Dirac Gauginos, Negative Supertraces and Gauge Mediation
aa r X i v : . [ h e p - t h ] J u l UCI-TR-2010-12June, 2010
Dirac Gauginos, Negative Supertraces and Gauge Mediation
Linda M. Carpenter
Department of Physics and AstronomyUniversity of California Irvine,Irvine, CA [email protected]
Abstract
In an attempt to maximize General Gauge Mediated parameter space, I propose simple modelsin which gauginos and scalars are generated from disconnected mechanisms. In my models Diracgauginos are generated through the supersoft mechanism, while independent R-symmetric scalarmasses are generated through operators involving non-zero messenger supertrace. I propose severalnew methods for generating negative messenger supertraces which result in viable positive masssquareds for MSSM scalars. The resultant spectra are novel, compressed and may contain lightfermionic SM adjoint fields. NTRODUCTION
Gauge mediation is a simple and flavor blind mechanism for the communication of SUSYbreaking [1] [2] [3]. In gauge mediation, SUSY breaking is communicated from a hiddensector to the MSSM via SM gauge interactions only. In its simplest implementation, gaugemediation requires a SUSY breaking spurion which gets an F term as well as an R symmetry-breaking vev.This spurion couples to a set of fields with SM gauge interactions, the messengers gener-ating a superpotential W = XM M → vM M + θ F X M M (1)X is the SUSY breaking spurion and M are the messengers, here in a fundamental anti-fundemental of the SM gauge group SU(5). Loops proportional to SM gauge couplings arethen generated giving masses to the MSSM fields. Majorana gauginos masses are generatedat one loop while scalar masses squared are generated at two loops. In the minimal case,all MSSM fields get masses proportional to a single mass parameter Λ =
F/v . The theoryis thus simple and predictive, however, like many minimal SUSY breaking models, MinimalGauge Mediation(MGM) is highly constrained as it produces a hierarchichal spectrum withvery heavy squarks. There is thus significant fine tuning in the Higgs potential. Meade et.al. have proposed a generalization of gauge mediation, defining Gauge Mediation as anymediation mechanism such that MSSM masses go to zero when the SM gauge couplingsare turned off. Barring A and B terms, a model within the framework of General GaugeMediation(GGM) may have up to six distinct mass parameters[4]. This framework allowsgauge mediated models with non-standard spectra and the hope of less fine tuning. SimpleGGM extensions have been built, however not every model manages to cover the entireGGM parameter space.There are many regions of MSSM parameter space which produce highly non-standardspectra with rich phenomenology. Many of these regions of parameter space are not yethighly constrained by LHC searches, for example ’supersoft’ spectra [5], compressed spectra,and -strikingly - spectra with stop masses under 400 GeV [6]- [10]. The General GaugeMediated framework should allow near complete models which express these spectra to bebuilt. 2owever, many simple weakly coupled models retain spectra very similar to MinimalGauge Mediation. In particular, squarks remain the heaviest sparticles with masses 500GeV or above due to a persistent relation between gaugino and scalar masses. To get thegist of this consider an example from a set of weakly coupled renormalizable models [11].For a model containing messenger pairs in a 5, 5 and 10, 10 of SU (5) and for multiple SUSYbreaking spurions, the MSSM mass spectrum is given by five parameters. However, thelarge number of parameters does not necessarily guarantee light scalars. In particular gluinomasses are given by the sum of three mass parameters m g = α π (Λ q + 2Λ Q + Λ u ) (2)One is free to cancel the mass parameters to produce an arbitrarily light gluino. Thelargest contribution to the squark mass, however, is given by a mass parameter which is the sum of the squares of the gluino mass parameters m s ∼ α π Λ c → α π (Λ q + 2Λ Q + Λ u ) (3)The squarks may not be made arbitrarily light with respect to the gluinos, in fact manysmall gluino masses which rely on a cancelation between large mass parameter will ensure aheavy squark mass. Given the details of tuning in the EWSB sector, this feature of weaklycoupled models leads to the general occurrence of an irreducible fine tuning at the 5 percentlevel [12]. As Seiberg et. al. have