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- Local models of gauge mediated Abelian hidden sectors at a GeV supersymmetry breaking in Iñaki García-Etxebarria, Fouad Saad and Angel M. Uranga To cite this article: David E. Morrissey et al JHEP07(2009)050 - Common gauge origin of discrete symmetries in observable sector and hidden sector Taeil Hur, Hye-Sung Lee and Christoph Luhn View the article online for updates and enhancements. - Semi-direct gauge mediation Nathan Seiberg, Tomer Volansky and Brian Wecht

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This content was downloaded from IP address 131.215.225.165 on 13/06/2019 at 19:20 JHEP07(2009)050 x Supersym- July 15, 2009 May 19, 2009 June 22, 2009 , : : : idden sectors in Received Published Accepted visible sector by gauge resent specific models of han the visible sector, as es can arise when hidden if the hidden sector is se- nergy collider searches. b,c s kinetic mixing of a U(1) We study these mechanisms 10.1088/1126-6708/2009/07/050 which couple to both sectors, sible relevance of such sectors doi: Laboratory, Published by IOP Publishing for SISSA [email protected] , and Kathryn M. Zurek a David Poland a 0904.2567 Beyond , Cosmology of Theories beyond the SM, We discuss mechanisms for naturally generating GeV-scale h [email protected] SISSA 2009 Batavia, Illinois 60510, U.S.A. Department of Physics, UniversityAnn of Arbor, Michigan, Michigan 48109, U.S.A. E-mail: Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138, U.S.A. Particle Astrophysics Center, Fermi National Accelerator [email protected] c b a c

Abstract: David E. Morrissey, the context of weak-scalesectors supersymmetry. are more Such weaklyhappens low coupled mass when to scal supersymmetry supersymmetryinteractions breaking breaking under is t communicated which to thequestered the from hidden -mediated sector supersymmetryin is breaking. detail uncharged, in or theAbelian context GeV-scale of hidden gaugegauge sectors. and force gaugino with In mediation, hypercharge,and particular, and singlets additional we p or loop discus bi-fundamentals effects.for dark Finally, matter we phenomenology, investigate as the well pos as for low-Keywords: and high-e Abelian hidden sectors at a GeV metric , Supersymmetry Breaking ArXiv ePrint: JHEP07(2009)050 4 5 7 8 9 9 2 3 20 22 24 25 25 26 27 28 30 30 31 32 36 36 12 13 15 17 18 26 33 34 36 11 – 1 – colliders − e + e hid hid hid hid hid hid m m m m m m & & ≪ & ≪ ≪ model model 2 2 2 2 2 2 / / / / / / ′ ′ 3 3 3 3 3 3 µ µ m m m m m m 4.3.2 Lower-energy 4.1.1 Elastic4.1.2 dark matter Inelastic dark matter 4.3.1 High-energy hadron colliders 3.3.2 3.1.2 3.2.1 3.2.2 3.3.1 3.1.1 B.1 Minimal B.2 Hidden sector NMSSM 4.2 Applications to4.3 PAMELA and ATIC Collider phenomenology 3.4 Multi-mediator models 4.1 Dark matter direct detection and DAMA 3.2 Hidden sector NMSSM 3.3 Singlet-mediated SUSY breaking 2.6 Additional mediator fields 3.1 Minimal 2.1 effects 2.2 Hypercharge kinetic2.3 mixing and D Little terms gauge2.4 mediation Little gaugino2.5 mediation MSSM renormalization group effects B Renormalization group equations 5 Conclusions A Kinetic mixing mediation 4 Signatures in dark matter searches and colliders 3 Models Contents 1 Introduction 2 Supersymmetry breaking and the hidden sector JHEP07(2009)050 g ]. However, 3 rough kinetic , 2 sector. Effects eir cosmological x ] under which cer- 5 e found around the (1) , 4 ], which can cause the ayet-Illiopoulos term in e consider in the present el (MSSM), the scale of to the hidden sector. In order of the scale of soft c mixing corresponds to 13 rimental bounds provided – urally less than or on the mmunicate supersymmetry he scales of supersymmetry inetic mixing, the symmetry ic mixing. Renormalization er into the hidden sector in tions [ gain be around a GeV. metry breaking at the corre- 11 municated predominantly by ons (e.g., assuming gauge or ymmetry breaking is commu- particle will typically be long If the gravitino is much lighter how that this is indeed possible to one another [ esis or be overabundant. If the f the gravitino mass compared red in turn to parameters in the be stable and one still needs to ce soft parameters in the hidden o the MSSM. With such singlets, ed to be present, though their size eaking is typically very similar for ]. 14 – 6 – 2 – term for hypercharge [ , and whether or not there is sequestering of generic 2 D / 3 ]. m 16 , ]. Similarly, the effective amount of supersymmetry breakin 15 1 sector can also have a renormalizable coupling to the MSSM th x ]. The detailed phenomenology of these hidden sectors and th 17 [ 2 − All these effects combine to suggest that hidden sectors may b A simple and concrete example of the class of scenarios that w The U(1) If singlets are present in the hidden sector, they may also co -suppressed operators [ 10 Pl . electroweak symmetry breaking issupersymmetry determined breaking by [ and is on the 1 Introduction In the minimal supersymmetric extension of the standard mod viability, however, depends stronglywith on the the mass of relative theand size lightest the o hidden-sector hidden particle sector (LHP). lived respects and R-parity, give the rise lightest togravitino R-odd problematic is decays heavier, after then nucleosynth ensure the that lightest it has R-odd an particle efficientin annihilation will channel. the context We will of s simple hidden-sector models. breaking if they couple directly tono the messenger kinetic sector mixing or t isthis necessary case, the to SUSY-breaking communicate scale SUSY in breaking the hidden sectorGeV can scale. a Suchthey new are sectors sufficiently areǫ consistent hidden, with which current in expe the case of gauge kineti in other sectors of thesponding theory mass can scale. naturally If induce thegravitational gauge breaking interactions, of sym the supersymmetry scale is of com all supersymmetry sectors br of theory, evenif if they supersymmetry do breaking not is coupletain communicated appreciably by sectors gauge of interac thebreaking theory can are arise uncharged, between a the hierarchy different among sectors t [ work consists of the MSSM augmented by an additional hidden U hidden gauge group to break.breaking For scale natural values is of on the the gaugenicated order k to of a the GeV. visible Ingaugino sector addition, mediation), through if SUSY-breaking supers effects the will SMhidden be gauge sector transfer interacti at thegroup messenger effects from scale the in visible-sectorsector gauginos the can through presence also of the indu kinet kineticorder mixing of the term. GeV scale. These effects are nat M mixing with hypercharge.the Such hidden a sector term when can there induce is an a effective F proportional to the scaleseveral ways. of Supergravity supersymmetry interactions are breaking alwaysdepends can expect on ent the gravitino mass JHEP07(2009)050 , ], ]. we 12 24 18 4 , 8 he mes- tings and GeV/TeV; ] or gaugino ∼ 5 erved by the , 3 4 − ng of GeV-mass nt, but surprising, . In section 3 MeV/TeV. However, scale supersymmetric ], can arise from dark cuss here have already ∼ plied to MeV sectors as 23 6 of size 10 – d under the hidden-sector hich for electroweak-scale − vant there is the strength etry breaking can be medi- es seen by PAMELA [ y through standard model on of supergravity interac- s, supersymmetry breaking 0 s. Using these results, we of the hidden sector to the dark sectors, motivated by esults. 21 an annual modulation signal hter than a few GeV [ x n, we assume that the hidden- is reserved for our conclusions. n section lation rate today relative to the we investigate various ways to cent hints for dark matter, and 5 tered away from supersymmetry ure can arise from a low-velocity 2 pling to new GeV-mass states [ ]. The difference between the GeV ion 39 – ] that appeared while the present work 37 14 , , 17 13 , 6 – 3 – gauge group with hypercharge, bi-fundamentals gauge symmetry. Throughout this discussion, we x x ], as well as the WMAP haze [ 20 ], or by heavier inelastic dark matter whose inelastic split gauge interactions in the form of gauge mediation [ Y 31 – 26 U(1) ]. In the context of gauge mediation, we assume further that t × ] experiment. 41 L ]. This can potentially be explained by the elastic scatteri 36 , 25 40 ], and PPB-BETS [ SU(2) 19 × c ]. A GeV sector may also help to account for the 511 keV line obs The outline of this paper is as follows. In section New hidden sectors at a GeV may help to explain some of the rece Some of the mechanisms to generate light sectors which we dis 35 – INTEGRAL [ the possibility of MeV-mass dark matter [ assume that the MSSMSU(3) feels supersymmetry breaking primaril 32 was in preparation. Where there is overlap, we confirm their r investigate some applications of thesewe discuss models briefly to their explain collider re signatures. Finally, sect mediation [ sengers of supersymmetry breaking togauge the group, MSSM and are not thatsource charge there of supersymmetry is breaking. no Withinsector significant gaugino fields mediatio direct (including the coupling Abelianbreaking. gauge fields) In are both seques thecan gauge be and communicated gaugino to mediation thetions, framework hidden kinetic sector mixing through of a the combinati hidden U(1) ATIC [ matter annihilation, but seem to requirevalue an yielding enhanced the annihi correct thermalSommerfeld relic enhancement density. of This feat thedark matter annihilation requires in an ourNew attractive GeV-mass galaxy, states force are w with also a suggestedat by mediator DAMA the lig [ observation of dark matter states [ scattering cross-section emerge naturally through its cou mediate supersymmetry breakingconstruct to several GeV-scale concrete hidden sector Abelian hidden-sector models i 2 Supersymmetry breaking andWe the begin with hidden an sector overview ofated the to different a ways hidden that sector supersymm containing a U(1) hints for dark matter (DM). The positron and electron excess sectors which are theof focus the of coupling thissectors, of study typical and the couplings MeV hidden to sectors the sector rele MSSM to and SUSY SUSY breaking breaking. are In GeV- been used to construct natural supersymmetric MeV U(1) by contrast, MeV sectors must have weaker couplings of size 1 some of the mechanisms wewell. discuss Our in study the also present has work overlap can with be refs. ap [ JHEP07(2009)050 (2.3) (2.1) (2.2) -suppressed Pl . Sequestering M sses in both the When sequestering ric 1 ediated soft terms do essenger masses close ]. ugino mediation must 42 nd hidden sectors can be auge-mediated soft terms from the source of super- -suppressed operators me- sequestering , inglets that couple to both ymmetry breaking, relative 2 Pl / dden sectors are generically y TeV-scale soft masses. For to other fields then give con- 3 iation mechanisms provide an M Even so, residual supergravity y on the order of the gravitino m elow. ough try breaking to all sectors of the tion to the suppressed soft terms  ]. In addition to allowing for anomaly , in the absence of any other physics symmetry in particular. 2 Pl 43 / M 3 R M , ], m also recently been proposed as a solution to the  3 Pl 2 2 , ) ) 2 M 2 2 F π [ g π ]. 3 g 2 (4 46 √ (4 / – 3 – 4 – ], generating soft masses on the order of ∼ = ∼ 44 m ], but can induce unacceptable tachyonic slepton 16 2 / , F 47 M 3 2 / 2 15 AMSB 1 m ) 2 π m g (4 ∆ ∼ ] or through conformal running effects [ vis soft 16 m , 15 sector, and those that break U(1) ]. x 15 . This leads to a quite general statement — is the messenger mass scale. Thus, gravity-mediated soft ma parametrizes the underlying supersymmetry breaking. Gene 2 / represents a coupling of the corresponding field. Anomaly-m 3 M F g m -problem in gauge and gaugino mediation [ The typical size of supergravity effects in both the visible a An exception to this statement occurs when the generic In comparison to these supergravity-mediated soft terms, g For a pedagogical review of conformal sequestering, see [ 1 where described in terms of the gravitino mass diating supersymmetry breaking are further suppressed thr sectors. We describe each of these possible2.1 contributions b Supergravity effects A strong motivation forto gauge generic or gravity gaugino mediation, mediation isexplanation of that for supers the these absence gauge-based ofthis med strong to flavor be mixing induced effective,strongly b the dominate over MSSM those soft fromeffects terms can supergravity still induced couplings. potentially by providein gauge an a important or hidden contribu ga U(1) operators connecting the sourcetributions of to supersymmetry the breaking softmass parameters in all sectors of the theor charged under both the hidden and visible gauge groups, and s can arise either bysymmetry localizing breaking [ a hidden sector on a brane away µ/Bµ mediation to dominate, conformal sequestering effects have occurs, supergravity effects will stilltheory mediate through supersymme anomaly mediation [ scalar masses [ where where connecting the visible andcomparable to hidden the gravitino sectors, mass. mass scales in hi are on the order of not generate too much flavor mixing [ visible and hidden sectors on the order of a GeV can arise for m JHEP07(2009)050 x ]. ]. . 51 tric 2 49 / (2.7) (2.4) (2.6) (2.5) , 3 in the 48 m c 100 GeV, istent with ∼ undamentals, θHH 2 4 / 3 d m R 100) hierarchy between on length) and Λ is ∼ − hen ate visible-sector super- , h.c. (10 2 O / avor symmetries) [ nt if we shift the basis of + suppressed by sequestering 3 l sectors of the theory will 2 s generated are the visible- s charged under both U(1) ive contributions to hidden-   m , or in the context of certain 2 2 α are no explicit supersymmetric , c µ Λ Pl x X GeV. . Conversely, the kinetic mixing  V α M -th field. This leads to values of M 2 i ǫ 14 X − ln s  quire a mild 4 1 c i 10 10 − Y Λ ]. In this case we would need + i M . Λ is less than unity and can be as small Y , and the higher-dimensional Planck scale [ − x / α 50 V c  4 c , 2 B i − M g M α → X 16 10 ) B Y ∼ -th field, Λ is the UV cutoff scale, and the log , µ 4 1 i – 5 – ≃ c ( 15 2 [ Y F + ǫ M π g 2 α ) , V /  . Thus, in this case the cutoff scale must be close to x 16 µ 3 X ]. is the mass of the c ( V Pl α ǫ x m Λ i 55 c M g B M , m ǫ  2 ≃ → Λ) 2 54  ) / g x c µ θ V ( 2 ∼ M ǫ d ( 2 ∆ , where or holomorphic potential K¨ahler operators vis soft g i Z gauge group, one can write down a renormalizable supersymme c m m x ∼ c ≃ L⊃ HH ], ′ M denote the charges of the µ 56 i θµ GeV. This is about as large as possible while still being cons – 2 Y can be highly suppressed or absent if there exist no such bi-f d 52 14 [ ǫ R is the compactification scale (inverse of the compactificati 10 and Y c i ∼ M x ∼ Even with sequestering, residual supergravity effects in al If a gauge kinetic mixing term is generated, it will communic Within gaugino mediation, generic supergravity effects are In order to maintain a perturbative description, this may re M 2 corresponding to the Planck scale. Note that this counting assumes that there masses arise from anomaly mediation. These will be at the GeV scale w as a loop factor. kinetic mixing term connecting it to hypercharge the higher-dimensional cutoff scale. The ratio 2.2 Hypercharge kineticIf mixing there and is D a terms new U(1) to where hidden sector — ifsector there are, parameters conformal proportional compensator to effects g symmetry breaking effects togauge fields the to hidden eliminate sector. the gauge This kinetic mixing, is evide the source of supersymmetrysector breaking. gaugino masses, The on leading the soft order term of GeV, which requires a somewhat lower cutoff, constraints on new sources of flavor mixing (assuming no new fl the kinetic mixing in the typical range where Such a term will beand generated U(1) radiatively when there are field the cutoff of the higher-dimensional effective field theory, Λ is cut off below parameter if the underlying gaugestring-theoretic structure constructions consists [ of a simple group JHEP07(2009)050 (2.9) (2.8) ]. We (2.10) (2.11) (2.12) (2.13) 6 term induces ], such as can a contribution sector [ ]. D ] in the hidden it can induce a x 60 59 57 charges, sector, it is itself a x x , while the hypercharge ]. e for natural values of i or soft supersymmetry- -flatness [ x mphasize, however, that 61 rsymmetry breaking, and D -term potential is given by sector comes from the hy- ortional to supersymmetry D hypercharge hidden U(1) nger parity [ , x he U(1) ers [ x ctive U(1) 2 . 2 charge ! ǫ 3 , but this leads to the hierarchy problem x Y ξ − Y 1 . ξ x ǫ 1 g Y 2 = 1 to ensure . ξ . √ / i i 2 1 β − x v Y  ≡ 2 x β | x i Y 2 g i ǫ Y g g x c 2 ǫ φ ǫ x | Y i ǫξ s 2 g ǫ c g gauge multiplets and x − – 6 – term arises when the visible-sector Higgs fields  − − , c Y i = 2 = X D ǫ = i i≃

