLAS EPS 2011 (1800) -1 ∫ L dt = 4.71 fb , s=7 TeV ATLAS EPS 2011

squark mass [GeV] σ = 1 fb SUSY ∼ 500 τ LSP 1400 ~ q (1400) LEP Chargino ~ supersymmetry... No EWSBg (1200) 1200 400 q ~ σSUSY = 10 fb (1000) ~g (1000) 1000 300 ~g (800)

q~ 800 σSUSY = 100 fb (600)

200 ~g (600) 600 600 800 1000 1200 1400 1600 1800 2000 500 1000 1500 2000 2500 3000 3500 4000 gluino mass [GeV] m0 [GeV]

Figure 7: 95% CLs exclusion limits obtained by using the signal region with the best expected sensitivity at each point in a simplified MSSM scenario with only strong production of gluinos and first- and second-generation squarks, and direct decays to jets and neutralinos (left); and in the (m0 ; m1/2) plane of MSUGRA/CMSSM for tan = 10, A0 = 0 and µ>0 (right). The red lines show the observed limits, the dashed-blue lines the median expected limits, and the dotted blue lines the 1⇥ variation on the expected ± limits. ATLAS EPS 2011 limits are from [17] and LEP results from [59]. R-parity violation. 7 Summary LSP decays, This note reports a search for new physics in final states containing high-pT jets, missing transverse 1 momentum and no electrons or muons, based on the full dataset (4.7 fb ) recorded by the ATLAS 1st,2nd generation experiment at the LHC in 2011. Good agreement is seen between the numbers of events observed in the data and the numbers of events expected from SM processes. no missing energy. The results are interpreted in both a simplified model containing only squarks of the first two genera- heavy (> 1.5-2 TeV), tions, a gluino octet and a massless neutralino, as well as in MSUGRA/CMSSM models with tan = 10, A0 = 0 and µ>0. In the simplified model, gluino masses below 940 GeV and squark masses below 1380 GeV are excluded at the 95% confidence level. In the MSUGRA/CMSSM models, values of m1/2 < 300 GeV are excluded for all values of m0, and m1/2 < 680 GeV for low m0. Equal mass squarks if LSP light and gluinos are excluded below 1400 GeV in both scenarios. (< 200-300 GeV) References [1] L. Evans and P. Bryant, LHC Machine, JINST 3 (2008) S08001. Too simplified [2] H. Miyazawa, Baryon Number Changing Currents, Prog. Theor. Phys. 36 (6) (1966) 1266–1276. [3] P. Ramond, Dual Theory for Free Fermions, Phys. Rev. D3 (1971) 2415–2418. a model [4] Y. A. Golfand and E. P. Likhtman, Extension of the Algebra of Poincare Group Generators and Violation of p InvarianceToo, JETP Lett. simplified13 (1971) 323–326. [Pisma Zh.Eksp.Teor.Fiz.13:452-455,1971]. (compressed) LSP heavier [5] A. Neveu and J. H. Schwarz, Factorizablea model dual model of pions , Nucl. Phys. B31 (1971) 86–112. 14 (at least 300-400 GeV) (cascades) Dirac Gluino in Supersymmetry Dirac Gluino

Solve EDMs “Supersafe” (Hall,Randall) -- Suppressed σ’s (Kribs,Martin)

Reduced Supersoft R-Symmetric Fine-Tuning Supersymmetry Supersymmetry (Kribs,Martin) (Fox,Nelson,Weiner) -- Flavor safe! (Kribs,Poppitz,Weiner) II. R-SYMMETRY IN SUPERSYMMETRY assignments of the spurions are necessarily +2 and +1 respectively. The W ! can be considered a hidden sector ! The supersymmetry algebra automatically contains a U(1) that acquires a D-term. We assume that the sizes continuous R-symmetry. It was argued long ago [14] that of the F -type and D-type breaking are roughly compa- the existence of an R-symmetry in the hidden sector is a rable up to an order of magnitude or so. Coupling these necessary condition for supersymmetry breaking. A va- spurions in an R-preserving manner to a low energy su- riety of supersymmetric theories exhibit supersymmetry persymmetric theory gives rise to the most general theory breaking without breaking the R-symmetry, notably the with softly broken supersymmetry and an R-symmetry. recently discovered nonsupersymmetric metastable vacua Assuming ordinary Yukawa couplings are R- in supersymmetric gauge theories [15, 16, 17]. Why, then, symmetric, and that electroweak symmetry breaking expectation values H do not break R-symmetry, has unbroken R-symmetry not played a larger role in su- ! u,d" persymmetric model building? the quark and lepton superfields must have R-charge There are three basic reasons. The phenomenological +1 and the Higgs superfields have R-charge 0. Gauge lore has been that gaugino masses require R-symmetry superfields Wi have their usual R-charge +1. breaking. This is true for Majorana gaugino masses, but For the MSSM, writing all operators consistent with perfectly viable Dirac gaugino masses (see [18, 19, 20]) the SM gauge symmetries and the extended R-symmetry, are possible when the gaugino is paired up with the we find: fermion from a chiral superfield in the adjoint represen- Majorana gaugino masses are forbidden. tation. Similarly, the µ term also breaks R-symmetry, in • the presence of the Bµ term, and is also needed to give The µ-term, and hence Higgsino mass, is forbidden. the Higgsinos a mass. • The second reason is that models of dynamical su- A-terms are forbidden. • persymmetry breaking generally break the R-symmetry. Left-right squark and slepton mass mixing is absent However, as already alluded to above, nonsupersymmet- • (no µ-term and no A-terms). ric vacua do not always break the R-symmetry. For example, O’Raifeartaigh models may preserve an R- The dangerous ∆B =1and∆L =1operators, • symmetry, and, intriguingly, some simple models of su- QLLLDR, URURDR, LLLLER,andHuLL,arefor- persymmetry breaking in meta-stable vacua also preserve bidden. So far we havethe notR included-symmetry, any for explicit a review Majorana see [16]. mass for the ESP fields. Since a is massive, we can integrateThe last it out, reason yielding is related the condition to embedding supersymme- Proton decay through dimension-five operators, • try breaking in supergravity. At the very least, two con- QLQLQLLL and URURDRER,isforbidden[68]. ∂exclude flavor violation is to communicate supersymmetry breaking from a flavor independent ditions must be satisfied:L =0 theDj gravitino=0. must acquire a (2.7) ∂Reinteraction.(a ) → Various possibilities include gauge∆L mediati=2Majorananeutrinomass,on [14–16], anomaly mediationHuHuLLLL [1,,is 17] mass, and the cosmologicalj constant must be tunable to • (virtually) zero. Theand second gaugino condition mediation is usually [18, 19]. satisfied allowed. Since D-flatness is an automatic consequence of these fields, in the absence of a Majorana by adding a constant term in the superpotential, breaking mass, no low-energy D-term quartic couplingsAs an will alternative be present,includingtheveryimportant to F -term SUSY breaking,Already supersymmetrywe see that the extended can alsoR be-symmetry broken by leads a D- the R-symmetry explicitly. Indeed, it is this term that Higgs quartic potential terms. In thecomponent presence of explicit vev of supersymmetric a hidden sector Majorana vectorto masses superfield, several improvements with gaugefieldstrength over the MSSM.W However,! .However, the ensures the R-axion that results from a spontaneously MSSM gauginos and Higgsinos are massless,α in obvious M1,2 for the U(1) and SU(2) ESPs, the quartic coupling will not vanish. For example, the broken R-symmetrythe is lowest given a dimension small but gauge non-zero invariant mass operatorconflict with which experiment. directly contributes We must therefore to scalar augment masses Higgs quartic coupling rescales as [21]. There are potentialsquared loopholes is to this generic argu- the MSSM in such a way that allows for R-symmetric ment, however. One is that, in some cases, the cosmo- α β g!2 + g2 1 M 2g!2 M 2g2 gaugino! ! † and! Higgsino! masses. logical constant could also1 be canceled2 by fields in the4 (W Wα) W Wβ † 2 2 + 2 2 . d θ (2.8) Q Q. (2.3) Kähler potential8 → 8 that!M1 acquire+4m1 largeM2 +4 expectationm2 " values M 6 [22]. Second, we show in Sec. VI that even with! only As we will discussexclude shortly, flavor there violation are theIf M usual is to communicate one-loopM ,thistermwillbesubdominanttoanomalymediatedsoftmass contributions supersymmetry to the quartic breaking coupling, from a flavor independentA. Gaugino masseses, while in gauge an approximate R-symmetry,∼ Pl with small R-violating ef- including thoseinteraction. fromfects top (as loops, Various in the which “supersymmetrymediated possibilities become very models include important without it gaugein actually this supergravity” mediati scenario. contributeson [14–16],negatively anomaly mediationto sfermion [1, 17] masses squared [20]. Since The first obstacle to overcome is to generate a gaug- andframework gaugino mediation of [23], [24]), [18, 19]. much of the benefits to reduc- D-terms do not break an R-symmetry,ino they mass. cannot Remarkably, contributeR-symmetric to Majorana gaugino gaugino masses masses. are 2.2 Other supersoftingAs the an operators alternative supersymmetric to F -term contributions SUSY breaking, to flavor supersymmetry violation can also be broken by a D- In our framework, D-terms can bepossible the only when source the of gauginos supersymmetry are Dirac. breaking. Such a possibil- We will With the extendedcomponentcarry field content through. vev of and a hidden the U(1) sector! D-term, vector there superfield, is one other with supersoft gaugefieldstrength operator W ! .However, assume the presence of an hidden sectorityU(1) has! beenwhich explored acquiresα in a numberD-component of contexts vev. previously.5 With the which we canthe write: lowest dimension gauge invariant operator which directly contributesFor instance, to in scalar [25, masses 26], gluinos were made Dirac by W ! W !α squared is additionald2θ α fieldsA2. from the gauge extension,adding(2.9) we a can color add octet, the and operator electroweak gauginos acquired III. BUILDINGDiracM AN2 GauginosRj -SYMMETRIC in Supersymmetry SUPERSYMMETRIC# MODEL!α ! † !β ! their masses via marrying the superpartners of the Gold- 4 (W Wα) W Wβ † ! α While we have written it for the ESP fields, this termd canθ be written for any realQ representationQ. stone modesWαW inA thej Higgs(2.3) supermultiplet. In [19], Dirac M 6 2 √ j of a gauge group. This term splits the scalar and! pseudoscalarmassessquaredbyequaldgauginosθ 2 were motivated. as an ultraviolet insensitive and(2.4) Our starting point is thus supersymmetry breaking Polchinski, SusskindM (1982) amounts, leavingIf M someM component,thistermwillbesubdominanttoanomalymediatedsoftmassSUSY with breaking a negative to contributigauginoson communicated to its mass squared. ! flavor If that blindes, means while of in mediating gauge SUSY breaking, which originating∼ Pl from hidden sector spurions that preserve the Hall, Randall (1991) is the scalar, whichmediated already models hasthrough a it positive actuallyAs D-term we contribution, shall contributes spurions: discuss thisnegatively is shortly not troublesome. into section sfermion If, 2.3, instead,resulted massesFox, this Nelson, inoperatorsquared theWeiner so-called (2002) [20]. is supersoft Since “supersoft”,inthatitdoesnotgive spectrum with gaug- R-symmetry. Both F -type and D-type supersymmetry 1/2 it is the pseudoscalar, then we must require a Majorana ESP mass from an N =1preservinginos a factor... of (4π/α) above the scalars. They have D-termsbreaking do not is allowed, breaklog an which divergent R-symmetry, we can radiative write they cannot in contributions terms contribute of the to to Majorana other soft gaugino parame masses.ters, as would, e.g., aMajorana superpotential term, in order to prevent2 color and! charge breaking. additionally been considered in a variety of phenomeno- spurionsIn our framework,X = θ F andD-termsWα = canθα beD,wherethe the only sourceR-charge of supersymmetry breaking. We will Although there is no symmetry whichgaugino allows mass. the terms Including in (2.4) but this forbids operator, those inlogical the (2.9), Lagrangian contexts recently contains [27, the 28, terms 29, 30, 31, 32, 33, 34]. assume the presence of an hidden sector U(1)! which acquires a D-component vev.5 With the these terms are technically independent, as (2.4) will not generate (2.9) and vice versa. additional fields from the gauge extension, we can add the operator 1 Dirac gaugino masses arise mfrom:λ a˜ √2m2 (a + a∗)D D ( g q∗t q ) D2 (2.5) D j j D j j j j k i j i 2 j 2.3 Radiative Corrections L ⊃− ! α − − i − W W Aj " d2θ√2 α j . (2.4) Below the scale M,where(2.4)isgenerated,thegauginohasamass,sowewouldM naively expect that it would give a logarithmicallyoffshell, divergent and “gaug! ino mediated” contribution to the messenger scale scalar massesAs squared. we shall However, discussgiving from shortly a general in section argument, 2.3, we thiscan operator see that is thissupersoft is not the,inthatitdoesnotgive 2 ∗ 2 ∗ ∗ case. log divergent radiative contributions to othermD softλja˜ paramej m ters,(aj + asa would,) √e.g.,2mDaMajorana(aj + a )( gkq taqi)(2.6) L ⊃− − D j − j i We have agaugino renormalizable mass. Including effective theory this with operator, only soft the supe Lagrangianrsymmetry cont breaking.chiralains fermion the Fur- termsin adjoint rep "i thermore the supersymmetry breaking can be parametrized by aspurionWgaugino! /M = θ m , ! α α D onshell, where m = D /M , a is the! complex scalar component of A,andq represents all and written as the gauge invariant, supersymmetric term ofD (2.4),∗ with mD = D /M .Ifthis∗ 1 2 mDλja˜j √2mD(aj + aj )Dj Dj( gkqi tjqi) Dj (2.5) soft supersymmetry breaking introducesL ⊃−fields divergent charged− correct underions to the the group soft− massesGj.Noticethatthegauginonowhasa of squarks− 2 Dirac mass with "i and sleptons, we should be able to writethe down ESP a supersymmetri fermiona ˜.(WeusetildestodesignatefieldswhichareR-parityodd.)Dc, gauge invariant counterterm irac gluino offshell, and masses were considered previously in theories with a U(1)R symmetry [21,22]. The possibility of adding triplets2 to∗ the2 theory, one of∗ which could∗ marry the SU(2) gauginos was considered mDλja˜j mD(aj + aj ) √2mD(aj + aj )( gkqi taqi)(2.6) L ⊃− 5 − − by [23], who noted that such masses could"i be explained by the presence of the term in (2.4). ! However, the gaugino mass is only one effect of this term. We additionally have given a onshell, where mD = D /M , a is the complex scalar component of A,andq represents all mass to the real scalar piece of a,leavingthepseudoscalarmassless.Therearenewtrilinear fields charged under the group Gj.NoticethatthegauginonowhasaDirac mass with the ESP fermiona ˜.(WeusetildestodesignatefieldswhichareR-parityodd.)Dterms between a and the MSSM scalar fields which haveirac no gluino analog in the MSSM. masses were considered previously5The presence in theories of such a withD-term a U(1) makesR symmetry a kinetic [21,22]. mixing between The possibilityU(1)! and hypercharge potentially very of adding triplets to thedangerous. theory, However, one of which if hypercharge could marry arises the asSU a generator(2) gauginos of anon-AbeliansymmetrysuchasaGUT,thiswill was considered by [23], who noted thatnaturally such masses be absent could and be radiatively explained stable. by the presence of the term in (2.4). However, the gaugino mass is only one effect of this term. We additionally have given a mass to the real scalar piece of a,leavingthepseudoscalarmassless.Therearenewtrilinear terms between a and the MSSM scalar fields which have no analog in the MSSM.

5The presence of such a D-term makes a kinetic mixing between U(1)! and hypercharge4 potentially very dangerous. However, if hypercharge arises as a generator of anon-AbeliansymmetrysuchasaGUT,thiswill naturally be absent and radiatively stable.

4 Dirac Gauginos in Supersymmetry II

Dirac gaugino masses require extending the MSSM with chiral adjoint superﬁelds:

Aj j =1...8 color octet A j =1...3 weak triplet 8 j < Aj j =1 singlet : Gauge coupling uniﬁcation... (for those who still care)

...still perturbative, but requires unifons. exclude flavor violation is to communicate supersymmetry breaking from a flavor independent interaction. Various possibilities include gauge mediation [14–16], anomaly mediation [1, 17] and gaugino mediationDirac [18, 19].Gauginos in Supersymmetry III As an alternative to F -term SUSY breaking, supersymmetry can also be broken by a D- ! component vev of a hidden sector vector superfield, with gaugefieldstrengthWα.However, the lowestScalar dimension masses gauge invariant could arise operator from: which directly contributes to scalar masses squared is (W !αW ! )†W !βW ! d4θ α β Q†Q. (2.3) M 6 ! If M M ,thistermwillbesubdominanttoanomalymediatedsoftmasses, while in gauge ∼ Pl mediated modelswhich it is actually finite! contributes This is becausenegatively theto sfermion only counterterm masses squared [20]. Since D-terms do not break an R-symmetry, they cannot contribute to Majorana gaugino masses. 2 ¯2 4 4 ✓ ✓ mD In our framework, D-terms can bed the✓ only sourceQ†Q of supersymmetry breaking. We will M 2 assume the presence of an hidden sectorZ U(1)! which acquires a D-component vev.5 With the additional fields from the gauge extension, we can add the operator is suppressed by 1/M2. ! α W W Aj d2θ√2 α j . (2.4) M Scalar masses! are “supersoft” As we shall discuss shortly in section 2.3, this operator is supersoft,inthatitdoesnotgive log divergent radiative contributions to other soft parameters, as would, e.g., aMajorana gaugino mass. Including this operator, the Lagrangian containsFox, the Nelson, terms Weiner (2002)

1 m λ a˜ √2m (a + a∗)D D ( g q∗t q ) D2 (2.5) L ⊃− D j j − D j j j − j k i j i − 2 j "i oﬀshell, and

m λ a˜ m2 (a + a∗)2 √2m (a + a∗)( g q∗t q )(2.6) L ⊃− D j j − D j j − D j j k i a i "i ! onshell, where mD = D /M , a is the complex scalar component of A,andq represents all fields charged under the group Gj.NoticethatthegauginonowhasaDirac mass with the ESP fermiona ˜.(WeusetildestodesignatefieldswhichareR-parityodd.)Dirac gluino masses were considered previously in theories with a U(1)R symmetry [21,22]. The possibility of adding triplets to the theory, one of which could marry the SU(2) gauginos was considered by [23], who noted that such masses could be explained by the presence of the term in (2.4). However, the gaugino mass is only one effect of this term. We additionally have given a mass to the real scalar piece of a,leavingthepseudoscalarmassless.Therearenewtrilinear terms between a and the MSSM scalar fields which have no analog in the MSSM.

5The presence of such a D-term makes a kinetic mixing between U(1)! and hypercharge potentially very dangerous. However, if hypercharge arises as a generator of anon-AbeliansymmetrysuchasaGUT,thiswill naturally be absent and radiatively stable.

