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Gaugino mediated supersymmetry breaking

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Please note that terms and conditions apply. JHEP01(2000)003 b on January 7, 2000 , and Eduardo Pont´ Accepted: a term can be generated by the Giu- µ [email protected] , [email protected] , Ann E. Nelson, b Novemver 30, 1999, Received: Markus A. Luty, a Field Theories in Higher Dimensions, Supersymmetry Breaking, We consider supersymmetric theories where the standard-model quark [email protected] HYPER VERSION Department of Physics, BoxSeattle, 351560, Washington, University 98195, of USA Washington Department of Physics, UniversityCollege of Park, Maryland Maryland 20742,E-mail: USA [email protected] b a Abstract: dice-Masiero mechanism. The supersymmetricviolation CP occurs problem only is on naturally the solved observablein sector if the 3-brane. CP literature These that are solve the all simplest models supersymmetric naturalness problems. Keywords: and lepton fields areand localized Higgs on fields a3-brane, propagate ‘3-brane’ supersymmetry in in breaking extra the is dimensions,rect communicated bulk. higher-dimension to while interactions, gauge and the to and If gauge quarkloops. Higgs and supersymmetry fields lepton We fields by show is via that di- standard-model broken thismetry gives on breaking. rise another to The a sizetimes realistic of larger and the than predictive extra fundamental model dimensionsto scale for is (but (e.g. supersym- required the distinguishable to string from)neutral be scale). the currents of predictions are The order naturally of spectrum 10–100 suppressed. ‘no-scale’ is The similar models. Flavor-changing Supersymmetric Standard Model. Gaugino mediated supersymmetry breaking Zacharia Chacko, JHEP01(2000)003 . Because r & M if rava and Witten [4].) Mr − e between the visible and hidden branes is 1 r are suppressed by a Yukawa factor M If contact interactions between the hidden and visible sector fields can be ne- Supersymmetry (SUSY) provides anproblem, attractive but framework it for introduces solvingis naturalness the the puzzles hierarchy ‘SUSY of flavor its problem:’solution own. is why Perhaps given do the by the mostU(1)’ models squark serious masses of models conserve gauge-mediated [2]. flavor? SUSYtheories A breaking In where natural [1] the ref. or visible sector by [3],and fields ‘anomalous Randall are the localized hidden and on sector Sundrum a fieldsof ‘3-brane’ suggested are this in type localized extra another were dimensions on introduced solution a inRef. the spatially in [3] context separated pointed of out ‘3-brane’. string that theory (Models in byfields such Hoˇ theories are contact terms between suppressed the visible if and hidden the separation 1. Introduction Contents 1. Introduction2. Bulk gauge and Higgs3. fields Phenomenology4. Conclusions 3 1 8 11 the suppression is exponential,larger the than the separation fundamental need scaleinteractions. only (e.g. be the string an scale) order to of strongly suppress magnitude contact glected, other effectspossibility become is the important recently-discovered mechanism for ofindependent anomaly-mediation communicating [3, supergravity 5], SUSY a effect model- breaking. thatanomaly is mediation One always present. in anately, (For a specific if careful higher-dimensional anomaly-mediation discussion model,supersymmetric dominates, of standard see model and ref. (MSSM), if then [6].)ative. slepton the mass-squared This Unfortu- visible terms problem are sectorwe can neg- will be is explore avoided the the in alternate minimal extensions possibility of that the standard-model MSSM gauge and [7]. Higgs In fields this paper, sufficiently large. The reasonout states is with simply mass that contact terms arising from integrating JHEP01(2000)003 )inor- 1 − The leading Figure 1: diagram that contributes to SUSY-breaking scalar masses in the models con- sidered in this paper. The bulk line is a gauginopagator pro- withinsertions two on mass thebrane. hidden , M ,thethe- /r term can be 1 µ ∼ 2 c µ is the number of ‘large’ D ,where 4 − D ) Mr ( / In the higher-dimensional theory, the standard-model In this scenario, SUSY breaking masses for gauginos ory matches onto a 4-dimensionaltheory, effective the theory. couplings of In the this gaugepressed and Higgs by fields are 1 sup- der to explain thewith gauge a hierarchy. hidden