i eff i 2 φ − Y ǫ 2 ǫ φ x ξ h c m 1 2 x This vanishes in pure gauge mediation with messenger 2 ∆ √ g and U(1) 4 ≡ = x . ǫ x s D V 6= 0. 6= 1 induced by SUSY breaking ) β 2 ]. A hypercharge Ym 58 ( are the U(1) , T r Y 54 . . Alternatively, the hypercharge FI term can be thought of as V term, which induces an effective Fayet-Illiopoulos term [ 3 , Pl − M 12 D 10 and , represents a hidden-sector scalar field with U(1) ≪ − x i 4 11 Y V φ ξ − However, a usually more important effect on the U(1) Including the effect of the hypercharge FI term, the U(1) When the FI term dominates the dynamics in the hidden sector, Of course, there could be a supersymmetric contribution to 10 EWSB at the supersymmetric level necessarily has tan 3 4 -term potential retains its usual form. Thus, we see that the ∼ acquire VEVs with tan The visible-sector fields then act as gauge messengers to the percharge Doing so, one finds that the visible-sector fields acquire effe where will discuss this in more detail below. parity, but can bearise generated if if the there Higgs are fields couple violations directly of to messe the gauge messeng sector [ an effective FI term for U(1) hidden-sector VEV The hypercharge FI termbreaking can when also receive contributions prop of why where for one orǫ several of the scalars. This is close to the GeV scal This contribution willbreaking be scalar in masseseven addition present though in to the the induced anycan FI hidden supersymmetric term itself sector. is trigger generated spontaneous Let (in supersymmetry part) us breaking by e supe in t to the hidden sector scalar masses in the amount D supersymmetric coupling. JHEP07(2009)050 ) and 2.5 , and 3 (2.16) (2.15) (2.14) − vis soft 10 ) gaugino uch terms m x 4 ∼ ) . 2 , λ π ǫ ǫ Y ing in eq. ( (4 λ ∼ arge gaugino mass. -terms are generated the hidden sector are B t the gauge messengers ) through the method of - and ctor by gauge mediation in- n by n-sector trilinear or bilinear ), the mass matrix becomes so be generated for the fields charges, the ( asis where the kinetic mixing A mportant implications for the F/M ale with size , x group effects, which we discuss 2.7 gaugino soft mass, we find that ! 1) x little gauge mediation 1 , -preserving scalar soft masses. We 1 . Let us emphasize that this result c , R M 2 E M ǫ M ]. In the field basis where the gaugino ! 2 ǫ s m 0 s 2 63 − 1  1 0 0 x M Y , which is close to a GeV for 1 g M g ]. We present a derivation using the analytic ǫ

M  s vis soft 63 – 7 – 2 i = − , x ǫm 2

] gauge mediation scenarios. 62 ǫ . The leading order result for the soft scalar masses ∼ = 64 = A gaugino i relative to the U(1) 2 φ hid soft M ǫ is m gaugino mass generated can be understood as an example m ], we call this mechanism gaugino x M 9 M sector if there is gauge kinetic mixing. The typical size of s x gaugino soft mass is a bit more involved since the kinetic mix x is the standard gauge-mediated contribution to the hyperch -breaking soft terms generated by little gauge mediation in 1 TeV. Following ref. [ R M ∼ As in gauge mediation to the visible sector, hidden-sector The hidden-sector soft terms that arise from integrating ou The U(1) vis soft which clearly also contains a zero eigenvalue. at the two-loop levelcouplings. in These the terms will presence be generated of at corresponding the messenger hidde sc all U(1) will generally be subdominantbelow. relative to Note renormalization that, together with our result for the U(1) analytic continuation into superspace [ 2.3 Little gauge mediation If supersymmetry breaking is communicated to the visible se volving only the MSSM gaugein interactions, the soft hidden terms U(1) will al holds both for minimal and general [ is less than or on the order of suppressed by a least a factor of kinetic mixing is eliminated by the transformation of eq. ( can be computed diagrammatically or (to leading order in also generates an off-diagonal gauginoappears explicitly kinetic and term. the In visible-sector fields the carry b no U( continuation technique in appendix at the gauge messenger scale mass matrix at the messenger scale at one-loop is simply give That there is no explicit U(1) where of the “gaugino screening” effect discussed in ref. [ with all quantities evaluated at the messenger scale m will see in thehidden-sector following phenomenology. section that this feature can have i JHEP07(2009)050 , , e ]. Y on 41 ξ c 45 with , , (2.18) (2.20) (2.17) (2.19) M 40 44 sectors will 6= 0 at the ) x d 2 H m t terms in the four- − s for the possibility ]. Gaugino mediation u e, it may be possible to 2 H 41 bulk between the branes, persymmetry breaking is gate in the bulk [ m , ral and U(1) tional contribution to tering can also be induced from brane-localized higher rmal hidden sector [ istent with flavor constraints 40 cribe below), and additional is the compactification scale. o supersymmetry breaking sses, with all other soft terms work. rate this operator (necessarily c , ugino mass. While it would be α he compactification scale e the MSSM chiral multiplets as M , W α α . B c , α 2 1 F XW M ], and spectra similar to that of gaugino c M  1 XD † 42 M c ∼ Λ X 2 M  2 c  1  – 8 – Λ Λ 2 M Λ a F θ g 2 ]   d ∼ θ 41 ∼ 2 a term generated by having ( Z , d ξ M 40 D Z L⊃ L⊃ gaugino will have an approximately vanishing soft mass at th x sector (gauge and chiral multiplets) are confined to a brane, x provided it is sequestered on the MSSM brane. The leading sof c M An additional possibility in gaugino mediation that is cons Allowing only the MSSM vector multiplets to propagate in the In fact, without specifying the complete UV and GUT structur ]. This can be important for the hidden sector in that it allow scale dimensional low-energy effective theory in both the MSSM chi supersymmetry breaking confined toby a approximately separate conformal brane. strong dynamics Seques [ Such operators generate visible-sector gaugino masses at t then arise from renormalizationsupergravity group effects. running (which we des is that the MSSM Higgs chiral multiplets are allowed to propa In this scenario, the U(1) which is the same orderinteresting as to the further visible-sector explore hypercharge which ga involving UV GUT-breaking structures effects), may we gene postpone this to future the order of 65 2.4 Little gauginoA mediation GeV-scale hidden sector can also arise in a natural way if su communicated to the visible sector by the MSSM gauginos [ where Λ is the cutoff of the higher-dimensional theory and can arise in a sequesteredwell extra-dimensional as scenario the wher entire U(1) of a non-vanishing hypercharge mediation can arise from coupling gauge mediation to a confo the leading-order soft terms consistvanishing of MSSM up gaugino to soft small ma dimension corrections. operators of The the gaugino form masses [ arise which is gauge invariant and yields an FI term proportional t compactification scale. RG running will then provide an addi simply write down the brane-localized FI-term operator beyond that induced by the Higgs VEVs. JHEP07(2009)050 - k R Φ j Φ (2.21) (2.22) (2.23) i Φ mentals ijk . Note that y or compact-  6 1 rs to the hid- relative to the + M h.c. ǫ j breaking, thereby -symmetry break- Φ inear and trilinear + i R R k hidden sector come breaking in the hid- Φ φ ij j R ..., he visible-sector gauge φ i M + factor of 2 1 φ auge groups, and singlets  ituations, RG running (or shold scale 1 . . . n group (RG) equations of is broken spontaneously by ijk = -function from hidden-sector generate case a pseudo-Goldstino can a s, we will focus on two cases: M β + 1 R y of little gauge (and gaugino) 1 6 rce of U(1) 2 ..., x s that follow, we will construct  mportant in relation to U(1) e den sectors to be approximately g -symmetry breaking by at least M 1 ) spectrum which mediate between + + R 2 k hidden j M  x 2 2 x φ | W i g 1 + ) φ 2 j 2 j M ij x | x b 2 x 1 2 + g + 2 i 2 i 2 i x x x 8 4( 4( − ⊃− – 9 –   (1) correction to the soft masses generated at the 2 ǫ ij ] . Soft scalar masses in the hidden sector receive a s ijk O 1 M y 66 2 ǫ = 2 ǫ M hidden s s V 2 i − − m = = d dt 2 - can emerge if the U(1) ij ) b ijk R π a d dt (4 d dt 2 ) 2 ) π π (4 (4 , the visible-sector states will themselves act as messenge , act as gauge messengers to the hidden sector. Such bi-funda c x ] M 66 -terms in the presence of supersymmetric hidden-sector bil . If there is no source of explicit supersymmetric U(1) B ǫ - and The leading RG effects of the visible-sector soft terms on the Perhaps more importantly, RG effects proportional to Light bi-fundamentals in the spectrum, charged under both t A hidden-sector VEVs. In addition, itsupersymmetric is prior even to possible for gauge-symmetry hid emerge breaking, in if which supersymmetry ispossibly supergravity spontaneously effects) broken. can provide In the dominant these sou s ification scale a factor of den sector, a light pseudo- breaking in the hidden sector.mediation Indeed, is a that remarkable it propert shields the hidden sector from U(1) den sector. Thesethe effects hidden-sector soft are parameters. captured in They are the particularly renormalizatio i setting the mass of the light state. from the hypercharge gaugino mass where this is in addition to the standard contributions to th contribution [ 2.5 MSSM renormalizationIn group addition effects to the soft terms generated at the messenger thre and the soft parameters defined as interactions. This term can lead to an interactions. These are generated as [ messenger scale if there is a moderate amount of running. the mass parameters generated in this way are suppressed by a ing where the hidden-sector superpotential is taken to be soft scalar masses. 2.6 Additional mediatorFinally, fields there may exist additional fields inthe the visible low-energy and hiddenbi-fundamentals sectors. charged Among under the many boththat possibilitie couple the directly visible to fieldsexplicit and in examples hidden both that sectors. g realize both In cases. the section group and U(1) JHEP07(2009)050 F ≫ due 2 F ǫ µ (2.24) (2.26) (2.25) gaugino breaking. x gino mass. gauge cou- term arises R sector. The x F x ) ceptably large mmetry breaking Bµ ] implies that the 63 states suppressed by in the limit of , ctor by gauge-singlet ] . [ x ]. An important special d to) kinetic mixing be- with superpotential cou- mess h.c. cale below the messenger of the U(1) , ation scale. The only dif- 67 connected to the situation S + n pass on this supersymme- ! . [ c e U(1) t rresponding generalization of ithmic enhancement in erence that the supertrace of eters contain U(1) function renormalization of < M 2 2 bf estored. Up to the logarithmic umed to have been integrated d gauge-mediated models (with Λ F F F M µ F