4 Several phenomenological implications of Dirac gauginos scalar components of the adjoint superfields. The Mi as well as fully R-symmetric supersymmetry have been are the Dirac masses for the gauginos. Assuming the explored in [39–60]. contribution to the squark masses is dominated by the In this study we do not consider bounds on the third Dirac gluino, generation squarks. Third generation squarks receive M 2 logr ˜ modifications to their masses through their interactions M 2 (700 GeV)2 3 3 (2) with the Higgs supermultiplets. Given that supersoft su- q˜ ⇤ 5 TeV log 1.5 ⇥ persymmetry has a suppressed D-term for the Higgs po- wherer ˜ m˜ 2/M 2. Somewhat smaller or larger soft tential, typically this requires heavier stop masses as well i ⇥ i i as separating the scalar masses of the adjoint superfields masses can be achieved by adjusting the ratior ˜3,since from the corresponding Dirac gaugino masses. This could we hold the Dirac gluino mass M3 =5TeVfixedinthe be accomplished through additional R-symmetric F -term SSSM. contributions to their masses. In any case, third generation squarks have distinct signals involving heavy flavor B. Naturalness (with or without leptons), and thus require incorporating a much larger class of LHC search strategies. We believe The up-type Higgs mass-squared m2 receives positive there are interesting di⇥erences between the third gen- Hu eration phenomenology of a supersoft model versus the one-loop finite contributions from the Dirac electroweak MSSM, but we leave this for future work. gauginos as well as negative one-loop contributions from We also do not consider potentially large flavor- the stops. As was emphasized in Ref. [21], the latter violation in the squark-gaugino (or squark-gravitino) in- contribution can easily overwhelm the former, leading to teractions, as could occur in an R-symmetric model [30]. a negative Higgs mass-squared and thus radiative elec- This would add to the heavy flavor component of signals troweak symmetry breaking. Unlike the MSSM, however, the usual logarithmic divergence from the stop contribu- while subtracting from the nj +/ET signals that concern us in this paper. In the interests of demonstrating the tions to the Higgs mass is cuto⇥ by the Dirac gluino mass, di⇥erences between the SSSM and the simplified models giving of the MSSM, the latter of which cannot have large fla- 3⇤2 M 2 vor violation, we do not consider flavor-violation in the ⇥m2 = t M 2 log 3 . (3) Hu 8⌅2 t˜ M 2 squark interactions of the SSSM. t˜ Using Eq. (1), and approximating log[M 2/M 2] 3 t˜ ⇤ log[3⌅/(4s)], we obtain III. ASPECTS OF DIRAC GAUGINO MASSES M 2 logr ˜ ⇥m2 3 3 . (4) A. Supersoftness Hu |SSSM ⇤ 22 log 1.5 ⇥ Contrast this expression with the analogous one from the A supersoft supersymmetricSquark/Slepton model contains Masses chiral su- MSSM [7] perfields in the adjoint representation of each gauge group of the SM in addition to the superfields of ˜ 2 ˜ 2 theOne-loop MSSM. contributions: Supersymmetry breaking communicated 2 M3 log /M3 ⇥mHu MSSM . (5) through a D-term spurion leads to Dirac gaugino masses | ⇤⇤ 4 ⌅ ⇤ 3 ⌅ that pair up the fermionic component from each field ˜ strength with the fermionic component of the corre- where M3 corresponds to the Majorana gluino mass. sponding adjoint superfield. The adjoint superfields also This makes it clear that a Dirac gluino can be several contain a complex scalar, whose real and imaginary com- times larger than a Majorana gluino in an MSSM-type ponent masses are not uniquely determined in terms of model and yet be just as natural, even when compar- the Dirac gaugino mass. The Lagrangian for this setup, ing against an MSSM model with a mediation scale that ˜ in terms of four component spinors, is given in Ap- is as low as conceivable, 20M3. Our choice of ⇤ pendix A. Dirac gluino mass M3 =5TeVwith˜r3 1.5isthus ⇤ The scalar components of chiral superfields receive one- roughly equivalent, in the degree of naturalness, to a low- loop finite contributions to their soft masses from gaug- scale mediation MSSM model with Majorana gluino mass Figure 2: Loop contributions to scalar masses. The new contribution from the purely˜ scalar loop inos and adjoint scalars, as was shown clearly by [21] M3 900 GeV. cancels theGiving logarithmic divergence resulting from a gauginomassalone. ⇤ C (f) M 2 m˜ 2 M 2 = i i i log i . (1) for the masses involvingf˜ this spurion.⌅ The only possibleM 2 suchcountertermisproportionaltoC. Colored Sparticle Production (2.3), and gives i i ⇧ 2 θ2θ m4 The sum runs over the threed4θ SM gaugeD Q†Q. groups where For LHC(2.10) phenomenology, there are several impli- Λ2 Ci(f) is quadratic Casimir! of the fermion f under the cations of a heavy Dirac gluino. First, gluino pair Since we have four powers of mD,wehavetointroduceanotherscaletomakethisdimen- gauge group i.The˜mi are the soft masses for the real production and associated gluino/squark production is sionfully consistent. Since the only other scale is the cutoffΛ,thisoperatorissuppressed by Λ2,and,inthelimitthatΛ ,mustvanish.Consequently,weconcludeall radiative →∞ corrections to the scalar soft masses are finite. 3 While a gaugino mass (including a Dirac mass) would ordinarily result in a logarithmic divergence, here this is cancelled by the new contribution from the scalar loop. The contribution to the scalar soft mass squared is given by

d4k 1 1 m2 4g2C (φ) + i , (2.11) i i (2π)4 k2 − k2 m2 k2(k2 δ2) ! − i − i 2 where mi is the mass of the gaugino of the gauge group i,andδ is the SUSY breaking mass squared of the real component of ai.Ifthetermin(2.9)isabsent,thenδ =2mi.Asexpected, this integral is ﬁnite, yielding the result

2 2 2 Ci(r)αimi δ m = log 2 . (2.12) π "mi #

Note that as δ approaches mi from above, these one loop contributions will vanish! If A has aMajoranamassofM,thenthisformulageneralizes

C (r)α m2 M 2 + δ2 M 2∆ + M m2 = i i i log log , (2.13) π m2 − 2∆ 2∆ M $ " i # % − &' 2 2 2 where ∆ = M /4+mi . These contributions, arising from gauge interactions, are positive and ﬂavor blind as in gauge and gaugino mediation, but there are two other remarkable features of this result.

6 Several phenomenological implications of Dirac gauginos scalar components of the adjoint superfields. The Mi as well as fully R-symmetric supersymmetry have been are the Dirac masses for the gauginos. Assuming the explored in [39–60]. contribution to the squark masses is dominated by the In this study we do not consider bounds on the third Dirac gluino, generation squarks. Third generation squarks receive M 2 logr ˜ modifications to their masses through their interactions M 2 (700 GeV)2 3 3 (2) with the Higgs supermultiplets. Given that supersoft su- q˜ ⇤ 5 TeV log 1.5 ⇥ persymmetry has a suppressed D-term for the Higgs po- wherer ˜ m˜ 2/M 2. Somewhat smaller or larger soft tential, typically this requires heavier stop masses as well i ⇥ i i as separating the scalar masses of the adjoint superfields masses can be achieved by adjusting the ratior ˜3,since from the corresponding Dirac gaugino masses. This could we hold the Dirac gluino mass M3 =5TeVfixedinthe be accomplished through additional R-symmetric F -term SSSM. contributions to their masses. In any case, third generation squarks have distinct signals involving heavy flavor B. Naturalness (with or without leptons), and thus require incorporating a much larger class of LHC search strategies. We believe The up-type Higgs mass-squared m2 receives positive there are interesting di⇥erences between the third gen- Hu eration phenomenology of a supersoft model versus the one-loop finite contributions from the Dirac electroweak MSSM, but we leave this for future work. gauginos as well as negative one-loop contributions from We also do not consider potentially large flavor- the stops. As was emphasized in Ref. [21], the latter violation in the squark-gaugino (or squark-gravitino) in- contribution can easily overwhelm the former, leading to teractions, as could occur in an R-symmetric model [30]. a negative Higgs mass-squared and thus radiative elec- This would add to the heavy flavor component of signals troweak symmetry breaking. Unlike the MSSM, however, the usual logarithmic divergence from the stop contribu- while subtracting from the nj +/ET signals that concern us in this paper. In the interests of demonstrating the tions to the Higgs mass is cuto⇥ by the Dirac gluino mass, di⇥erences between the SSSM and the simplified models giving of the MSSM, the latter of which cannot have large fla- 3⇤2 M 2 vor violation, we do not consider flavor-violation in the ⇥m2 = t M 2 log 3 . (3) Hu 8⌅2 t˜ M 2 squark interactions of the SSSM. t˜ Using Eq. (1), and approximating log[M 2/M 2] 3 t˜ ⇤ log[3⌅/(4s)], we obtain III. ASPECTS OF DIRAC GAUGINO MASSES M 2 logr ˜ ⇥m2 3 3 . (4) A. Supersoftness Hu |SSSM ⇤ 22 log 1.5 ⇥ Contrast this expression with the analogous one from the A supersoft supersymmetric model contains chiral su- MSSM [7] perfields in the adjointSquark/Slepton representation of Masses each gauge group of the SM in addition to the superfields of ˜ 2 ˜ 2 the MSSM. Supersymmetry breaking communicated 2 M3 log /M3 One-loop contributions: ⇥mHu MSSM . (5) through a D-term spurion leads to Dirac gaugino masses | ⇤⇤ 4 ⌅ ⇤ 3 ⌅ that pair up the fermionic component from each field ˜ strength with the fermionic component of the corre- where M3 corresponds to the Majorana gluino mass. sponding adjoint superfield. The adjoint superfields also This makes it clear that a Dirac gluino can be several contain a complex scalar, whose real and imaginary com- times larger than a Majorana gluino in an MSSM-type ponent masses are not uniquely determined in terms of model and yet be just as natural, even when compar- the Dirac gaugino mass. The Lagrangian for this setup, ing against an MSSM model with a mediation scale that ˜ in terms of four component spinors, is given in Ap- is as low as conceivable, 20M3. Our choice of ⇤ pendix A. Dirac gluino mass M3 =5TeVwith˜r3 1.5isthus ⇤ The scalar components of chiral superfields receive one- roughly equivalent, in the degree of naturalness, to a low- loop finite contributions to their soft masses from gaug- scale mediation MSSM model with Majorana gluino mass Figure 2: Loop contributions to scalar masses. The new contribution from the purely˜ scalar loop inos and adjoint scalars, as was shown clearly by [21] M3 900 GeV. cancels theGiving logarithmic divergence resulting from a gauginomassalone.Would-be log divergence⇤ 2 2 2 Ci(f)iMi m˜ i is cutoff by adjoint scalar for the masses involvingM ˜ this= spurion. The onlylog possible. suchcountertermisproportionalto(1) f ⌅ M 2 contribution. C. Colored Sparticle Production (2.3), and gives i i ⇧ 2 θ2θ m4 The sum runs over the threed4θ SM gaugeD Q†Q. groups where For LHC(2.10) phenomenology, there are several impli- Λ2 Ci(f) is quadratic Casimir! “Supersoft” of the fermion f underFox, theNelson,cations Weiner (2002) of a heavy Dirac gluino. First, gluino pair Since we have four powers of mD,wehavetointroduceanotherscaletomakethisdimen- gauge group i.The˜mi are the soft masses for the real production and associated gluino/squark production is sionfully consistent. Since the only other scale is the cutoffΛ,thisoperatorissuppressed by Λ2,and,inthelimitthatΛ ,mustvanish.Consequently,weconcludeall radiative →∞ corrections to the scalar soft masses are finite. 3 While a gaugino mass (including a Dirac mass) would ordinarily result in a logarithmic divergence, here this is cancelled by the new contribution from the scalar loop. The contribution to the scalar soft mass squared is given by

2 2 2 Ci(r)αimi δ m = log 2 . (2.12) π "mi #

Note that as δ approaches mi from above, these one loop contributions will vanish! If A has aMajoranamassofM,thenthisformulageneralizes

6 exclude flavor violation is to communicate supersymmetry breaking from a flavor independent interaction. Various possibilities include gauge mediation [14–16], anomaly mediation [1, 17] and gaugino mediation [18, 19]. As an alternative to F -term SUSY breaking, supersymmetry can also be broken by a D- ! component vev of a hidden sector vector superfield, with gaugefieldstrengthWα.However, the lowest dimension gauge invariant operator which directly contributes to scalar masses excludesquared flavor violation is is to communicate supersymmetry breaking from a flavor independent interaction. Various possibilities include gauge mediation [14–16], anomaly mediation [1, 17] !α ! † !β ! and gaugino mediation [18, 19]. (W Wα) W W d4θ β Q†Q. (2.3) As an alternative to F -term SUSY breaking, supersymmetryM 6 can also be broken by a D- component vev of a hidden sector vector superfield,! with gaugefieldstrengthW ! .However, If M M ,thistermwillbesubdominanttoanomalymediatedsoftmassα es, while in gauge the lowest∼ dimensionPl gauge invariant operator which directly contributes to scalar masses squaredmediated is models it actually contributes negatively to sfermion masses squared [20]. Since !α ! † !β ! D-terms do not break an R-symmetry,(W Wα) W Wβ they cannot contribute to Majorana gaugino masses. d4θ Q†Q. (2.3) M 6 In our framework,! D-terms can be the only source of supersymmetry breaking. We will If M MPl,thistermwillbesubdominanttoanomalymediatedsoftmass! es, while in gauge 5 assume∼ the presence of an hidden sector U(1) which acquires a D-component vev. With the exclude flavor violation is to communicate supersymmetry breakingmediated from models a flavor it independent actually contributes negatively to sfermion masses squared [20]. Since So far we have not included any explicit Majorana mass for the ESP fields. Since a is interaction. Various possibilities include gauge mediation [14–16],D-termsadditional anomaly do not mediation break fields an from R-symmetry, [1, 17] the gauge they cannot extension, contribute we to canMajorana add the gaugino operator masses. massive, we can integrate it out, yielding the condition and gaugino mediation [18, 19]. In our framework, D-terms can be the only source of supersymmetry breaking. We will ! α As an alternative to F -term SUSY breaking, supersymmetry can also be broken by a D- ! 5 ∂ assume the presence of an hidden sector U(1) which acquires2 aWDα-componentWj Aj vev. With the L =0 D =0. ! (2.7) d θ√2 . (2.4) component vev of a hidden sector vector superfield, withj gaugefieldstrengthWα.However, ∂Re(aj) → additional fields from the gauge extension, we can add the operatorM the lowest dimension gauge invariant operator which directly contributes to scalar masses ! ! α squaredSince D is-flatness is an automatic consequence of theseAdjoint fields, in the Scalars absence of a Majorana W W Aj As we shall discuss shortlyd in2θ√ section2 α j 2.3,. this operator is supersoft(2.4),inthatitdoesnotgive mass, no low-energy D-term quartic(W couplings!αW ! )†W ! willβW ! be present,includingtheveryimportant M d4θ α β Q†Q. log divergent radiative(2.3) contributions! to other soft parameters, as would, e.g., aMajorana Higgs quartic potential terms. InGauginos the presenceM married6 of explicit off with supersymmetric fermionic components Majorana masses of ! As we shall discuss shortly in section 2.3, this operator is supersoft,inthatitdoesnotgive M for the U(1) and SU(2) ESPs, the quartic coupling willgaugino not vanish. mass. For example, Includingthe this operator, the Lagrangian contains the terms If M1,2 MPl,thistermwillbesubdominanttoanomalymediatedsoftmasschiral adjoint superfields:log divergent radiativees, while in contributions gauge to other soft parameters, as would, e.g., aMajorana Higgs∼ quartic coupling rescales as mediated models it actually contributes negatively to sfermiongaugino masses mass.a˜ squared Including [20]. this Since operator, the Lagrangian contains the terms 1 D-terms do not break an R-symmetry, they cannot contributeA to Majorana= j gaugino masses. m λ a˜ √2m (a + a∗)D D ( g q∗t q ) D2 (2.5) g!2 + g2 1 M 2g!2 M 2gj2 D j j D j j j j k i j i j 1 2 aj L ⊃− − ∗ ∗ − 1 2 − 2 In our framework, D-terms can be the only2 source2 + of supersymmetry2 2 ✓. breaking.◆ mD Weλja˜ wj ill(2.8)√2mD(aj + aj )Dj Dj( gkqi tjqi) Dj i (2.5) 8 → 8 !M! 1 +4m1 M2 +4m2 " L ⊃−5 − − − 2 " assume the presence of an hidden sectorAlso Ucontain(1) which scalars acquires in aadjointD-component representation vev. With the(e.g. “sgluons”). "i additional fields from the gauge extension, we can add the operator As we will discuss shortly, there are the usual one-loop contoffshell,ributionsoffshell, and to and the quartic coupling, including those from top loops, which becomeW ! W veryαA important inalso this scenario. 2 √ α j j 2 ∗ 2 2 ∗ 2∗ ∗ ∗ ∗ d θ 2 . mDλj(2.4)a˜j mmD(λaj a˜+ aj ) m √(2amD+(aja+)aj )( √g2kmqi taq(ia)(2.6)+ a )( g q t q )(2.6) M L ⊃− − D j j −D j j D j j k i a i 2.2 Other supersoft operators! L ⊃− − − i " "i As we shall discuss shortly in section 2.3, this operator! is supersoft,inthatitdoesnotgive! With the extended field contentAdditional and the U(1) contributionsD-term, thereonshell, is one where othermD supersoft= D /M operator, a is the complex scalar component of A,andq represents all log divergent radiative contributions to other soft parameters,onshell, as would, e.g., whereaMajoranam = D!/M , a is the complex scalar component of A,andq represents all which we can write: fields charged under the groupD Gj.NoticethatthegauginonowhasaDirac mass with gaugino mass. Including this operator, the LagrangianW ! W !α contains the terms 2 α 2 the ESPfields fermionMasses chargeda ˜.(WeusetildestodesignatefieldswhichareR-parityodd.)D for under Re[aj] the and group Im[aj] Gj.Noticethatthegauginonowhasairac gluino Dirac mass with d θ 2 Aj . (2.9) M masses were1 considered previously in theories with a U(1)R symmetry [21,22]. The possibility m λ a˜ √2m (a# + a∗)D D ( g q∗thet q ) ESP(oppositeD2 fermion signs)a ˜(2.5).(WeusetildestodesignatefieldswhichareR-parityodd.)Dirac gluino While we haveL written⊃− D itj forj − the ESPD fields,j thisj termj − canj beofk wri addingi ttenj i − tripletsfor2 anyj real to the representation theory, one of which could marry the SU(2) gauginos was considered i masses were considered previously in theories with a U(1) symmetry [21,22]. The possibility of a gauge group. This term splits the scalar and pseudoscala"by [23], whormassessquaredbyequal noted that such masses could be explained by the presence of theR term in (2.4). offamounts,shell, and leaving some component with a negative contributiofHowever,on adding to its massthe triplets gaugino squared. mass to If the that is only theory, one e oneffect of of this which term. could We ad marryditionally the haveSU given(2) a gauginos was considered is the scalar, which already has a positive contribution, thmassisby is to not [23], the troublesome. real who scalar noted piece If, instead, that of a,leavingthepseudoscalarmassless.Therearenewtrilinea such masses could be explained by the presencer of the term in (2.4). m λ a˜ m2 (a + a∗)2 √2m (a + a∗)( g q∗t q )(2.6) it is the pseudoscalar,D thenj j we mustD j requirej a MajoranaD j ESPtermsj ma betweenssk fromi a ai anandN =1preserving the MSSM scalar fields which have no analog in the MSSM. L ⊃− − − i However, the gaugino mass is only one effect of this term. We additionally have given a " superpotential term, in order to prevent color and charge br5Theeaking. presence of such a D-term makes a kinetic mixing between U(1)! and hypercharge potentially very ! mass to the real scalar piece of a,leavingthepseudoscalarmassless.Therearenewtrilinear onshell,Although where m thereD = D is no/M symmetry, a is the complexwhich allows scalar the component termsdangerous. in (2.4) of A However,but,and forbidsq ifrepresents hypercharge those in all (2.9),arises as a generator of anon-AbeliansymmetrysuchasaGUT,thiswill fieldsthese charged terms are under technically the group independent,Gj.Noticethatthegauginonowhasa as (2.4) will notnaturally generateterms be (2.9) absent betweenDirac and and vice radiativelymassa versa.and with stable. the MSSM scalar fields which have no analog in the MSSM. the ESP fermiona ˜.(WeusetildestodesignatefieldswhichareR-parityodd.)Dirac gluino 5The presence of such a D-term makes a kinetic mixing between U(1)! and hypercharge potentially very masses2.3 Radiative were considered Corrections previously in theories with a U(1)R symmetry [21,22]. The possibility of adding triplets to the theory, one of which could marry the SUdangerous.(2) gauginos However, was considered if hypercharge arises as a generator of anon-AbeliansymmetrysuchasaGUT,thiswill Below the scale M,where(2.4)isgenerated,thegauginohasamass,sowewouldnaively by [23], who noted that such masses could be explained by the pnaturallyresence of the be absent term in and (2.4). radiatively stable.4 expect that it would give a logarithmically divergent “gaugino mediated” contribution to the However, the gaugino mass is only one effect of this term. We additionally have given a scalar masses squared. However, from a general argument, we can see that this is not the mass to the real scalar piece of a,leavingthepseudoscalarmassless.Therearenewtrilinear case. terms between a and the MSSM scalar fields which have no analog in the MSSM. We have a renormalizable effective theory with only soft supersymmetry breaking. Fur- 5 ! The presence of such a D-term makes a kinetic mixing between U(1) and hypercharge potentially! very 4 thermore the supersymmetry breaking can be parametrized by aspurionWα/M = θαmD, dangerous. However, if hypercharge arises as a generator of anon-AbeliansymmetrysuchasaGUT,thiswill! naturallyand written be absent as and the radiatively gauge invariant, stable. supersymmetric term of (2.4), with mD = D /M .Ifthis soft supersymmetry breaking introduces divergent corrections to the soft masses of squarks and sleptons, we should be able to write down a supersymmetric, gauge invariant counterterm