supersymmetry Models breaking similarstandard-model sector gauge to sequestered and the on Higgs one a fieldsmodels different considered in 3-brane contained the here and an bulk, , were additional i.e. consideredthis U(1) in is gauge ref. not multiplet; [9]. required the These to present paper obtain a shows realistic that theory of SUSY breaking. generated by the Giudice-Masiero mechanismdirect [10]. contact Other interactionsbecause between the of hidden theirfor and spatial visible visible separation. sector sectorstrated fields are The in arises suppressed figure leading from 1. contributionbecause loops These to diagrams the of are SUSY spatial bulk ultraviolet breaking separationpoint-splitting convergent gauge (and of regulator. and hence the calculable) Higgs In hiddenloop fields, effective and momenta as field visible above theory illus- the braneswhile compactification language, acts the scale the as contribution is contribution from a aobtained from loop physical (finite) from momenta matching below the contribution, the 4-dimensional compactification effective scale theory. can be The higher-dimensional theory gauge and Higgsrenormalizable fields interactions. We therefore can treat the interactdimensional higher- theory only as an through effective non- theory with a cutoff propagate in the bulkand and visible-sector communicate SUSY matter breaking fields.the between gauge the Models and hidden with Higgs sector fieldsthose the localized models all on supersymmetry the a was MSSMconditions, 3-brane directly superfields were broken requiring also by except a considered the rather in compactification large ref. boundary extra [8]. dimension In (radius of order TeV which may be viewed asory. the fundamental Below scale the of compactification the scale the- spacetime dimensions. Therefore, themensions size cannot of be the too extrascale. di- large in However, units because of the theis suppression fundamental exponential, of there contact is terms apression range of of contact radii terms with to sufficientcurrents avoid sup- without flavor-changing exceeding neutral the strong-coupling boundsthe on couplings in the higher-dimension theory [9]. and Higgs fields aretact generated terms by between higher-dimension thefields, bulk con- assumed fields to and arise thesuch from hidden as a sector string more theory. fundamental theory In particular, the JHEP01(2000)003 , M (2.1) , )) x ( j ,φ ) j x, y spacetime dimensions, with (Φ( j D L ) j 4 compact spatial dimensions with y − MSB). − g D y ( 4 − 3 D δ j X )) + -dimensional effective lagrangean takes the form x, y D : nonzero gaugino masses and Higgs mass parameters, and c (Φ( µ bulk .The r L = D L We therefore consider an effective theory with The renormalization group has a strong effect on the SUSY breaking parameters, This paper is organized as follows. In section 2, we discuss the higher-dimensional linear size of order 3 + 1 non-compact spacetime dimensions and In this section, we discussgauge some and general Higgs features fields ofthe in higher-dimensional term the theories ‘3-branes’ bulk with to andstring-theory other mean D-branes) fields or either non-dynamical localized dynamicaltime features on surfaces (e.g. of ‘3-branes.’ orbifold (e.g. the fixed We higher-dimensional topologicalwe points). use space- defects will All or not of concern thesemental ourselves ingredients theory. with occur We the in simply derivation string write of theory, an the but effective model field from theory a valid more below funda- some scale 2. Bulk gauge and Higgs fields which may be the stringsmall scale, dimensions, the or compactification some scale other associated new with physics. additional therefore gives initial conditions forcompactification the scale 4-dimensional renormalization group at the loop-suppressed soft SUSY breakingis parameters similar for to the the squarksthe boundary and present case sleptons. conditions the of This boundarydimensional ‘no-scale’ conditions theory. are supergravity Since justified models the by SUSY [11], thethan breaking geometry but masses the of for in third the all higher- chiral generationscenario matter squarks fields ‘gaugino are other mediated dominated SUSY by breaking’ the (˜ gaugino loop, we call this and the soft masses atbe the the weak scale lightest are superpartner allof (LSP) of ‘no-scale’ in the supergravity this same models scenario. order. [11],scenario The with In