) small values of the U(1) -terms as well as the U(1) , B Bµ F ) ln ]. Hidden-sector scalar soft masses are ) [( 2 F bf 67 µ − Bµ M ( 2 - and | 2 bf c 2 F A 2 x ( x F π | 2 x – 10 – 8 c g 2 F Str ≃ 2 i 4 m denotes the bi-fundamental mass matrix, and Λ is ) x x 4 x π + g c M bf 2 (4 2 | M F | F F gaugino mass at the scale 2 F ∼− F x m µ 2 i m ⊃ ⊃ charge, ∆ W x is a genuinely supersymmetric threshold (i.e., the ( soft is typically on the order of cancel at this loop order, leading to a highly suppressed gau V F . F x ǫ ) µ M Bµ ( 1 (assuming order unity charges) to avoid generating an unac and hypercharge, which in turn will further mediate supersy . & 0 x is the U(1) c . 2 F i ). With this provision, the gaugino screening theorem of ref x x m c g F Bi-fundamentals also can contribute to Bi-fundamental fields in the spectrum will also induce (or ad Supersymmetry breaking can also be mediated to the hidden se = 2 F to the hiddenconsidered sector. previously, where In allout fact, bi-fundamentals above this the were scenario scale ass ference of is is the continuously that gauge we messengersscale. have or now Even the so, lowered compactific the let us bi-fundamental also mass mention s that the additional logar to lighter bi-fundamentals typically requires relatively relevant diagrams are analogous tothe those arising bi-fundamentals in as standar messengers),the with bi-fundamental the multiplets important may diff beminimal non-vanishing. gauge The mediation co is worked out in ref. [ develop soft masses from gauge or gaugino mediation, and the try breaking through gauge loops connecting them to the rest case occurs when contributions to generated on the order of where with the general expression for the gaugino mass given in ref a loop factor relative to the visible sector. tween U(1) (running) enhancement, this leads to soft masses for the pur approximately the scale at which a vanishing supertrace is r low-scale value of chiral superfields. As an example, consider the gauge single pling and entirely from supersymmetry breaking contained in the wave For bi-fundamental couplings of the form m the contribution to the U(1) mass, with a necessary condition being that their soft param JHEP07(2009)050 c r H are ζ term. (2.27) (2.29) and µ or λ nd pick up H term to a hidden . . . ′ µ )+ 2 . . . | sector that illustrate the λ are a vector pair of states x A ) (2.28) sses are typically positive. c )+ | 2 2 | bility is that the ario is only viable for a very be to construct simple viable | hidden-sector parameters. H ζ onal viable scenarios as long + persymmetry breaking to the λ nimal scenarios, is then driven , because of these constraints, ng parameters through larger positive. As long as thesis or generate dark matter lic density unless supergravity mediated model whose matter . In many cases, the models we c A | A 2 c ors allow the LHP to decay. We | 2 H . . In this case, they play a similar and c + H S m + term. We will see that this model d c ′ H + 2 H µ 2 H to be heavier than the lightest hidden- and m 2 H m , and 2 masses negative. This can in turn cause d / m + H λSHH 3 + c H u + m + , 2 H H 2 H 2 S u gauge boson. This regime also gives a natural d m m H x m H ( – 11 – + + and u 2 | 2 S 2 S λ H | may or may not condense to generate the m m term, but has the disadvantage that the spectrum ( ( 2 2 ζSH S ′ | | + 2 µ ζ λ | | ⊃ W = 4 = 2 ) will then generate a running contribution to the soft scala ) 2 S c ( m 2 H 2.27 d dt m 2 d . The singlet ) dt can couple directly to the supersymmetry-breaking sector a , x π c 2 ) S are the MSSM Higgs multiplets and (4 H π d (4 H and H and u H We then turn to a hidden NMSSM model which promotes the Alternatively, depends on unknown UV physics. generically contains a lighteffects fermion push with its mass an above overly that large of re the U(1) explanation of the origin of the content is a pair of hidden Higgs fields with a bare sector particle (LHP). We begin with a simple little-gauge- a large soft mass that then drives the singlet. When the gravitinolow is supersymmetry-breaking lighter scale, than or the ifwill LHP, additional the see operat scen that making the gravitino heavier allows for additi plings Here, The interactions of eq. ( consider run into problems within constraints excess of from the nucleosyn observedhidden density. sectors As that such, our avoid main theseit goal difficulties. is will generally We favorable will for see the that gravitino mass masses of At the messenger orThe compactification singlet soft scale, mass, the which vanishesnegative. Higgs at This the soft input in ma scale turn in drives mi the soft masses for the hidden-sector gauge group to break. An additional possi fields receive weak-scale massescouplings and and possible supersymmetry-breaki (auxiliary) VEVs of charged under U(1) somewhat small, this can lead to GeV-scale contributions to supersymmetry-breaking mechanisms discussed in section role as the bi-fundamentalsrest considered of above, hidden mediating sector. su 3 Models We present here a handful of simple models for the hidden U(1) JHEP07(2009)050 ulti- (3.4) (3.1) (3.3) GeV can entions, the . ′ µ is positive and the must not be much ′ ξ . µ iable candidate to be a teresting possibility for amical matter fields, and = 0 w-energy scalar potential i imilar to the case of little . c broken. gauge bosons, with the mass 2 rms in the hidden sector, the H r. With bi-fundamentals, the tion by bi-fundamentals. The  0 so that h ξ rs. For the time being we leave an be viable provided the axion . − a non-vanishing FI term for either 2 GeV. In analyzing this model, we ǫ> 2 | v , c 2 β ∼ ) 2 H c | 2 H . / ) (3.2) x Y c H 3 0 and 2 2 x g x | g m c x > or 0 (or very large!), and we include in this ( ǫ − g / HH H 2 H | 2 2 ′ / | | − ′ x 3 µ + – 12 – µ H = m | 2 ⊃ | H Y − | ξ x H 6= 0. W | H x ( ) -term part of the potential arises from the hypercharge ǫ 2 2 2 g x | 2 while sequestering supergravity effects. In this case the g ′ D ξ/x µ ≡ 0. To permit symmetry breaking, + | Ym hid ξ p are either ( = ′ → m = µ T r ′ dark hidden sector consists of a vector-like pair of chiral m V ∼ η µ x 2 / has kinetic mixing with hypercharge as discussed above. 3 i≡ x , or if m H x h model a negative mass-squared contribution. With these sign conv ′ appearing in the µ with the superpotential unspecified, although we will comment on how values of ξ H ′ c µ H and H In the absence of supersymmetry breaking, the tree-level lo Lastly, we discuss models where the mediation occurs via dyn Without loss of generality, we assume of the theory is given by arise naturally from supergravity effects when The parameter will assume that U(1) FI term set by the VEV of the MSSM Higgs fields, and is given by doing this is to take as the LHP retains a large enough annihilation channel. An in Thus, even in the absencegauge of symmetry soft (as supersymmetry-breaking well te as supersymmetry) is spontaneously larger than other contributionsthe to hidden-sector origin paramete of splitting set by anomalycomponent mediation of effects. the dark The matter. LHP is thenconstruct a an v explicit modelsinglet for scenario singlet often mediation contains andis a media light able pseudo-axion, to but decaylow-energy c through spectrum small couplings and togauge phenomenology the mediation. is visible secto frequently very s 3.1 Minimal LHP still has phase space to annihilate to nearly degenerate The minimal viable U(1) class of models the limit plets The most natural values of This term will receive additional contributionshypercharge if or there U(1) is potential gives minimum of the potential lies at JHEP07(2009)050 . , ǫ 3 0, . − ′ √ GeV (3.5) (3.8) (3.6) (3.7) → Bµ ′ 14 , which = 10 ǫ µ ǫ 1, . = 0 H x ure of the Higgsinos 1 GeV. As y a factor of x g ymmetry-breaking op- . . ), on the order of 2 of a massive gauge boson 2 | x FI term by a factor of ) c Z enology of the model. origin, whether from gauge x . In general, however, the tion effects then provide the . For g red. H rically smaller by a power of on scale well below 10 2.22 e Goldstino corresponding to m | 2 ng to the scale of the hidden- | H ) bed above. ′ 2 x . | µ ponding to this state becoming ( ′ | 2 / µ  ) | . ξ 2 . . We can thus treat their effects as | 2 x ′ + ξ is shifted to η − 2 Z µ c | 2 2 H . Thus, we consider the distinct cases | 2 H m H x 2 c + / 2 x m + 3 g H term is genuinely supersymmetric in origin 2 H | 2 ) m ′ | , both with mass with mass 2 ′ H + ( m µ term is then generated within little gauge or ( = 2 x µ c 2 H | | ′ h.c. x – 13 – − H − 2 Z q H | + 2 H | ) Bµ m c = 2 | H ′ 3 | = , ξ/x µ f 2 | H 2 h HH q x ′ M + m = 2 x 2 H . Bµ 2 derived from g ( η m h hid − + m i≡ = ( & H h V 2 / 3 hid m m gaugino with mass ≪ and x 2 / hid 3 , and is parametrically smaller than the scalar soft masses b 1 m generated only by the MSSM Higgs VEVs, we find M ′ ≪ ξ Among the fermionic states, two are comprised of a Dirac mixt The tree-level scalar potential becomes The corresponding spectrum of bosonic states then consists The spectrum will be deformed by the inclusion of soft supers With the inclusion of soft terms, the VEV of µ 2 compared to the symmetry breaking induced by 2 / ǫ 3 ǫ 2 x gaugino mediation primarily through RG running as in eq. ( and neglect supergravity effects. The For the time being, we will assume that the as well as a complex scalar derived from and the U(1) the potential acquires amassless flat and supersymmetry direction in at the tree-level hidden corres sector being resto m g small perturbations on the supersymmetric spectrum descri and a physical Higgs boson The third fermionic state isthe a spontaneous massless breaking Weyl of fermion. supersymmetry It in is this th sector. erators. The precise effector of gaugino the mediation softphenomenology terms or of depends due the on hidden to their sectorsector residual can masses supergravity be relative classified effects accordi to the gravitino mass 3.1.1 m Such a hierarchy can arise with a messenger or compactificati This has important implications for the spectrum and phenom in turn are smaller than the symmetry breaking induced by the in gauge or gaugino mediation.dominant contributions Little√ to gauge the or gaugino soft media terms, which are paramet and JHEP07(2009)050 h (3.9) ) are 0 (3.11) (3.13) (3.12) (3.10) Z , , ] e e 6 -symmetry R >m

