Status of Supersymmetry Breaking Scenarios. Lisa Everett University of Wisconsin, Madison

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1 Status of Supersymmetry Breaking Scenarios Lisa Everett University of Wisconsin, Madison

2 Outline of Presentation Introduction/Motivation The MSSM Parameter Space (Incomplete) Taxonomy of SUSY Models and (qualitative) LHC Implications Standard mediation mechanisms: minimal models (paradigm: msugra/cmssm) Examples of theory-motivated models (top-down and bottom-up). (example: Deflected Mirage Mediation) Conclusions and Outlook

3 Introduction/Motivation TeV scale SUSY: intriguing hypothesis, here since 70 s, 80 s Many benefits/features: SUSY (i) Higgs hierarchy problem (ii) Gauge coupling unification (iii) Higgs sector/radiative EW breaking (iv) Dark matter candidate, LSP (for free ) (v) May provide the baryon asymmetry (v) Sparticles decouple from low energy processes

4 Good for some phenomenology, but not all... (i) CP and flavor problems (unlike SM) (ii) protection from B,L violation requires extra symmetry (unlike SM) SUSY (iii) no superpartners yet: mild tension of SUSY mass scale wrt EW scale (little hierarchy) (iv) cosmological gravitino, moduli problems Still, arguably most robust known framework. Definitive tests in LHC era! Focus here on MSSM: 2 Higgs doublets, conserved R-parity

5 The MSSM and its Parameter Space MSSM fields: tan β = H u H d Supersymmetric interactions: MSSM reviews: Martin 97, Chung et al. 03, many others...

6 Soft supersymmetry breaking: gaugino masses M 1,2,3 bilinear scalar coupling b Bµ trilinear scalar couplings à αij = A αij Y αij soft scalar mass-squares m 2 f ij 105 new parameters!

7 How to cope with this impractically vast # SUSY flavor/cp problems. of parameters? No cartography of the full viable parameter space exists, but many constraints! absence of FCNC (1st and 2nd generations, 3rd weaker) Reδ ( f) i=j Re m2 f i=j m 2 f O(10 2 ) Imδ ( f) i=j O( ) SUSY (flavor-indep.) CP problem. EDM constraints on flavor-diagonal phases (or cancellations) (φ 1f = φ µ + φãf φ b, φ 2λ = φ µ + φ Ma φ b ) O(10 2 )

8 Assumption: invoke Minimal Flavor Violation (MFV) also set flavor-diagonal CP phases to zero relevant for collider phenomenology gaugino masses: M 1,2,3 scalar mass-squares: trilinears (3rd gen): A t,b,τ 1st, 2nd gen: m 2 Q,u,d,L,e Higgs parameters: 3rd gen: µ, Bµ m 2 Q 3,u 3,d 3,L 3,e 3 Note: flavor-diagonal phases can be nonzero (care needed with EDMs). If nonzero, they are relevant for collider physics. Won t consider this here.

9 1. Study this set (or just certain regions that are phenomenologically motivated) explicitly. Supersymmetry Without Prejudice see also: Minimal Reasonable Models (subset of above+flavor-diagonal CP phases) C. Berger et al. 08, Djouadi et al. 02 Brhlik, Kane Build models of SUSY breaking to reduce the ~20 parameters to a manageable set. Here: (incomplete) taxonomy of models +LHC implications. Start w/hidden sector paradigm (example: msugra/cmssm). Go further to explore other theory-motivated examples.

10 Theoretical and Experimental Constraints on the Soft Breaking Sector (I) Neutral stable LSP (lightest superpartner) consequence of assumed R-parity Electroweak symmetry breaking radiative EWSB, stable minimum, no CCB or UFB,... mu/bmu problem missing transverse energy collider signatures often avoid it and trade Z mass, tan(beta) challenge in many scenarios to generate mu and B at the same order Fine-tuning and little hierarchy problem

11 Theoretical and Experimental Constraints on the Soft Breaking Sector (II) Direct collider bounds on (s)particle masses m h > 100 GeV (soft) m τ1 > 98.8 GeV m χ ± 1 m t 1 > GeV > GeV Note: many bounds depend on sufficient mass splitting b/w LSP, NLSP Indirect constraints < ρ < a µ Br b sγ =( ) 10 4 Br Bs µµ < electroweak constraints, rare decays, muon g-2,...

12 Theoretical and Experimental Constraints on the Soft Breaking Sector (III) neutralino LSP dark matter hypothesis Assumption: standard cosmology, WMAP3 WMAP7 neutralino as thermal wimp (2σ) (1σ) generically need well-tempered neutralino (admixing of EW-inos) Note: not necessary (or possible) in some scenarios other options: gravitinos, axinos, non-susy...