shown, breaking these mass relations requires morecomplex messenger sectors [13]. In many models with hidden sector gauge dynamics massrelations between scalars and gauginos still persist; for example, in current semi-direct gaugemediated models there is an irreducible bound on the ratio of scalars and gaugino masses[14].In attempting to cover gauge mediated parameter space, there are unexplored theoreticaloptions. In this paper I will generate scalar and gaugino masses from disconnected mech-anisms. My models require messenger fields with non-holomorphic masses and a hiddensector gauged U (1) field which gets a D-term vev. Integrating out sets of messengers willproduce two distinct kinds of MSSM masses, Dirac gaugino masses generated using the su-persoft mechanism, and R-symmetric, log-divergent scalar masses. In particular I proposeseveral new mechanisms to generate positive scalar mass squareds from negative messengersupertraces. 3irac gauginos have proven theoretically useful, yielding mediation mechanisms suchas supersoft SUSY breaking[15], supersoft hybrids [16], gaugino mediation [17] and theMRSSM [18]. Models in this paper will employ the supersoft mechanism. Supersoft SUSYbreaking yields a Dirac gaugino mass when gauginos mix with an additional SM adjoint field[15]; masses are proportional to a SUSY breaking D-term [15]. Generating Dirac gauginosthrough gauge mediation was proposed by Nelson et. al. , [15][19], and larger explorations ofDirac gauginos in the formalism of general gauge mediation have been made [20]. Supersofttype gauginos offer several model building advantages. First, they naturally allow threedistinct gaugino mass parameters with minimal theoretical structure. Second, the scalarmass contribution resulting from supersoft generates scalars masses a square root of a loopfactor below gaugino masses.When supersoft is the only mass giving mechanism, producing a 100 GeV mass spectrumfor MSSM scalars requires multi-TeV gaugino masses. Since the aim in this paper is todisconnect gaugino and scalar masses however, one is free to generate 100 GeV gauginomasses from supersoft mediation. The bulk of the scalar masses are generated not fromsupersoft, but from the independent R symmetric contributions which do not affect gauginomasses. In this way the gaugino and scalar masses become largely independent of oneanother. In addition I resolve a problem found in previous GM implementations of supersoftin which large negative mass squared contributions to adjoint scalar masses were generates.In my models, adjoint scalar mass squared are large and positive. The existence of SMadjoints offers novel solutions to old theoretical problems such as the µ term-less MSSM[19].The effect of non-holomorphic messenger masses on the MSSM scalar spectrum was firstdiscussed by Poppitz and Trivedi [21]. When messengers have non-holomorphic masses theyresult in two loop gauge mediated masses for MSSM scalars, that are proportional to themessenger supertrace. As these scalar mass operators are R symmetric, they do not affectgaugino masses. The catch to using this mechanism to generate scalar masses is that thescalar mass squareds have the opposite sign as the messenger supertrace. Many models areknown to generate positive messenger supertrace and hence disastrous negative messengermass squareds, however few methods are known to generate negative messenger supertrace.One of the few methods for generating negative messenger supertrace was proposed byRandall [22]. This ’mediator mechanism’ involved generating two-loop non-holomorphic4essenger masses. I build several models where negative messenger supertrace is achievedat lower loop order.This paper proceeds as follows, section 2 reviews supersoft mediation. Section 3 presentsa SUSY breaking superpotential that generates Dirac gauginos. Section 4 adds to thissuperpotential terms which are capable of generating R symmetric MSSM scalar massesthrough negative messenger supertrace. Section 5 concludes. REVIEW OF DIRAC GAUGINOS