allows the spectrum fact, a important the is Fayet-Iliopoulos difference Bino similar termeffect can that to for the on that hypercharge present the that can sleptontuning have spectrum. for an neutralino important We and obtainthat slepton realistic these masses spectra superpartners below are without approximately relatively excessive 200 light GeV, fine- in suggesting this scenario. theory. We show that the sizeFCNC’s of the while extra still dimensions having can gauge bealso large and show enough how Higgs to the couplings suppress SUSY ofIn CP order section problem 1 3, can we at be discuss low naturallyour the energies. solved phenomenology conclusions. in We of this this class class of of models. models. section 4 contains JHEP01(2000)003 .  1, 2 1 . (2.3) (2.4) (2.2)  . is the 4 M 4 ,which − Mr − D − D D ) e r , at the scale −  ! ∼ Mr ( 4 ∂ / ıve dimensional M − 1 , D in eq. (2.3) do not j V ∼ dimensions, and all ˆ ˆ φ φ M 4 , g D ˆ Φ M

ˆ Φand j L -dimensional gauge coupling 4 4 in the semiclassical expansion) D ,wehave ` M 4 ~ brane. This effective theory can ) − j 4 compact spatial dimensions, Φ is D th y . j , 4 1 (as observed), we require the gauge − − 4 − /M D . However, it presumably does not make . This follows from ‘na¨ y − 1 2 D D ∼ D ( D g ` 4 4 M M V ∼ 4 M − g 4. When we match onto the 4-dimensional -dimensional theory and D are coordinates for the 4 non-compact space- D = δ ∼ g D x 2 4 2 D j g 1. g X D> ∼ +  ! ∂ 4 extra spatial dimensions are compactified on a distance M , − are order 1. Note that the fields 2) is the geometrical loop factor for ˆ D Φ j M L D/

is a field localized on the are coordinates for the Γ( j 2 and bulk y . We also assume that the distance between different branes is also φ larger than its strong-coupling value, defined to be the value where D/ L π D D /M D bulk g D act as loop-counting parameters (like 1 L ` M j  L =2 is the gauge coupling in the . This ensures that contact interactions between fields on different branes ∼ r r runs over the various branes, D D D ` g j and L We assume that the standard-model gauge and Higgs fields propagate in the We assume that the We can use eq. (2.3) to read off the value of the We neglect the effects of gravitational curvature. For an explicit supersymmetric example and calculations, see ref. [12]. 2 1 , the lagrangean is [9] bulk M where which is unacceptable. In order to have have canonical kinetic terms. TheL idea behind eq. (2.3) is that the factors multiplying volume of the compact dimensions. If of order arising from states above the cutoff are suppressed by the Yukawa factor where loop corrections are orderanalysis’ 1 (NDA) [14, at 15], thetheories which scale [16]. is known If to we assume work that extremely the well loop in corrections supersymmetric are suppressed by bulk. Bulk gaugeis fields an have irrelevant a interaction gauge for coupling all with mass dimension 4 theory at the compactification scale, the effective 4-dimensional gauge coupling is coupling to be larger than unity in units of sense to take where be treated using the usualmost techniques general of interactions effective of field the theory, assumed and degrees parameterizes of the freedom below the scale of order couplings in that cancel the loopStrong coupling factors corresponds and to ensure that loop corrections are suppressed by time dimensions, a bulk field, and JHEP01(2000)003 =1 (2.7) (2.6) (2.5) , N  i ) . c . . 4 − +h D 4 d V /` 4 H − D u 8 5 4 4 4 4 52 ` , D − − − − − − H − ) max M 10 10 10 10 10 10 10 obs Mr 2 +( 2 φ × × × × × × hid − d × ˆ e M F H † obs † d φ ∼ H )( d + is the maximum length of a cycle of -dimensional theory, we find 2 H + 72 03 84 84 max hid  + . . . . . are the Higgs fields, normalized to ˆ u D 1811 2 3 φ 8 8 7 7 c 118 4 ,m .  max H . u Mr † hid Sphere: † u L c u,d 2 H . ˆ φ +h H ( H h 2 d θ 7 5 4 4 3 / 5 14 +h 4 162 − − − − − H 1 and using eq. (2.2). The results are shown − d hid − α u max ˆ φ 10 10 10 10 10 10 ∼ W H 10 Z α dimensions. (More precisely, these are  † hid ML × × × × × × × † hid ˆ 2 φ − Mr ˆ W φ e 4 D ,Bµ,m − M  − e 4 hid 1 D 3 ˆ − φ − ∼ 3 D 4 M 1 D max − V is the maximum radius of the sphere. /` 4 2920 6 16 5 14 3 13 9 1 63 2 1 D + 740 3 M − D Torus: ` brane D ML M 1 by setting  max L r θ θ M ∼ 4 2 ∆ d d 7 8 9 5 6 4 D 10 11 hid g M ˆ Z Z F  4 D ` ∼ ` 4 D ` ` + ,µ is the gauge field strength and 2 Estimates of the maximum size and exponential suppression factor for