13 SUSY Model Building Hidden sector paradigm: hey, SUSY s broken cool. Hidden sector (SUSY broken) Φ F Φ order parameter of SUSY breaking Observable sector (SM) mediation mechanisms: gravity, gauge, anomaly/ bulk

14 Standard Scenario: Gravity Mediation Polonyi; Chamseddine, Arnowitt, Nath, s Soft terms depend on details of Plancksuppressed couplings between sectors Hidden sector (SUSY broken) Φ F Φ hey, SUSY s broken Observable sector (SM) cool. scale of soft terms: m SUSY example of high scale mediation F M Pl

15 msugra/cmssm Minimal Supergravity (msugra) tree-level gaugino mass generation (universal gauge kinetic functions) 5 parameters: (4 + 1 sign) universal gaugino mass universal scalar mass universal trilinear coupling plus tan β and sign(µ) + canonical Kahler potential a.k.a. constrained MSSM (CMSSM) specified at high (unification) scale m 1/2 m 0 A 0

16 LHC7 reach in msugra/cmssm Baer, Barger, Lessa, Tata

17 LSP Dark Matter in msugra/cmssm DM-allowed regions Ellis, Olive, et al. (updated regularly),...

18 General features of msugra/ CMSSM models colored sparticles heavier than uncolored sparticles lighter electroweak -inos can also have light sleptons gaugino code: M 1 : M 2 : M 3 =1:2:6 Choi, Nilles 08 relatively easy to solve mu/bmu problem

19 Feldman, Liu, Nath 07

20 Lessons to learn (and not to learn) from msugra/cmssm Useful, practical framework. But beware of standard lore! For example, msugra DM indicates that bulk region (1.): many light sfermions that can be seen at LHC funnel region (3.): only at large tan(beta), affects cascade decays well-tempered neutralino only in focus point region (4.) All of these conclusions can be invalidated even in simple 1-parameter extensions of msugra! (more on extended models shortly) Baer et al,

21 Gauge Mediation Mediator X (gauge singlet), SM charged messengers ψ, ψ hey, SUSY s broken cool. Hidden sector (SUSY broken) X F X Xψ ψ m SUSY 1 F X 16π 2 X mediation scale can be low--high Observable sector (SM) Dine, Fischler, s, Dine, Nelson, Shirman, 96,... Seiberg, Shih et al., 08

22 General features of minimal GMSB models Parameters: M mess = X, Λ = g2 F X 16π 2 X,N, tan β (N= # messenger pairs) stretched spectrum similar gaugino code as msugra gravitino LSP NLSP: stau or neutralino solve flavor problem!

23 Anomaly Mediation* Loop-order SUSY breaking from scale invariance anomaly chiral compensator hey, SUSY s broken Konishi; Kaplunovsky; s -90 s, Randall + Sundrum; Luty et al, 99 cool. Hidden sector (SUSY broken) C F C m SUSY 1 F C 16π 2 C Observable sector (SM) negative slepton mass problem: add common m0 in minimal models *caveat: claim (de Alwis) that standard results are not correct (more later)

24 General features of minimal AMSB models Parameters: m aux = F C C,m 0, tan β stretched spectrum (details depend on fix of slepton problem) gaugino code M 1 : M 2 : M 3 =3.3 :1:9 wino LSP NLSP: chargino (nearly degenerate) may solve flavor problem

25 Mediators side-by-side Gravity: Gauge: Anomaly: m SUSY m 3/2 F F M Pl M Pl m SUSY 1 F X 16π 2 X m 3/2 F X M Pl m SUSY 1 F C 16π 2 C m 3/2 F C C!!!"! #$%&!!!"! #$%&! #$%&!!!" tree level one-loop level one-loop level 4-*(2,,5(2*$*2

26 Mediators side-by-side (II) Gravity Gauge Anomaly* m SUSY F m M SUSY 1 F X Pl 16π 2 X m SUSY 1 F C 16π 2 C Lightest sparticle (LSP): U(1) Y gaugino/higgsino gravitino SU(2) L gaugino Solves: mu/bmu problem flavor problem flavor problem (?) UV sensitivity problem Distinctive features: variable spectrum long lived NLSP stretched spectrum long lived chargino depends on fix of tachyonic slepton

27 Beyond Minimal Models Theory-motivated models involving some or all of the previous mediation mechanisms, or new mechanisms (i) Bottom-up motivation solve problems of MSSM, improve/extend known scenarios (ii) Top-down motivation GUT or string-derived (or -motivated) models not a clean taxonomy! next level of classification: single or multiple mediation mechanisms

28 Extensions of msugra (i) Supergravity theories: msugra+ separate common soft mass for 1st, 2nd gen separate soft mass(es) for Higgses nonuniversal gaugino masses lowered unification scale wide variety of possible DM-allowed spectra! Baer, Tata et al., Ellis, Olive et al.,...