In Supersoft SUSY breaking scenarios, gaugino masses are Dirac. In the simplest case,they arise from the coupling of SM gauge adjoints to gauginos and a hidden sector U (1) ′ gauge field which gets a D term. One must add to the MSSM three adjoint fields, one foreach gauge group. In the low energy, the super-potential operator generating such massterms is W = c i W ′ W i A i Λ (4)where the A is the adjoint and W ′ is the hidden sector U(1) gauge field. Gauge indiciesare contracted between W and A while Lorentz indicies are contracted between W and W ′ .Inserting the D term and pulling the proper components the above expression becomes c i D Λ λ i ψ Ai (5)which is a Dirac gaugino mass for gauginos of size c i D/ Λ. As the couplings c i are differentfor all of the gauginos, each gaugino is determined by a distinct mass parameter.Finite one loop scalar masses are then generated after gauginos get mass. In the absenceof extra operators, the scalar masses are m s = C i α i m λi π log( δ i m λi ) (6)where m λi are the gaugino masses and δ i is the mass squared of the real part of the adjoint.The ratio between the masses of the gauginos and the MSSM scalars (with the exception ofthe adjoints) is thus m s m λ = r C i α i π log( δ i m λi ) (7)5hich means that scalar masses from the supersoft mechanism may be a few percent ofthe gaugino masses. If gauginos masses are fixed at 100 GeV and there are R symmetriccontributions to scalar masses, then the gaugino and scalar masses are largely independent.It is interesting to note that if δ i equals m λi , the gaugino masses make no contribution toscalar masses at all. SUSY BREAKING AND DIRAC GAUGINOS
I now attempt to implement supersoft mediation by building a hidden sector with a U (1) ′ D-term that couples to an adjoint and gaugino. This is accomplished by integratingout messengers which are charged both under the hidden sector U(1) and the standard modelgauge interactions. Consider the following hidden sector superpotential with a gauged U(1)symmetry W = λX ( φ + φ − − µ ) + m φ + Z − + m φ − Z + + W ′ W ′ (8)The subscripts indicate U (1) ′ charges. This model was studied in [23]. The fields φ get U (1) ′ breaking vevs φ = m m φ − (9) φ − = r m m µ − m The field X as well as the Z’s get F terms of order m/λ .The D term is nonzero as long and m is unequal to m , and is given by D = g ′ ( m m µ − m )( m m −
1) (10)The coupling of the D term to the gaugino and adjoint requires the addition of a set ofmessengers in the fundamental representation of the SM gauge groups, and which are alsocharged under the U (1) ′ . The messengers require a supersymmetric mass-term. Adoptingthe notation of Nelson, the messenger superpotential is given by6 T = m T T T + y i T AT (11)where the fields T are the messengers. At tree level there are no off-diagonal bosonic messen-ger masses but there are diagonal scalar messenger masses resulting from the D term. Sincethe messenger fundamental and anti-fundamental have opposite U (1) ′ charge for anomalycancelation, the supertrace of these messengers is zero. A one loop mass for gauginos isgenerated and, is given by the diagram found below. The resulting gaugino mass is m λ i = g i π y i Dm T (12)Some notes are in order. First, one may call this implementation of supersoft a sub-setof semi-direct gauge mediation; that is the messengers have charge under a hidden sectorgauge group but do not themselves participate in SUSY breaking [24]. In this model thereis a flat direction, and one may do a Coleman-Weinberg calculation to lift it. For certainvalues of the parameters R symmetry is broken, and X gets a non zero vev. One may finda vev for X in the region of large m and m for order 1 values of λ and the gauge couplingg. Here an X vev means that a messenger B-term is generated at two loops and hence aMajorana gaugino mass is generated at three loops.The one loop R-symmetric Dirac mass will by far be the dominant gaugino mass con-tribution and the three loop mass will be small. A multi-loop gaugino mass seems genericfor models where messengers are charged under the hidden sector gauge group but do notparticipate in SUSY breaking; both the Mediator Models of Randall and Semi-Direct GaugeMediation have this feature. Operators from the Kahler Potential
In addition to gaugino masses, important mass contributions to the real and imaginarypart of the adjoint are generated at one loop. As the original superpotential contains neitherthe supersoft gaugino mass nor the adjoint mass contributions, one must extract them fromthe Kahler potential. In order to keep careful track of one loop operators, I will now producethem from the Kahler potential, including a rederivation of the supersoft gaugino mass.7 AD FIG. 1: 1-loop diagram for gaugino masses.