propaga- / ∼ α 1 W m brane To see how much suppression is required, note that the dangerous contact terms L ∆ where superfields obtained by projectingspecific the example, bulk see supermultiplets ref. onto [12].) the Matching branes. to the For a in table 1.the We extra see dimensions that can the beconclusions exponential substantial hold suppression even for for factor the many Higgs due extra interactions. to dimensions [9]. the large Similar have size the of form (using eq. (2.3)) where the observable fields (butized. not the This hidden fields) must have beHiggs been SUSY compared canonically breaking normal- with parameters. the From operators eq. that (2.3) give we rise obtain to the gaugino and a symmetric torus, and We can obtain thewith the maximum fact value that for the size of the extra dimension consistent Table 1: tion between two branes of maximal separation. have canonical kinetic terms in JHEP01(2000)003 , 4 5 ). − 2 D / /M 10 2 1 (2.8) coun- (2.10) × 16 43 85 3.4 130 3 =16 Sphere: local Bµ/m L , ' Estimates of  8 2 / − ˜ 2 1 s e for the symmetric m 10 28 69 3.4 1TeV 160 . 2 Torus: /  4 2 1 Bµ/m ) /M 4 − =8 6 5 7 8 9 D 10 torus and thesize sphere. of theis The chosen extra so dimension nential that the suppressionis expo- of factor order (approximately the maximum suppression forThis large meanshas that cycle the length and torus ther sphere has radius TableBµ/m 2: , × 4 ` (4 ∼ . (2.9) 4 4. As − ! ˜ s D ˜ ∼ 2 s ˜ 2 d V 2 m 4 m / 2 1 − 6

D . M Im , the exponential 2 4 D ` Bµ/m ` ! /M =5compactifiedon ∼ hid , M ˆ 20 and 2 F D  / 1toobtainthelastes- 5 2 1

∼ − Bµ ˜ s ∼ m L 10 m Mr 4 − g 1TeV is plausibly sufficient to suppress FCNC’s. × e  4 5 ) − ∼ 3 − ∼ 2 vis term and the Higgs mass-squared terms are enhanced by a volume -dimensional theory, this diagram is therefore calculable. From the 200 GeV. Using the experimental constraints 10 10 -dimensional theory that can cancel a possible overall divergence. m to 10 D − ∼ D × e ∆ 3 Bµ − 1% to obtain all SUSY breaking parame- (6 /M 10 ∼ . vis 4 ∼ For example, ˜ ˆ s ˜ 2 s F ˜ d 2 /` 3 m m Mr The contribution to visible sector scalar masses We now discuss the loop effects that communicate SUSY breaking to the visible The values eq. (2.7) are the values renormalized − This point was missed in an earlier version ofFor a this complete paper. discussion, It seeMultiloop was e.g. diagrams pointed ref. may out [17]. have in subdivergences, ref. but [13], these which can always be cancelled by countert- e 3 4 5 suppression is wherewehaveimposed so the number of extracoupling dimensions estimate increases, is the approached rapidly. strong See table 2. from contact terms is ters of the same sizeof [9]. extra dimensions, However, for the abe fundamental small theory strongly number need coupled not atcan the naturally fundamental obtain scale, all and SUSYthe we breaking same terms size. close For to examplea for circle with circumference Given a specific timate. We see thatat if the the fundamental theory scale,order is we 1 strongly require coupled a fine tuning of Note that the factor. sector fields, such as those illustratedcause in the figure separation 1. of the These hiddenregulator are and ultraviolet for visible convergent branes these be- acts diagrams. as a Another physical way point-splitting to see this is that there is no at the compactification scale; werequire will later see that we appeared while this paper was being completed. See also ref. [9]. erms localized on one of the branes. terterm in the JHEP01(2000)003 (2.12) (2.11) .This 2 / 1 m , 2  4 , hid 2 M F / 1 2 2 4 π m g 2 16 2 4 π g  16 ∼ ∼ d , generated from higher-dimension 2 H 2 vis / can be rotated away using a combi- 1 m A m ∆ B ∆ , u terms of order 2 H 7 and A m ,and , µ ∆ 2 B / , 2 1 µ m 2 , 2 4 π 4 g transformations, leaving a single phase in hid 16 M F R 2 to the weak scale gives large additive contributions to the ∼ 2 4 π c g 2 vis µ . The effects of this cutoff can be absorbed into a counterterm 16 m -dimensional theory. However, we will see that the RG running /r ∼ 1 ∆ D λ and U(1) ∼ m is the 4-dimensional Planck scale [3, 5]. The other soft terms also get c PQ ∆ µ M is the gaugino mass. The precise value of the counterterms is calculable if & 2 / 4 1 M m There are many other aspects of the higher-dimensional theory that we could Note that the soft terms arising from contact terms are larger than the anomaly- The higher-dimensional origin of these