5 Several phenomenological implications of Dirac gauginos scalar components of the adjoint superfields. The Mi as well as fully R-symmetric supersymmetry have been are the Dirac masses for the gauginos. Assuming the explored in [39–60]. contribution to the squark masses is dominated by the In this study we do not consider bounds on the third Dirac gluino, generation squarks. Third generation squarks receive M 2 logr ˜ modifications to their masses through their interactions M 2 (700 GeV)2 3 3 (2) with the Higgs supermultiplets. Given that supersoft su- q˜ ⇤ 5 TeV log 1.5 ⇥ persymmetry has a suppressed D-term for the Higgs po- wherer ˜ m˜ 2/M 2. Somewhat smaller or larger soft tential, typically this requires heavier stop masses as well i ⇥ i i as separating the scalar masses of the adjoint superfields masses can be achieved by adjusting the ratior ˜3,since from the corresponding Dirac gaugino masses. This could we hold the Dirac gluino mass M3 =5TeVfixedinthe be accomplished through additional R-symmetric F -term SSSM. contributions to their masses. In any case, third generation squarks have distinct signals involving heavy flavor B. Naturalness (with or without leptons), and thus require incorporating a much larger class of LHC search strategies. We believe The up-type Higgs mass-squared m2 receives positive there are interesting di⇥erences between the third gen- Hu eration phenomenology of a supersoft model versus the one-loop finite contributions from the Dirac electroweak MSSM, but we leave this for future work. gauginos as well as negative one-loop contributions from We also do not consider potentially large flavor- the stops. As was emphasized in Ref. [21], the latter violation in the squark-gaugino (or squark-gravitino) in- contribution can easily overwhelm the former, leading to teractions, as could occur in an R-symmetric model [30]. a negative Higgs mass-squared and thus radiative elec- This would add to the heavy flavor component of signals troweak symmetry breaking. Unlike the MSSM, however, the usual logarithmic divergence from the stop contribu- while subtracting from the nj +/ET signals that concern us in this paper. In the interests of demonstrating the tions to the Higgs mass is cuto⇥ by the Dirac gluino mass, di⇥erences between the SSSM and the simplified models giving of the MSSM, the latter of which cannot have large fla- 3⇤2 M 2 vor violation, we do not consider flavor-violation in the ⇥m2 = t M 2 log 3 . (3) Hu 8⌅2 t˜ M 2 squark interactions of the SSSM. t˜ Using Eq. (1), and approximating log[M 2/M 2] 3 t˜ ⇤ log[3⌅/(4s)], we obtain III. ASPECTS OF DIRAC GAUGINO MASSES M 2 logr ˜ ⇥m2 3 3 . (4) A. Supersoftness Hu |SSSM ⇤ 22 log 1.5 ⇥ Contrast this expression with the analogous one from the A supersoft supersymmetric model contains chiral su- MSSM [7] perfields in the adjoint representation of each gauge group of the SM in addition to the superfields of ˜ 2 ˜ 2 the MSSM. Supersymmetry breaking communicated 2 M3 log /M3 ⇥mHu MSSM . (5) through a D-term spurion leads to Dirac gaugino masses | ⇤⇤ 4 ⌅ ⇤ 3 ⌅ that pair up the fermionic component from each field ˜ strength with the fermionic component of the corre- where M3 corresponds to the Majorana gluino mass. sponding adjoint superfield. The adjoint superfields also This makes it clear that a Dirac gluino can be several contain a complex scalar, whose real and imaginary com- times larger than a Majorana gluino in an MSSM-type ponent masses are not uniquely determined in terms of model and yet be just as natural, even when compar- the Dirac gaugino mass. The Lagrangian for this setup, ing against an MSSM model with a mediation scale that ˜ in terms of four component spinors, is given in Ap- is as low as conceivable, 20M3. Our choice of ⇤ pendix A. Dirac gluino mass M3 =5TeVwith˜r3 1.5isthus ⇤ The scalar components of chiral superfields receive one- roughly equivalent, in the degree of naturalness, to a low- Finiteloop Squarkfinite contributions Masses to their from soft Dirac masses from Gauginos gaug- scale mediation MSSM model with Majorana gluino mass ˜ inos and adjoint scalars, as was shown clearly by [21] M3 900 GeV. ⇤ C (f) M 2 m˜ 2 M 2 = i i i log i . (1) Several phenomenological implications of Dirac gauginos scalar componentsf˜ of the adjoint⌅ superfields.M 2 The M C. Colored Sparticle Production i i i as well as fully R-symmetric supersymmetry have been are the Dirac masses for⇧ the gauginos. Assuming the explored in [39–60]. contributionThe sum to runs the over squark the masses three SM is dominated gauge groups by the where For LHC phenomenology, there are several impli- Plugging in numbers: In this study we do not consider bounds on the third DiracC gluino,i(f) is quadratic Casimir of the fermion f under the cations of a heavy Dirac gluino. First, gluino pair generation squarks. Third generation squarks receive gauge group i.The˜mi are the soft masses for the real production and associated gluino/squark production is M 2 logr ˜ modifications to their masses through their interactions M 2 (700 GeV)2 3 3 (2) with the Higgs supermultiplets. Given that supersoft su- q˜ ⇤ 5 TeV log 1.5 ⇥ 3 persymmetry has a suppressed D-term for the Higgs po- wherer ˜ m˜ 2/M 2. Somewhat smaller or larger soft tential, typically this requires heavier stop masses as well or i ⇥ i i as separating the scalar masses of the adjoint superfields masses can be achieved by adjusting the ratior ˜3,since we hold the Dirac gluino mass M =5TeVfixedinthe2 from the corresponding Dirac gaugino masses. This could 2 M33 logr ˜3 M 2 (760 GeV) be accomplished through additional R-symmetric F -term SSSM. q˜ ' 3TeV log 4 contributions to their masses. In any case, third genera- ✓ ◆ tion squarks have distinct signals involving heavy flavor B. Naturalness (with or without leptons), and thus require incorporating Dirac gluino ≈ (5-7) x squark mass a much larger class of LHC search strategies. We believe The up-type Higgs mass-squared m2 receives positive there are interesting di⇥erences between the third gen- Hu eration phenomenology of a supersoft model versus the one-loop finite contributions from the Dirac electroweak MSSM, but we leave this for future work. gauginos as well as negative one-loop contributions from We also do not consider potentially large flavor- the stops. As was emphasized in Ref. [21], the latter violation in the squark-gaugino (or squark-gravitino) in- contribution can easily overwhelm the former, leading to teractions, as could occur in an R-symmetric model [30]. a negative Higgs mass-squared and thus radiative elec- This would add to the heavy flavor component of signals troweak symmetry breaking. Unlike the MSSM, however, the usual logarithmic divergence from the stop contribu- while subtracting from the nj +/ET signals that concern us in this paper. In the interests of demonstrating the tions to the Higgs mass is cuto⇥ by the Dirac gluino mass, di⇥erences between the SSSM and the simplified models giving of the MSSM, the latter of which cannot have large fla- 3⇤2 M 2 vor violation, we do not consider flavor-violation in the ⇥m2 = t M 2 log 3 . (3) Hu 8⌅2 t˜ M 2 squark interactions of the SSSM. t˜ Using Eq. (1), and approximating log[M 2/M 2] 3 t˜ ⇤ log[3⌅/(4s)], we obtain III. ASPECTS OF DIRAC GAUGINO MASSES M 2 logr ˜ ⇥m2 3 3 . (4) A. Supersoftness Hu |SSSM ⇤ 22 log 1.5 ⇥ Contrast this expression with the analogous one from the A supersoft supersymmetric model contains chiral su- MSSM [7] perfields in the adjoint representation of each gauge group of the SM in addition to the superfields of ˜ 2 ˜ 2 the MSSM. Supersymmetry breaking communicated 2 M3 log /M3 ⇥mHu MSSM . (5) through a D-term spurion leads to Dirac gaugino masses | ⇤⇤ 4 ⌅ ⇤ 3 ⌅ that pair up the fermionic component from each field ˜ strength with the fermionic component of the corre- where M3 corresponds to the Majorana gluino mass. sponding adjoint superfield. The adjoint superfields also This makes it clear that a Dirac gluino can be several contain a complex scalar, whose real and imaginary com- times larger than a Majorana gluino in an MSSM-type ponent masses are not uniquely determined in terms of model and yet be just as natural, even when compar- the Dirac gaugino mass. The Lagrangian for this setup, ing against an MSSM model with a mediation scale that ˜ in terms of four component spinors, is given in Ap- is as low as conceivable, 20M3. Our choice of ⇤ pendix A. Dirac gluino mass M3 =5TeVwith˜r3 1.5isthus ⇤ The scalar components of chiral superfields receive one- roughly equivalent, in the degree of naturalness, to a low- loop finite contributions to their soft masses from gaug- scale mediation MSSM model with Majorana gluino mass ˜ inos and adjoint scalars, as was shown clearly by [21] M3 900 GeV. ⇤ C (f) M 2 m˜ 2 M 2 = i i i log i . (1) f˜ ⌅ M 2 C. Colored Sparticle Production i i ⇧ The sum runs over the three SM gauge groups where For LHC phenomenology, there are several impli- Ci(f) is quadratic Casimir of the fermion f under the cations of a heavy Dirac gluino. First, gluino pair gauge group i.The˜mi are the soft masses for the real production and associated gluino/squark production is

3 Several phenomenological implications of Dirac gauginos scalar components of the adjoint superfields. The Mi as well as fully R-symmetric supersymmetry have been are the Dirac masses for the gauginos. Assuming the explored in [39–60]. contribution to the squark masses is dominated by the In this study we do not consider bounds on the third Dirac gluino, generation squarks. Third generation squarks receive M 2 logr ˜ modifications to their masses through their interactions M 2 (700 GeV)2 3 3 (2) with the Higgs supermultiplets. Given that supersoft su- q˜ ⇤ 5 TeV log 1.5 ⇥ persymmetry has a suppressed D-term for the Higgs po- wherer ˜ m˜ 2/M 2. Somewhat smaller or larger soft tential, typically this requires heavier stop masses as well i ⇥ i i as separating the scalar masses of the adjoint superfields masses can be achieved by adjusting the ratior ˜3,since from the corresponding Dirac gaugino masses. This could we hold the Dirac gluino mass M3 =5TeVfixedinthe be accomplished through additional R-symmetric F -term SSSM. contributions to their masses. In any case, third generation squarks have distinct signals involving heavy flavor B. Naturalness (with or without leptons), and thus require incorporating a much larger class of LHC search strategies. We believe The up-type Higgs mass-squared m2 receives positive there are interesting di⇥erences between the third gen- Hu eration phenomenology of a supersoft model versus the one-loop finite contributions from the Dirac electroweak MSSM, but we leave this for future work. gauginos as well as negative one-loopNaturalness contributions from I: Gluino We also do not consider potentially large flavor- the stops. As was emphasized in Ref. [21], the latter violation in the squark-gaugino (or squark-gravitino) in- contribution can easily overwhelm the former, leading to teractions, as could occur in an R-symmetric model [30]. a negative Higgs mass-squaredMSSM and thus radiative elec- This would add to the heavy flavor component of signals troweak symmetry breaking. Unlike the MSSM, however, the usual logarithmic divergence from the stop contribu- while subtracting from the nj +/ET signals that concern one-loop us in this paper. In the interests of demonstrating the tions to the Higgs mass is cuto⇥ by the Dirac gluino mass, giving 2 2 di⇥erences between the SSSM and the simplified models 2 3⇥t 2 mH = M˜ log of the MSSM, the latter of which cannot have large fla- u 8⇤2 3⇤t2 M 2M 2 vor violation, we do not consider flavor-violation in the ⇥m2 = t M 2 logt˜ 3 . (3) Hu 8⌅2 t˜ M 2 squark interactions of the SSSM. two-loop t˜ 2 2 Using Eq. (1), and approximating log[M 2/M ] ⇤2 2 3 t˜ ⇤ log[3⌅/(4s2)], we obtaint s 2 ⇥m = M˜ 3 log III. ASPECTS OF DIRAC GAUGINO MASSES Hu 2⌅2 ⌅ | | M˜ 2 M ✓2 logr ˜ 3 ◆ ⇥m2 3 3 . (4) A. Supersoftness Hu |SSSM ⇤ 22 log 1.5 evaluate ⇥ Contrast this expression with the analogous one from the A supersoft supersymmetric model contains chiral su- MSSM [7] perfields in the adjoint representation of each gauge group of the SM in addition to the superfields of ˜ 2 ˜ 2 the MSSM. Supersymmetry breaking communicated 2 M3 log /M3 ⇥mHu MSSM . (5) through a D-term spurion leads to Dirac gaugino masses | ⇤⇤ 4 ⌅ ⇤ 3 ⌅ that pair up the fermionic component from each field ˜ strength with the fermionic component of the corre- where M3 corresponds to the Majorana gluino mass. sponding adjoint superfield. The adjoint superfields also This makes it clear that a Dirac gluino can be several contain a complex scalar, whose real and imaginary com- times larger than a Majorana gluino in an MSSM-type ponent masses are not uniquely determined in terms of model and yet be just as natural, even when compar- the Dirac gaugino mass. The Lagrangian for this setup, ing against an MSSM model with a mediation scale that ˜ in terms of four component spinors, is given in Ap- is as low as conceivable, 20M3. Our choice of ⇤ pendix A. Dirac gluino mass M3 =5TeVwith˜r3 1.5isthus ⇤ The scalar components of chiral superfields receive one- roughly equivalent, in the degree of naturalness, to a low- loop finite contributions to their soft masses from gaug- scale mediation MSSM model with Majorana gluino mass ˜ inos and adjoint scalars, as was shown clearly by [21] M3 900 GeV. ⇤ C (f) M 2 m˜ 2 M 2 = i i i log i . (1) f˜ ⌅ M 2 C. Colored Sparticle Production i i ⇧ The sum runs over the three SM gauge groups where For LHC phenomenology, there are several impli- Ci(f) is quadratic Casimir of the fermion f under the cations of a heavy Dirac gluino. First, gluino pair gauge group i.The˜mi are the soft masses for the real production and associated gluino/squark production is