29 Extensions of minimal GMSB (i) Gauge mediation models many examples, including gauge messenger models direct mediation models (eliminate messenger sector) semi-direct gauge mediation Unified approach of Seiberg et al. General Gauge Mediation (GGM): obs. and hidden sectors decouple if gauge couplings set to zero more parameters than minimal GMSB, wider variety of spectra

30 Bulk Mediation Models (i) extra-dimensional scenario: mediation by bulk field couplings (may be at tree or loop level) bulk field hey, SUSY s broken cool. Hidden sector (SUSY broken) brane Φ F Φ Observable sector (SM) brane examples: standard (RS0) anomaly mediation, gaugino mediation...

31 Gaugino mediation Chacko et al., Kaplan, Kribs 99 ways out: SM gauge, Higgs fields in bulk SM quarks, leptons on observable sector brane M 1/2 =0,m 0 = A 0 =0 simple, predictive, solves flavor+cp problems difficulty: stau is LSP gravitino LSP, running above GUT scale, include anomaly mediation contributions (gaugino-assisted anomaly mediation) mixed SUSY breaking (but why are terms of same order?) Schmaltz, Skiba 00; Kaplan, Kribs 00

32 Extensions of minimal AMSB (i,ii) Deflected anomaly mediation Pomarol, Rattazzi 99 naturally comparable anomaly and gauge mediation terms F X X 2 n 1 F C C W Xn Λ n 3 Hypercharged anomaly mediation unusual spectrum with heavy bino, sleptons Dermisek,Verlinde, Wang 07 AMSB+ Z gaugino mediation NMSSM-like scenario, addresses mu/bmu problem Note: can also consider Z mediation alone. Addresses mu/bmu problem, split spectrum with heavy scalars de Blas et al. 09 Langacker et al. 07

33 Gaugino anomaly mediation (inoamsb) (i,ii) anomaly-mediated contributions only to gaugino masses so no slepton AMSB problem! de Alwis 08; Baer, de Alwis et al. 10 Parameters: m 3/2, tan β can get viable models (stau LSP avoided) gaugino code same as std AMSB very minimal, predictive scenario

34 Theory-motivated models: supergravity theories from string theory (ii) Moduli as mediator fields e.g. Kahler modulus T hey, SUSY s broken cool. Hidden sector (SUSY broken) T F T Observable sector (SM) m SUSY F M Pl F T T + T T M Pl primary issue is moduli stabilization: many recent developments many talks at SVP workshop!

35 Models based on G2 constructions of M theory. moduli stabilized from non-pert. hidden sector dynamics mixed SUSY breaking scenario: gravity+anomaly mediation strongly split spectrum: very heavy scalars + higgsinos light gauginos --wino LSP Acharya, Kane, Bobkov, Kumar, Kuflik, Shao, Torabian... Models based on Large volume compactifications of Type IIB supergravity theory with stringy effects moduli stabilized from fluxes and quantum corrections remarkably: flavor-diagonal at leading order (i) Conlon, Quevedo, et al... Other examples: F theory GUTs, intersecting D brane models

36 Theory-motivated mixed scenarios (ii) Motivation: top-down (KKLT: moduli stabilization in Type IIB) all 3 mediation mechanisms can have comparable contributions.,1=*6?6b$1%? mirage mediation (MM) and deflected mirage mediation (DMM)

37 Mirage Mediation (MM) KKLT scenario (Type IIB string theory) Kachru, Kallosh, Linde, Trivedi 03 Observable sector (SM) T, C stabilization of T modulus Hidden sector (SUSY broken) /75")/-)&*%'6'8%$.'9':"-5/7)$7+*)&;/ mixed modulus-gravity/anomaly mediation F T T + T 1 log(m Pl /m 3/2 ) F C C 1 F C 4π 2 C Choi et al. 05, Endo et al. 05,... >?7@ A&?7@

38 Why mirage? Apparent unification of soft terms at mirage scale Choi et al., 05 4(%&2$+,)&*$7! αm " m3/2 2 M mirage = M G M Pl ratio of anomaly to modulus mediation terms

39 Deflected Mirage Mediation L.E., I.-W. Kim, P. Ouyang, K. Zurek, , B. Altunkaynak, L.E., I.-W. Kim, B. Nelson, Y. Rao, Observable sector (SM) X T, C stabilization of T,X moduli (KKLT) Hidden sector (SUSY broken) /75")/-)&*%'6'8%$.'9':"-5/7)$7+*)&;/ X, messengers: give comparable gauge-mediated terms! F X X m 3/2 F C C m (grav) soft m (anom) soft m (gauge) soft