is much smaller than that of tan 4 2 2 h 2 √ | field to develop a VEV as well. Since this term is subleading, c ǫ ≃ ). The third fermion state is much lighter, and coincides wit √ 4 m c fx | H f GeV, 1 − U H | 3.6 fx M    ∼ U 2 W | , we find ′ c ≃ i 2 2 µ . ′ e π | g f ′ 3 H 2 H π h 2 H µ x 4 | x M 2 x / 2 x / g i g 1 c M      H 2 to be even), and is only able to decay or annihilate into visib is the typical velocity during freeze-out and h ǫ 100 GeV, c term forces the = i≃ ∼ ∼ ′ f.o. H α v 1 α σv h Bµ The bosonic spectrum still contains a single real Higgs scal The very light pseudo-Goldstino fermion state is evidently The fermion mass matrix becomes M and -channel gauge boson exchange into state. The additional suppression for Two of the masswith eigenvalues mass are given relatively by heavy, eq. and ( corres The where and CP-odd scalars derived primarily from the massless Goldstino fermion found above. Explicit super breaking in the form of the subleading the corresponding VEV of this state. Including the effect of by tan tion final state consists of neutrinos. For electromagnetism and couplings to neutrinos (due to a resid With our assumption of a supersymmetric origin of the through kinetic mixing. We estimates the corresponding anni For tree-level) with the gauge boson with mass given again by eq. cle (LHP) in thisH sector. It is metastable due to of tan These states are split slightly by the JHEP07(2009)050 GeV. (3.14) . 2 sweet-spot / 3 he dominant , m can also arise e relic density, . Thus, if the 2 2 2 /  / 3 his case lie on the 3 3 erms will be of the − m m ǫ , we could still have 10 supersymmetry break- hid |∼  ′ m -sector fermion onto the GeV in gauge or gaugino 2 al supergravity-mediated ravitino after BBN) or if x mion is unstable to decay tino. If the light fermion tions to the hidden-sector  1 GeV arises in 14 Bµ ≪ | | ermion has too high a relic se. Since the relic density of γ order of 2 ǫ 10 ∼ we should have p / P | hter than the lightest fermion l generically have too large of 3 tands. 2 ∼ / ∼ e.  m 3 ′ ]. The precise effect on the hidden 5 M µ m  ]. The precise particle spectrum will 49 50 , such as might emerge with a messenger χ 2 / m 3 1 MeV . m 0 , the light fermion state decouples while it is e  4 – 15 – depends on whether or not supergravity-mediated ! 2 < m ], as well as in certain GUT constructions based on / i -mediated mixing with the photino. The correspond- 3 f 1 ǫ 68 F m h M p 100 TeV is the projection of the light U(1) ). The primary effect would be to push up the mass of the

ǫ x ) s M ∼ 2 2 | 23 i γ γ P F 10 P h | (and . Indeed, for × π 5 χ e ′ hid , in which case residual supergravity effects would provide t m 16 (3 1 m Bµ ]. Residual supergravity-induced flavor-mixing effects in t M > m = ≃ | ]. This cross-section is much too small to yield an acceptabl ′ & 72 f 1 τ µ – GeV supergravity contributions to the hidden-sector soft t 11 2 | / 2 M 3 69 ǫ ∼ 2 x is the auxiliary VEV parametrizing the underlying source of 2 g / F 3 & In the case of gauge mediation without sequestering, residu Under our assumption of a very light gravitino, the light fer So far, we have completely neglected supergravity contribu m 2 / 2 3 -theory [ For hidden sector is to be light (and to avoid flavor constraints) same order as those due to kinetic mixing. A value of effects are sequestered. We consider both possibilities her effects will generate contributions to all soft masses on the still relativistic. into a photon and a gravitino via its suppressed [ therefore depend on unknown UV physics. F sector spectrum for a given value of border of what is consistent with current constraints [ even with ing lifetime is through the standard Giudice-Masiero mechanism [ where ing in all sectors, and soft parameters. However, even though we have assumed photino. This lifetime isthe on light the state order is of too the large, age this of scenario the is univer ruled out as it s light fermion, which wouldis weigh lighter nearly than the thea same gravitino relic as it density. the is gravi in In then the either stable, hidden case, and sector whetherthe will (in the gravitino stil which gravitino is case is heavier thedensity), than lig this fermion the scenario decays fermion is to (in not the viable. which g case3.1.2 the f m m Our results lead us to consider larger values of contribution to models of supersymmetry breaking [ mediation. Indeed, the case of gauge mediation with or compactification scale on the order of or greater than JHEP07(2009)050 ]. no, ] 14 [ 73 (3.15) (3.17) (3.16) 2 ) π (4 / 2 . This allows / h 3 ith rate [ asily avoid too m . , 5 ∼ . 4 is somewhat small, term, we must have |  ′  x hid fh g h U m Bµ h | m t is possible for anomaly- 4 calar Higgs ng m ed for (high-scale) gaugino that we estimate to be of 1 GeV  ecays to four electrons via 1 GeV  H gsino states that could make oblem that the hidden-sector 1 ed by anomaly mediation are ector  4 . ependent, phenomenology. x predictive assuming there are hrough Higgs mixing is on the , with 0 (3.18) 4 0 x in the potential. K¨ahler In this  : , as well as decays to electrons g ǫ  c 0 <  3 h 2 0 2 − / ǫ h 2 3 HH ! 10 m m  f 1 115 GeV 4 2 4 H )  x M will be longer-lived, with decays to photon  π 2 will themselves decay rapidly to the visible 4 x 1 GeV h H g  1 (4 h 4 . x

3 0 x h − − ǫ – 16 – g s) 1 m / 10  3 = 4 1 ǫ ) c  0 s 5 h cm 2 H 4 h ) -odd fermion. 4 4 W 4 s | 2 m c 3 m m − R f 24 2 1 4 fh π 2 e − − 1 = 10 ǫ M U 2 H | 3 10 10 × 2 H 256 x 4 h π 2 2 x π × x × m g α (1 4 x 64 g 256 (6 (2 -parity odd state in the spectrum is lighter than the graviti ≃ ≃ R ≃ e ≃ ≃ 4 i ≃ → γγ h σv τ → h h τ -odd fermion to annihilate very efficiently to gauge bosons, w R is an order unity mixing factor into Higgsinos. One can thus e fh U When supergravity effects are sequestered, such as is requir When the lightest The gauge boson and the hidden Higgs = 0 in the superpotential and forbid the operator ′ µ This is typically longerkinetic mixing, than though the it goes lifetime through for a hidden higher power Higgs of d mediation to be the dominantmediated source contributions of to the set MSSM the soft scale masses, of i the hidden sector There is also asimilar size. related Thus, loop-mediated this decay scenario to leads to two a electrons viable, but UV-d However, in order to avoid generating too large of a hidden-s case, the scenario withno additional vanishing non-decoupling superpotential effects. ispotential However, highly is it unstable. has the Thisgiven pr by is because the soft masses induc sector. Of these two states,pairs the by hidden mixing Higgs with the visible SM-like Higgs boson the lightest large a relic density for the stable supergravity contributions can pushup all the the stable gaugino state and to Hig be heavier than the gauge boson and the s where through kinetic mixing. Theorder lifetime of for di-photon decays t it will be a stable dark matter candidate. If the gauge coupli JHEP07(2009)050 5 to S (3.20) (3.19) (3.21) . The glet λ η a massive = λ subgroup, but still m ional operators. whose origin can 3 ′ Z µ have opposite charges. generates a joint super- um consists of a massive c 2 | . At this minimum, the i H . S H c ee-level scalar potential in | oupling seen from the fermion mass global symmetry in addition 2 all at tree-level. |      H c h fermion (necessary on account test state in the sector derived and , e overcome by adding a singlet 0 H λ η 2 requires additional contributions | e sum of the squared soft masses S  2 e supersymmetry-breaking sector. | ξ 0 0 λ λ η | − =0= η 2 + | . x i c c  g 2 S | H H h 0 0 0 | S x | H 2 x + √ , while the VEV of 2 is given by − η is not stabilized. Including an FI term in the λSHH | – 17 – η c 2 0. The supersymmetric global minimum of this H x  i | ⊃ g c x ˜ H S | x H > H 00 0 0 0 0 | , H g ), and often gives rise to a light fermion state or an c W x h 2 2 H ˜ 2 | H , along with x H hid √ x = √ H H | m producing two chiral multiplets of mass 2 x i ˜ = 2 2      H, g | x S H ∼ ξ/x λ h + | = ˜ λ, m 2 p 0 and  f / = 3 and ≃ M m V c ξ > η H chiral multiplet gets eaten by the gauge multiplet yielding . Such a symmetry can also prevent a direct coupling of the sin x term in the superpotential breaks the global U(1) down to a i ≡ H 3 absolutely stable up to explicit breaking by higher-dimens H S h c H and S Neglecting soft supersymmetry-breaking operators, the tr The spectrum of the theory within this supersymmetric minim Including an 5 to the theory and taking the superpotential to be gives rise to a stable state in this sector. fermion states of these multipletsof mix to the form accidental a U(1)), single while Dirac the scalar states do not mix at symmetric mass for unstable potential. Both ofS these possible difficulties can b the visible-sector Higgs fields, the gauge messengers, or th this theory is be problematic (unless We can enforce this form byto imposing the a gauged discrete U(1) or continuous where again we take The condensing vector multiplet with mass potential does not help stabilizedoes not this change direction (and because is still th to negative). the Thus, potential this in scenario order to be viable. 3.2 Hidden sector NMSSM The minimal model described above contains a dimensionful c theory has an exact global U(1) symmetry under which As a result, the theoryfrom breaks into two sectors, with the ligh and so the D-flat direction vector multiplet and amatrix, pair which of in chiral the multiplets. basis This can be potential has JHEP07(2009)050 ∼ and 2 H (3.25) (3.24) (3.23) (3.22) global 0, and hid he VEV t contri- η/m ≤ m -terms, it λ 2 s A A ≪ m . 2 ) / 0, 4 3 e supersymmet- | c ≥ m h.c. ) H | 2 s + coupling on the RG 2 x m g H λ 2 2 H eaking soft terms to the c + x c with degenerate real and ermion state derived from . on the order of 2 H + . In general, however, the SH s , ng to the scale of the hidden 2 m λη , the bosonic states consist of ir origin, whether from gauge hiral multiplets, although the h λ | 2 r masses. c S ) + = x H , g λ A | λ 2 H 2 and ( ) o the running from the H and η 2 m c m | x 2 − c | h ( . 2 2 H / λ | | | H η c 2 2 H 2 | | + H λ m | λ | | 4 2 2 H | | with mass − + + S m H | S 2 | H 2 s | 2 | 2 + x . We again consider the cases – 18 – m g 2 H λ c | | / 2 ξ/x 2 H 3 2 H = 2 H x + q x m s m with mass 2 2 x 2 h | + c are oppositely charged. The spectrum of states still = g = S m 2 | H η | scalar will be the lightest on account of the soft mass term. The unbroken accidental global U(1) in this sector c S − ) 2 h 2 λ s H ξ | | 2 m x h A ) i≡ H g ξ | and 2 x 2 H H | h g c x λ | H H scalar derived from + x + c s as before. As a result, the potential maintains an exact U(1) − , the VEV is now shifted to -sector soft terms, which are parametrically smaller than t h 2 S 2 H ) i , little gauge or gaugino mediation then provides the larges x c ( 2 H m m hid S h sector of the theory derived from hid 2 H m m +( +( λ m m ≪ scalar derived from = ( ≫ , allowing us to again treat them as small perturbations on th ≪ . c 2 ξ =0= / V ξ h 2 is pure Dirac, and its tree level mass is still 3 2 x hid i / c g 3 c m H H m H h x & Within the This simple picture is deformed by adding supersymmetry-br Among these states, the 2 induced by the subleading . This mass runs negative in the IR due to the effect of the / and 3 2 s ǫ There will be a very small additional mixing between √ a complex as well as a complex With components within these multiplets will now be split in thei consists of a massive vector multiplet and a “Dirac” pair of c symmetry under which while potential. The precise effect ofor the gaugino soft terms mediation dependsphenomenology or on of due the the to hiddenmasses sector residual relative can supergravity to be the effects classified gravitino accordi mass m 3.2.1 m ensures that the mixed mass eigenstates are complex scalars imaginary components. This sameS U(1) also ensures that the f When butions to the U(1) induced by ric spectrum. The tree-level scalar potential then becomes evolution. In fact, neglecting subleading contributions t m is not hard to show that (to one-loop order) we have ( JHEP07(2009)050 (3.28) (3.27) (3.26) in the -channel s , denotes the o mediation 2 ǫ  √ 3 . f.o scalar is stable to ∼ 0 tate is metastable v . For example, the s relative to the tree-  4 2 cs h 2 π 4 . On account of this  U ch of the two sectors -suppressed Majorana η 1  . ǫ 16 x 3 rrections. The fermionic eff M /  Z − 2 2 s ǫ Q s ǫ m 2 h 4 10 m icles through the 1 GeV = η effects also split these states 2  m ∼ ale. The 4  2 h o mediation on account of the | λ c tive corrections. The dominant heir masses of the same order. 4 ly broken. assive gauge sector, the lightest λ 2 2 h λ m | ators break the accidental U(1)   A 2 el masses due to loop suppression | f.o. m nsity is overly large. This scenario v ǫ ]. cs  4 s √ | U 14 h along with the properties of their RG | ln cs s 2 analogously to the Higgs quartic in the m  1 GeV 4 2 U 2 h . η | | -even) and annihilates efficiently into the π 0 2 λ x 2 m eff 8 | but acquire a tiny R ǫ g  Q 2 2 η 2 H + )  x x is given by and x 2 x g H 2 Z g c – 19 – 1 h H . x 2 h 2 H m x = 2 0 x s x 2 m 2 h g 2 h states induced by − 2  √ m . s m c ) 2 h h → = ǫ η sector is lighter, the unbroken global U(1) ensures that /s m 2 x 3 x √ g λ (4 m 2 H and ∼ cm x 2 W s c 36 h 2 soft − e = 2 π m 2 H 10 3 ] x eff gauge boson. We estimate the cross-section for this process 2 × x 39 Q g x 2 (1 ≃ -parity (assuming all fields are scalar is stable, while the slightly heavier Dirac fermion s i ≃ 0 throughout the RG flow to the IR, given little gauge or gaugin R s σv h ≥ is the typical particle velocity at thermal freeze-out and h c 2 H f.o. m v = The phenomenology of this scenario depends primarily on whi All states in the gauge sector have equal masses up to small co scalar can only annihilate into lighter visible sector part 2 H s level value. The otherThese states splittings are receive all a veryas radiative small well shifts relative as in to the the t hierarchy tree-lev flow discussed above. This pushes up the real scalar mass where small mixing between the tree-level mass of the physical real scalar m is lighter. Whether or not the The logarithm is non-negativesoft within masses little appearing gauge in or the gaugin masses of as for the fermions and theeffect gauge boson, is but to is lifted raise by the radia effective quartic coupling additional mixing suppression, the singletis scalar therefore relic de unacceptable unlessand allow higher-dimensional for oper an efficient decay of the singlet scalar [ boundary conditions at the messenger or compactification sc splitting from the subleadingapart gaugino from soft the mass. gauge boson Radiative by an amount on the order of MSSM. This produces the shift the extent that the accidental global U(1) is not accidental states retain a Dirac mass of the lightest on account of h lighter scalar. When this chiral sector is lighter than the m exchange of a U(1) early universe to be [ JHEP07(2009)050 x ]. 13 . As (3.29) (3.30) hid GeV or m 14 & 10 2 , ∼ / 3 2 GeV, the MSSM ,  m scalar will also be annihilation cross- The corresponding 3 ∼  mess s − 2 ǫ h 6 3 / M . 3 f.o. 10 0 v he m  s sector is metastable on tures. airs.  ihilate efficiently into the 2 or LHP, the fermionic relic 2 ecise spectrum depends on with imit was considered in [ soft terms will receive addi-   | lue, though such a candidate rent flavor bounds. The U(1) γ ǫ x gauge boson and the real scalar P e of about the same size. ), but now with a gaugino soft additional supergravity-induced y viable for extremely low gauge | Z x on photodissociation during BBN. ature at thermal freeze-out.  m 1 GeV 3.21 5 . Assuming   2 ] indicates that this lifetime must be 4 / 3  x 74 m H m 1 -sector fermion onto the photino. Energetic . x x 1 GeV 0 x g   4 – 20 – ! s) / 3 i f.o. , the theory will again split into two subsectors. The F v h cm H x 24 p 2 Z 1 − 100 TeV lead us to consider the opposite limit, m 10