3 Several phenomenological implications of Dirac gauginos scalar components of the adjoint superfields. The Mi as well as fully R-symmetric supersymmetry have been are the Dirac masses for the gauginos. Assuming the explored in [39–60]. Several phenomenologicalcontribution implications to the squark of Dirac masses gauginos is dominatedscalar by the components of the adjoint superfields. The Mi In this study we do not consider boundsas well on theas fully third R-symmetricDirac gluino, supersymmetry have been are the Dirac masses for the gauginos. Assuming the generation squarks. Third generation squarks receive explored in [39–60]. 2 contribution to the squark masses is dominated by the modifications to their masses through their interactions 2 2 M3 logr ˜3 Mq˜ (700 GeV) Dirac gluino,(2) with the Higgs supermultiplets. Given thatIn supersoft this study su- we do not consider⇤ bounds on5 the TeV thirdlog 1.5 ⇥ persymmetry has a suppressed D-termgeneration for the Higgs squarks. po- Third generation squarks receive 2 2 2 M logr ˜ tential, typically this requires heavier stopmodifications masses as well to theirwhere massesr ˜i throughm˜ i /Mi . their Somewhat interactions smaller or larger soft 2 2 3 3 ⇥ Mq˜ (700 GeV) (2) with the Higgs supermultiplets.masses can be Given achieved that by supersoft adjusting su- the ratior ˜3,since ⇤ 5 TeV log 1.5 as separating the scalar masses of the adjoint superfields ⇥ from the corresponding Dirac gaugino masses.persymmetry This could has awe suppressed hold the DiracD-term gluino for mass the HiggsM3 =5TeVfixedinthe po- SSSM. wherer ˜ m˜ 2/M 2. Somewhat smaller or larger soft be accomplished through additional R-symmetrictential, typicallyF -term this requires heavier stop masses as well i ⇥ i i contributions to their masses. In any case,as separating third genera- the scalar masses of the adjoint superfields masses can be achieved by adjusting the ratior ˜3,since tion squarks have distinct signals involving heavy flavor we hold the Dirac gluino mass M3 =5TeVfixedinthe from the corresponding Dirac gauginoB. masses. Naturalness This could (with or without leptons), and thus requirebe accomplished incorporating through additional R-symmetric F -term SSSM. a much larger class of LHC search strategies. We believe contributions to theirThe masses. up-type In Higgs any case, mass-squared third genera-m2 receives positive there are interesting di⇥erences between the third gen- Hu tion squarks have distinctone-loop signals finite contributions involving heavy from the flavor Dirac electroweak eration phenomenology of a supersoft model versus the B. Naturalness MSSM, but we leave this for future work.(with or without leptons),gauginos and as well thus as require negative incorporating one-loopNaturalness contributions from I: Gluino We also do not consider potentiallya much large larger flavor- classthe of LHC stops. search As was strategies. emphasized We in believe Ref. [21], the latter contribution can easily overwhelm the former, leadingThe up-type to Higgs mass-squared m2 receives positive violation in the squark-gaugino (or squark-gravitino)there are interesting in- di⇥erences between the third gen- Hu teractions, as could occur in an R-symmetriceration model phenomenology [30]. a negative of a supersoft Higgs mass-squaredMSSM model versus and thus the radiativeone-loop elec- finite contributionsSupersoft from the Dirac electroweak This would add to the heavy flavor componentMSSM, of but signals we leavetroweak this for symmetry future work. breaking. Unlike the MSSM,gauginos however, as well as negative one-loop contributions from the usual logarithmic divergence from the stop contribu- while subtracting from the nj +/ET signalsWe that also concern do not considerone-loop potentially large flavor- the stops.one-loop As was emphasized in Ref. [21], the latter us in this paper. In the interests of demonstrating the tions to the Higgs mass is cuto⇥ by the Dirac gluinocontribution mass, can easily overwhelm the former, leading to violation in the squark-gauginogiving (or squark-gravitino)2 2 in- 2 2 di⇥erences between the SSSM and the simplified models 2 3⇥t 2 a negative Higgs mass-squared2 3⇥t and2 thusm˜ 3 radiative elec- teractions, as could occur inm anH R=-symmetricM˜ modellog [30]. mH = M˜ log of the MSSM, the latter of which cannot have large fla- u 8⇤2 3⇤t2 M 2M 2 troweak symmetry breaking.u 8⇤2 Unliket theM MSSM,2 however, vor violation, we do not consider flavor-violationThis would in add the to the heavy flavor⇥m2 component= t M of2 log signalst˜ 3 . (3) t˜ Hu 8⌅2 t˜ M 2 the usual logarithmic divergence from the stop contribu- squark interactions of the SSSM. while subtracting fromtwo-loop the nj +/ET signals that concernt˜ two-loop us in this paper. In the interests of demonstrating the tions to the Higgs mass is cuto⇥ by the Dirac gluino mass, Using Eq. (1), and approximating log[M 2/M 2] 2 2 3giving2 t˜ di⇥erences between the SSSM and the⇤ simplifieds models ⇤ log[3⌅/(4s2)], we obtaint ˜ 2 ⇥mH = M3 log (finite) III. ASPECTS OF DIRAC GAUGINOof the MASSES MSSM, the latter of whichu cannot2⌅2 ⌅ have| large| fla-˜ 2 2 2 Several phenomenological implications2 of DiracM gauginos3 scalar components of the2 adjoint superfields.3⇤t 2 The MMi 3 as well as fully R-symmetric supersymmetryM ✓ log haver ˜ been◆ are the Dirac masses⇥m for the= gauginos. AssumingM log the . (3) vor violation, we do not consider2 flavor-violation3 in the 3 Hu 2 t˜ 2 explored⇥m in [39–60].SSSM . contribution(4) to the squark masses is8 dominated⌅ by theM A. Supersoftness squark interactions of the SSSM.Hu | ⇤ 22 log 1.5 t˜ In this study we do not consider bounds⇥ on the third Dirac gluino,evaluate using mstop and: evaluategeneration squarks. Third generation squarks receive 2 M 2 32⇥ 2 Contrastmodifications this expression to their masses with throughthe analogous their interactions oneUsing from the Eq.2 (1), and2 M approximating3 logr ˜3 log log[3 logM /M ] Mq˜ (700 GeV) (2) 2 3 t˜ A supersoft supersymmetric model contains chiral su- with the Higgs supermultiplets. Given that supersoft su- ⇤ 5 TeV log 1.5 Mt˜ ' 4s ⇤ MSSM [7] log[3⌅/(4s)], we obtain ⇥ perfields in the adjoint representation of each gauge persymmetry has a suppressed D-term for the Higgs po- 2 2 III. ASPECTS OF DIRACtential, typically GAUGINO this requires MASSES heavier stop masses as well wherer ˜i m˜ i /Mi . Somewhat smaller or larger soft 2 2 ⇥ group of the SM in addition to the superfields of as separating the scalar masses˜ of the adjoint superfields˜ masses can be achieved by adjusting the ratior ˜3,since2 the MSSM. Supersymmetry breaking communicated from2 the corresponding DiracM3 gaugino masses.log / ThisM could3 we hold the Dirac2 gluino mass M3 =5TeVfixedintheM3 logr ˜3 ⇥m MSSM . SSSM.(5) ⇥m . (4) A. SupersoftnessbeH accomplishedu through additional4 R-symmetric3 F -term Hu SSSM through a D-term spurion leads to Dirac gaugino masses contributions| to⇤ their masses.⇤ In⌅ any⇤ case, third genera-⌅ | ⇤ 22 log 1.5 tion squarks have distinct signals involving heavy flavor ⇥ that pair up the fermionic component from each field B. Naturalness where M˜(withcorresponds or without leptons), to and the thus Majorana require incorporating gluinoContrast mass. this expression with the analogous one from the strength with the fermionic componentA of supersoft the corre- supersymmetrica3 much model larger class contains of LHC search chiral strategies. su- We believe Dirac gluino can be Thesubstantially up-type Higgs mass-squared mheavier2 receives positive sponding adjoint superfield. The adjoint superfields also This makesthere it are clear interesting that di⇥erences a Dirac between gluino the third can gen-MSSM be several [7] Hu perfields in the adjoint representationeration phenomenology of of a each supersoft gauge model versus the one-loop finite contributions from the Dirac electroweak contain a complex scalar, whose real and imaginary com- times larger than a Majorana gluino in an MSSM-typegauginos as well as negative one-loop contributions from group of the SM in additionMSSM, but tothan we leave the this Majorana superfields for future work. of gluino while just as natural.2 2 ponent masses are not uniquely determined in terms of model andWe yet also be dojust not consider as natural potentially, even large when flavor- compar-the stops. As was emphasized in Ref.M˜ [21], the latterlog /M˜ the MSSM. Supersymmetryviolation breaking in the squark-gaugino communicated (or squark-gravitino) in- contribution2 can easily overwhelm the former,3 leading to 3 the Dirac gaugino mass. The Lagrangian for this setup, ing againstteractions, an MSSM as could model occur in an withR-symmetric a mediation model [30]. scalea negative that⇥mH Higgsu MSSM mass-squared and thus radiative elec- . (5) troweak symmetry| breaking.⇤ Unlike the MSSM,4 however, 3 through a D-term spurionis as low leadsThis as would conceivable, to add Dirac to the gaugino heavy flavor component20 massesM˜ 3. of Our signals choice of ⇤ ⌅ ⇤ ⌅ in terms of four component spinors, is given in Ap- the usual logarithmic divergence from the stop contribu- while subtracting from the nj +/⇤ET signals that concern pendix A. that pair up the fermionicDirac gluino component mass M3 =5TeVwith˜ from each fieldr3 1.5isthustions to the Higgs mass is cuto⇥ by the Dirac gluino mass, us in this paper. In the interests of demonstrating⇤ the ˜ The scalar components of chiral superfieldsstrength receive with one- theroughly fermionic equivalent,di⇥erences component between in the the SSSM degree of andthe theof corre- naturalness, simplified modelswhere togiving a low-M3 corresponds to the Majorana gluino mass. of the MSSM, the latter of which cannot have large fla- 3⇤2 M 2 loop finite contributions to their soft massessponding from adjoint gaug- superfield.scale mediation The adjointMSSM model superfields with Majorana also gluinoThis mass makes⇥ itm2 clear= t thatM 2 log a3 . Dirac gluino(3) can be several vor violation, we do not consider flavor-violation in the Hu 2 t˜ 2 ˜ 8⌅ M˜ inos and adjoint scalars, as was showncontain clearly by a complex[21] scalar,M3 900 whosesquark GeV. interactions real and of imaginary the SSSM. com- times larger than a Majoranat gluino in an MSSM-type ⇤ Using Eq. (1), and approximating log[M 2/M 2] model and yet be just as natural3 t˜ ,⇤ even when compar- 2 ponent2 masses are not uniquely determined in terms of log[3⌅/(4s)], we obtain 2 Ci(f)iMi m˜ i III. ASPECTS OF DIRAC GAUGINO MASSES M = log the. Dirac gaugino(1) mass. The Lagrangian for this setup, ing against an MSSM model2 with a mediation scale that f˜ 2 M3 logr ˜3 C. Colored Sparticle Production ⇥m2 . (4) ⌅ M Hu SSSM ˜ i ini terms of four component spinors,A. is Supersoftness given in Ap- is as low as| conceivable,⇤ 22 log 1.5 20M3. Our choice of ⇧ ⇥ ⇤ Contrast this expression with the analogous one from the pendix A. A supersoft supersymmetric model contains chiral su-Dirac gluino mass M3 =5TeVwith˜r3 1.5isthus The sum runs over the three SM gauge groups where For LHC phenomenology, there are severalMSSM impli- [7] ⇤ The scalar components ofperfields chiral in superfields the adjoint representation receive one- of each gaugeroughly equivalent, in the degree of naturalness, to a low- Ci(f) is quadratic Casimir of the fermion f under the cations ofgroup a ofheavy the SM Dirac in addition gluino. to the superfields First, gluino of pair 2 2 M˜ log /M˜ the MSSM. Supersymmetry breaking communicatedscale mediation⇥m2 MSSM3 model3 with. Majorana(5) gluino mass gauge group i.The˜mi are the soft massesloop finite for thecontributions real production to their and soft associated masses gluino/squark from gaug- production is Hu MSSM through a D-term spurion leads to Dirac gaugino masses˜ | ⇤⇤ 4 ⌅ ⇤ 3 ⌅ inos and adjoint scalars, asthat was pair shown up the fermionic clearly component by [21] from each fieldM3 900 GeV. ˜ strength with the fermionic component of the corre- where⇤ M3 corresponds to the Majorana gluino mass. 3 sponding2 adjoint superfield.2 The adjoint superfields also This makes it clear that a Dirac gluino can be several 2 Ci(fcontain)iM ai complex scalar,m˜ i whose real and imaginary com- times larger than a Majorana gluino in an MSSM-type M = log . (1) model and yet be just as natural, even when compar- f˜ ponent masses are not2 uniquely determined in terms of C. Colored Sparticle Production the⌅ Dirac gauginoM mass. The Lagrangian for this setup, ing against an MSSM model with a mediation scale that i i ˜ in terms of four component spinors, is given in Ap- is as low as conceivable, 20M3. Our choice of ⇧ ⇤ pendix A. Dirac gluino mass M3 =5TeVwith˜r3 1.5isthus ⇤ The sum runs over the threeThe SM scalar components gauge groups of chiral superfields where receive one- Forroughly LHC equivalent, phenomenology, in the degree of naturalness, there to a low- are several impli- loop finite contributions to their soft masses from gaug- scale mediation MSSM model with Majorana gluino mass ˜ Ci(f) is quadratic Casimirinos of and the adjoint fermion scalars, asf wasunder shown clearly the by [21] cationsM3 900 of GeV. a heavy Dirac gluino. First, gluino pair ⇤ gauge group i.The˜mi are the soft massesC (f) forM 2 them˜ 2 real production and associated gluino/squark production is M 2 = i i i log i . (1) f˜ ⌅ M 2 C. Colored Sparticle Production i i ⇧ The sum runs over the three SM gauge groups where For LHC phenomenology, there are several impli- Ci(f) is quadratic Casimir of the fermion f under3 the cations of a heavy Dirac gluino. First, gluino pair gauge group i.The˜mi are the soft masses for the real production and associated gluino/squark production is

3 exclude flavor violation is to communicate supersymmetry breaking from a flavor independent excludeinteraction. flavor violation Various is to possibilities communicate include supersymmetry gauge mediati broneaking [14–16], from anomaly a flavor mediation independent [1, 17] interaction.and gaugino Various mediation possibilities [18, include 19]. gauge mediation [14–16], anomaly mediation [1, 17] and gauginoAs mediation an alternative [18, 19]. to F -term SUSY breaking, supersymmetry can also be broken by a D- component vev of a hidden sector vector superfield, with gaugefieldstrengthW ! .However, As an alternative to F -term SUSY breaking, supersymmetry can also be brokenα by a D- the lowest dimension gauge invariant operator which directly contributes to scalar masses component vev of a hidden sector vector superfield, with gaugefieldstrengthW ! .However, squared is α the lowest dimension gauge invariant operator!α which! † ! directβ ! ly contributes to scalar masses (W Wα) W W squared is d4θ β Q†Q. (2.3) M 6 ! !α ! † !β ! 4 (W Wα) W Wβ † If M MPl,thistermwillbesubdominanttoanomalymediatedsoftmassd θ Q Q. es, while in(2.3) gauge ∼ M 6 mediated models it actually! contributes negatively to sfermion masses squared [20]. Since If M DM-termsPl,thistermwillbesubdominanttoanomalymediatedsoftmass do not break an R-symmetry, they cannot contribute to Majoranaes, while gaugino in gauge masses. ∼ mediated modelsIn our framework, it actuallyD contributes-terms cannegatively be the onlyto source sfermion of supersymmetry masses squared breaking. [20]. Since We will D-termsassume do not the break presence an R-symmetry, of an hidden sector they cannotU(1)! which contribute acquires to aMajoranaD-component gaugino vev.5 masses.With the In ouradditional framework,Naturalness fields fromD-terms the gauge canII: beDirac extension, the only Electroweak we source can add of supersymmetry the ope Gauginos?rator breaking. We will ! 5 assume the presence of an hidden sector U(1) which acquires! α a D-component vev. With the W W Aj additional fields from the gauge extension, wed2θ can√2 addα thej ope. rator (2.4) With just D-term spurion M ! ! α W W Aj As we shall discuss shortly in sectiond2θ√ 2.3,2 α thisj operator. is supersoft,inthatitdoesnotgive(2.4) M log divergent radiative contributions! to other soft parameters, as would, e.g., aMajorana gaugino mass. Including this operator, the Lagrangian contains the terms As we shall discussin components: shortly in section 2.3, this operator is supersoft,inthatitdoesnotgive log divergent radiative contributions to other soft∗ parameters, as would,∗ e.g.,1 2 aMajorana mDλja˜j √2mD(aj + a )Dj Dj( g q tjqi) D (2.5) gaugino mass. IncludingL ⊃− this operator,− the Lagrangianj cont− ains thek i terms− 2 j "i Integrate out massive Re[aj], forces Dj = 0, hence 1 offshell, and √ ∗ ∗ 2 tree-levelmDλ jquartica˜j 2 mvanishesD(aj + a. j )Dj Dj( gkqi tjqi) Dj (2.5) L ⊃− − − i − 2 2 ∗ 2 " ∗ ∗ mDλja˜j mD(aj + aj ) √2mD(aj + aj )( gkqi taqi)(2.6) 3 mt˜ mt˜ L ⊃−2 2 − 2 −2 2 2 1 i2 offshell, and mh = mZ cos 2⇥ + 2 cos yt mt ln 2" 4⇤ mt ! onshell, where mD = D /M ,2 a is the∗ complex2 scalar component∗ of∗A,andq represents all Naively...amDλja˜ DISASTER!j mD(aj + a Onlyj ) stop√2m Dloop(aj +contributionsaj )( gkqi ta qtoi)(2.6) fields charged under the group Gj.NoticethatthegauginonowhasaDirac mass with L ⊃− − − i the ESP fermionHiggs mass.a ˜.(WeusetildestodesignatefieldswhichareR-parityodd.)D (Requires >> 10 TeV mass stops.)" irac gluino ! onshell,masses where weremD considered= D /M , previouslya is the complex in theories scalar with component a U(1)R symmetry of A,and [21,22].q represents The possibility all fields chargedof adding under triplets the to group the theory,Gj.Noticethatthegauginonowhasa one of which could marry the SU(2) gauginosDirac wasmass considered with the ESPby fermion [23], whoa ˜.(WeusetildestodesignatefieldswhichareR-parityodd.)D noted that such masses could be explained by the presence of theirac term gluino in (2.4). However, the gaugino mass is only one effect of this term. We additionally have given a masses were considered previously in theories with a U(1)R symmetry [21,22]. The possibility of addingmass triplets to the to real the scalar theory, piece one of ofa,leavingthepseudoscalarmassless.Therearenewtrilinea which could marry the SU(2) gauginos was considered r by [23],terms who noted between thata and such the masses MSSM could scalar be fields explained which by have the no p analogresence in of the the MSSM. term in (2.4). However,5The the presence gaugino of such mass a D-term is only makes one a kinetic effect mixing of this between term.U We(1)! adandditionally hypercharge have potentially given a very mass todangerous. the real However, scalar piece if hypercharge of a,leavingthepseudoscalarmassless.Therearenewtrilinea arises as a generator of anon-AbeliansymmetrysuchasaGUT,thiswillr naturally be absent and radiatively stable. terms between a and the MSSM scalar fields which have no analog in the MSSM.

4 Naturalness II: Higgs Mass

“Pure” Supersoft (Dirac gauginos; D-term & no F-terms) dead.

Need either Majorana winos and binos, or other additional contributions to Higgs mass, e.g.

• NMSSMology • R-symmetric contributions (λ couplings) • Composite stops (Csaki, Randall, Terning) • ...

I’m not directly concerned with Higgs mass. Arguably, the MSSM needs to be extended anyway to minimize EW tuning... II. THE MINIMAL R-SYMMETRIC Unlike the µ-terms, which are required to achieve exper- SUPERSYMMETRIC STANDARD MODEL imentally viable chargino masses, there is no direct phenomenology that dictates that the ⇤i couplings in Eq. (4) First we review the field content and new couplings must be nonzero (being superpotential couplings, they present in the minimal R-symmetric supersymmetric will not be generated radiatively if set to zero initially). standard model (MRSSM). In the MRSSM, the gaugi- However, these ⇤i couplings play a vital important role nos acquire Dirac masses through the Lagrangian terms in driving the phase transition to be first order. The im- portance of the ⇤i couplings can be seen already from the ⇥a scalar potential; the operators in Eqs. (3,4) lead to new 2 ⌦ ⇤ a d ⇥ 2 W W + h.c. , (1) trilinear and quartic operators involving Higgs fields and mess ⇤ the scalars in ⇥B, ⇥W ,Ru,Rd. where a is the field strength superfield for one of the B 0 2 B 0 2 W V µ (⇤ A ) H + µ (⇤ A ) H + c.c., (5) II.SM THEgauge MINIMAL groups (labelled R-SYMMETRIC by a, is a spinor index) andUnlike the µ⇤-terms,u u whichB are| u required| d tod achieveB | d exper-| SUPERSYMMETRICa STANDARD MODEL ⇥ is a “R-partner” chiral superfield transforming underimentallyTrilnear viable scalarchargino interactions masses, there involving is no direct the Higgs phe- multi- the adjoint representation of the appropriate gauge groupnomenology that dictates that the ⇤i couplings in Eq. (4) a plets, especially those with large couplings, are well First wewith reviewR-charge theR field[⇥ ] content = 0. Supersymmetry and new couplings breakingmust is beknown nonzero to impact (being superpotentialthe strength of couplings, the electroweak they phase presentcommunicated in the minimal throughR-symmetricR-symmetry supersymmetric preserving spurionswill nottransition be generated [10, radiatively15, 23, 26, 33, if set 78–83]. to zero initially). standardthat model include (MRSSM).⇤ which In the parameterizes MRSSM, the a D-type gaugi- spurion,However, these ⇤i couplings play a vital important role W Turning to the supersymmetry breaking parameters of nos acquire⇤ Dirac= D ⇥ masses. Expanded through into the components, Lagrangian theterms abovein op- driving the phase transition to be first order. The im- W the theory, scalar soft masses can arise from an additional erator becomes portancesource of the of⇤iFcouplings-term supersymmetry can be seen already breaking. from So the long as ⇥a scalar potential; the operators in Eqs. (3,4) lead to new 2D⌦ ⇤ a the supersymmetry breaking spurions X have R-charge d ⇥ 2a W W +⌦h.c. , a a (1) trilinear and quartic operators involving Higgs fields and (⇤ ⌃a+messh.c. + 2 Da (A + A )) = R[X] = 2, the R-symmetry is preserved and no Majorana ⇤ the scalarsgaugino in ⇥B masses, ⇥W ,R areu,R generated.d. 1 The soft masses from the a ⌦ a where a is the fieldMD strength⇤ ⌃a + superfieldh.c. +2 2 forDa oneRe(A of) the, (2) KählerB terms are0 2 B 0 2 W V µu (⇤u AB ) Hu + µd (⇤d AB ) Hd + c.c., (5) SM gauge groups (labelled by a, is a spinor index) and⇥ ⇤ | | | | a a X†XQ†Q ⇥ is a “thatR-partner” contains chiral the masssuperfield term transforming between the under gaugino (Trilnear⇤ ) scalarK interactionsd4⇥ involving, the Higgs multi- (6) ⇤ 2 the adjointand representation its “R-partner” of the(⌃a) appropriate as well as a gauge coupling group of the realplets, especially those⇤ withmess large couplings, are well a a c c c a with R-chargepart ofR the[⇥ scalar] = 0. field Supersymmetry within ⇥ to breaking the D-term is of the Q Qi,U ,D ,Li,E ,Hu,d,Ru,d, ⇥ . known to impact the⌅ strength{ i ofi the electroweaki phase} communicatedcorresponding through gaugeR-symmetry group. preserving spurions transitionIn [10,addition, 15, 23, holomorphic 26, 33, 78–83]. soft masses for each ⇥a are of that includeThe⇤ secondwhich term parameterizes in Eq. (2) a hasD-type two spurion, important con-Turning to the supersymmetry breaking parameters of W a the form ⇤ = Dsequences:⇥. Expanded First, into the components, equation of motion the above for Re( op-A )setsthe theory, scalar soft masses can arise from an additional W ⇥a⇥a erator becomesDa 0 for all three SM gauge groups. The Higgs quarticsource of F -term supersymmetry2 ⇤ ⇤ breaking. So long as ⇥ d ⇥ W W2 + h.c. . (7) coupling in the MSSM is contained in the SU(2) and Uthe(1) supersymmetry breaking spurionsmess X have R-charge D a a a ⇤ D-terms,(⇤ ⌃ so+ eliminatingh.c. + ⌦2 D these(A terms+ A will)) = clearly have an a a R[X] =We 2, the assumeR-symmetry the coe is⇧ preservedcients for and the no holomorphic Majorana soft impact on the Higgs potential. Second, while the real 1 gauginomasses masses are are real. generated. The fullThe set of soft soft masses masses from for the the scalar partsM of⇤Aa a⌃acquire+ h.c. a+2 mass⌦2 D(MRe()A froma) , Eq. (2),(2) Im(Aa) D a a D Kähler termscomponents are of ⇥ and ⇥ are given in the Appendix remains massless at this level.O B W ⇥ in Eq. (A5).X XQ Soft-breaking,Q trilinear scalar couplings be- that containsIn order the mass to enforce termR between-symmetry the on gaugino the superpotential, (⇤a) K d4⇥ † † , (6) tween⇤ the Higgs2 and squarks or sleptons are forbidden and its “theR-partner” Higgs sector (⌃a) of as the well MRSSM as a coupling must of be the enlarged. real The ⇤ mess a by R-symmetry.c Forc viablec phenomenology,a we allow the part of theµ-term scalar of the field MSSM within is⇥ replacedto the byD-term the R-symmetric of the µ- Q Qi,U ,D ,Li,E ,Hu,d,Ru,d, ⇥ . relative⌅ { size ofi the supersymmetryi i breaking} contributions correspondingterms gauge group. In addition,to be holomorphic within roughly soft one masses order for of magnitude each ⇥a are in of mass. The second term in Eq. (2) has two important con- the form Throughout this paper we will take the Dirac gaug- sequences: First, the equationW µu ofHu motionRu + µ ford Rd Re(HdA,a)sets (3) ⇤ ino masses to be large. a Thisa limit simplifies our calcu- ⇤ ⇤ ⇥ ⇥ Da 0 for all three SM gauge groups. The Higgs quartic lations andd2⇥ isW motivatedW by phenomenology.+ h.c. . Specifically,(7) ⇥ where Ru,d are new, R-charge R[Ru,d] = 2 fields that 2 coupling in the MSSM is contained in the SU(2) and U(1) to avoid conflict withmess precision electroweak observables transform as (1, 2) under the standard model gauge ⇤ D-terms, so eliminating these1/2 terms will clearly have an Ref. [35] found the SU(2) gaugino masses should be groups. This choice⇥ of R-partners ensures that elec-We assume the coe⇧cients for thew holomorphic soft impact on the Higgs potential. Second, while the real larger than 1 TeV. Such heavy electroweak gauginos de- troweaka symmetry breaking by the Higgs fieldsa Hmasses are real. The full set of soft masses for the scalar parts of A acquire a mass (MD) from Eq. (2), Im(A ) u,d couple from the rest of the theory and play little role in does not spontaneouslyO break R-symmetry. The MRSSMcomponents of ⇥B and ⇥W are given in the Appendix remainsExample: massless at this R-Symmetric level. with λ couplingsthe electroweak phase transition. The higgsino masses in also defines the R-charges of the matter fields toin be Eq. (A5). Soft-breaking, trilinear scalar couplings be- In order to enforce R-symmetry on the superpotential, the MRSSM, on the other hand, come from µ ,µ ,which R[Q ,Uc,Dc,L ,Ec] = 1, allowing the usual Yukawa cou-tween the Higgs and squarks or sleptons are forbiddenu d the Higgs sectori i of thei i MRSSMi must be enlarged. The we take to be closer to the electroweak scale. In anplings R-Symmetric in the superpotential. model, a tree-level quarticby isR -symmetry. For viable phenomenology, we allow the µ-term of the MSSM is replaced by the R-symmetric µ- relative sizeFurthermore, of the supersymmetry heavy Dirac breaking gauginos, contributions when combined terms Given the extra matter content, there are new super- with the MRSSM Higgs superpotential structure and generatedpotential by operators “mu” [35]terms one canand write “λ” in theterms:R-symmetricto be within roughly one order of magnitude in mass. Throughout this paper we will take the Dirac gaug- theory,W µ H R + µ R H , (3) ⇤ u u u d d d ino masses to be large. This limit simplifies our calcu- u d W ⇤B ⇥B Hu Ru + ⇤B ⇥B Rd Hd lations and1 R-symmetry is motivated is not by essential phenomenology. here. Majorana Specifically, gaugino masses can where Ru,d are new,⇤ R-charge R[Ru,d] = 2 fields that u a a d a a to avoid conflictbe avoided with as long precision as X is not electroweak a singlet [50]. observables transform as (1, 2) + ⇤underW ⇥W H theu ⇧ standardRu + ⇤W model⇥W Rd gauge⇧ Hd . (4) 1/2 Ref. [35] found the SU(2) gaugino masses should be groups. This choice⇥ of R-partners ensures that elec- w larger than 1 TeV. Such heavy electroweak gauginos de- troweak symmetry breaking by the Higgs fields H Example (not optimized for maximal Higgsu,d withcouple minimal2 from thestops): rest of the theory and play little role in does not spontaneously break R-symmetry. The MRSSM the electroweak phase transition. The higgsino masses in also defines the R-charges of the matter fields to be the MRSSM, on the other hand, come from µ ,µ ,which R[Q ,Uc,Dc,L ,Ec] = 1, allowing the usual Yukawa cou- u d i i i i i we take to be closer to the electroweak scale. plings in1 the superpotential. 125 Furthermore, heavy Dirac gauginos, when combined M2 =1TeV Given the extra matter content, there are new super- with the MRSSM Higgs superpotential structure and potential0 operators [35] one can write in the R-symmetric ⇥W µu = µd = 200 GeV theory, 100 ˜ 1 u 75 d m(tL,R)=3TeV W ⇤ ⇥ H R + ⇤ ⇥ R H 1 ⇤ B B u u 50 B B d d R-symmetry is not essential here. Majorana gaugino masses can u a a d a a be avoided as long as X is not a singlet [50]. 2 + ⇤W ⇥W Hu ⇧ Ru + ⇤W ⇥W Rd ⇧ Hd . (4) 2 1 0 1 Fok, Martin, Tsai, GK