The Kahler potential term which generates the one loop supersoft gaugino mass is K = Z d θ W DV ′ A Λ + h.c. (13)Where V is the U (1) ′ vector field, W is the SM field strength and A is the adjoint. In thisoperator gauge indicies are contacted between W and A, while Lorentz indicies are con-tracted between W and the superspace derivative D. Acting with the superspace derivative,integrating over θ , and replacing V ′ by its vev one gets W = Z d θ D ′ Λ W A (14)which is exactly the supersoft term in the superpotential.There are other operators of the same order only involving the adjoint field. Theseoperators are K = Z d θ W ′ DV ′ AA Λ + h.c. and K = Z d θ W ′ DV ′ AA † Λ + h.c. (15)which are soft mass contributions to the real and imaginary parts of the adjoint A. Theseterms are represented by two one loop diagrams involving messengers which are given in theAppendix. If one takes the first operator and acts with derivatives, integrates over θ , andinserts D-terms, the result is a term in the superpotential W = Z d θ D ′ D ′ Λ AA (16)This operator was discussed by Nelson and is recognizable as the ’lemon twist’ operator; infact presented a challenge for previous incarnations of Supersoft mediation. This and similar8perators can be quite useful for model building, for example [16] [25]. In this context,however, the operator is problematic because it gives a negative mass squared contributionto one component of A. This mass contribution is large, in fact it is a square root of aloop factor larger than the gaugino mass. If only this first operator existed, one wouldrequire a very large majorana mass for A in order to preserve the SM gauge symmetries.However, the second operator is of the same order as the first and gives both components ofA positive mass squared. Adding up the contributions to A one indeed finds a cancelation,to order D /M to real part of A while the imaginary gets a positive mass squared. Thefull scalar adjoint masses consists of the D term-mass for the real component, the aboveone loop masses, and whatever R symmetric gauge mediated masses the adjoints may get.One expects the gauge mediated masses will be large and positive and both components ofA thus end up with large positive mass squareds. Operators of the type found in equation15 seem to be generic to GM models of Dirac gauginos, for example one may notice thatslightly reminiscent operators may be found in [18]. In calculating masses, one will only findall relevant operators by keeping careful track of the Kahler potential, keeping track of thesuperpotential alone is not sufficient. SCALAR MASSES AND NEGATIVE MESSENGER SUPERTRACES
One may create R symmetric scalar masses which are independent of the gaugino masses.The scalar mass contributions arise at two loops from diagrams where messengers havenon-holomorphic masses. Such terms are log divergent and proportional to the messengersupertrace. The MSSM scalar masses from such contributions were calculated by Poppitzand Trivedi [21] and are given by m i = − f X a g a π S Q C ai Str M mess log( M Λ ) (17)where S is the Dynkin index of the messengers, C ai is the Casimir for the scalars, and Mis the supersymmetric messenger mass. These mass terms come from R symmetric physicsand hence do not effect gaugino masses. The scalar mass squareds have signs which areopposite of the sign of messenger supertrace; positive scalar mass squareds require negative messenger supertraces. 9ne of the only fleshed out examples of negative messenger supertrace are the MediatorModels of Randall [22]. In this model, there are low scale messengers which are chargedunder SM gauge groups, and high scale messengers-uncharged under SM gauge groups- whichtalk to the SUSY breaking sector. The argument is as follows, the hidden sector messengersget SUSY breaking masses though direct mediation, and thus have positive supertrace. Thelow scale messengers, in addition to having a supersymmetric mass, get two-loop SUSYbreaking masses from the high scale messenger sector. Since the high scale messengers hadpositive supertrace, they will contribute negatively to the SUSY breaking masses of the lowscale messengers. Thus the low scale messengers get a negative supertrace which results ina positive mass squared for MSSM scalars. The entire mechanism generates MSSM scalarmasses at four loops, but one would like to achieve scalar masses