4 H π ) hid × x s 4 2 x 2 16 m | 3 . From this, we obtain the strong upper bound on the scale of i g (7 sector, and its corresponding relic density will be tiny. s γ F 10 4 P x h ≪ | ≃ × π 5 x 10 2 i ≃ / 3 m 16 (3 . hid σv h m τ m = ≃ τ & is the projection of the light U(1) -parity. It is nearly degenerate with the U(1) 2 ǫ denotes the typical relic velocity during freeze-out. This / R 3 ∼ f.o. γ v P Since we assume the gravitino is lighter than the gauge-sect When the gauge sector is lighter, the lightest fermion in thi With high-scale gauge mediation without sequestering, all If the only field to condense is The radiative mass splitting is much smaller than the temper 6 , and thermal effects allow it to annihilate into gauge boson p where h where electromagnetic decays are strongly constrained by limits For the fermion relic density we estimate, ref. [ section leads to amay relic constitute density a smaller than subdominant the component measured of va the dark matter. T before, we study the two cases of high-scale gauge mediation will decay at a later time into a gravitino and a photon. This l The corresponding lifetime is less than about account of cross-section at freeze-out is estimated to be stable in the presentscalar scenario. state in the However, U(1) it is now able to ann supersymmetry breaking, implying that thismessenger scenario is scales. onl 3.2.2 m tional supergravity contributions on the order of lower-scale gaugino mediation with a compactification scal fermion mass matrix will take the same form as eq. ( Our findings for superpartner spectrum is only slightly perturbed,flavor mixing with being any on the limit of what is consistent with cur sector, on the otherunknown hand, UV is physics. significantly Even modified so, we and can the identify pr a few general fea JHEP07(2009)050 . | . x λ n- cs , can 2 A f.o. U | v 2 λ (3.31) (3.32)  -sector h λ 3 . f.o. 0 v  trilinear soft 4 -parity or very λ -channel U(1)  s A R ction is somewhat x ction will be given Z its coupling to the , -wave factor of 2 ), but now with -sector scalar m p 1 GeV  λ xλ U  3.28 x 2 LHP, it will not have any responding cross-section is  irs of the LHP scalar with test ding on the size of the soft m gravity contribution to ate a gaugino-Higgsino state sses, larger gauge couplings, s sector. Both are stable. If ction. The heavier te. 1 GeV aller masses, larger couplings, an acceptable level for slightly x sufficiently into two Majorana mass is now of the same order ion cross-section, assuming the as well as the  y eq. ( m e on account of nihilate through 4 c | 2 f.o. 1 GeV v H xλ  x 4 U 2 Z | | and without the 4 m and fh x  λ U 2 Z | S 1 ), and the resulting scalar relic density is . m λ 2 0  gauge coupling, or if there is a resonant en- condenses, supergravity effects make a signif- +Γ  3 → 3.32 2 x 2 x − ǫ x ) s) H – 21 – x m / 10 m 2 Z 3 2 x  1 m 2 m cm  4 − | 23 H 2 x − 1 xλ . x m 0 x U 10 | g (4 × π  4 4 | λ -sector scalars, and the lighter of the two complex mass eige s) 16 (2 fh / λ 3 U ≃ | 2 i ≃ ǫ cm σv 29 2 W h c − 2 sector is lighter and only π e 10 λ 2 H 12 × x 2 x -sector Dirac fermion is the LHP, its annihilation cross-se ), but with the replacement g is the mass of the lightest gauge-sector fermion and (2 λ is the mixing between the Higgsino and the LHP. This cross-se x ≃ fh 3.31 m i ≃ U When the If the σv h -sector fermion and the LHP scalar. fermion now has itscross-section relic abundance set by annihilation to pa This abundance can potentiallyor be with acceptable for a smaller resonant ma enhancement of the annihilation cross-se icant contribution to the soft scalar masses for long lived, and hence potentially a good dark matter candida coupling. This mixes the mass of a similar size to the other mass terms. This will gener that is at leastmass somewhat for lighter than the the hiddenhidden-sector gauge gaugino. annihilation boson, modes, If it depen will the only be gauge able sector to an contains the expected to be safely small. too small for the samplelighter parameters chosen, hidden-sector but masses, increases to a larger U(1) where typically on the order of unity due to the unsuppressed super where hancement of the annihilationas process. the Since hidden-sector the masses, gravitino this state will either be stabl This can provide an acceptable relicor density with for somewhat a sm resonant enhancement of the annihilation. The ligh by eq. ( states can be heavierthe or lightest lighter scalar than is the the LHP, Dirac its fermion relic in abundance is thi given b λ gauge boson exchange into thegravity-mediated visible gaugino sector. soft The mass annihilat states, splits is the Dirac states now annihilate efficiently intoapproximately the four Dirac times fermion the LHP. The value cor in eq. ( JHEP07(2009)050 tions (3.34) (3.33) ount for ble sector . This is 2 ) -odd hidden π R (4 / 2 x t fermion, there is g 2 / ario, it is possible to ]. ) may also be gener- 3 -preserving) source of such that the anomaly- atter. As in the case of 14 m R gravitino and a photon, -sector spectrum (which iation, additional contri- 3.33 x hid ∼ gauge boson. In this case, ither a Majorana Higgsino- m y, the fermion can still have mately degenerate with the between the supersymmetry- onal operators allowing for a precise spectrum in this case field couples directly to the x so the possibility of having a n, but they are suppressed by hid in ref. [ ≫ -term ( s and obtain an acceptable relic m S 2 3 coupling to the superpotential, D / / 3 3 . scalar soft mass 3 m . 2 S κS 3 κ in this situation, we obtain an acceptable + is desirable for a viable phenomenology. c positive sector is broken spontaneously leading to a hid hid λ ]. As in the case of high-scale gauge mediation m m (100 GeV) – 22 – 14 ∼ λSHH & ≃ 2 sector of the theory, and in both cases leads to too 2 / 2 S ⊃ / sector will annihilate efficiently to gauge bosons, and 3 λ 3 m x m W m couples primarily to a . As above, this implies that the lightest S hidden sector. This gives rise to several new features which . For < λ x 2 / x 3 fields all condense due to additional supergravity contribu g m corresponding to the interaction of eq. ( S -parity which is mostly singlet, whose relic density can acc κ , even when the cross-section for annihilation into the visi A R , this leads to a significant change in the U(1) , and 3.29 c hid and H m λ , model, we have found A is small. Since the gravitino can be heavier than the lightes ∼ H ′ 2 µ / 3 3.31 m When supergravity effects are sequestered, as in gaugino med If the Sequestering of supergravity effects also allows for particle will behidden a gauge gaugino-Higgsino boson. mixture Sincephase there that space is available is to an annihilate approxi approximate intodensity degenerac hidden as gauge in boson eq. will typically have astable safely LHP small due relic to density. There is al the lightest stable state in the U(1) or if there iswill explicit be breaking UV by dependent, supergravitymake but effects. all by states The analogy in with the the usual hidden NMSSM sector scen heavier than the U(1) to the soft masses, the global U(1) in the phenomenology provided massless boson. This can be avoided by including a the observed dark matter abundance. butions to the softa masses loop still arise factor from relative anomaly to mediatio supersymmetry-breaking sector, generating a Soft terms The new ingredient is that we now assume that the ated, but will be suppressed if 3.3 Singlet-mediated SUSYWe breaking now consider a scenario where abreaking singlet sector field communicates and the U(1) we investigate below. The superpotential is taken to be in eq. again no problem withand BBN this constraints state from can latethe again bare be decays stable into and a a component of the dark m with mediated soft-mass contributions are on the order of ∆ rapid decay of this state to the visible sector, as suggested large of a relic density. This can be avoided by adding additi is now largely calculable),gaugino with mixture, a or similar comes effect. from The the LHP is e precisely the situation considered in ref. [ JHEP07(2009)050 c ), 2, 0, c H √ h → / ) in the (3.41) (3.40) (3.37) (3.39) (3.35) (3.36) (3.42) (3.38) − S and η h λ,κ ( iA A 2 H 1 √ + gauge boson s implifying as- x 0 or ≡ h . 1 , both → ), but with addi- h c + ( ! κ 2 s H 3.22 dstone state eaten by gauge field a mass = λκ η and x its of ly broken by the VEVs, are somewhat suppressed 4 S eq. ( λκηs is somewhat small and the κ rom the axion mass matrix 2 , given by H − A λ √ s  κ communicates supersymmetry . e c hid , 2 and + 2 2 H Λ and κA 2 S 2 H 2 2 H m η √ m λ η m λ λ / λ )  m . 2 A + 3 2 s 2) λ η. 2 λA ln λ and s λA 0. This yields typical values of η is generated. These hidden-sector soft √ 2 2 H 2 S / ≃− λ x > H √ 2 S − x m 2 H 2 g ≃− 2 2 η x m ) 2 to g 2 π iA 2 x 2 2 λ ≡ g η 2 H . η 2 √ S 2 S 16 + 2 λ 2 2 S x 2 – 23 – − i ) λ m = c c 2 λκηs λA 2 m (4 ( λA 2 x gauge symmetry and giving the U(1) λ h H ≃− ( λκs Z ≃ ≃ ≃ √ x 2 c = − m s 2 1 + ( 2 H ≃ h s 2 h 2 h 2 h − 4 x + 2 2 η g m s m m m i η 1. Under these assumptions, and assuming further that λ i≡ λ = with approximate masses H = . With negative soft masses for h S s κ ) ≪ h 2 H λ A λA c h 2 ( 2 m κ = H √ s