⇥B 2 LHC Squark & Gluino Production LHC

Squark Production

˜ q q

- q -q˜

g Gluino exchange diagrams

g ˜ ought to dominate

g˜ LHC production of g

q (1st generation) squarks ˜ -q q- q˜

But for heavier gluino... Majorana versus Dirac

qL sqL qL sqL

˜ ˜ q q q q

- - - q q˜ q -q˜

g g g ˜ g

g˜ g˜ g

X g

q q˜ ˜ - - -q q q˜ q- q˜ qL sqL qR sqR

Requires Majorana mass Dirac and Majorana. insertion. Scales as Scales as

1/M |p|/M2

Suppressed Suppression of t-channel Dirac Gluino

Squark mass Comparison Plot 1+2 1 only

t-channel 1500 dominant squark mass 1000 [GeV] s-channel 500 dominant

DiracDirac gluino gluino mass mass 6 Squark masses 2 at which the 4 cross-section of the final 8state sqL,sqR surpasses that of the final state sqL/R,sq*L/R. Red: Both generations,Dirac Gluino blue: justmass the [TeV]first generation. Sunday, November 11, 2012 Kribs & Raj Squark and/or gluino production (LO)

q q˜ g g˜ - q- q˜ Squark and/or gluino production (LO) with heavy gluino

q q˜ g g˜ - q- q˜ X X X X X X Squark production (LO)

q q˜ g g˜

q- q˜

˜ q q

- q -q˜ q q˜

g g

g ˜

g˜ g˜ g

q ˜ -q - q- q˜ q- q˜ LL, RR absent suppressed 1/M2 & PDFs LR suppressed 1/M2 Bottom Line:

Colored Sparticle Production in Supersoft Supersymmetric Models Substantially Suppressed at LHC

(numbers in 5 slides) Simpliﬁed Models Examples of Simpliﬁed Models Bounded @ LHC

~ ~ ~ ~ ~ ~ ~ ~ ∼0 ~ ~ Squark-gluino-neutralino model, m(χ∼0) = 0 GeV MSUGRA/CMSSM:pp → tan q qβ ,= q 10, → Aq =+ 0,LSP; µ>0 m(g)>>m( )q pp → g g, g → q q χ ; m(q)>>m( )g

1 0 ) 2000 ) s 1200 CMS Preliminary s 1200 ATLAS Preliminary ATLAS Preliminary CMS Preliminary 700 -1 Combined s = 7 TeV L L=1.1dt = 4.71 fb-1, s=7 TeV -1 [GeV] ∫ s = 7 TeV L=1.1 fb (GeV)

1800 CLs observed 95% C.L. limit 0 1/2 ∼ αT Combined χ (GeV) CLs median expected limit m 1000 10 αT prod NLO-QCDCL observed 95% C.L. limit m 1000 10 = s prod NLO-QCD (pb) (CL Expected limit ±1 σ σprod σ NLO-QCD σ = σ 600 σ ~ prod NLO-QCD q σ = 3 ×CL σ median expected limit LSP s ATLAS EPS 2011 (1800) prod NLO-QCD σ = 3 × σ 1600 σ = 1/3 × σ prod NLO-QCD L dt = 4.71 fb-1, s=7 TeV (pb) (CL σ = 1/3 × σ ∫ m ATLAS EPS 2011 σ squark mass [GeV] σ = 1 fb 800 SUSY ∼ 800 500 τ LSP 1400 ~ q (1400) LEP Chargino 1 ~ 1 No EWSBg (1200) 600 600 1200 400 q ~ σSUSY = 10 fb (1000) ~g (1000) 1000 400 -1 400 300 10 10-1 ~

g (800) 95% CL upper limit on

q~ 800 σ = 100 fb (600) SUSY 200 200 200 ~g (600) -2 600 10 -2 600 800 1000 1200 1400 1600 1800 2000 500 1000 1500400 2000 600 2500 3000 800 3500 1000 4000 1200 10 gluino mass [GeV] 400 600 800 1000 1200 m0 [GeV] 95% CL upper limit on on limit upper CL 95% m~g (GeV) m~q (GeV) Figure 7: 95% CLs exclusion limits obtained by using the signal region with the best expected sensitiv- q q ity at each point in a simpliﬁed MSSM scenario with only strong production of gluinos and ﬁrst- and P2 q second-generation squarks, and direct decays to jets and neutralinos (left); and in the (m ; m ) plane of P2 0 1/2 χ˜0 g˜ MSUGRA/CMSSM for tan = 10, A = 0 and µ>0 (right). The red lines show the observed limits, the χ˜0 0 q˜ dashed-blue- massless lines the median expected LSP limits, and the dotted blue lines the 1⇥ variation on the expected 0 ± 0 χ˜ limits. ATLAS EPS 2011 limits are from [17] and LEP results from [59].P1 q˜ χ˜ g˜ q P1 7 Summary q q

This note reports a search for new physics in final states containing high-pT jets, missing transverse - bounds in 1 momentum and no electrons or muons, based on the full dataset (4.7- fbgluino ) recorded by >> the ATLAS sq - sq >> gluino experiment at the LHC in 2011. Good agreement is seen between the numbers of events observed in the data and the numbers of events expected from SM processes. The(M3, results are interpretedMsq) in both a simplified model containing only squarks of the first two generations, a gluino octet and a massless neutralino, as well as in MSUGRA/CMSSM models with tan = 10, A0 =plane0 and µ>0. In the simplified model, gluino masses below 940 GeV and squark masses below 1380 GeV are excluded at the 95% confidence level. In the MSUGRA- bounds/CMSSM models, valuesin of - bounds in m1/2 < 300 GeV are excluded for all values of m0, and m1/2 < 680 GeV for low m0. Equal mass squarks and gluinos are excluded below 1400 GeV in both scenarios. (Msq, LSP) (M3, LSP) References plane plane [1] L. Evans and P. Bryant, LHC Machine, JINST 3 (2008) S08001.

[2] H. Miyazawa, Baryon Number Changing Currents, Prog. Theor. Phys. 36 (6) (1966) 1266–1276.

[3] P. Ramond, Dual Theory for Free Fermions, Phys. Rev. D3 (1971) 2415–2418.

[4] Y. A. Golfand and E. P. Likhtman, Extension of the Algebra of Poincare Group Generators and Violation of p Invariance, JETP Lett. 13 (1971) 323–326. [Pisma Zh.Eksp.Teor.Fiz.13:452-455,1971].

[5] A. Neveu and J. H. Schwarz, Factorizable dual model of pions, Nucl. Phys. B31 (1971) 86–112.

14 Dirac versus Majrorana Gluino Simpliﬁed Models

Construct a supersoft supersymmetric simpliﬁed model (SSSM) and perform apples-for-apples comparison against MSSM.

SSSM “equal MSSM” “intermediate MSSM” “heavy MSSM”

g˜ g˜ M3 = 5 TeV M˜ = 5 TeV g˜ 3 M˜ 3 =2Mq˜ g˜,˜qL,R;1,2 M˜3 = Mq˜ q˜L,R;1,2 q˜L,R;1,2 M3 q˜L,R;1,2 Mq˜ Mq˜ Mq˜ 5 10 ⇤

LSP LSP LSP LSP Mq˜ to < Mq˜ Mq˜ Mq˜ Mq˜ ⇥

FIG. 1. The spectra for the simplified models considered in this paper. The left-most pane illustrates our primary interest – the supersoft supersymmetric simplified model (SSSM). It contains a gluino with a large Dirac mass M3 = 5 TeV, first and second generation squarks that are roughly 5 10 times lighter than gluino, and an LSP that is generally assumed to be much lighter than the squarks. The three right-most panes illustrate the three simplified models of the MSSM to which we compare. We write the gluino Dirac mass as M3 to be distinguished from a Majorana mass written as M˜ 3. Two of the comparison simplified models of the MSSM (“equal MSSM” and “intermediate MSSM”) are designed to provide comparisons between typical MSSM spectra and the SSSM. The third comparison model, “heavy MSSM”, directly compares the results for a Dirac gluino versus a Majorana gluino of the same mass. Generally the LSP mass is taken to be kinematically negligible, however we also comment on the relaxation of the bounds on the SSSM when the LSP is heavier.

II. SIMPLIFIED MODELS AND THE SSSM contrast to the MSSM. The “equal MSSM” and “intermediate MSSM” simplified models are chosen to provide a comparison with typical MSSM spectra. The “heavy We are interested in calculating the bounds on su- MSSM” simplified model is highly unnatural within the persymmetric models with Dirac gaugino masses. Our usual MSSM as we have already discussed. Nevertheless, approach is to first construct a supersoft supersymmet- it illustrates the dierences in squark mass bounds that ric simplified model (SSSM) on which we can apply the remain between a heavy Majorana gluino versus a heavy nj +/ET limits from LHC. This is completely analogous Dirac gluino even when they have the same mass. to the construction of simplified models of the MSSM [22, 23], which are now widely used in presenting the re- Our analyses generally assume the LSP has a kine- sults from LHC searches for supersymmetry. The SSSM, matically negligible mass. In the Discussion we also con- illustrated in the far left pane of Fig. 1, has a gluino with sider the weakening of the bounds as the LSP mass is a large, purely Dirac mass, degenerate first and second increased. The LSP could be light gravitino, or could generation squarks (of both handedness), and the light- instead be some other light neutral superpartner, so long est supersymmetric particle (LSP) at the bottom of the as the squark decay proceeds directly to the LSP in the spectrum. In defining the SSSM, we have explicitly cho- one step processq ˜ q +LSP. We also assume all decays sen the Dirac gluino mass to have a fixed large value, into the LSP are prompt. The assumption of short decay M3 = 5 TeV. The large gluino mass implies gluino pair chains from heavy squarks to a massless LSP implies the production is kinematically forbidden while associated bounds we obtain are the most optimistic possible using gluino/squark production is highly suppressed, leaving the jets plus missing energy searches with no leptons in squark production as the only potentially viable colored the final state. sparticle production at the LHC. Squarks decay through Mapping the bounds from the SSSM onto theories q˜ q + LSP, where the quark flavor and chirality de- with Dirac gaugino masses is straightforward in princi- pends on the initial squark. ple, though model-dependent in practice. In particular, To perform an apples-for-apples comparison of the con- we do not include electroweak gauginos or Higgsinos in straints on supersoft supersymmetry versus the MSSM, our spectrum. The supersoft supersymmetric model has we calculate the bounds not only on the SSSM, but also heavy Dirac gaugino masses, with an ordinary MSSM three other simplified models of the MSSM. In all of µ-term for the Higgs sector [21]. Several other models the simplified models, the first and second generation incorporate Dirac gauginos [24–38]. In several cases, the squarks are degenerate and the LSP is massless. The gaugino sector approximately preserves a U(1)R symme- spectra of the three comparison simplified models of the try, while the Higgs sector does not. In [30] a fully R- MSSM are shown in the three right-most panes of Fig. 1. symmetric supersymmetric model was constructed that The purpose of the comparison models is to both vali- incorporated not only Dirac gaugino masses but also R- date our analysis against the actual bounds from exper- symmetric Higgsino masses. In this model, additional R- imental analyses (where available), as well as to directly symmetric contributions to the soft masses were allowed, show the weakness of the bounds on the SSSM in direct and notably, could be nearly arbitrary in flavor-space.

2 Simulations

Signal simulation | Depends only on squark mass!

Pythia with NLO K-factors from Prospino CTEQ6L DELPHES jet deﬁnitions appropriate to experiments

Backgrounds from ATLAS, CMS analysis notes.

Use simpliﬁed models of MSSM as cross checks that we are approximately matching expt analyses limits. Colored Sparticle Cross Sections

100 neutralinos, such as same-sign lepton ﬁnal states, may ⌅ MSSM, M3 ⇥ Mq

⇥ ⌅ not yield strong bounds if the model is approximately R- MSSM, M3 ⇥ 2 Mq pb 10 MSSM, M3 ⇥ 5 TeV symmetric, and so again we are left to model-dependent ⇥ SSSM investigations to make quantitative statements. 1

superpartners 0.1

colored 0.01 ⇧ pp IV. RECASTING LHC LIMITS 0.001 ⇤

104 To recast LHC limits on colored superparticle produc- 400 600 800 1000 1200 M⌅ GeV tion into the SSSM, we follow the analyses searching for q supersymmetry through nj +/ET signals performed by FIG. 3. Cross sections at the 7 TeV ⇥ LHC for coloredKribs & super- Martin ATLAS [61] and CMS [62–64]. Of the existing supersym- partner production. The four lines correspond to the four metry searches, jets plus missing energy is the simplest, simplified models shown in Fig. 1, where the first and second and involves the fewest assumptions about the spectrum. generation squarks are degenerate with mass Mq˜.Thesolid line shows the cross section for the SSSM where the cross To simulate the supersymmetric signal, we use section is dominated byq ˜q˜ final states, while the dashed PYTHIA6.4 [65]; the first and second generation squarks lines show cross sections for the three simplified models of the are set to have equal mass, the gravitino is chosen to be MSSM. All cross sections are calculated to next-to-leading or- the LSP, and all other superpartners are decoupled (set der using PROSPINOv2.1 [68], CTEQ6L1 parton distribution to 5 TeV). We use CTEQ6L1 parton distribution func- functions, and default scale choices. For event generation, we tions, generating a su⌅cient number of events such that use PYTHIA6.4 [65] and rescale the cross section to match statistical fluctuations have negligible eect on our re- those shown here. sults. To incorporate detector eects into our signal simulations, all events are passed through the Delphes [66] program using ATLAS or CMS detector options and statistic [69]: adopting the corresponding experiment’s jet definitions: N (µ +µ ) N (µ +µ ) i,obs e i,b i,s anti-k ,R =0.4 for the ATLAS search [61], and anti- ⇤ i,obs i,b i,s T 0 db⇥ 0 (N )! G(µb,b⇥) 0.05 = i,obs . kT ,R=0.5 for the CMS searches [62–64]. We repeat the Ni,obs N µ e µb ⇥ i,obs b same steps for the three simplified models of the MSSM ⇤ db G(µb,b) 0 ⇥ 0 (Ni,obs)! ⇥ (c.f. Fig. 1) allowing all combinations ofq ˜q˜,˜qq˜,˜qq˜ as (6) well as gluino pair production and associated squark plus ⇥ gluino production. Note that our “heavy MSSM” simpli- Here µ N is the number of expected SM back- i,b ⇥ i,exp fied model is an existing CMS simplified model, “T2” ground events and µi,s Ni,SUSY is the number of signal [67]. events. To estimate the⇥ eects of systematic errors, the Colored superpartner production cross sections receive number of SM events is modulated by a Gaussian weight- ing factor [70]. Specifically, we shift µ µ (1 + f ), sizable next-to-leading order (NLO) corrections. To in- b ⇤ b b corporate these corrections, we feed the spectra into where fb is drawn from a Gaussian distribution centered PROSPINO [68], restricting the processes appropriately at zero and with standard deviation ⇤f = ⇤i,SM /Ni,exp, where ⇤i,SM is the quoted systematic uncertainty (taken for each simplified model (i.e., just pp q˜q˜ for the SSSM). The cross sections are shown in Fig.⇤ 3 for each of directly from [61–64]). Whenever the systematic error is the simplified models as a function of squark mass. De- asymmetric, we use the larger (in absolute value) num- pending on the scale choice and the squark mass, we find ber. To combine channels (when appropriate), we simply the K-factor ranges from 1.7-2.1. This takes into account replace the right-hand side of Eq. (6) with the product the increased rate at NLO, through not the kinematic over all channels. distribution of events. The number of supersymmetry events in a particular channel is the product of the cross section, luminosity, The analyses we are interested in [61–64], are broken acceptance and e⌅ciency, up into several channels. For some analyses the channels are orthogonal, while in other analyses one event can Ni,SUSY = K(Mq˜) ⇤(Mq˜) A(Mq˜) , (7) fall into multiple channels. To set limits we begin by L· · · counting the number of supersymmetry events in each where K(Mq˜) is the mass-dependent K-factor to account analysis channel for several squark masses. The number for the larger rate at NLO. Within our simplified setup, of supersymmetric events passing cuts is translated into the only parameter the cross section and acceptance de- a mass-dependent acceptance for each channel. We then pend upon is the mass of the squark – thus Eq. (6) is form the 95% CL limit, using the likelihood ratio test simply a limit on the squark mass.