theories can also solve the ‘SUSY CP phase can vanish naturallyin the in lagrangean the localizedcause present on loop model effects the do if visible notbrane. CP brane. generate This local is This situation CP-violating violated can is terms ariselocalized in only a (for the on by natural example) bulk if assumption the or terms CP the be-moment, visible is hidden broken we brane. spontaneously must by also fields pressed (In assume [19].) order that to the effects avoid of a the large QCD neutrondiscuss, vacuum but electric angle the dipole basic are features sup- that of the the visible scenario and depend hiddenof only sectors the on are higher-dimensional the spatially model qualitative separated. feature would have A to complete take specification into account the fact that there for the visible sector scalar masses and operators in eq. (2.6).nation The of phases U(1) in visible soft masses, and thethe final counterterm. results We are will rather therefore insensitive be to content the with precise themediated value simple contributions, of estimate which above. give contributions larger than theirabove. anomaly-mediated values Therefore, from we the canmodels. neglect RG, the as anomaly-mediated discussed contribution in this class of problem’ [18]. This problem arisesing terms from the must be fact that muchelectric less the than phases dipole 1, in moments otherwise the theyness SUSY in give break- problem conflict rise because to with electron CPand experimental and is it neutron bounds. (apparently) must be maximally ThisCP-violating explained violated phases is why in can it appear a the in is natural- CKM not matrix, violated in all terms. In the present model, point of view ofcutoff of 4-dimensional order effective field theory, the extra dimensions act as a where of the soft masses from we fully specify the where JHEP01(2000)003 Z M (3.1) .(Wedo , 2 / GUT 1 in making our M m ∼ GUT , is one to two orders 2 M / c 1 µ m ,µ,B and 2 = / c 2 1 3 µ to be close to the unification m M renormalized at c , t ∼ = µ 2 2 . y / d 2 2 π 2 2 1 / 2 H π 1 m 16 M , which is most naturally taken to be m 16 ,m = ∼ M ,and u ∼ 1 2 H 2 B 8 from the observed value of the top quark. , A m M m β µ , d 2 H m . We have also seen that terms: , u /r 1 2 H A m , as suggested by the success of gauge coupling unifica- ∼ , solutions, so we neglect all other Yukawa couplings.) The 2 GeV. We therefore identify c Higgs masses: / µ 1 GUT β : 16 Gaugino masses: m M 10 GUT × M 2 ∼ orbifold is easily constructed [12, 9]. Another important feature of the at the weak scale fixes tan 2 Squark and slepton masses: then fixes two more parameters. We see that we are left with essentially 4 t Z y β GUT / 1 M S We will further assume that the theory is embedded in a grand-unified theory = 5 or 6. If we neglect the small loop-suppressed parameters, the model is defined value of not consider large tan scale The requirement that electroweak symmetry breaks with the correct value of close to the string scale. Therefore, we expect of magnitude below the fundamental scale We have argued above that theseD conditions can emerge naturally inby this the scenario 6 for parameters estimates. (GUT) at the scale tion in the MSSM.renormalized We at therefore consider the following SUSY breaking parameters and tan parameters. 3. Phenomenology We now turn to thebreaking phenomenology parameters of in thesecompactification models. the scale We effective have 4-dimensional seen that theory the are SUSY determined at the are more supersymmetries in higheror dimensions. explicitly This (e.g. may bymust be an be broken orbifold), consistent spontaneously and with SUSY. couplingson An between a explicit bulk example and with boundary 5 dimensions fields compactified higher-dimensional theory is themechanisms stabilization that of are the appropriate extra forrefs. dimensions. the [20, scenario Stabilization we 6]. are We consideringfield conclude are that theory discussed there in models is ofthis no the obstacle type type to can outlined constructing beleft here. realistic derived for effective The future from work. question a of more whether fundamental a theory model such of as string theory is JHEP01(2000)003 & β (3.2) (3.3) ;weuse β GeV down 16 no in ref. [24] 10 × , and the values of , which is important µ =2 β by imposing electroweak and GUT 2 B 3). We use input values of 2 . We also find that tan / . M ) 1 β u m (24 H and / † u , µ H ( ∂c =1 ∂v taken to be the heaviest of the stop )tobe[23]  c ˜ t v ˜ t t m . These approximations could be refined, m m GUT GUT W α 9 M ln µ at the GUT scale. This distinguishes this 2 4 t y π u 3 8 , we easily obtain spectra where the LSP is a 2 H u  and determine 2 H sensitivity = = >m H GUT >m V d mainly influences the value of tan M 2 H d ∆ t 2 H m y at renormalized at m t t = 500 GeV, using y y 20). However, it is argued by Anderson and Casta˜ W & µ ,and d 2 H (a coupling renormalized at m c , u is the Higgs VEV and the derivative is taken with all other couplings at the 2 H ) = 165 GeV, which includes 1-loop QCD corrections. We minimize the Higgs v m W , We evolve the 1-loop RG equations from the scale Some parameter choices that give rise to realistic spectra are given in table 3. An important issue when analyzing the spectrum at the weak scale is the ra- An important feature of these results is the amount of fine-tuning required to 2 µ / ( t 1 5 is preferred in order to have a sufficiently large mass for the lightest neutral . to the Higgs potential. because the lightest Higgs boson is light for small tan where GUT scale held fixed. The largest sensitivity is to neutralino. The value of m to the weak scale model from ‘no-scale’ models.points This in is table illustrated in 3. the second For and third parameter mass eigenstates, and potential including the term eq. (3.2) with the sensitivity parameter arestrongly given in as table the 3. superpartnerwhere We masses the see are superpartner that increased. masses theparameter are is sensitivity Note large increases close ( that to even the for experimental parameters limits, the sensitivity but they will sufficemodels. to illustrate the main features of theWe spectrum find that of the this dependence onis class the what of overall scale would of be thefine-tuning expected: initial required SUSY to the breaking achieve electroweak masses superpartners symmetryThe right-handed breaking become sleptons increases heavier, get (see an and below). importantFayet-Iliopoulos positive the contribution term amount from a if of hypercharge diative corrections to thebe lightest viewed neutral as Higgs apotential mass below top the [21]. loop stopthe contribution mass The term [22]. to largest an We effect include effective can an quartic estimate term of this in effect the by effective adding achieve electroweak symmetry breaking.parameter We define the fractional sensitivity to a Higgs. 2 symmetry breaking. Them value of the top quark mass is used to fix tan JHEP01(2000)003 2 / 1 m allowed choices of 2 2 50 78 0.8 2.5 160 285 280 690 875 945 910 945 905 400 725 510 165 315 630 650 315 645 100 860 860 860 1050 (400) (400) Point 3 apriori 2 2 50 78 0.8 2.5 200 275 265 685 875 945 905 950 910 400 755 635 165 315 650 670 315 670 100 995 1000 1000 1000 (400) (600) Point 2 10 implies that the parameter 2 2 ∼ 16 19 78 90 0.8 2.5 105 140 125 350 470 470 450 475 455 520 200 370 315 140 320 360 140 350 490 490 495 (200) (300) 10 Point 1 2 2 0 d u β ± 0 1 0 2 0 3 0 4 0 L ± 1 ± 2 1 2 R L L L R R 3 / / A ˜ ˜ t t ˜ t ˜ ˜ ˜ h ˜ ˜ e χ χ χ χ ν ˜ e d u d u 2 H χ χ H 2 H 1 1 H µ µ y B M m m m m m m m m m m m m m m m m m m m m m m m tan 400 GeV. stops: Higgs: gluino: ∼ inputs: sleptons: charginos: sensitivity: neutralinos: other squarks: Sample points in parameter space. All masses are in GeV. In the first two points, should be less than parameters. From this point ofmasses view, the is fine-tuning much ofwith points less with light low severe, superpartner superpartner and massesparameter naturalness [24]. defined clearly in In ref. favors particular, [24] regions requiring be of that less parameters the than naturalness that sensitivity does not captureif the idea the of physical fine-tuning: quantities significantly the more theory is sensitive fine-tuned than only Table 3: the LSP is mostlyparameter Bino, is defined while in in the the main third text. it is a right-handed slepton. The sensitivity JHEP01(2000)003 B Nucl. Phys. (1997) , , (1997) 18 ]; ]; B 414 79 Nucl. Phys. , (1981) 353; Phys. Lett. , ]; Dynamical soft terms with hep-ph/9705307 hep-ph/9507378 Phys. Rev. Lett. B 192 , Low-energy supersymmetry New tools for low-energy dynamical Theories with gauge-mediated super- (1998) 12 [ (1996) 2658 [ hep-ph/9408384 ]; Supersymmetric technicolor Nucl. Phys. , 11 Low-energy dynamical supersymmetry breaking B 510 . D53 Supercolor (1995) 1362 [ Dynamical supersymmetry breaking at low-energies Nucl. Phys. Phys. Rev. , hep-ph/9303230 , D51 ]; hep-ph/9801271 , ]; A model of direct gauge mediation (1982) 96; (1993) 1277 [ Simple gauge-mediated models with local minima Phys. Rev. , B 207 D48 (1981) 575; hep-ph/9706554 hep-ph/9705271 S. Dimopoulos and S. Raby, 189 M. Dine, A.E. Nelson and Y.simplified Shirman, L. Alvarez-Gaume, M. ClaudsonPhys. and M.B. Wise, Rev. M. Dine and A.E. Nelson, M. Dine, A.E. Nelson, Y. Nir and Y. Shirman, supersymmetry breaking H. Murayama, S. Dimopoulos, G. Dvali, R. Rattazzi and G.F. Giudice, [ unbroken supersymmetry For a review, see G.F. Giudice and R. Rattazzi, M.A. Luty, 71 [ symmetry breaking While this work was being completed, we received ref. [13], which considers very [1] M. Dine, W. Fischler and M. Srednicki, References Acknowledgments M.A.L. and E.P. areA.E.N. supported are by supported the by the NSF DOE under under grant contract PHY-98-02551. DE-FGO3-96-ER40956 Z.C. and similar ideas. This model is thean simplest acceptable supersymmetric spectrum for theorystandard the in flavor-changing superpartners the processes while literature anddictive, explaining that electric with the generates squark dipole absence and of moments.supergravity non- models. slepton masses It The nonuniversality qualitatively is ofthe similar the GUT highly scale up- to pre- can and those distinguish down-type thisdifference of Higgs theory between masses the from ‘no-scale’ up at ‘no-scale’ and supergravity—the down expected Iliopoulos type Higgs term masses which generates affects a hypercharge theand Fayet- slepton the lightest mass neutralino spectrum. areobtaining The significantly lighter natural right-handed than electroweak sleptons the symmetry other breakingroughly superpartners, requires 200 and that GeV. these be lighter than 4. Conclusions JHEP01(2000)003 , , ]; ]; B J. , D55 (1999) 08 (1999) 503 Phys. Lett. (1998) 329 (1990) 377; Nucl. Phys. , U(1), Phys. Rev. B 544 hep-ph/9702359 hep-ph/9710204 B 246 , B 431 ]; soft masses in theories ]. Gaugino mass without sin- symmetry for the more mini- (1998) 70 [ ]; Phys. Lett. Nucl. Phys. (1997) 1598 [ Realistic anomaly-mediated su- , , Phys. Lett. J. High Energy Phys. ]. ]; , U(1) mediated SUSY breaking, fermion Dynamical supersymmetry break- , ]; B 516 D56 hep-th/9310151 U(1) as a mediator of supersymmetry breaking hep-ph/9810442 Millimeter range forces in superstring theo- ; Heavy thresholds, slepton masses and the mu 12 U(1) hep-th/9510209 Nucl. Phys. Phys. Rev. Out of this world supersymmetry breaking ]; , , hep-th/9603142 (1994) 69 [ hep-ph/9903448 ]; hep-ph/9607383 Anomalous (1998) 027 [ Sparticle masses from the superconformal anomaly . ]; Limits on extra dimensions in orbifold compactifications Radius stabilization and anomaly-mediated supersymme- Horizontal, anomalous 12 B 326 Heterotic and type-I string dynamics from eleven dimen- Gaugino condensation and the anomalous Anomalous (1996) 506 [ Eleven-dimensional supergravity on a manifold with bound- (1996) 94 [ hep-ph/9905390 (1999) 013 [ ]. , (1996) 3728 [ 05 hep-th/9607172 B 460 ]. ]; B 475 . 77 hep-th/9602070 Phys. Lett. , A possible new dimension at a few TeV hep-th/9910202 hep-ph/9608441 , Strong coupling expansion of Calabi-Yau compactification (1996) 503 [ Nucl. Phys. J. High Energy Phys. rava and E. Witten, rava and E. Witten, , hep-ph/9906296 (1996) 135 [ Nucl. Phys. , , hep-ph/9803432 hep-ph/9810410 Phys. Rev. Lett. B 389 P. Binetruy and E. Dudas, R.N. Mohapatra and A. Riotto, masses and natural suppression(1997) of 1138 FCNC [ and CP-violatingA.E. Nelson effects and D. Wright, mal supersymmetric standard model [ N. Arkani-Hamed, M.ing in Dine models and with S.P. a Martin, green- schwarz mechanism hep-th/9810155 sions P. Hoˇ ary E. Witten, 471 glets High Energy Phys. try breaking Z. Chacko, M.A. Luty, I.persymmetry breaking Maksymyk and E. Ponton, E. Katz, Y. Shadmiterm and in Y. anomaly Shirman, mediated supersymmetry breaking 015 [ I. Antoniadis and K. Benakli, of superstrings I. Antoniadis, S. Dimopoulos and G.ries Dvali, with weak scale compactification I. Antoniadis, S.with Dimopoulos, supersymmetry A. breaking by Pomarol TeV compactification and M. Quiros, [ [2] G. Dvali and A. Pomarol, [3] L. Randall and R. Sundrum, [4] P. Hoˇ [5] G.F. Giudice, M.A. Luty, H. Murayama and R. Rattazzi, [7] A. Pomarol and R. Rattazzi, [6] M.A. Luty and R. Sundrum, [8] I. Antoniadis, JHEP01(2000)003 , , , ]. B Nucl. (1998) , (1999) 001 Nucl. Phys. supergravity ]. , D57 11 Nucl. Phys. , =1 hep-ph/9812489 N Benjamin/Cummings, problem in supergravity Phys. Rev. ]; , ]. µ ’s in strongly coupled super- . hep-th/9712214 A complete analysis of FCNC π 4 (1999) 095008 [ Theroadtonoscalesupergravity J. High Energy Phys. , D60 Supersymmetry breaking through trans- Counting hep-ph/9803258 No scale supersymmetric guts A very light gravitino in a no scale model hep-ph/9706275 . Implication of exact SUSY gauge couplings Massive higher-dimensional gauge fields as (1998) 065002 [ hep-ph/9909248 Supersymmetry and electroweak breaking from 13 , CP-violation in the minimal D58 Phys. Rev. Transmission of supersymmetry breaking from a 4- ]. , A natural solution to the Yang-Mills theory (1997) 301 [ Soft supersymmetry breaking in deformed moduli spaces, Chiral quarks and the nonrelativistic quark model (1988) 480. (1999) 035005 [ Flavor conserving CP-violation in invisible axion models (1985) 413. =2 hep-ph/9911293 , N Phys. Rev. ]; B 412 , D59 B 206 B 255 (1986) 241. (1984) 99; ]. hep-ph/9604387 (1987) 1. ıve dimensional analysis and supersymmetry (1984) 189; Weak interactions and modern particle theory, B 276 Na¨ B 147 145 Phys. Lett. Phys. Rev. , Phys. Lett. , , Nucl. Phys. (1984) 373; B 234 , hep-ph/9706235 (1996) 321 [ hep-th/9908085 A. Delgado, A. Pomarol and M. Quiros, extra dimensions at the TeV scale messengers of supersymmetry breaking dimensional boundary theories Phys. Lett. B 247 For a review, see A.B.Phys. Lahanas, Rep. D.V. Nanopoulos, J. Ellis, C. Kounnas and D.V. Nanopoulos, parent extra dimensions Phys. Menlo Park 1984; H. Georgi and L. Randall, H. Georgi, Nucl. Phys. 1531 [ symmetry A.G. Cohen, D.B. Kaplan and A.E. Nelson, for QCD M.A. Luty and R.conformal Rattazzi, theories and [ and CP constraints in general SUSY extensions of the standard model 477 theory [9] Z. Chacko, M.A. Luty and E. Ponton, [10] G.F. Giudice and A. Masiero, [12] E.A. Mirabelli and M.E. Peskin, [11] J. Ellis, K. Enqvist and D.V. Nanopoulos, [13] D.E. Kaplan, G.D. Kribs and M. Schmaltz, [15] M.A. Luty, [14] A. Manohar and H. Georgi, [16] L. Randall, R. Rattazzi and E. Shuryak, [17] F. Gabbiani, E. Gabrielli, A. Masiero and L. Silvestrini, [18] M. Dugan, B. Grinstein and L. Hall, JHEP01(2000)003 ]. Nucl. Phys. Phys. Phys. (1991) (1995) , , , , ]. Phys. Rev. Phys. Rev. Phys. Lett. , , , (1991) 1; B 347 B 267 85 hep-ph/9307201 (1991) 1815; (1984) 387; 66 Phys. Lett. Phys. Lett. , hep-ph/9412322 , B 136 (1978) 223; (1993) 4280 [ On radiative corrections to super- 40 Prog. Theor. Phys. D48 , (1995) 1693 [ The supersymmetric Higgs for heavy su- Phys. Rev. Lett. Phys. Lett. , , ? (1991) 83; Upper bound of the lightest Higgs boson mass z 14 ]. D52 M Phys. Rev. Radiative corrections to the masses of supersym- Modulus stabilization with bulk fields Measures of fine tuning , Current mass ratios of the light quarks Phys. Rev. Lett. B 257 , The renormalization group improved Higgs sector of (1991) 167; no, CP conservation in the presence of instantons Can the mass of the lightest Higgs boson of the minimal Upper bounds on supersymmetric particle masses (1977) 1791; Phys. Rev. Constraints imposed by CP conservation in the presence of , B 258 Naturalness and superpartner masses or when to give up on D16 ]; hep-ph/9907447 Phys. Lett. , (1978) 279; (1984) 329; (1977) 1440; (1988) 63. A new light boson? Naturally weak CP violation Phys. Lett. Problem of strong P and T invariance in the presence of instantons Nucleosynthesis constraints on cosmic strings Phys. Rev. Solving the strong CP problem without the Peccei-Quinn symmetry , 40 53 38 , (1986) 2004. (1999) 4922 [ (1991) 477; B 306 56 83 hep-ph/9409419 J. Ellis, G. Ridolfimetric and Higgs F. bosons Zwirner, S. Weinberg, instantons Rev. Lett. symmetric Higgs boson massesB and 262 their implicationsR. for Barbieri, LEP M. searches Frigeniperpartners and F. Caravaglios, M. Quiros, 27. the minimal supersymmetric model F. Wilczek, Rev. Lett. A.E. Nelson, Phys. Rev. Lett. D.B. Kaplan and A.V. Manohar, S.M. Barr, 300 [ weak scale supersymmetry Lett. in the minimal supersymmetric standard model H.E. Haber and R. Hempfling, supersymmetric model be larger than Lett. [19] R.D. Peccei and H.R. Quinn, [22] H.E. Haber and R. Hempfling, [23] R. Barbieri and G.F. Giudice, [24] G.W. Anderson and D.J. Casta˜ [20] W.D. Goldberger and M.B. Wise, [21] Y. Okada, M. Yamaguchi, T. Yanagida,