h = 2 A ), and M ) basis c , and that S h 2 S ]. To analyze the mass spectrum of this scenario, we make the s m + gauge boson, , A 9 h , H x ( 6 A 2 1 0 at the low scale, we obtain √ The resulting scalar potential is identical to that given in The Higgs VEVs break the gauge symmetry, giving the U(1) > ≡ 2 S 2 For the CP-odd scalar masses we must take more care. In the lim breaking to the hidden sector, generating soft masses of siz This minimum is stable provided logarithm is not too large. supersymmetry breaking. The coupling of masses are on the order of a few GeV provided the coupling where Λ is the scale at which the soft mass tional terms proportional to as well as the approximate mass eigenstates of the CP-even scalars are sumptions that the kinetic mixing is suppressed, that the theory hasleading a to global a Abelian massless Nambu-Goldstonein symmetry boson, the that as ( can is be spontaneous seen f range of 20–60 GeV and somewhat smaller values of h Expanding the scalarsthe around U(1) their VEVs and removing the Gol can develop VEVs, breaking the U(1) m relative to a mass [ JHEP07(2009)050 7 S = m 4 , f 3 (3.43) (3.46) (3.45) (3.44) M -parity. R g in the hid- -term parameter- ner of the pseudo- F cond pseudoscalar is , or gauginos and Hig- . 2 | ˜ a      1 χ ravitino mass, so we again P 0 0 -breaking source of super- r hand, these terms can be | λ η λ η mall, there remains a light R 5 preserves an R-symmetry. In η s ization group effects, and the  x 2 S g . provided the , the lightest state in the hidden ) m H χ n. Depending on the mass of the κ s x κ m A 2 -terms can be the same order as . 1 GeV and two fermions with mass √ A κA  hid η − and 4 + x m η g are all even. λ 2 ! x c H A g & i x H 2 H 0 0 0 0 λκη / F λη λη x 3 , and the expression for its mass implies that 3 h 2 c – 24 – = 2 − m ( p √ , and H 2 100 TeV , . 2 2 f H 1 η -sector fermion will be unstable against decaying to 2 S s η η ,