40 X Stabilization Case 1. Radiative stabilization (Coleman-Weinberg): F X e K 2 K XX ( X W + ( X K)W ) e K 2 W (T + T ) n X (T + T ) n X X = m 3/2 X F X X m 3/2 F C C Case 2. Stabilization by superpotential self-couplings: W Xn Λ n 3 F X n < 0, n 3 X = 2 n 1 F C same result as deflected anomaly mediation! C

41 Moral: if include X, messengers (generic): gravity, anomaly, gauge mediation all comparable! F T T + T 1 log(m Pl /m 3/2 ) F C C F X X 2 n 1 F C C n 3 or n < 0 F T T + T = m 0 F C C = α m log(m Pl /m 3/2 )m 0 F X X = α g F C C Parameters: m 0, α m, α g, tan β, X, N, {n i }, signµ usually fix these

42 MSSM MSSM +Ψ, Ψ MZ Mmess = X MG 4)56#(+%7)$$0%! " "!! $! $ # % % % % &! &' (! " '! " "! "#$$ $! #* & ""! "#$$ $ &'!"#$%&'!!"#!!! "! " "! # $ $ )! $ $ ) % $ % "!! #" $ $! ##! $! $ % % & " &! '! % & %&(! ) '!! #" "#$$ $! ( ()*#"+,-.-%"&-++/+01-%$2' *!! #" $ $! ##+)! $! $ % %!!& " *&! " #!,!! % % & % % )+(! & " *& *) " -./. '*!! #" "#$$ $! $ ' +/ ' 0 1! '#" "#$$ $ %&(!!!,'!! #%&(! $! % ( 2 " % & )!!! % & )! "! DMM Soft Terms thresholds large for α g > 0, small for α g < 0

43 Why deflected mirage? m 0 = 2 TeV, N = 3, α g = 1 Deflected mirage unification scale for gauginos: M mirage = M G m3/2 M P αm ρ/2 ρ = 1 + 2Ng π 2 1 α mα g Ng π 2 ln M GUT M mess ln M P m 3/2

44 From phenomenological viewpoint: dial between scenarios with tunable α m, α g Anomaly Mediation mirage mediation Deflected Mirage Mediation deflected anomaly mediation Gravity Mediation Gauge Mediation

45 Mirage and Deflected Mirage models: tremendous variety of superpartner mass spectra Relatively squeezed gaugino mass spectrum Consequence of mirage unification in gaugino sector. Strongest effect for large thresholds ( ) α g > 0 gluino often light (can be the next lightest superpartner) well-tempered neutralino can be easily obtained scalars can be significantly heavier than all gauginos (but still only of order several TeV or so)

46 Mirage Mediation Example: EW/TeV Mirage unification α m = 2 Mass (GeV) 1000 M 1 N = M M log 16 (µ (GeV)) 10 Mass ( GeV ) M M D3 D1 U3 M U1-500 M Q3 Q Log 16 (µ (GeV) ) 10 Mirage unification at electroweak scale, wino LSP highly compressed mass spectrum, reduced fine-tuning

47 DMM 1: nonperturbative stabilization intermediate messenger scale: M mess = GeV α m = 1 N = 3 W 1 X α g = 1 (large thresholds)

48 DMM 2: nonperturbative stabilization low messenger scale: M mess = 10 5 GeV α m = 1 N = 3 W 1 X α g = 1 (large thresholds) wino LSP

49 DMM 3: nonrenorm. op. stabilization intermediate messenger scale: M mess = GeV α m = 1 N = 3 W X 5 α g = 0.5 (small thresholds) heavier gluino

50 DMM Collider Phenomenology Parameter Set α g Value α m M 0 M mess Line A 1 2 TeV GeV τ LSP Line B 1 1 TeV 10 8 GeV g LSP g LSP Line C TeV GeV Line D TeV GeV Missing E Distribution T 2000 Events Data Set D1 D2 D3 D4 D5 MET (GeV) Model Point σ susy (pb) Trigger Eff. Line A A % A % A % A % Line B B % B % B % Line C C % C % C % C % C % Line D D % D % D % D % D % MET (GeV)

51 The LHC Era is Here! CMS first collision candidate, 11/23/09 LHC signatures dictated by soft SUSY breaking: superpartner masses collider phenomenology

52 LHC Signatures Huge variety of mass spectra in our model list: compressed, squeezed, stretched (minimal models), split SUSY signatures: well explored in minimal models but new patterns have new signatures: Example: light gluino and heavy scalars gluino decays dominantly through off-shell squarks with a preference for (lighter) 3rd generation compressed: harder to discover (soft decay products), but sparticle production rates larger

53 Summary and Outlook SUSY model building of great importance in LHC era Mediation mechanisms: gravity, gauge, anomaly/bulk Minimal models. Prototype msugra/cmssm. Must be careful not to extrapolate results naively to more general theories. Many theory-motivated non-minimal models. Deflected mirage mediation: simple but rich framework w/ distinctive phenomenology variety of spectra