at lower loop level.Achieving a negative messenger supertrace is challenging. To get a negative supertrace,the bosonic messenger mass squared must be less than the square of the fermionic messengermass. Any supersymmetric mass does not contribute to the supertrace. In addition, at treelevel any F term type SUSY breaking leads to zero supertrace.One sees that the only way to achieve negative supertraces at tree level is with D-terms.Messengers that couple to a D-term may get tree level gauge mediated mass squared whichare negative [26].Getting negative messenger supertraces with F-terms alone requires that the messengersget nonsupersymmetric mass contributions at loop level. I will build several models withnegative messenger supertrace at different loop order levels, one with and one without hiddensector gauge dynamics. Tree Level SuperTrace
To generate tree-level non-supersymmetric messenger masses I require a hidden sectorgauge group which gets a D term. For the sake of simplicity I will be using a hidden sector U (1) ′ gauge group. I will consider the superpotential from section 3 W = λX ( φ + φ − − µ ) + m φ + Z − + m φ − Z + (18)as it breaks SUSY and has a U (1) ′ D term. I must now add the messenger content in sucha way that the messengers pick up a non-zero supertrace from the D term. This means10hat the messengers will be spectators which are charged under the hidden sector U (1) ′ butwill not participate in SUSY breaking. Building a viable model with the correct messengersector has several constraints; first, the messenger content must be such that there are no U (1) ′ or mixed anomalies. Second, the messenger supertrace must actually be non-zero; if,as in the previous section, one adds a pair of messengers M , M with opposite U (1) ′ chargesand identical supersymmetric mass, the tree level supertrace contributions to M and M willexactly cancel. Finally, if messenger bi-linears have a U (1) ′ charge that does not sum tozero, they cannot be given an explicit mass term, their mass must come from the vev of acharged field.To meet the above requirements, consider a superpotential which is a variant of the onein section 3, with two sets of messengers M and N W = λX ( φ + φ − − µ ) + m φ + Z − + m φ − Z + + λ φ + M N + λ φ − N M (19)The fields M and N have charges which sum to 1 while N and M have charges that sum to-1. For simplicity we may take N and N to have U (1) ′ charge zero so M and M have oppositecharge. The M’s do not have equal supersymmetric mass. M has mass λ v φ + and will makea contribution to the supertrace proportional to +D, while M has a mass λ v φ − and willmake a contribution to the supertrace proportional to -D. However, the contributions toMSSM scalar masses do not exactly cancel since the supersymmetric messenger masses aredifferent. Applying the Poppitz Trivedi formula for scalar masses one gets m s = − f X a g a π S Q C ai D log( M Λ ) + f X a g a π S Q C ai D log( M Λ ) (20)Summing the two non-canceling contributions yields m i = − f X a g a π S Q C ai D log( M M ) (21)where M and M are the unequal supersymmetric messenger masses.As one expects, the scalar mass squareds go to 0 as supersymmetric messenger massesbecome degenerate. One may understand the scalar mass formula as follows; both themessenger fundamental and anti-fundamental contribute to the scalar mass from running.The contributions to scalar masses from M and M have opposite signs and would cancel if11heir supersymmetric mass thresholds were equal. Since the thresholds are unequal however,a scalar mass squared remains which is proportional to the mismatch of the running of bothcontributions. The sign of the mass squared depends on the relative size of the parameters M and M ; it can be made both negative and arbitrarily small.To the above superpotential one may easily add the messenger sector of section 3.4 for acomplete superpotential, λX ( φ + φ − − µ ) + m φ + Z − + m φ − Z + + λ φ + M N + λ φ − N M + m T T T + y i T AT (22)Since the messengers T have equal and opposite U (1) ′ charges and equal mass, they will noteffect the scalar mass relation just derived. The messengers M and N do not couple to theadjoint and hence do not contribute to the gaugino masses. The ratio M M that appears inthe scalar mass is a parameter completely separate from the gaugino sector.In order to cover more scalar mass parameter space, one