x x and x 6 M g S m ) and g s H ≃ H 0 0 2 ≃ hid x 3 2 | H 1 x i 2 ) the fermion mass matrix is 2 − ˜ a 2 a m 2 2 a ˜ χ S F √ if the dynamics generating 10 h m , √ P fermion will be stable or metastable on account of m | c − ≪ 2 S π × ˜ x 5 χ 2 H      m / 16 3 m (3 ˜ = H, m = ≃ f ˜ λ, τ hid M , the lightest U(1) -parity requires that R m hid -terms will be set by the dominant contribution to R-breakin m ≪ A 2 ≪ is the projection of the lightest fermion onto the superpart / 3 2 ˜ a / χ 3 P sector is the pseudo-axion. In principle, these m 0 is needed for the stability of the perturbed minimum. The se . x With our simplifying assumption of small The scalar VEVs also induce a mixing between the hidden-sect Preservation of λη 7 2 This state derives mostly from λκ < consider the two cases Thus, the phenomenology of the hidden sector depends on the g pseudo-axion in the spectrum with mass Under our assumption that these parameters are relatively s axion. This decay will occur safely before nucleosynthesis izing supersymmetry breaking is not too large. 3.3.1 m where With a pseudo-axion and a gravitino. The lifetime for this decay i if the singlet receivessymmetry its breaking, such soft as mass thesignificantly through gauge smaller messengers. couplings than On to the an othe This gives two fermions with mass U(1) this case the den sector, which couldlightest arise hidden-sector from state supergravity will orgravitino, be renormal the the lightest light U(1) pseudo-axio gsinos. In the basis ( mostly singlet and has mass √ JHEP07(2009)050 L (3.47) (3.49) (3.48) (3.50) ’s. 5 ⊕ . has a small 5 3  S e made safe in 1 n a similar cross- a , m 1 GeV 2 . 0  into a set of sector consists of a pair sector will typically be completely stable, they c  xample, if the absence of any inter- x er hand, they will decay 2 doublets under SU(2) x λη F 2 / 2 1)  1 √ 3 GeV and ±  ough this state may compose a F llider timescales. . η mentals to be = 4 ] | e Y hx 40 GeV h.c. U  | , and leads to a pseudo-axion lifetime , the pseudo-axion will mix with the , such as the models described above. 4 4 + S d x ,  c  c H 1 ]. The leading coupling in this case comes u . This cross-section is large enough that . λ 0 H F F A 76 F F x  F , F m x ) ζSH 2 µ g s) 75 ) – 25 – 2 / 100 GeV Bµ ⊃ -parity. This state can annihilate efficiently into 3 √  In addition to these states, we assume that there λη 1 [( R 2 2 cm W 8 that transform as  √ . , the annihilation cross-section is on the order of ( 1 x x c 23 . λ > ⊃− 4 λ g | 0 − F 2 hx  10 soft √ , the lightest fermion in the U(1) 2 U V | × and -term potential due to  when 4 1 hid π 3 3 a F λ 4 (1 λ< 4 A F m − H ζ m x m 2 under U(1) = ≃ 10 x & η g i  F 2 2 2 / 3 x ) ζ 3 σv √ π s 2 hid h ± m λ 6 . 2 m → 256 α (0 & λ 2 ≃ ≃ is a gaugino-Higgsino mixing factor close to unity. We obtai / is the mass of the MSSM pseudoscalar. This lifetime can thus b 3 τ A hx U m The light pseudo-axion in the hidden sector will be stable in To preserve MSSM gauge unification, we could also incorporat 8 on the order of where CP-odd Higgs and decay to photon pairs [ coupling to the visible sector of the form section with also exists a set of fields charged only under U(1) from the cross-term in the actions with the SM.create If a these problem with areaway the efficiently heavier if cosmological than they abundance. an couple eV even On and very the weakly oth to the SM. For e For simplicity, we take the superpotential for the bi-funda along with the soft-breaking operator the relic abundance of thefraction stable of fermion the is dark safely matter. small, th 3.4 Multi-mediator models A minimal model with bi-fundamental mediators to a hidden U( and have charges where of chiral bi-fundamentals the LSP, and ispseudo-axions. stable When on the account of terms of cosmology, but is very slow relative3.3.2 to particle-co m In the case that JHEP07(2009)050 ). with sector. 2.6 ]. Both x 1, to avoid 25 . [ 0 0, we could model with σ . ′ augino mass. 3 is a genuinely e lighter than → . µ x g F odel with larger F ) µ sectors described gaugino mass will -based scintillation x x Bµ , if ) ic, the mediators will 2.6 ctors might be probed at he phenomenology of the y modify the soft masses erpretation, however, is to ume to be of TeV size, they e is an enhancement of the seen in DAMA, PAMELA, through RG effects, eq. ( Conversely, if the mass term th dark matter scattering off ). ter direct detection searches, gaugino mass will be on the through their contribution to ǫ significance of 8 r depends importantly on the d the U(1) rs studied above to help provide x masses in the light U(1) soft operator will arise from RG In particular, the 3.31 ( he NMSSM scenario with a lighter F 9 , the shifts in the soft masses are ust be relatively small, ) x g Bµ netic mixing GeV are viable scenarios. ∼ 2 / – 26 – 3 m or ]. 2 / 67 [ 3 m F ]. On the other hand, if the bi-fundamental threshold is not /µ 63 F ) Bµ to be larger than the gauge messenger scale with ( )( 2 F ) model with residual supergravity effects and the NMSSM model condensing) will have a problematic gaugino-Higgsino stat µ π ′ gaugino mass they induce. As discussed in section µ H (4 x / 2 F x can be phenomenologically acceptable. However, the NMSSM m gauge boson, on account of the mediator contribution to the g 2 x 2 g x / 3 m (and only In the screened case, mediator effects will only significantl When the bi-fundamental mass threshold is not supersymmetr Bi-fundamental mediators can be added to any of the light U(1 2 is supersymmetric in origin, the corresponding ( With lighter bi-fundamental mediators the gauge coupling m / 9 3 F GeV-scale residual supergravity contributions as wellgauge as t sector with either small subleading relative to thelight effect states will of remain the similar induced to FI that described term, above. and t While we do not specify the origin of these terms, which we ass could originate dynamically from an NMSSM-likeµ mechanism. the U(1) This tends to produceannihilation too cross-section relative large to of the a estimate relic in density eq. unless ther 4 Signatures in darkIn matter this section searches we and consider using colliders dark the GeV-scale matter hidden secto explanationsATIC, for and some PPB-BETS. We of also discusspresent the how and intriguing these future light signals particle-collider hidden experiments. se 4.1 Dark matterThe direct detection DAMA/NaI and and DAMA detectors, DAMA/LIBRA have experiments, reported an consisting annualthe modulation of period signal NaI with and a the phasedetector of nuclei. this modulation The are mainmaintain consistent consistency challenge wi with of the such null a results dark of matter other int dark mat completely supersymmetric, the contribution to the U(1) order of ( of the light hidden-sector scalar fields. For smaller generating an unacceptably large low-scale value for the ki supersymmetric threshold, gaugino screening will occur an small arise only at 5-loop order [ running. Pushing Here, both the m contribute significantly to both the gaugino and scalar soft previously. Their effect onsize of the the properties U(1) of the light secto integrate these states out andkinetic their mixing. effect would be felt only JHEP07(2009)050 ǫ he he ]. 30 (4.1) (4.2) charge x ] denotes the 86 Q ), the factors of symmetry breaking 4.1 x dent scattering cross- ate arises if there is a ]. There is an exception, , where x . 85 2 , the multi-GeV mass range ǫ/g  oton equal to [ r value. Such a state could 84 W , H gauge boson. This state can DAMA, while remaining con- l are taken into account [ 10 GeV) elastically-scattering DM -sector fields, such as through ssion. In this case, we obtain a x ed model. rs in a window where the dark x king up either the majority or a x r, provided it has an acceptable 2 DM ], but there remains an allowed , and in the gauge diagonal basis eQc g mechanism in these scenarios k matter state with U(1) . ], but it has been essentially closed by  x − 28 83 2 m β , , or if the U(1) 2 2 , 1  50 GeV) inelastically-scattering dark c Y in the sun [ ǫ 27 82 ξ 2 , x & W ch case the constraints vanish. g  29 p e c p m Plugging this into eq. ( µ m  . 2 4   – 27 – ) ǫ v 2 , and depends importantly on the phenomenon of | x 2 x Z H , this cross-section is too large (assuming the local charges equal to g cm x M H cm x ) by about two orders of magnitude. It can, however, β ]. Two possibilities that are potentially consistent with 3  38 2  /x c − 2 p | 78 39 π cm µ Y − 10 DM / ], and heavier ( g x x ≃ 10 × 80 g p , − (5 σ ≃ The allowed window is constrained by the spectral shapes of t 79 41 3 GeV x ≃ . − 2 Z , 10 p breaking is dominated by the hypercharge FI term induced by t ]. σ m ]. 10 31 – x 29 81 , ] and XENON [ 29 , , is the reduced mass of the proton-DM system. 26 77 35 , – p 26 25 m 32 [ , ≃ 12 p amazingly cancel out, and we find µ x has an effective nuclear-scattering cross-section off of a pr g When the U(1) There is also a spin-dependent scattering window [ The models constructed above often contain a stable state in A second possible scattering mechanism for a light DM candid 10 DM visible-sector Higgs VEVs, we cangauge further boson reduce mass this of expre where matter [ effectively mix with electric chargethe through kinetic visible mixing sector states acquire U(1) such as CDMS [ however, if the dark matter is not self-annihilating, in whi Super-Kamiokande constraints on annihilating dark matter region even after constraints from the spectrum of thewith signa a thermal relicpotentially density act close as to a the lightsignificant elastic measured fraction dark dark of matter matte candidate, the ma totalnucleon relic scattering density cross-section. of darkconsists matte The of nuclear simplest scattering scatterin mediated by the light U(1) both DAMA and other null result bounds are light ( 4.1.1 Elastic darkLight matter elastic dark mattersistent can with produce other observable recoils directmatter at detection has null a results. masssection between This in about occu the 3 range and 10 GeV and aDAMA spin-indepen modulated and unmodulated signal rates [ electric charge of that state. Consequently a potential dar dark matter [ x and channeling Unless there is a hierarchy in be reduced if there are additional contributions to dark matter density is 0 is driven by other soft parameters, as in thehidden-sector singlet-mediat singlet which has a small coupling to visible JHEP07(2009)050 (4.3) , the 3.3 , is a hidden- 4 and  1 h 1 3.2 h he target nucleus, r light elastic DM, m ge boson then con- or if there are other 2 3 GeV sector can induce an ar whose real compo-  H  3 al modulation signal is c mixing. The effective x 4 − ile being consistent with off a proton mediated by ζ  ermanium used in CDMS. ll fraction of the total dark 10 h a large nucleon scattering kinematics of the scattering n sections lightly heavier state. This gets, such as the iodine in and , assuming a single dominant is dominated by the induced  DM 0 keV and an effective nucleon 2 masses (above about 50 GeV). 2 h x 2 n inelastic interaction. Among lear scattering is a light hidden  DM m cm rimarily through a massive gauge ge x 1 .  λ 115 GeV 0 38   ]. Consider introducing a vector pair − 2 4 |  87 10 is the MSSM Higgs, and U , | − 0 2 14 h η 40 –  sector fermion off a nucleon is approximately − ). As for light elastic DM, this cross-section is n 1 or smaller values of the hidden-sector scale. . 11 20 GeV x ]. In contrast to elastic-scattering dark matter, 0 N 10 , – 28 – ζ 1  4.1 8 4 h 81  1 2 , ∼ m ].  2 n 35 p 81 n – σ  , µ m η 32 0 u 35  , 2 h – ) . Such couplings induce a small mixing among the visible- m 12 2 d 32 λζ v , H  cm u 12 4 | 41 − U | ζSH 2 n 10 + N × c 2 n π µ (2 ≃ ≃ n λSHH comes from the effective coupling of the exchanged scalar to t -even Higgs scalar. This cross-section is somewhat small fo σ ]. The couplings of the resulting mass eigenstates to the gau n 32 CP N that couples to the visible sector only through gauge kineti x Coupling a TeV-scale dark matter state to a GeV-scale hidden IDM can arise naturally from a Dirac fermion or a complex scal corresponds a mixing factor of order unity, contributions to the gauge bosoncross-section mass. can On be the acceptable other ifmatter hand, the density. suc IDM makes up only a sma inelastic mass splitting of the right size [ the terms nents are split slightly in mass, andboson that [ couples to nuclei p slightly too large when thehypercharge hidden FI sector term symmetry unless breaking there is a hierarchy between IDM scatters preferentiallyenhances off the target annual modulation nuclei ofprocess the into signal such a and modifies that second the DAMA, the s is scattering enhanced rate relativeInelastic off to dark lighter heavier matter elements, nuclear can suchother then tar direct as detection account the bounds for for g a theThis wide DAMA range requires of signal dark an wh matter inelasticscattering mass cross-section splitting in the on range the order of 100 nect states with differentthe masses, possibilities naturally for giving the rise massiveU(1) to gauge a boson mediating nuc scattering cross-section of the lightest U(1) where scattering cross-section for a dark matter particle of char and hidden-sector Higgs states. For the models considered i dark matter component [ U sector but may be enhanced for larger values of such a gauge boson was estimated in eq. ( inelastic dark matter (IDM) [ 4.1.2 Inelastic darkA matter second potential dark matter explanation for the DAMA annu JHEP07(2009)050 er oo , we TeV (4.8) (4.6) (4.9) (4.7) (4.4) (4.5) D at the ∼ x 2 x ∓ X M 2 = / states carry SM , and H 1 1 and c x . X 0 D ± , blematic because the , ∼ , 2 2 N 2 and X N λ nelastic splitting consists 1 to be SU(2) doublets with , generates the effective D uced by the Higgs VEVs. 2 . ∼ , c X charges 2 2 n the symmetry breaking in x 1 X and D urally on the order of a few x λ X M 1 1 ically develops an unacceptably litting operator TeV. Note, however, that this N . X + for and . 2 and x / 2 ) 2 2 . ζ DHN ) D S 2 M 1 H s ) + u X u + 2 M state to get the effective superpotential 2 GeV DH with U(1) 2 2 ( 2 1 2 . Integrating out N 2 i DH DH 1 ( 1 H N ( ∼ + X 2 N x x HX , and coupling them to the condensing Higgs N gauge boson. Furthermore, the cross-section H 2 S x 2 2 h 2 N ± 2 2 2 ζ 2 M 0 x λ λ ξ s N λ 2 1 and Z – 29 – ξ 2 1 M λ + + M 2 2 λ 1 HX c , and the superpotential 2 1 2 2 exchange is roughly the correct size to account for X λ ⊃ X X 0 u ⊃− charges DD + ⊃− eff Z 1 x 1 eff W N DH eff and X , as the heavier inelastic state will now be able to decay to 1 W D u x 1 W λ ξ , which implies a nucleon scattering cross-section that is t X ⊃ ⊃ DH 1 DM charged under U(1) ]. This difficulty can be avoided if the λ W W x c 89 2. An inelastic mass splitting can then be generated in a numb ⊃ D = / , 1 H W 88 now have U(1) ∓ x and 2 TeV, we can integrate out the = X D in addition to GeV. Y i∼ S 1 and N i∼ 1 H X h → h The simplest way to realize this scenario is to take A second related scenario that is able to induce the correct i Unfortunately, the minimal IDM model presented above is pro 1 in the hidden sector as well as a pair of chiral singlets N supersymmetric level then generates the inelastic mass-sp superpotential where the DAMA signal. H which, after supersymmetrically integrating out obtained from scattering through of chiral states This operator can generate the correct inelastic splitting If charges in addition to thethe U(1) lighter state and neutrinos through a This operator yieldshundred an inelastic keV mass through splitting the that numerology is MeV nat when of a singlet of ways. Introducing a pair of states hypercharge can write operator requires heavier inelastic state tends tolarge be relic density very [ long-lived, and typ large for acceptable IDM makingthe up hidden the sector is full relic dominated by density the whe hypercharge FI term ind JHEP07(2009)050 . - x 0 ∼ 1. s Z & state ance- M x Z ons will ∼ x /m ], and more M DM 95 m x ]. Annihilation of α 8 sector in a number x nihilate efficiently into . We found that these ensity, while for scalars cade decays is unstable le can lead to a variety 3.4 g observational constraints fields described above are e dominated by the U(1) se signals could potentially by its annihilation to gauge oss-section mediated by the le U(1) c uch an explanation to work, be mediated both by the SM be dominated by the SM atically due to kinematics for eter space [ er of 100 keV for ion an still potentially account for nt provided D g the correct thermal relic den- as discussed in ref. [ ctor final states. Second, at high gauge bosons in our local region of ], these dark gauge bosons should y high-energy colliders such as the and x 24 ] experiments observe excesses in cos- D ]. However, lighter IDM that makes up 20 90 – 30 – 5. . 0 ∼ gauge boson is also lighter than twice the mass of any 2 λ x ] and anti-protons [ ∼ 1 94 gauge boson (provided there is kinetic mixing). Somewhat -doublet IDM, this implies that the mass of the state must ], and PPB-BETS [ λ – L x ]. The hidden-sector particles may then cascade further, po 19 91 11 , can have the correct properties to induce the necessary enh , x 9 , models outlined above, when coupled to a heavier dark matter 8 x , ], ATIC [ machines, such as the B and charm factories, heavy-flavor mes 6 2 GeV, and -charged dark matter state into U(1) 18 x − e i∼ + e H h 3 GeV provided the U(1) . 0 ]. gauge boson. 24 . x The light U(1) The two IDM scenarios with bi-fundamental as well as the light U(1) x Z 0 ment in a subset of the phenomenologically consistent param In this case, we obtain an inelastic mass splitting on the ord 4.2 Applications toThe PAMELA PAMELA and [ ATIC tentially giving rise toluminosity additional visible- and hidden-se the heavy U(1) subsequently decay primarily to leptons.m This occurs autom recently in refs. [ only a small fraction of the total dark matter relic density c models can lead to a phenomenologically acceptable GeV-sca the DAMA signal owing toU(1) the often large proton scattering cr mic ray positrons and electronsoriginate at from energies dark above matter 10the GeV. annihilating dark in The matter our state galaxy. mustleptons be with For heavier a s than cross-section aboutsity larger [ 100 than GeV the and value providin an of the other hidden-sector states. 4.3 Collider phenomenology The presence of supersymmetricof interesting hidden signals sectors atTevatron at particle and colliders. the the GeV First, LHC, sca against at subsequently ver the decaying into visible-sector hidden-sector LSP states, produced in cas the galaxy will generically receive a Sommerfeld enhanceme 300 GeV, charged under the U(1) To account for the signals aton PAMELA or fluxes ATIC without violatin of gamma rays [ very similar to the multi-mediator models discussed in sect of ways. Scattering of theZ bi-fundamental IDM off nuclei will amusingly, the scattering of this IDM state off protons will b gauge boson exchange, while its scattering off neutrons will be greater than about 1000 GeV to provide the observed relic d the mass should be in excess of about 500 GeV [ The relic density of thebosons. IDM will For be fermionic determined in SU(2) a large part JHEP07(2009)050 x o us , and hidden + γ gauge bosons can scalar fields in the x )). This necessarily 1. This coupling is → ]. In the models we further visible-sector production of hidden- ≪ paratively quiet decay 98 Υ 3.47 utralino, and the U(1) hains with a squark or n. The dominant decay ζ , igher fraction of the total an hidden sector at high- → te leptons will tend to be re U(1) ), ( 97 ng the “lepton jet”. Note, ible-sector Higgs fields and he hidden sector and visible , − ighter hidden sector. Hidden- and we can consider the model of ] have characteristically busy e llimated leptons (and possibly essarily) heavy bi-fundamental 3.17 11 d ncluding the R-even states) are + der time scales in the scenarios ecays of heavier states carrying future work. lf be produced through cascade are hidden Higgs and Higgsino 98 tons plus missing energy, and in e , H s. ( nematically incapable of decaying 8 , u gauge boson decay predominantly ˜ tates may also have decay modes to 8 H x ζSH and ]. We give a brief overview of potential ⊃ 11 H , gauge groups. This is a very simple example W 8 x – 31 – , where gauge boson decays primarily to hidden states, the ˜ H x H → ]. For both cases, additional visible-sector states may als 0 96 χ through an ISR photon. For the models discussed in the previo hidden with the superpotential coupling + γ ]. These states then cascade down to the lightest fermion and 3.3 11 → Consider the case where the visible-sector LSP (vLSP) is a ne The subsequent cascade in the hidden sector can be a source of An alternative possibility is that the connection between t − e + fields [ into the visible sector, whichto usually pairs requires of that hidden-sector particles. it is Otherthe ki hidden-sector visible s sector, butconsidered they are above. generally very When slow the on colli U(1) hidden-sector cascades will unfortunately remain hidden. particles. The general condition for this is that U(1) gauge boson decaysslepton mainly vLSP back will to bemode visible similar, of states. but the with The neutralino one decay is more c quark or lepto be emitted in the LSP or bi-fundamental decay. have rare exotic decays into the hidden sector, such as of a hidden valley scenario [ e be emitted. These will typicallypions), decay giving promptly to rise highly to co low-invariant mass “lepton jets” [ hidden sector allowed by phase space. Along the way, one or mo gives rise to ahowever, large that component the of non-Abelian missing models energy considered accompanyi in [ sector is via aa singlet large which coupling has to asection hidden-sector small Higgs coupling fields. with For the example, vis 4.3.1 High-energy hadronWe colliders consider first someenergy of hadron the colliders potential suchsector signatures particles as of will the an arise TevatronSM primarily Abeli and charges. through the In the LHC. particular, cascadedecays The in the d the visible-sector usual way, LSP and may willsector subsequently states decay itse into can the also l be producedstates through charged the under decays of both (nec the SM and U(1) have considered, both the finallong-lived state on fermions collider and scales scalars and (i leave the detector (see eq events due to showeringsomewhat in soft. the hidden Onchains the sector in other and the hand, the hidden the final-sta momentum sector of Abelian and the models the event. have leptons com will thus carry a h collider signatures here, leaving a more detailed study for sections, we find that theirsome collider cases signatures highly involve pho collimated “lepton jets” [ JHEP07(2009)050 , ]. 1, ¯ X gh- 106 X ≪ gauge ζ . These x → 3 Z − d models, − 2 e − ], where the + e 10 105 . , ǫ onstraint on these 104 [ machines are typically , as discussed in [ hoton, with the MSSM e stronger constraint at γ sector particles must go sible way to ensure that dden-sector states which − he previous discussion on onent of the neutralino is e with subsequent decays of upling of the Higgs to the w invariant mass. + + hidden Higgs. Since gauge boson, e den decays of SM resonances, hidden ecent studies of hidden-sector x these machines. Search modes, ates which are meta-stable. s by production of the hidden- . The related production cross- imply for a photon plus missing and similar signatures as before. + then depend on the decay chains x n Higgs and Higgsinos, γ hidden ˜ hidden H with electric charge, hidden-sector factories, this implies hundreds to . The hidden Higgs may then decay γ Z h H x → → → B colliders are also typically very weak. → where the hidden states have invisible or − → e γ c − − 0 + e h e χ e gauge boson with the photon. Potentially + + ) + e x S + hidden e – 32 – ]. + Υ(1 γ 103 – → → , which should be satisfied as long as collected at the 99 ) 3 ], which find that for GeV-scale mediators and a kinetic − S 1 − e ]. The simplest signatures result when the hidden states 2 − + colliders 100 10 e S, -channel exchange of the U(1) , 100 × s − 5 e , 99 . + 2 99 e < ) machines, such as Belle, BaBar, DAΦNE, KLOE and CLEO, offer hi , production cross-sections at low-energy 3 ). We discuss signatures in both gauge- and singlet-mediate − − e S + 10 -channel electron exchange, e t invisible ∼ ǫ → ) S collider signatures, see refs. [ ) decays to hidden particles via photon mixing. Belle finds th When there is gauge kinetic mixing of the U(1) The Belle and CLEO collaborations have already put a strong c For the singlet-mediated models, any production of hidden- S − e (Υ(1 + the hidden particles producing SMsuch final as states, as the well Υ(1 as hid leaving more detailed studiese for future work. For related r decay modes and the photon arises from ISR, interesting processes include luminosity precision tests ofsector these particles low-mass through hidden mixing sector of the U(1) sections are given in refs. [ thousands of hidden-sector particles haveand been the produced corresponding at constraints fromof existing searches, the hidden particles [ or through a in the fb range. Given the ab 4.3.2 Lower-energy states are produced by the Lower-energy not necessary to communicate SUSY breaking, but it is one pos the lightest axion hasthe a singlino, decay which mode. will again In lead this to case, the a decay small comp Υ(1 The Υ can decay topseudoscalar an Higgs mixing (off-shell) with MSSM a pseudoscalar hidden Higgs Higgs, and p mixing of remain stable on collider timescales,energy. so This that type the search ofhadron-collider is general signatures, s search in remains the to cascadebosons be decays may of done. be hidde radiated As which in decay t to pairs of leptonssectors with by lo searching for Υ(3 to two LHPs, resulting in a completely invisible decay of the however, these constraints also turn out to be quite weak. B bounds apply for bothare direct either decays meta-stable to on collider the time LHP, scales and or heavier decay hi through to st mixing of visibleinitial and state hidden is Higgses. very Because weak, the constraints co from A possible exception is through the exotic decay Υ JHEP07(2009)050 x of absence If the U(1) tor is to consider a for explaining some owever. For example, 100 keV, with the new PAMELA, ATIC, and les feel supersymmetry ∼ ved by the recent results DAMA can potentially be vitino mass. On the other V-scale gauge bosons can g. Even in the oo large of a relic density. annihilation today, giving a king into the hidden sector breaking scale or if higher- an potentially be probed at ing is communicated to the den sector. rs can be quite generic, and ommunicated to the visible hough its mass is much less or, there is always a danger percharge, SUSY breaking is visible sector, one generically ’t too large. This light stable ises when supergravity effects idden-sector states which then lly different mass scales. This t of dark matter, or by heavier cale fields charged under both that are not charged under the ier by ns to their soft masses. If there -scale hidden sectors. tuation is generally alleviated if rticle, provided it retains a large uples to both the SUSY-breaking ons reported by PAMELA, ATIC, colliders. – 33 – − e + e — the lightest fermion is kinematically not allowed to hid m ∼ 2 / 3 m gauge group and a vector-like pair of fields charged under it. x Perhaps one of the simplest ways to add a GeV-scale hidden sec Some care must be taken in the construction of these models, h Whether these sectors are responsible for the signals obser New particles and forces at the GeV scale may also be relevant couples to the visiblecommunicated sector to through the kinetic hidden mixing sector with through hy the kinetic mixin 5 Conclusions As long as there is an asymmetry in the way that various partic breaking, it is genericseems to end particularly up likely with whensector sectors through supersymmetry at gauge hierarchica breaking interactions,messenger is in gauge which c group case will particles are receive suppressed no contributio additional couplingsexpects between the these mass particles scale andhand, of the the it hidden is sector easyvisible to for be and additional set hidden by mediator gaugethrough the groups) fields loop-suppressed gra to (e.g., contributions, feed high-s giving supersymmetry rise brea to GeV new U(1) kinetic mixing, viable scenarios can ariseand when hidden a sectors, singlet co but with a suppressed coupling to the hid if the gravitino isof lighter quasi-stable than states the whichIn states either this in decay case, the after viabledimensional hidden BBN scenarios operators sect or arise allow have for only t the additional for gravitino decays. a is This very heavier si low thanenough the SUSY- annihilation lightest channel hidden-sector so pa particle that is its typically relic a abundancethan good isn the candidate weak for scale.are the sequestered A dark and particularly matter, interesting t scenario ar from the dark matter experiments, the presence of such secto sector at thealso GeV give rise scale to naturally apossible Sommerfeld inducing explanation enhancement for of the the the splitting. excess dark inand matter electrons PPB-BETS. and Ge In positr addition, theseboth GeV-scale future hidden and sectors present c hadron and decay to a gravitino and photon, but can still annihilate to h decay. This scenario ishidden viable sector when either the via supersymmetry kinetic break mixing or via aof singlet. the recent possiblePPB-BETS experiments. hints The for annual dark modulationexplained matter signal by the seen seen elastic at by scatteringdark of the matter a DAMA, GeV-scale scattering componen inelastically to a state that is heav JHEP07(2009)050 | ). 2 i (A.5) (A.4) (A.1) (A.2) (A.3) ]. F/M | 107 ) on the gauge µ h.c. ( i ed basis at leading + or a real superfield Z  . Upon transforming X α nology. Dark matter ediated to an Abelian (DP), and by the DOE s, we use the method of X an expansion in uge couplings appear in α racy Slatyer, and Tomer an Hooper, Markus Luty, B re perfields. In this basis, the ) part by the Harvard Center denotes the charge of field µ rammatic analysis [ ( 2 a i h q ǫ . + x, Y, ) α µ = ( X x α g ) if there are no fields charged under both , 2 X µ ) to a chiral superfield π i xY ( b 8 , a µ Y ( 2 . . . 1 g M 2 a x ]. For this, we determine the dependence of the ) and wavefunction factors = ) π b g + 8 µ µ – 34 – h 4 63 ( ( i ǫ a , h φ = + ǫ g d x dt 62 V α  i 2 x a B 1 )= e g α † i µ (  φ B ǫ ) ) takes the form d µ dt µ ( ( µ i 1 2 Y Z and hadron colliders, can then give us many possible windows g h 4 − θ , and then promote  e 4 θ d is the beta function coefficient (and + . From this, we see that: M 2 i e a i d Y Z q i a i x + Z q , the holomorphic kinetic mixing does not run at all i i Y = P P is related to the kinetic mixing in the canonically normaliz L − − h U(1) ǫ = = a . The result of this procedure represents the leading term in and b sector by gauge kinetic mixing. In order to study these effect xY b X x x It is convenient to work in the holomorphic basis where the ga † X √ the dynamics and signatures very different from MSSM phenome experiments, as well analytic continuation into superspace [ John Mason, Peter Ouyang,Volansky for Frank helpful Petriello, discussions. Mattfor Schwartz, the This T Fundamental work Laws of isincluding Nature, supported grant by in DE-FG02-95ER40896 NSF (KMZ). grant PHY-0556111 A Kinetic mixing mediation Supersymmetry breaking inU(1) the visible (MSSM) sector can be m into the hidden world. Acknowledgments We thank Brian Batell, Doug Finkbeiner, Jonathan Heckman, D with messenger mass scale front of the gaugeeffective kinetic Lagrangian terms at and scale are promoted to chiral su running hidden-sector gauge couplings U(1) where The holomorphic-basis kinetic mixing runs according to of the soft terms, with the full result obtainable from a diag Note that order as The exact RG equations for the holomorphic gauge couplings a JHEP07(2009)050 , and (A.9) (A.8) (A.7) (A.6) F M 2 ) 2 2 π ǫ ) depends on (16 gaugino mass is ∼ A.7 . ) Y SM gauge groups, . . M (  c ) ortional to that of the 2.5 he one-loop anomalous 4 h 2 E . ǫ e messenger scale: er both hypercharge and ( m M ) alar masses are suppressed O with explicit kinetic mixing = ) canonical kinetic terms and ine of eq. ( ions through the messenger o not depend on the details ction -sector A-terms and B-terms on gauge boson propagators en-sector trilinear or bilinear µ e derived by considering the ale at order M