5 Basic Jets Plus Missing Energy Searches

ATLAS 4.7/fb CMS 1.1/fb B Excluded regions in supersymmetry parameter space showing the channel withATLAS the best jets expected + missing exclusion search at each pointstrategy

Squark-gluino-neutralino model, m(χ∼0) = 0 GeV 0 leptons;MSUGRA/CMSSM: all jets tanβ = pT10, A => 0, 40 µ>0 GeV 2000 1 0 ATLAS Preliminary At At Bt Bt ATLAS Preliminary 700 Combined L dt = 4.71 fb-1, s=7 TeV Cl CmDt Dt Bt [GeV] ∫ 1800 CLs observed 95% C.L. limit At At Bt Bt Channel Requirement1/2 Combined

CLs median expected limit m A A’ B C CLD s observedE 95% C.L. limit Expected limit ±1 σ 600 At At Bt Bt Cl Cm Dt Bt Bt miss q ~ CLs median expected limit ATLAS EPS 2011 (1800) 1600 ET [GeV] > 160 -1 ∫ L dt = 4.71 fb , s=7 TeV At Bt Bt Bt ATLAS EPS 2011

squark mass [GeV] pT( j1) [GeV] > 130 ∼τ LSP Cl Et Dt Bt Bt At At At 500 ~ 1400 pT( j2) [GeV] > At Bt q Bt Bt Dt 60 Ct Dt Dt Dt Dt Dt (1400) LEP Chargino ~ pT( j3) [GeV] > – – 60 60 60No EWSBg (1200)60 Am Dt Dt Et Dt Dt Dt Dt Dt Dt Dt Cm Et Et Dt At AtAt At 1200 pT( j4400) [GeV] > – – – 60 60 60 q ~ (1000) Cm Dt Dt Et Em Em Em Em Em Em Em pT( j5) [GeV] > – – – – 40 ~g (1000)40 Cm Cm Cm Am Am Am At At 1000 pT( j6) [GeV] > – – – – – 40 300 Bt Cm Et EtEm Em Em Em Em Em Em Cl Cl A’ Am Am Am Am Am miss ⇤(jet, E ) > 0.4 (i = 1, 2, (3) ) 0.4 (i = 1, 2, 3 ), 0.2 (p > 40 GeV~g (800) jets) T min { } { } T Cl Am Am Am A’ Am A’ A’ Cl Cl El El El El El El El El 800 miss q~ ET /me⇥(Nj) > (600) 0.3 (2j) 0.4 (2j) 0.25 (3j) 0.25 (4j) 0.2 (5j) 0.15 (6j) Cm Cm Cl Cm Am A’ A’ A’ 200 ~ me⇥(incl.) [GeV] > 1900Cl /1400Cl/– –/1200Cm/– Et1900/–/–Cl 1500/1200Cl /900Cl 1500g/– Cl(600)/– 1400/1200/900 600 600 800 1000 1200 1400 1600 1800 2000 500 1000 1500 2000miss 2500 3000mid 3500 4000 Table 1: Cuts used to definetightmid each of themid channelstight in the analysis.tight mid The E tight/m cut in any N jetloose channel gluino mass [GeV] looseT e⇥ tight m0 [GeV] uses a value of me⇥ constructed from only the leading N jets (indicated in parentheses). However, the final me⇥(incl.) selection, which is used to define the signal regions, includes all jets with pT > 40 GeV. FigureATLAS-CONF-2012-033 38: 95% CLs exclusion limits obtained by usingThe three me⇥ the(incl.) selections signal listed in region the final row denote with the ‘tight’, the ‘medium’ best and ‘loose’ expected selections sensitivity at each point in a simplified MSSM scenario withrespectively. only Not all channels strong include all production three SRs. of gluinos and first- and second-generation squarks, and direct decays to jets and neutralinosmiss (left); and in the (m⌅ miss0 ; m1/2) plane In Table 1, ⇤(jet, ET )min is the smallest of the azimuthal separations between PT and the re- miss of MSUGRA/CMSSM for tan = 10, A0 = 0 and µ>constructed0 jets. (right). For channels A, The A’ and B,red the selection lines requires show⇤(jet, ET the)min > observed0.4 using up to limits, miss three leading jets. For the other channels an additional requirement ⇤(jet, ET )min > 0.2 is placed on the dashed-blue lines the median expected limits, and the dotted blue linesmiss the miss1⇥ variation on the ex- all jets with pT > 40 GeV. Requirements on ⇤(jet, ET )min and ±ET /me⇥ are designed to reduce the pected limits. The labels A-E refer to the channel withbackground the from multi-jet best processes. expected exclusion at each point, while the suxes l, m and t refer to the loose, medium and tightStandard Model selections background processes for contribute each to the signal event counts in region. the signal regions. ATLAS The EPS 2011 limits are from [17] and LEP results from [59].dominant sources are: W+jets, Z+jets, top quark pair, single top quark, and multi-jet production, with a smaller contribution from diboson production. The majority of the W+jets background is composed of W ⇥ events, or W e,µ events in which no electron or muon candidate is reconstructed. The largest part of the Z+jets background comes from the irreducible component in which Z ¯ miss decays generate large ET . Top quark pair production followed by semileptonic decays, in particular tt¯ bb¯⇥qq with the ⇥-lepton decaying hadronically, as well as single top quark events, can also generate miss large ET and pass the jet and lepton requirements at a non-negligible rate. The multi-jet background in the signal regions is caused by misreconstruction of jet energies in the calorimeters leading to apparent missing transverse momentum, as well as by neutrino production in semileptonic decays of heavy quarks. Extensive validation of the MC simulation against data has been performed for each of these background sources and for a wide variety of control regions (CRs). Each of the six channels is used to construct between one and three signal regions with ‘tight’, ‘medium’ and/or ‘loose’ me⇥(incl.) selections. In order to estimate the backgrounds in a consistent and robust fashion, five control regions are defined for each of the eleven signal regions, giving 55 CRs in total. The orthogonal CR event selections are designed to provide uncorrelated data samples enriched in particular background sources. Each ensemble of one SR and five CRs constitutes a di⇥erent ‘stream’ of the analysis. The CR selections are optimised to maintain adequate statistical weight, while minimising as far as possible the systematic uncertainties arising from extrapolation to the SR. The control regions are chosen to be as close kinematically as possible to the corresponding SR in order to minimise theoretical uncertainties arising from extrapolation between them. The CRs are listed

34 sum over these cell clusters, measured at the electromagnetic scale, treating each as an (E, ⌅p) four-vector with zero mass. The jet energies are corrected for the e⇥ects of calorimeter non-compensation and in- homogeneities by using pT- and -dependent calibration factors based on Monte Carlo (MC) corrections validated with extensive test-beam and collision-data studies [22]. Only jet candidates with pT > 20 GeV are subsequently retained. Electron candidates are required to have p > 20 GeV and < 2.47, and to pass the ‘medium’ T | | electron shower shape and track selection criteria described in Ref. [23]. Muon candidates are required to have p > 10 GeV and < 2.4. T | | Following the steps above, overlaps between candidate jets with < 2.8 and leptons are resolved | | as follows [24]. First, any such jet candidate lying within a distance R = 2 + ⇥2 < 0.2 of an electron is discarded; then any lepton candidate remaining within a distance R = 0.4 of any surviving jet candidate is discarded. ⌅ miss miss The measurement of the missing transverse momentum two-vector PT (and its magnitude ET ) is based on the transverse momenta of all remaining jet and lepton candidates and all calorimeter clusters not associated to such objects. Following this step, all jet candidates with > 2.8 are discarded. There- | | after, the remaining lepton and jet candidates are considered “reconstructed”, and the term “candidate” is dropped. Meﬀ 4 Signal and Control Region Deﬁnitions

Following the object reconstruction described above, events are discarded if any electrons with pT > 20 GeV or muons with pT > 10 GeV remain, or if they have any jets failing quality selection criteria designed to suppress detector noise and non-collision backgrounds (see e.g. Ref. [25]), or if they lack a reconstructed primary vertex associated with five or more tracks. This analysis aims to search for the production of heavy SUSY particles decaying into jets and miss neutralinos, with the latter creating missing transverse momentum (ET ). Because of the high mass scale expected for the SUSY signal, the ‘e⇥ective mass’, me⇥, is a powerful discriminant between the signal and most Standard Model backgrounds. For a channel which selects events with N jets, me⇥ is miss defined to be the scalar sum of the transverse momenta of the leading N jets together with ET . The final signal selection uses cuts on me⇥(incl.) which sums over all jets with pT > 40 GeV. Cuts on me⇥ miss miss and ET , which suppress the multi-jet background, formed the basis of the previous ATLAS jets+ ET + 0-lepton SUSY search [26]. The same strategy is adopted in this analysis. The requirements used to select jets and leptons (which are referred to as physics objects) are chosen to give sensitivity to a broad range of SUSY models. In order to achieve maximal reach over the (mg˜ , mq˜)- plane, six analysis channels are defined. Squarks typically generate at least one jet in their decays, for instance throughq ˜ q⇤˜0, while gluinos typically generate at least two, for instance throughg ˜ qq¯⇤˜0. 1 1 Processes contributing toq ˜q˜,˜qg˜ andg ˜g˜ final states therefore lead to events containing at least two, three or four jets, respectively. Cascade decays of heavy particles tend to further increase the final state multiplicity. ATLAS-CONF-2012-033Five inclusive analysis channels, labelled A to E and characterized by increasing jet multiplicity from 2 to 6, are therefore defined. In addition, the two jet sample is divided into two channels, A and A’, using miss the ratio of the ET to the me⇥. Channel A’ is designed to improve the sensitivity to models with small sparticle mass splittings, where the presence of initial state radiation jets may allow signal events to be selected irrespective of the visibility of the sparticle decay products. The lower jet multiplicity channels focus on models characterised by squark pair production with short decay chains, while those requiring high jet multiplicity are optimised for gluino pair production and/or long cascade decay chains. The channels and signal regions (SRs) are summarised in Table 1.

2 Signal Region Signal Region Process Process SRC loose SRE loose SRCSRA loose medium SRA’SRE medium loose SRCSRA medium medium SRESRA’ medium medium SRC medium SRE medium tt¯+ Single Top 74 13 (75)tt¯+ Single66 Top26 (64) 74 7135 (75) (5.1) 6611 263.4 (64) (10) 127 45.5 (5.1) (10) 1711 5.38.4 (13) (10) 12 4.5 (10) 17 5.8 (13) ± ± ± ± ±± ±± ±± ± ± Z/+jets 70 22 (61) Z/+jets22 6.4 (13) 70 31229 (61).9 (34) 2264 620.4 (13)(69) 1731 59.9.9 (16) (34) 8642.920 (4.4) (69) 17 5.9 (16) 8 2.9 (4.4) ± ± ± ± ±± ±± ± ± ± ± W+jets 62 9.3 (61) W+jets23 11 (23) 62 199.34 (61).5 (21) 2326 114.6 (23) (30) 819.1 24.9.5 (11) (21) 526.9 34 (4.7).6 (30) 8.1 2.9 (11) 5.9 3 (4.7) ± ± ± ± ±± ±± ±± ± ± Multi-jets 0.39 0.4 (0.16)Multi-jets3.7 1.9 (3.8) 0.390.140.40. (0.16)24 (0.13) 30.7 0.113.9 (0.38) (3.8) 0.0240.14 0.0034.24 (0.013) (0.13) 0.08 00..5313 (0.64) (0.38) 0.024 0.034 (0.013) 0.8 0.53 (0.64) ± ± ± ± ±± ±± ± ± ± Di-Bosons 7.9 4 (7.9)Di-Bosons4.2 2 (4.2) 7.97.34 (7.9)3.7 (7.5) 415.2 72.4 (4.2) (16) 17.7.3 0.387.7 (1.7) (7.5) 2.157 1.73.4 (2.7) (16) 1.7 0.87 (1.7) 2.7 1.3 (2.7) ± ± ± ± ± ±± ±± ± ± Total 214 24.9 13 Total119 32.6 11.621464.824.109 .2 136.92 119115 3219.6 911.69.6 3864..68 610.68.2 4.776.92 341154.4719 5.579.69 38.6 6.68 4.77 34 4.47 5.57 ± ± ± ± ± ± ± ± ± ± ±± ±± ±± ± ± ±± ± ± ± ± B Excluded regions in supersymmetryData parameter210 Data 148 space21059 showing14885 the3659 chan-2585 36 25 ATLAS jets + missinglocal p-value (Gaus.search⇥) 0.55(-0.14)local p-value (Gaus.strategy0.21(0.8)⇥) 0.55(-0.14)0.65(-0.4) 0.21(0.8)0.9(-1.3) 0.6(-0.26)0.65(-0.4) 0.85(-1)0.9(-1.3) 0.6(-0.26) 0.85(-1) nel with the best expected exclusion at each44 point52 44 20 5232 1420 12 32 14 12 UL on NBSM 58(6083) UL on NBSM84(6993) 58(6025(2883)39) 84(6929(439360)) 18(1925(282739) ) 12(1629(4323)60) 18(1927) 12(1623) 9.3 11 9.3 4.3 116.7 34.3 2.56.7 3 2.5 UL on ⇥BSM /(fb) 12(1318UL) on ⇥BSM18(15/(fb)20) 12(135.3(618 )8.2) 18(156.2(9.22013)) 3.7(45.3(6.158.7.2)) 2.5(36.2(9.5.5213) ) 3.7(4.15.7) 2.5(3.55 )

Squark-gluino-neutralino model, m(χ∼0) = 0 GeV MSUGRA/CMSSM: tanβ Signal= 10, Region ASignal= Region0, µ>0 Signal Region 2000 1 Process Process At ProcessAm Am’0 Bt ATLAS Preliminary SRC loose At SRESRAAt loosetight Bt SRABtSRB medium tight SRASRA’ tightATLASSRC medium tight PreliminarySRCSRBSRD medium tight tight SRESRESRC medium tight tight SRD tight SRE tight 700 Combined L dt = 4.71 fb-1, s=7 TeV Cl CmDt Dt Bt [GeV] ∫ 1800 CLs observed 95% C.L.t t¯limit+ ¯+ At. .At ¯+ Bt . Bt ...... Single Top tt Single1/2 74 13 Top (75) 0 2266 0 2635 (0.046)(64)tt Single0 21 Top7 0533 (5.1) (0.066)0 22 11013583 (0.046)41 (10)6 (0.96) 0 2112 20433157 (10) (0.066) (0.92) 1713895 814 (13)6 (2.6) (0.96) 2 1 7 (0.92) 3 9 4 (2.6) ± ±± ±± ± ±Combined± ±±± ± ±± ± ± CLs median expected limit m /+ . . CLs observed. 95% C.L. limit. 13 13 Z jets Z/70+jets22 (61) 222.9 16.54 (3.1) (13)Z/+jets312.5 919.4 (34) (1.6) 2.9 6412..5120 (3.1)1 (69).1 (4.4) 217.50.9515.940 (16) (1.6).58 (2.7) 832..212 91 (4.4)1.4.1 (1.8) (4.4) 0.95 0.58 (2.7) 3.2 1.4 (1.8) Expected limit ±1 σ 600 At At Bt Bt ± ± ~ ± ± ± ± ± q ± ± ± ± ± ±± ± ± Cl Cm Dt Bt Bt CLs median expected limit 1600 ATLAS EPS 2011 (1800) -1 W+jets W62+jets9.3 (61) 2.231 011.99 (23) (1.9)W+jets019.97 40.5.6 (21) (0.84)2.1 2601.99.24. (1.9)61 (30).2 (2.7) 0.978.11.702..691 (0.84)(11).5 (2.5) 52.19..32 31 (4.7)1.7.2 (1.5) (2.7) 1.7 1.5 (2.5) 2.3 1.7 (1.5) ∫ L dt = 4.71 fb , s=7 TeV ± At ±± Bt Bt Bt±± ± ± ± ATLAS EPS±± ± 2011 ±±± ± ± squark mass [GeV] Multi-jets Multi-jets0.39 0.4 (0.16) 0 3.07.00241.9 (0.002) (3.8)Multi-jets0.140.00340.24 (0.0032) (0.13)0 0.000240 00.13.0058 (0.002) (0.38) (0.0023)∼τ LSP0.02400.003400..0340072 (0.0032) (0.013) (0.021) 00.08.2200.0058.530.25 (0.64) (0.0023) (0.24) 0 0.0072 (0.021) 0.22 0.25 (0.24) Cl Et Dt Bt Bt At At At 500 ~ 1400 ± At± ± Bt q Bt ± Bt± Dt ± Ct±± Dt Dt ± ±±Dt Dt Dt±± ± ± ± (1400) LEP Chargino Di-Bosons Di-Bosons7.9 4 (7.9) 14.7.2 02.95 (4.2) (2)Di-Bosons71..37 30..795 (7.5) (1.9) 1.7 150.049.957.40 (2). (16)26 (0.51) 11..77 2~.02.87951 (1.7). (1.9)2 (2.2) 20..7249.5 1.310.. (2.7)326 (2.5) (0.51) 2.2 1.2 (2.2) 2.5 1.3 (2.5) ± ±± ± ± ± ± No EWSB±±g (1200)± ± ± ± ± Am Dt Dt Et Dt Dt Dt Dt Dt Dt Dt Cm Et Et Dt At AtAt At 1200 Total 214400Total24.9 13 1197 0.99932.6 211.26.6Total645.39.8 100.951.2 6.292.017 1150.5999.681912..79269.691.515.3839.66.0846.951.681.742.77.201.1 34512.68.14.4741.59.795.573.104.51 6.84 1.7 2.1 12.1 4.59 3.04 ± ± q±~ ± ±± ±± ±± ± ± ± ± ± ±± ± ±± ± ± ±± ± ±± ± ± ± ± (1000) Cm Dt Dt Et Em Em Em Em Em Em Em Data Data210 1481 Data 591 1 85 14 ~g36 1(1000)9 251314 9 13 1000 Cm Cm Cm Am Am Am At At local p-value (Gaus.local⇥) p-value3000.55(-0.14) (Gaus. ⇥) Bt 0.98(-2.1)0.21(0.8)localCm p-valueEt (Gaus.0.65(-0.4)Et0.95(-1.7)⇥) Em 0.98(-2.1)Em0.9(-1.3)0.018(2.1) Em Em 0.95(-1.7)0.6(-0.26)Em0.29(0.55)Em Em0.85(-1)0.45(0.13)0.018(2.1) 0.29(0.55) 0.45(0.13) Cl Cl A’ Am Am Am Am Am ~ 44 524.2 203.8 4.232 7.6 g (800)143.8 6.4 128.57.6 6.4 8.5 UL on NBSM UL on58(60NBSM ) 2.9(684(69.1 ))UL on NBSM25(283.1(5.5 ) ) 2.9(629(43.116(11) ) ) 3.1(518(1910(8.5 .)9) ) 12(1612(1216(11) ) ) 10(8.9 ) 12(12 ) Cl Am Am Am A’ Am A’ A’ 83 Cl Cl939 El El 398.El3 El 9 El60 15 El El 278.3 13El 231715 13 17 800 q~ 9.3 (600) 110.89 4.3 0.8 0.896.7 1.6 30.81.4 2.51.81.6 1.4 1.8 Cm Cm Cl Cm Am A’ A’ A’ UL on ⇥BSM /(fb) UL on200⇥12(13BSM /(fb)18 ) 0.62(118(15.3201UL.9) ) on ⇥BSM /0.65(1(fb)5.3(68..2)1.8) 0.62(16.2(9.33.5(21..9213).3)3.2)~ 0.65(13.7(42.2(1.1.25.17..9)82).7) 2.5(32.6(23.5(2.55.5.3).53).2) 2.2(1.92.7) 2.6(2.53.5) Cl Cl Cm Et Cl Cl Cl g Cl(600) 600 Signal Region 600 800 1000 1200 1400 1600 1800Table 3: Observed 2000Process numbersTable of events 3: Observed500 in data and numbers 1000 fitted background of 1500 events components in 2000 data and in 2500fitted each SR. background For 3000 the total components 3500 background 4000 in estimates, each SR. the For quoted the total errors background estimates, the quoted errors gluino mass [GeV] SRA tight SRB tight SRC tight SRD tight mSRE [GeV] tight give the systematic and statisticalgive the (MC systematic and CR combined) and statistical uncertainties (MC and respectively. CR combined) For the uncertaintiesindividual background respectively.0 components, For the the individual total uncertainties background components, the total uncertainties are given, withtt¯+ Single the values Top inare parenthesis given,0.22 0.35 with (0.046)indicating the values0.21 the pre-fit0 in.33 parenthesis (0.066) predictions1.8 indicating for1.6 the (0.96) MC the expectations. pre-fit2 1.7 predictions (0.92) For W+jets,3 for.9 Z the4+ (2.6)jets MC and expectations.tt¯+jets, these predictions For W+jets, Z+jets and tt¯+jets, these predictions ATLAS-CONF-2012-033 ± ± ± ± ± Figure 38: 95% CLs exclusion limits obtainedare from ALPGEN by, andusing scaledare by from the additionalALPGEN signal factors, and of scaled 0.75, region 0.78 by additional and 0.73 with respectively, factors the of 0.75, determined best 0.78 expected byand normalisation 0.73 respectively, tosensi- data in determined corresponding by normalisation control to data in corresponding control 13 Z/+jets 2.9 1.5 (3.1) 2.5 1.4 (1.6) 2.1 1.1 (4.4) 0.95 0.58 (2.7) 3.2 1.4 (1.8) tivity at each point in a simplified MSSM scenario with only± strong± production± of gluinos± and± first- and regions in channelW+ A.jets In theregions case2 of.1 the in0 channel. multi-jet99 (1.9) A. background, In0.97 the0 case.6 (0.84) the of pre-fit the multi-jet values1.2 1. are2 (2.7) background, from the1 data-driven.7 the1.5 (2.5) pre-fit method. values2.3 The1 are.7 p-values (1.5) from thegive data-driven the probability method. of the The p-values give the probability of the second-generation squarks, and direct decays to jets andobservation neutralinos± being consistent± (left); with the estimated and±⇥ background, in the± and (m the0 “Gaus.; m1±⇥/”2 values) plane the number of standard deviations in a Gaussian approximation, observation beingMulti-jets consistent with0 the0.0024 estimated (0.002) background,0 0.0034 (0.0032) and the “Gaus.0 0.0058” (0.0023) values the0 number0.0072 (0.021)of standard0.22 deviations0.25 (0.24) in a Gaussian approximation, of MSUGRA/CMSSM for tan = 10, A0 =evaluated0 and for a singleµ> observationevaluated0 (right).± at a time.for a Thesingle last The observation± two lines red show at lines athe time.± upper The limits show last on two the linesexcess± the show number observed the of upper events,± limits and limits, the on excess the excess cross-section, number above of events, and the excess cross-section, above Di-Bosons 1.7 0.95 (2) 1.7 0.95 (1.9) 0.49 0.26 (0.51) 2.2 1.2 (2.2) 2.5 1.3 (2.5) the dashed-blue lines the median expectedthat limits, expected from and the Standard thethat expected Model. dotted± The from observed the blue Standard upper± lines limit Model. is followed the The± observed in brackets1⇥ upper byvariation the± limit expected is followed limit, with on± in the brackets the super-ex- and by the sub-scripts expected showing limit, with the super- and sub-scripts showing Total 7 0.999 2.26 5.39 0.951 2.01 5.68 1.79±1.51 6.84 1.7 2.1 12.1 4.59 3.04 pected limits. The labels A-E refer to thethe channel variation in the with expectationthe the variation from± best1⇥± inchanges the expected expectation in the± background.± from exclusion1⇥ changes± ± in the at background.± each± point,± ± while the suxes l, m and t refer to the loose, medium andData tight selections±1 for1 each± signal14 region.9 ATLAS13 EPS 2011 limits are from [17] and LEP results fromlocal [59]. p-value (Gaus. ⇥) 0.98(-2.1) 0.95(-1.7) 0.018(2.1) 0.29(0.55) 0.45(0.13) 4.2 3.8 7.6 6.4 8.5 UL on NBSM 2.9(6.19 ) 3.1(5.58.3) 16(1115 ) 10(8.913 ) 12(1217 ) 0.89 0.8 1.6 1.4 1.8 UL on ⇥BSM /(fb) 0.62(1.31.9 ) 0.65(1.21.8) 3.5(2.33.2) 2.2(1.92.7) 2.6(2.53.5)