may divide the complete SU (5)messenger multiplets M into fundamentals of SU (3) and SU (2) giving each separate cou-plings to the fields φ + and φ − . W = λ Q φ + QY + λ Q φ − Y Q + λ L φ + LE + λ L φ − EL (23)There are now two mass parameters given by the ratio of the couplings λ Q /λ Q and λ L /λ L . Determining which coupling in the ratio is larger determines the sign of the login the scalar mass formula. One is thus free by choice of couplings to give negative masscontribution to one set of scalar mass squared and positive contribution to another. There-fore, even if one scalar, say the squark, were to get large mass squared contribution fromsupersoft, it may be canceled by the log divergent mass while still maintaining positive masssquared for the other scalars. Much of GGM parameter space is thus accessible. Loop Level SuperTrace
Negative messenger supertraces may also be generated at loop level using only F termSUSY breaking. Using F terms I will attempt generate messenger masses at one loop, andthus MSSM scalar masses at three loops. 12he F-term method of generating one loop negative mass squareds for messengers isreminiscent of that used to generate one loop MSSM scalar masses through messenger-matter mixing [3]. In the following model messengers start with supersymmetric masses.They then mix with the fields that talk to SUSY breaking. As the result of mixing, themessengers get one loop scalar masses squared contributions which are negative, resultingin negative supertrace.In standard messenger-matter mixing the SUSY breaking sector talks to intermediaryfields, in this case the messengers, and the messengers would mix with Higgses which thenget negative mass squareds. In my scenario the role of the Higgses is played by the mes-sengers and the role of the messengers is played by new intermediary fields. I thus requirea superpotential in which messengers only talk to SUSY breaking spurions through mixingwith the new intermediary fields.For two sets of messengers, M and N, in the fundamental and anti-fundamental reps. ofthe SM gauge groups, the required superpotential is W = X ( H − µ ) + mHA + y HM N + y HN M (24)Where H and A are intermediary fields. Here H gets a vev of order µ − m and X getsan F term. The vev of H generates the supersymmetric messengers masses. The resultingscalar potential contains contributions V s = y ( h m + h n ) + y ( h m + h n ) (25)This scalar potential leads to one loop diagrams for messenger masses which have H inthe loop and insertions of the F term on the internal H lines. In analogy to matter-messengermixing, there are two diagrams that lead to mass squared contributions with opposite signs.When calculating the resulting bosonic messenger masses there is an accidental cancela-tion in the highest order terms in F, in this case F M . This means the scalar messenger masssquareds are given by the next highest order term proportional to F m s ∼ − y π F M (26)13he negative mass squared contribution to the bosonic messenger ensures a negative mes-senger supertrace. On expects that this messenger supertrace can not be made positive andit will always result in positive mass squared contributions to the MSSM scalars given by m i = f X a g a π S Q C ai y π F M log( v H Λ ) (27)Notice that the above superpotential has an R-symmetry. Its structure is also non-genericand requires and additional Z under which A, H, and certain messengers have negativeparity. The superpotential only contains fields with R charge 0 or 2. By a theorem [27] weexpect that once a Coleman-Weinberg calculation is made, the field X will get a vev at 0and R symmetry will remain unbroken. If there were no additional source of SUSY breakingthis would mean a massless gaugino. However, in the full model the gaugino mass is coveredsince there is an independent SUSY breaking source generating Dirac gaugino masses. CONCLUSIONS