ted with going into a canon- ( e reproduce the RG equations M c h )+ = 1), we obtain ( 2 x ǫ ) changes across the messenger E µ g is tiny, however, and will be of 2 Y 2 h ( , since it contributes to the phys- 2 i Y Z g ǫ i 4 x x x g . Z ) ln ) ∂M M or 2 is given by ! M ∂ x ( i 0 b 2 ) x ǫ µ, M 1 ( 0 0 M M 2 Y ( g 4 x )=

g 2 h 2 h 2 i ǫ M ǫ charge = – 35 – x ( 2 Y c (but not 2 h x g ǫ 2 E )+ 2 x 2 x Y g µ g m = b ( ) 2 x − gaugino g M communicating to the messengers through the kinetic M  1 = ( M i 2 2 µ 4 x 2 i 2 i

φ g π π with U(1) i x x 2 i 4 4 i 2 Z x φ 2 h = ≃ ln ǫ 2 ∂M i ∂ Z )= dt ln ) depends on the messenger mass, and only a U(1) M d µ ( ( 2 i . Y m g ]. F M 3 53 ) 2 2 h π group. In this case, only ǫ x (16 ∼ . Since this contribution to the anomalous dimension is prop We turn next to the scalar masses in the light hidden sector. T Let us assume the gauge messengers are charged only under the Finally, as in gauge mediation to the visible sector, hidden 2 h ǫ We stress that theseof results the are messenger quite sector. general,two-loop in Furthermore, graph that this for they result the d can scalar also b This can be obtained by resumming double insertions of dimension of a hidden field From this we can simply read off the soft masses generated at th will be subdominant relative to the RG effects discussed in se to the canonical basis with the kinetic mixing eliminated, w listed in ref. [ the messenger mass, so weby see immediately that the squared sc and that there arethe no U(1) fields at the messenger scale charged und in the mixed kinetic basis,no or explicit by kinetic transforming mixing. to a Only basis the with second term in the last l threshold, only can be generated at thecouplings. two-loop These level terms in the will presence be of generated hidd at the messenger sc mixing term. generated in this basis.is The then gaugino simply mass matrix in the basis The physical gaugino massesmass can dependence of receive the higher wavefunctionical renormalization loop gauge correct couplings throughical the basis rescaling for anomaly the associa kinetic terms. This correction to right-handed selectron (normalized to have hypercharge order JHEP07(2009)050 , , ]. (and (B.1) (B.5) (B.2) (B.7) (B.4) (B.3) (B.8) λ 108 ]; plications ) (B.6) (1984) 1 2 | κ )=0[ 2 2 A | | 110 1 SPIRES [ xm + M ( gauge interactions. | 2 s . 2 x ) x ′ m T r g µ 2 H (3 1 2 x )= | M 2 ǫ 2 κ Phys. Rept. ( s | ift the visible- and hidden- , , 2 x ns for the soft terms in the raction with coupling he U(1) 8 1 g Ym ( − M 2 H ) ) + 4 2 x hep-ph/9709356 x ]; 2 2 T r g , | | 2 ǫ ]. λ λ s 2 H 8 A A x | | 2 2 ǫ | − Locally supersymmetric grand unification ]; s + + 1 ) SPIRES ′ [ 8 2 2 S 2 S x M SPIRES | g . − m m λ 2 ] [ x Bµ ]. 2 H κ ( g A + + x ]; Supergravity as the messenger of supersymmetry 2 x A SPIRES 2 Gauge models with spontaneously broken local c c 2 H [ 4 g | – 36 – 2 x | 2 H 2 H λ | 2 H − 2 ǫ κ | m m s x (1982) 343 2 2 SPIRES | | [ 8 4 + + κ κ + 6 SPIRES | | [ − − ). 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