Table 3: Observed numbers of events in data and fitted background components in each SR. For the total background estimates, the quoted errors give the systematic and statistical (MC and CR combined) uncertainties respectively. For the individual background components, the total uncertainties are given, with the values in parenthesis indicating the pre-fit predictions for the MC expectations. For W+jets, Z+jets and tt¯+jets, these predictions are from ALPGEN, and scaled by additional factors of 0.75, 0.78 and 0.73 respectively, determined by normalisation to data in corresponding control regions in channel A. In the case of the multi-jet background, the pre-fit values are from the data-driven method. The p-values give the probability of the observation being consistent with the estimated background, and the “Gaus. ⇥” values the number of standard deviations in a Gaussian approximation, evaluated for a single observation at a time. The last two lines show the upper limits on the excess number of events, and the excess cross-section, above that expected from the Standard Model. The observed upper limit is followed in brackets by the expected limit, with the super- and sub-scripts showing the variation in the expectation from 1⇥ changes in the background. ±

34 ATLAS Search Bounds

SSSM MSSM MSSM MSSM M3 = 5 TeV M3 = Msq M3 = 2 Msq M3 = 5 TeV 1500 1250 1000 750 500 250 1st,2nd generation squark mass

0 AmAtAt'BtClCmDtEm AmAtAt'BtClCmDtEm AmAtAt'BtClCmDtEm AmAtAt'BtClCmDtEm Kribs & Martin CMS αT strategy 1.1/fb 3

+0.01 of the trigger over the period of data collection, a small inefﬁciency of 0.99 0.02 is encountered in the lowest HT = 275 GeV bin and corrected for. In the HT = 325 GeV (375 GeV) bins, the trigger is fully efﬁcient with a statistical uncertainty of 3.4% (3.2%).

A suite of prescaled HT triggers is used to select events which stem mainly in QCD multi-jet production. A photon control sample to constrain the background from Z ⌅⌅¯ events is ⇤ selected with a single object photon trigger.

The analysis follows closely Ref. [1]. Events with two or more high-pT jets, reconstructed using the anti-kT algorithm [10] with a size parameter of 0.5 are selected. Jets are required to have E > 50 GeV, ⇤ < 3 and to pass jet identiﬁcation criteria [11] designed to reject spurious T | | signals and noise in the calorimeters. The pseudorapidity of the jet with the highest ET (leading jet) is required to be within ⇤ < 2.5, and the transverse energy of each of the two leading jets | | must exceed 100 GeV.

Events with jets passing the ET threshold but not satisfying the jet identification criteria or the ⇤ acceptance requirement are vetoed, as this deposited energy is not accounted for in the event kinematics. Similarly, events in which an isolated lepton (electron or muon) with pT > 10 GeV is identified are rejected to suppress events with genuine missing energy from neutrinos. The electron and muon selection requirements are described in [12] and [13], respectively. Further- more, to select a pure multi-jet topology, events are vetoed in which an isolated photon [14] with pT > 25 GeV is found. αT strategy Events are required to satisfy HT > 275 GeV. As the main discriminator against QCD multijet production the variableCombineT ,n defined > 2 jets for into di-jet 2 events “pseudojets”, as: then calculate:

jet2 jet2 ET ET T = = , 2 2 2 MT 2 jet 2 jet 2 jet ⇥ E i ⇥ p i ⇥ p i i=1 T i=1 x i=1 y ⇤ ⇥ ⇥ ⇥ ET of 2nd hardest jet 3 is used and events are required to= have T > 0.55. In events with jet multiplicity n > 2, two pseudo-jets are formed following Ref.invariant [1] and mass Eq. 2 isof appliedhardest to2 jets the pseudo-jets. 4 10 SUSYSUSY SUSY To protect against multiple jets failing the EZ T > 50 GeV selection requirement, the jet-basedZ SUSY Z->νν+jets 4 4 Z QCDQCD 10 QCD 10 estimate of the missing transverse energy, H/ T, is compared to the calorimeter tower-based esti- QCD calo 103 calo 1 mate, E/ T ,1 and events with Rmiss = H/ T/E/ T > 1.25 are rejected.Cut3 on αT ≈ 0.5 1 − 3 − 10 − 10 highly effective Finally, to protect2 against severe energy losses, events with significant jet mismeasurements 10 2 caused by masked regions in the ECAL (which amount toat10 about suppressing 1% of the ECAL channel 102 events/bin/fb events/bin/fb count), or by missing instrumentation in the barrel-endcap gap, are removed with the follow- events/bin/fb 101 QCD background. 1 1 ing procedure. The jet-based estimate of the missing transverse10 energy, H/ T, is used to identify 10 jets most likely to have given rise to the H/ T as those whose momentum is closest in ⇥ to the ~ 100 total H/ T which results0 0.1 after 0.2 0.3 removing 0.4 0.5 0.6 them 0.7 0.8 from 0.9 the 1 Randall event. & The Tucker-Smith0 azimuthalπ/6 π/ 30806.1049 distanceπ/22 betweenπ/35π/6 π 0 100 200 300 400 500 600 700 α π − ∆φ M this jet and the recomputed H/ T is referred to as ⇥⇥ in what follows. Events with ⇥⇥ < 0.5 are T 2(0) (GeV) rejected if the distance in the (⇤, ⇥) plane between the selected jet and the closest masked ECAL region,FIG.RECAL 1:, is SUSY, smallerZ than→ ν 0.3.ν+jets Similarly, and events QCD are rates rejected for passing if the jet the points cuts within described 0.3 in ⇤ in the text,asfunctionsofα (left), ∆φ (middle), of the ECAL barrel-endcap gap at ⇤ = 1.5. and MT 2(0) (right). | | To increase the sensitivity to higher-mass states, we carry out a shape analysis over the entire HT > 275 GeV region. This requires that the Standard Model background estimation methods which are based on data controlIII. samples, RESULTS provide an estimate of the background for each of3 the 10 α alone > α with MT 2 > 400 GeV HT bins in the signal region with HT 275 GeV. The background estimation methods based(fb) on α with ∆φ < 2π/3 susy The plots in Figure 1 suggest that appropriate cuts σ 102 on α, ∆φ,and/orMT 2 can suppress both the QCD 6 background and the dominant background after cuts, 5 4 (Z νν)+jets. The SUSY parameter point used here is 3 → S/B 2 (M1/2,M0)=(300, 100) GeV, and we impose a hard cut 1 on the sum of the two hard jets’ transverse momenta, 0 0 0.2 0.4 0.6 0.8 1 α pT 1 + pT 2 > 500 GeV. (3) 3 To streamline the analysis, events were required to have 10 (fb) E/>T 100 GeV for Figure, 1 and at least one of α > 0.5, 2 susy 10 ∆φ alone σ ∆φ < 2π/3, and E/>T 100 GeV for Figure 2. Remov- ∆φ with MT 2 > 400 GeV ∆φ with α > 0.45 ing these requirements does not affect the results once 5 4 optimal cuts on α, ∆φ,and/orMT 2 are made. 3

Evidently signal dominates over background for S/B > < > 2 α 0.5, ∆φ 2π/3, and MT 2 300 GeV. We will soon 1 ∼ ∼ ∼ 0 see that α, ∆φ,andMT 2 can be used to discriminate 0 π/6 π/3 π/22π/35π/6 signal from background by themselves, but first we point π − ∆φ out that cuts on these variables can improve an anal- 103 ysis based on E/T or H/ T .Forexample,thecombi- (fb) 2 nation (α > 0.45,H/>300 GeV) selects 315 signal susy T 10 MT 2 alone σ −1 with ∆ 2 3 events per fb ,withS/B =4.3. The combination MT 2 φ < π/ MT 2 with α > 0.45 (∆φ < 2π/3,H/>T 450 GeV) gives a somewhat lower 6 5 S/B (3.1), but with more events (429). An MT 2 cut 4 3 of 450 GeV gives the largest S/B of all (5.0, with 304 S/B 2 events), and in fact there appears to be no benefit in 1 0 supplementing the MT 2 cut with the H/ T cut. 0 100 200 300 400 500 600 M 2(0) (GeV) Figure 2 suggests that each of α, ∆φ,andMT 2 can T be used independently to observe a clear signal, without 2 employing H/ T at all. Well-chosen cuts give afew 10 FIG. 2: For events preselected as described in the text, the signal events after 1 fb−1,withS/B 3 ∼5. × dependence of the signal cross section and S/B on a variable Figure 2 also shows how the three variables∼ − can be used α cut (top), a variable ∆φ cut (middle), and a variable MT 2 in pairs to improve S/B in conjunction with the signal cut (bottom). event-rate. We again find that MT 2 seems to dominate alittle,butsincewedonotknowifthisisthecleanest variable to use in practice, which can be determined nly With those cuts in place, Figure 3 shows signal and after a full detector simulation, we present all combina- background events binned in the sum of the two hard- tions. Any two on their own can potentially give a robust est jets’ transverse momenta. We see that Z+jets is the signal. dominant background, followed by W +jets. A total of As an exanple, we consider the combination ∆φ < four QCD events with p1T + p2T < 500 GeV passed the 2π/3andα < 0.45, which gives a good S/B and a decent cuts, out of a sample corresponding to over 1.5 fb−1 of event rate. As stated earlier, we do not optimize cuts, integrated luminosity, divided by the K factor. A higher but we use this combination that works rather well. luminosity sample would be needed to get a better esti- 2 2 Trigger, Event Selection and Analysis

1 Introduction In this note we present an update of the search for a missing energy signature in dijet and 1 multijet events using the T variable. The current results are based on 1.1 fb of LHC data recorded in 2011 at a centre-of-mass energy of ⌅s = 7 TeV. The presented search concentrates on event topologies in which heavy new particles are pair- produced in a proton-proton collision and where at the end of their decay chain a weakly interacting massive particle (WIMP) is produced. The latter remains undetected, thus leading to a missing energy signature. In the case of SUSY, squarks and gluinos could be the heavy 0 particles while the lightest (and stable) neutralino ⇤1 is the WIMP candidate. Although this 2.2 H Dependence of R search is carried out in the contextT of SUSY, the resultsT are applicable to other New Physics 5 scenarios as the missing energy signature is common to many models, e.g., Extra Dimensions and Little Higgs models. CMS Preliminary 2011 CMS Preliminary 2011

4 10 -1 -1 To interpret the results, a simpliﬁed and practical L dt = model 1.1 fb , s = of 7 TeV SUSY-breaking, the constrained L dt = 1.1 fb , s = 7 TeV

! Events 4 ! minimal supersymmetric extension of the standard modelData (CMSSM) [2, 3],10 is used. The CMSSMData 3 Standard Model Standard Model 10 QCD MultiJet QCD MultiJet is described by five parameters: the universal scalar andtt, W, Z gaugino + Jets mass103 parameters (m0 andtt, W, Z + Jets Events / 25 GeV LM4 LM4 m , respectively), the universal2 trilinear soft SUSY breaking parameter A , and two low- 1/2 10 LM6 0 LM6 energy parameters, the ratio of the two vacuum expectation values of the102 two Higgs doublets, tan ⇥, and the sign of the Higgs mixing10 parameter, sign(µ). Throughout this note, two CMSSM parameter sets, referred to as LM4 and LM6 [4] and not excluded by10 the 2010 analysis [1], are used to illustrate possible CMSSM1 yields. The parameter values defining1 LM4 (LM6) are m0 = 210 GeV, m1/2 = 285 GeV, (m0 = 85 GeV, m1/2 = 400 GeV) and A0 = 0, tan ⇥ = 10, and -1 -1 sign(µ) > 0 for both points. 10CMS αT Search Strategy 10 500 1000 1500 2000 2500 2 3 4 5 6 7 8 9 10 11 12 HT (GeV) NJets Events with n high-pT hadronic jets are studied and the missing transverse momentum is in- ferred through the measuredTriggered jet(a) Comparison>= momenta 2 jets of withH viaT between the0 leptons kinematic data and and MC forvariable0 photons. the (b) ComparisonT, which of was the jet initially multiplicity between data hadronic selection for HT 375 GeV and H/T > and MC for the hadronic selection, for HT 375 GeV inspired by Ref. [5]. The- ET analysis: all jets follows> 50 GeV; closely leading Ref. 2 [1] jets and > 100 two previousGeV Physics Analysis 100 GeV. and H/T > 100 GeV. Summaries [6, 7]. The- Cut main and difference count H withT bins respect to Ref. [1] is that rather than defining a specific signal region, we now search for an excess of eventsCMS Preliminary in data 2011 over the Standard Model n jeti expectation over the entire HT = ET range above4 275 GeV. This approach-1 is comple- i=1 10 L dt = 1.1 fb , s = 7 TeV mentary to the searches carried out in Refs. [8] and [9]. The dominant∫ background which arises Data - missing ET > 100 GeV 3 Standard Model Events / 0.025 10 from QCD multi-jets can be suppressed significantly with a selection requirementQCD MultiJet on the T - mild Δφ cut to reduce tt, W, Z + Jets variable. To estimate the remaining backgrounds we make use of data controlLM4 samples. These are a µ + jets sample for jet the mismeasurement background from W + jets102 and tt events, and aLM6 photon+jets sample to determine the background from Z ⇧⇧¯ events. ⇥ 10

1 2 Trigger, Event Selection and Analysis 10-1 The trigger strategy has changed from that of the 20100 analysis0.2 0.4 0.6 [1],0.8 1 where1.2 1.4 a1.6 pure1.8 2HT trigger α was used to collect both the signal and the control samples. WithCMS-SUS-11-003 the increase in instantaneousT luminosity seen in 2011, the HT thresholds of these(c) Comparison triggers of are the tooT distribution high for between the analysis. data In and MC for the hadronic selection, for H 375 GeV contrast to 2010, the High Level Trigger has moved to using energy correctedT jets to calculate and H/T > 100 GeV. HT which results in a much steeper trigger efficiency curve as a function of HT. To ensure that Figure 1: Comparisons of basic quantities before the T selection cuts. the trigger is fully efficient with respect to the final event selection, the offline HT bin edges have been shifted up by 25 GeV2.2 withHT Dependence respect to the of onlineRT values. The analysis therefore uses the following H binning: 275, 325, 375, 475, 575,T>⇤ 675,T< 775,⇤ and > 875 GeV. T The ratio RT = N /N exhibits no dependence on HT if ⇤ is chosen such that the nu- merator of the ratio in all H bins is dominated by tt, W +jets and Z ⇥⇥¯+jets events (referred T ⇥ To select candidate events withto in jets the + following missing as transverse EWK) and energy, there is no cross-object significant contribution triggers between from events from QCD ⇥ n jeti HT and H/ T = H/ T = i=1 p⇥Tmulti-jetare production used. Due [1]. to This evolving is demonstrated trigger thresholds in Figure 3, using on the MCH/ simulationsT part for the cut | | | value| ⇤ = 0.55 over the range 275 < HT < 975 GeV.

One important ingredient in the RT method is the scaling of the jet pT thresholds in the low HT bins to maintain jet multiplicities and thus comparable event kinematics and topologies in the different HT bins. This is especially important in the case of the tt background, which have on 4 2 Trigger, Event Selection and Analysis

data control samples as used in Ref. [1] were explicitly designed with this use-case in mind. In the following, the results for the different background prediction methods are presented when splitting the signal region into 8 bins, as deﬁned in Table 1. The results of this selection are documented in Table 1 and comparisons between Data and 4 2Monte Trigger, Carlo Event (MC) Selection simulation and Analysis for control variables are shown in Section 2.1.