To cover General Gauge Mediated parameter space I have constructed models with Diracgauginos and independent scalar masses from R-symmetric dynamics. These models allowfor a breaking of the relations between scalar and gaugino mass parameters and presentthe particular phenomenological possibility of light squark masses and a very degeneratesparticle spectrum. In implementing Dirac gaugino masses I have avoided previous phe-nomenological problems with adjoint masses. In addition, I have proposed several newmethods for generating negative messenger supertraces. Though I have presented simpleviable models here there is still much work to do, in particular unification scenarios presenta serious challenge.While I have chosen very simple hidden sectors which contain the U (1) ′ field gauge neededfor Dirac gauginos, one may pick hidden sector with more complicated dynamics, for examplethe 4-1 model. In using D-terms to generate R-symmetric scalar masses I chose the D-termsfrom a U (1) ′ gauge symmetry, while it is likely possible to use D-terms from non-abeliangauge groups. In addition it may be possible to marry gauge-messenger scenarios to theideas I have presented here [28].One experimental challenge for Gauge Mediation of any kind is the possible discovery of a14iggs Boson at a mass 126 GeV. In typical implementations of the MSSM it the Higgs massis lifted above its tree level value through large one loop corrections from stop masses whichmust be above several TeV in mass which some may find phenomenologically unappealing.Lighter stop masses may yield a Higgs mass of 126 GeV if large A terms are present(seefor example [29]) however minimal gauge mediation produces only small A terms which rununder the gaugino mass, and models with dirac gauginos produce no A terms at all.One should not despair however, the Higgs sector of MSSM models is incomplete until amechanism can be specified for generating a µ term and a suitable B µ term. Any theoreticaladditions made to the Higgs sector may well raise the Higgs mass at tree level or loop level.One example is the generation of large stop A-terms resulting from models with Higgs-messenger mixing [30], [31]. Another example of course is the NMSSM. It may also bepossible to raise the Higgs mass significantly in models with Dirac gauginos, by couplingadjoint fields to the Higgs as is done in the µ -less MSSM [32]. It is likely that many theoreticalcompletions to General Gauge Mediated models exist which satisfy the (probable) Higgsmass bound.In building these models I essentially required two disconnected SUSY breaking sectorswhich determine the masses of the scalars and gauginos respectively. There may be a slighthierarchy between the SUSY breaking scales depending on the the choice of method of thegeneration of scalar masses, however the two SUSY breaking scales are generally comparable.Though one may rely on anthropic arguments to explain a coincidence of SUSY breakingscales [33] (footnote 14), it may not be beyond belief that such a coincidence could naturallytake place. Most models of General Gauge Mediation rely on the existence of multipleSUSY breaking spurions which have similar mass parameters, in addition to multiple setsof messengers - see for example [11]. In principle these models are quite similar, it shouldnot be too unnatural to choose similar mass parameters in the SUSY breaking sectors whichlead to comparable masses for gauginos and scalars. However, for those unsettled by the thereliance on the non-renormalization of the Superpotential, it may require some invocation ofsymmetries to explain why the two SUSY breaking sectors are sequestered from each other.Finally, models with Dirac gauginos offer new fields with SM charges that make forinteresting collider phenomenology. In standard supersoft mediation, since gaugino massescome a loop factor above scalar masses, gauginos and adjoints are typically heavy, usuallyto 10 TeV to produce scalars several hundred GeV in mass. Since I have included in this15cenario independent mass contributions for the scalars, the adjoint fermions and gauginosare free to be of order 100 GeV, while maintaining weak scale MSSM scalar masses. Thoughscalar adjoints are heavy there remains the possibility of light adjoint fermions. Whensome small R-breaking is introduced there is a mass splitting between a mostly-adjoint andmostly-gaugino states. This may lead to the possibility of interesting cascade decays, andmay shift current particle mass bounds. APPENDIX
TT T
A A
T TT T
A, A A, A
One loop diagrams contributing to Adjoint soft masses. The first diagram is a mass AA † while the second is a mass term AA + AA † + h.c. Acknowledgments
This work was supported in part by NSF Grant No. PHY-0653656. Thanks to YaelShadmi and Yuri Shirman and Ann Nelson for helpful discussions.16
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