Table 1: Definition of the HT bins and the corresponding pT thresholds for the leading, second, data control samples as used in Ref. [1] were explicitly designed with this use-case in mind. In and all remaining jets in the event; the number of events passing and failing the T cut and the the following, the results for the different background prediction methods are presented1 when resulting R value, for 1.1 fb of data collected in 2011. splitting the signal region into 8 bins, as defined in Table 1. T CMS CutsHT Bin and (GeV) Counts275–325 325–375 375–475 475–575 leading The results of this selection are documented in Table 1 and comparisonspT between(GeV) Data73 and 87 100 100 second Monte Carlo (MC) simulation for control variables are shown in SectionpT 2.1.(GeV) 73 87 100 100 other pT (GeV) 37 43 50 50 Table 1: Definition of the HT bins and the corresponding pT thresholds forT > the0.55 leading, second,782 321 196 62 7 7 7 6 and all remaining jets in the event;a the numberb of events passingc and failingT d< 0.55 the T cut5.73 ande10 the 2.36f 10 1.62g10 5.12h10 1 5 · · · · resulting R value, for 1.1 fb of data collected in 2011. R (10 ) 1.36 0.05 1.36 0.08 1.21 0.09 1.21 0.15 T T ± stat ± stat ± stat ± stat HT Bin (GeV) 275–325 325–375 375–475 HT475–575Bin (GeV) 575–675 675–775 775–875 875–⇥ leading leading pT (GeV) 73 87 100 pT 100(GeV) 100 100 100 100 second second pT (GeV) 73 87 100 pT 100(GeV) 100 100 100 100 other other pT (GeV) 37 43 50 pT 50(GeV) 50 50 50 50 T > 0.55 782 321 196 T >620.55 21 6 3 1 7 7 7 6 6 5 5 5 T < 0.55 5.73 10 2.36 10 1.62 10 5.12T < 0.5510 1.78 10 6.89 10 2.90 10 2.60 10 5 · · · · 5 · · · · R (10 ) 1.36 0.05 1.36 0.08 1.21 0.09 1.21R (100.15 ) 1.18 0.26stat 0.87 0.36stat 1.03 0.60stat 0.39 0.52stat T ± stat ± stat ± stat T± stat ± ± ± ± HT Bin (GeV) 575–675 675–775 775–875 875–⇥ leading pT (GeV) 100 100 2.1100 Data to Monte100 Carlo Comparison for Analysis Variables second pT (GeV) 100 100 100 100 other In the following we show data–MC comparisons before the T > 0.55 selection and requiring pT (GeV) 50 50 50 50 HT > 375 GeV and H/ T > 100 GeV, slightly higher than the trigger requirement. The data– T > 0.55 21 6 3 1 6 5 MC comparison5 plots5 are used to demonstrate the quality of the simulation, but are not used T < 0.55 1.78 10 6.89 10 2.90 10 2.60 10 5 · · for the· background· prediction. The actual background yields are obtained from data control RT (10 ) 1.18 0.26stat 0.87 0.36stat 1.03 0.60stat 0.39 0.52stat ± ± samples,± as described± further below. The uncertainties displayed on the MC distributions only correspond to the statistical uncertainties and do not include systematic uncertainties due to, 2.1 Data to Monte Carlo Comparison for Analysise.g., jet Variables energy scale or resolution.

In the following we show data–MC comparisons before the T > 0.55 selection and requiring Figures 1a and 1b show the comparisons between data and MC simulation for the HT variable HT > 375 GeV and H/ T > 100 GeV, slightly higher than the trigger requirement. The data– and the number of reconstructed jets per event, before the requirement on T. Good agreement MC comparison plots are used to demonstrate the qualityis observed of the simulation, between data but and are notMC used simulation. for the background prediction. The actual background yields are obtained from data control samples, as described further below. The uncertainties displayedFigure 1c shows on the the MC distributionsT distribution only and demonstrates that this variable is an excellent discrimi- correspond to the statistical uncertainties and do not includenator between systematic QCD uncertainties background due and to, signal. The numberCMS-SUS-11-003 of expected QCD events quickly falls e.g., jet energy scale or resolution. to zero with increasing T.

Figures 1a and 1b show the comparisons between dataFigures and MC 2a, simulation 2b and 2c for show the H comparisonsT variable between simulated standard model distributions and and the number of reconstructed jets per event, before thedata requirement for events onpassingT. Good the agreementT selection. The ⇥⇤ distribution in Figure 2a shows an approxi- is observed between data and MC simulation. mately flat behaviour as expected from SM processes with real missing transverse energy such as tt, W + jets and Z ⇤⇤¯+jets events. No evidence for QCD multi-jet events which would Figure 1c shows the T distribution and demonstrates that this variable is an excellent⇧ discrimi- peak at small values of ⇥⇤ is seen. Generally, the observed distributions in data show no nator between QCD background and signal. The numberdeviation of expected from QCD the standard events quickly model falls prediction. to zero with increasing T. Figures 2a, 2b and 2c show comparisons between simulated standard model distributions and data for events passing the T selection. The ⇥⇤ distribution in Figure 2a shows an approximately flat behaviour as expected from SM processes with real missing transverse energy such as tt, W + jets and Z ⇤⇤¯+jets events. No evidence for QCD multi-jet events which would ⇧ peak at small values of ⇥⇤ is seen. Generally, the observed distributions in data show no deviation from the standard model prediction. CMS Bounds on Simplified Models

0 pp → ~g ~g, ~g → q q χ∼ ; m(~q)>>m(~)g ) 1200 CMS Preliminary s s = 7 TeV L=1.1 fb-1 (GeV) 0 ∼ χ αT m 1000 10

q prod (pb) (CL σ = σNLO-QCD σprod = 3 × σNLO-QCD σ σprod = 1/3 × σNLO-QCD P2 q 800 g˜ 1 0 χ˜ 600

0 χ˜ 400 g˜ 10-1 q 95% CL upper limit on P1 200

q -2 400 600 800 1000 1200 10 ~ ~ ~ ~ ~ m~ (GeV) pp → q q, q → q + LSP; m(g)>>m( )q g )

1200 s q CMS Preliminary s = 7 TeV L=1.1 fb-1

αT (GeV) 1000 10 σprod = σNLO-QCD σprod = 3 × σNLO-QCD P2 0 LSP σprod = 1/3 × σNLO-QCD χ˜ (pb) (CL m

800 σ q˜ 1 600 0 P1 q˜ χ˜ 400 10-1

q 200

10-2 400 600 800 1000 1200 95% CL upper limit on on limit upper CL 95% CMS-SUS-11-003 m~q (GeV) CMS αT Search Bounds

SSSM MSSM MSSM MSSM M3 = 5 TeV M3 = Msq M3 = 2 Msq M3 = 5 TeV 1500 1250 1000 750 500 250 1st,2nd generation squark mass 0 a b c d e f g h a b c d e f g h a b c d e f g h a b c d e f g h Kribs & Martin Comparisons Eﬀectiveness of ATLAS strategy

1500 100 neutralinos, such as same-sign lepton ﬁnal states, may ⌅ MSSM, M3 ⇥ Mq 1250

⇥ ⌅ not yield strong bounds if the model is approximately R- MSSM, M3 ⇥ 2 Mq pb 10 MSSM, M3 ⇥ 5 TeV 1000 symmetric, and so again we are left to model-dependent ⇥ SSSM investigations to make quantitative statements. 750 1 500

superpartners 0.1 250

0 AmAtAt'BtClCmDtEm AmAtAt'BtClCmDtEm AmAtAt'BtClCmDtEm AmAtAt'BtClCmDtEm

colored 0.01 ⇧ pp IV. RECASTING LHC LIMITS 0.001 ⇤

104 To recast LHC limits on colored superparticle produc- 400 600 800 1000 1200 M⌅ GeV tion into the SSSM, we follow the analyses searching for q supersymmetry through nj +/ET signals performed by Kribs & Martin FIG. 3. Cross sections at the 7 TeV ⇥ LHC for colored super- ATLAS [61] and CMS [62–64]. Of the existing supersym- partner production. The four lines correspond to the four metry searches, jets plus missing energy is the simplest, simplified models shown in Fig. 1, where the first and second and involves the fewest assumptions about the spectrum. generation squarks are degenerate with mass Mq˜.Thesolid line shows the cross section for the SSSM where the cross To simulate the supersymmetric signal, we use section is dominated byq ˜q˜ final states, while the dashed PYTHIA6.4 [65]; the first and second generation squarks lines show cross sections for the three simplified models of the are set to have equal mass, the gravitino is chosen to be MSSM. All cross sections are calculated to next-to-leading or- the LSP, and all other superpartners are decoupled (set der using PROSPINOv2.1 [68], CTEQ6L1 parton distribution to 5 TeV). We use CTEQ6L1 parton distribution func- functions, and default scale choices. For event generation, we tions, generating a su⌅cient number of events such that use PYTHIA6.4 [65] and rescale the cross section to match statistical fluctuations have negligible eect on our re- those shown here. sults. To incorporate detector eects into our signal simulations, all events are passed through the Delphes [66] program using ATLAS or CMS detector options and statistic [69]: adopting the corresponding experiment’s jet definitions: N (µ +µ ) N (µ +µ ) i,obs e i,b i,s anti-k ,R =0.4 for the ATLAS search [61], and anti- ⇤ i,obs i,b i,s T 0 db⇥ 0 (N )! G(µb,b⇥) 0.05 = i,obs . kT ,R=0.5 for the CMS searches [62–64]. We repeat the Ni,obs N µ e µb ⇥ i,obs b same steps for the three simplified models of the MSSM ⇤ db G(µb,b) 0 ⇥ 0 (Ni,obs)! ⇥ (c.f. Fig. 1) allowing all combinations ofq ˜q˜,˜qq˜,˜qq˜ as (6) well as gluino pair production and associated squark plus ⇥ gluino production. Note that our “heavy MSSM” simpli- Here µ N is the number of expected SM back- i,b ⇥ i,exp fied model is an existing CMS simplified model, “T2” ground events and µi,s Ni,SUSY is the number of signal [67]. events. To estimate the⇥ eects of systematic errors, the Colored superpartner production cross sections receive number of SM events is modulated by a Gaussian weight- ing factor [70]. Specifically, we shift µ µ (1 + f ), sizable next-to-leading order (NLO) corrections. To in- b ⇤ b b corporate these corrections, we feed the spectra into where fb is drawn from a Gaussian distribution centered PROSPINO [68], restricting the processes appropriately at zero and with standard deviation ⇤f = ⇤i,SM /Ni,exp, where ⇤i,SM is the quoted systematic uncertainty (taken for each simplified model (i.e., just pp q˜q˜ for the SSSM). The cross sections are shown in Fig.⇤ 3 for each of directly from [61–64]). Whenever the systematic error is the simplified models as a function of squark mass. De- asymmetric, we use the larger (in absolute value) num- pending on the scale choice and the squark mass, we find ber. To combine channels (when appropriate), we simply the K-factor ranges from 1.7-2.1. This takes into account replace the right-hand side of Eq. (6) with the product the increased rate at NLO, through not the kinematic over all channels. distribution of events. The number of supersymmetry events in a particular channel is the product of the cross section, luminosity, The analyses we are interested in [61–64], are broken acceptance and e⌅ciency, up into several channels. For some analyses the channels are orthogonal, while in other analyses one event can Ni,SUSY = K(Mq˜) ⇤(Mq˜) A(Mq˜) , (7) fall into multiple channels. To set limits we begin by L· · · counting the number of supersymmetry events in each where K(Mq˜) is the mass-dependent K-factor to account analysis channel for several squark masses. The number for the larger rate at NLO. Within our simplified setup, of supersymmetric events passing cuts is translated into the only parameter the cross section and acceptance de- a mass-dependent acceptance for each channel. We then pend upon is the mass of the squark – thus Eq. (6) is form the 95% CL limit, using the likelihood ratio test simply a limit on the squark mass.

5 Eﬀectiveness of CMS αT strategy

100 1500 neutralinos, such as same-sign lepton ﬁnal states, may ⌅ MSSM, M3 ⇥ Mq

⇥ ⌅ not yield strong bounds if the model is approximately R- MSSM, M3 ⇥ 2 Mq 1250 pb 10 MSSM, M3 ⇥ 5 TeV symmetric, and so again we are left to model-dependent ⇥ SSSM 1000 investigations to make quantitative statements. 1 750 500 superpartners 0.1 250

0 a b c d e f g h a b c d e f g h a b c d e f g h a b c d e f g h colored 0.01 ⇧ pp IV. RECASTING LHC LIMITS 0.001 ⇤

104 To recast LHC limits on colored superparticle produc- 400 600 800 1000 1200 M⌅ GeV tion into the SSSM, we follow the analyses searching for q supersymmetry through nj +/ET signals performed by Kribs & Martin FIG. 3. Cross sections at the 7 TeV ⇥ LHC for colored super- ATLAS [61] and CMS [62–64]. Of the existing supersym- partner production. The four lines correspond to the four metry searches, jets plus missing energy is the simplest, simplified models shown in Fig. 1, where the first and second and involves the fewest assumptions about the spectrum. generation squarks are degenerate with mass Mq˜.Thesolid line shows the cross section for the SSSM where the cross To simulate the supersymmetric signal, we use section is dominated byq ˜q˜ final states, while the dashed PYTHIA6.4 [65]; the first and second generation squarks lines show cross sections for the three simplified models of the are set to have equal mass, the gravitino is chosen to be MSSM. All cross sections are calculated to next-to-leading or- the LSP, and all other superpartners are decoupled (set der using PROSPINOv2.1 [68], CTEQ6L1 parton distribution to 5 TeV). We use CTEQ6L1 parton distribution func- functions, and default scale choices. For event generation, we tions, generating a su⌅cient number of events such that use PYTHIA6.4 [65] and rescale the cross section to match statistical fluctuations have negligible eect on our re- those shown here. sults. To incorporate detector eects into our signal simulations, all events are passed through the Delphes [66] program using ATLAS or CMS detector options and statistic [69]: adopting the corresponding experiment’s jet definitions: N (µ +µ ) N (µ +µ ) i,obs e i,b i,s anti-k ,R =0.4 for the ATLAS search [61], and anti- ⇤ i,obs i,b i,s T 0 db⇥ 0 (N )! G(µb,b⇥) 0.05 = i,obs . kT ,R=0.5 for the CMS searches [62–64]. We repeat the Ni,obs N µ e µb ⇥ i,obs b same steps for the three simplified models of the MSSM ⇤ db G(µb,b) 0 ⇥ 0 (Ni,obs)! ⇥ (c.f. Fig. 1) allowing all combinations ofq ˜q˜,˜qq˜,˜qq˜ as (6) well as gluino pair production and associated squark plus ⇥ gluino production. Note that our “heavy MSSM” simpli- Here µ N is the number of expected SM back- i,b ⇥ i,exp fied model is an existing CMS simplified model, “T2” ground events and µi,s Ni,SUSY is the number of signal [67]. events. To estimate the⇥ eects of systematic errors, the Colored superpartner production cross sections receive number of SM events is modulated by a Gaussian weight- ing factor [70]. Specifically, we shift µ µ (1 + f ), sizable next-to-leading order (NLO) corrections. To in- b ⇤ b b corporate these corrections, we feed the spectra into where fb is drawn from a Gaussian distribution centered PROSPINO [68], restricting the processes appropriately at zero and with standard deviation ⇤f = ⇤i,SM /Ni,exp, where ⇤i,SM is the quoted systematic uncertainty (taken for each simplified model (i.e., just pp q˜q˜ for the SSSM). The cross sections are shown in Fig.⇤ 3 for each of directly from [61–64]). Whenever the systematic error is the simplified models as a function of squark mass. De- asymmetric, we use the larger (in absolute value) num- pending on the scale choice and the squark mass, we find ber. To combine channels (when appropriate), we simply the K-factor ranges from 1.7-2.1. This takes into account replace the right-hand side of Eq. (6) with the product the increased rate at NLO, through not the kinematic over all channels. distribution of events. The number of supersymmetry events in a particular channel is the product of the cross section, luminosity, The analyses we are interested in [61–64], are broken acceptance and e⌅ciency, up into several channels. For some analyses the channels are orthogonal, while in other analyses one event can Ni,SUSY = K(Mq˜) ⇤(Mq˜) A(Mq˜) , (7) fall into multiple channels. To set limits we begin by L· · · counting the number of supersymmetry events in each where K(Mq˜) is the mass-dependent K-factor to account analysis channel for several squark masses. The number for the larger rate at NLO. Within our simplified setup, of supersymmetric events passing cuts is translated into the only parameter the cross section and acceptance de- a mass-dependent acceptance for each channel. We then pend upon is the mass of the squark – thus Eq. (6) is form the 95% CL limit, using the likelihood ratio test simply a limit on the squark mass.

5 “Mixed Gauginos”

(Dirac gluino and Majorana wino & bino) 8 wino bino ui,L;˜ui,L g/p2 g0/3p2 di,L; d˜i,L g/p2 g0/3p2 ui,R;˜ui,R 0 4g0/3p2 di,R; d˜i,R 0 2g0/3p2 (a) Mode Wino Bino q˜Lq˜L X X q˜Rq˜R X X q˜Lq˜L⇤ X X q˜Rq˜R⇤ X X q˜L⇤ q˜L⇤ X X q˜R⇤ q˜R⇤ X X q˜Lq˜R X X q˜Lq˜R⇤ X X q˜L⇤ q˜R X X q˜L⇤ q˜R⇤ X X (b)

TABLE I: (a) Quark-squark-electroweakino couplings of the wino and the bino for di↵erent chiralities. The index i runs over quark generation; (b) Truth table FIG. 7: Impact of turning on electroweak gauginos showing whether the the wino and bino mediate the when both the Majorana wino and Majorana bino distinct individual modes of squark production via the masses are within an order of magnitude of the sweet t-channel. The wino participates in only the spot. The peaks are values of QECD/QCD. left-handed (anti)squark production, yet contributes much more to the total cross-section than a bino of the same mass. This happens on account of the wino’s stronger coupling strengths. 10

1 in its most interesting district, that is, where the L pb masses of the bino and wino are in the neigh- H 0.1 squarks

bourhood of the squark mass. Speciﬁcally, we s vary the neutralino or chargino mass in the range 0.01 0.1Mq˜, 10Mq˜ . The symmetry spoken of in our 1 { } .5 second observation, namely, the amplitudes for 5 .2 QCD only 0.001 5 .1 same-handed squark production are identical when 5 400 600 800 1000 1200 Mf /Mq˜ is the same as Mq˜/Mf ,isreﬂectedinthe Mé GeV near-mirror symmetry of the contours in Fig. 7. q

Once again we perceive that the region where the FIG. 8: Impact of turning onH electroweakL gauginos at squark mass is high and the electroweak gaugino di↵erent masses, with Mw˜ = M˜b. The ratio Mw˜ /Mq˜ is masses are close to the squark mass (by a factor represented by the di↵erent colors; green: 1, black = .5, of 2) is where the colored superpartner production blue: .2, red = .1. The solid purple line is the cross-section is most enhanced compared to a Dirac- QCD-only cross-section provided for comparison. gluino-only situation. Di↵erent regions of the con- tour plot of Fig. 7 are dominated in cross-section by the production of di↵erent final states. Fig. 9 is a representation of these relative dominances. The curves show that as the squark mass exceeds a TeV, ratio (mode)/(total) is plotted against squark the contribution of the same-handed squark produc- mass for three di↵erent kinds of final state modes: tion surpasses the same-handed squark-antisquark (i) same-handed squark-antisquark (solid lines), (ii) production. As Mw˜ = M˜b is lowered (that is, as same-handed squark-squark (dash-dotted), and (iii) red is approached), the final statesq ˜Lq˜L⇤ andq ˜Rq˜R⇤ opposite-handed squark-squark (dashed). The color dominate the cross-section irrespective of the squark code is green, black, blue, red = 1, .5, .2, .1 mass. These subprocesses, as seen before, occur where the{ numbers on the RHS are} the{ ratios of the} chiefly through an s-channel gluon with the initial weak gaugino mass to the squark mass. The green state as two gluons or a quark and an antiquark. Fractional Increase in Squark Cross Section wino=bino=10x msquark Contours showing the ratio of QCD-only XS over XS with gaugino interference. wino=bino=msquark The wino mass = bino mass is on the Y axis, given as factors of squark mass. wino=bino=msquark/10 Kribs & Raj

Sunday, November400 11, 2012 600 800 1000 1200 Summary

* Heavy Dirac Gluino in “supersoft”, “R-symmetric” natural and suppresses colored sparticle production substantially

* Bounds on 1st,2nd generation squarks 680-750 GeV;

(up to about 800 GeV with 12/fb @ 8 TeV CMS αT)

* Best search is αT (Mar 2012); optimize over range of HT crucial (but, “razor” T2 confusion, for oﬀ-line...)

* Very high mass searches (e.g. ATLAS Meﬀ > 1400-1900 GeV) not eﬀective at constraining lighter squarks

* SUSY not ruled out yet...even models not tuned to avoid bounds!

* What is “minimally” necessary? (Majorana EW versus Dirac gluino…)