(Extra)Ordinary Gauge Mediation

Transcription

1 (Extra)Ordinary Gauge Mediation David Shih IAS Based on: Clifford Cheung, Liam Fitzpatrick, DS, hep-ph/ DS, hep-th/

2 The LHC is coming... What will we see?

3 The MSSM The MSSM is still the most well-motivated possibility. Names spin 0 spin 1/ SU(3) C, SU() L, U(1) Y squarks, quarks Q (ũ L d L ) (u L d L ) ( 3,, 1 6 ) ( 3 families) u ũ R u R ( 3, 1, 3 ) d d R d R ( 3, 1, 1 3 ) sleptons, leptons L ( ν ẽ L ) (ν e L ) ( 1,, 1 ) ( 3 families) e ẽ R e R ( 1, 1, 1) Higgs, higgsinos H u (H + u H 0 u ) ( H + u H d (H 0 d H d ) ( H 0 d H 0 u ) ( 1,, + 1 ) H d ) ( 1,, 1 ) Table 1.1: Chiral supermultiplets in the Minimal Supersymmetric Standard Model. The spin-0 fields are complex scalars, and the spin-1/ fields are left-handed two-component Weyl fermions. Names spin 1/ spin 1 SU(3) C, SU() L, U(1) Y gluino, gluon g g ( 8, 1, 0) winos, W bosons W ± W 0 W ± W 0 ( 1, 3, 0) bino, B boson B 0 B 0 ( 1, 1, 0) Table 1.: Gauge supermultiplets in the Minimal Supersymmetric Standard Model.

4 MSSM, cont d But even if we are fortunate enough to discover the MSSM at the LHC, the main theoretical challenge will still be ahead of us: explaining the origin of the 100+ soft SUSY breaking parameters. L MSSM soft = 1 ( M 3 g g + M W W + M B B ) 1 + c.c. (ũ QH au u d a QH d d ẽ a LH ) e d + c.c. Q m Q Q L m L L ũ m u ũ d m d ẽ m d e ẽ m H u HuH u m H d HdH d (bh u H d + c.c.). Any explanation will have to address various problems, including: SUSY flavor problem SUSY CP problem little hierarchy problem

5 Gauge Mediation Alvarez-Gaume, Claudson, Dimopoulos, Dine, Fischler, Nappi, Ovrut, Raby, Srednicki, Wise; Dine, Nelson, Nir, Shirman Gauge mediation is a successful theory of the soft masses. It has many attractive features, including: flavor blindness calculability predictivity distinctive phenomenology SUSY sector Messengers SM gauge interactions MSSM

6 Ordinary Gauge Mediation

7 Ordinary Gauge Mediation The details of the hidden sector are generally irrelevant for determining the low-energy MSSM spectrum. Thus, it is useful to parametrize the SUSY-breaking sector in a model independent way, through a singlet spurion field X: X = M + θ F

8 Ordinary Gauge Mediation The details of the hidden sector are generally irrelevant for determining the low-energy MSSM spectrum. Thus, it is useful to parametrize the SUSY-breaking sector in a model independent way, through a singlet spurion field X: X = M + θ F By coupling X directly to messenger fields φ i, φ i transforming in vector-like representations of the SM gauge group, we obtain a simple family of gauge mediation models known as ordinary or minimal gauge mediation. W = N i=1 λ i Xφ i φi

9 Ordinary Gauge Mediation The details of the hidden sector are generally irrelevant for determining the low-energy MSSM spectrum. Thus, it is useful to parametrize the SUSY-breaking sector in a model independent way, through a singlet spurion field X: X = M + θ F By coupling X directly to messenger fields φ i, φ i transforming in vector-like representations of the SM gauge group, we obtain a simple family of gauge mediation models known as ordinary or minimal gauge mediation. W = N i=1 λ i Xφ i φi Simplest choice consistent with unification: φ i 5 φ i 5 of SU(5)

10 OGM Spectrum

11 OGM Spectrum M r = α r 4π Λ G, m f = where C r f 0 only if f is charged under the gauge group r. 3 r=1 C r f ( αr 4π Λ G = NΛ S = NF/M 100 TeV ) Λ S (leading order in F/M)

12 OGM Spectrum M r = α r 4π Λ G, m f = where C r f 0 only if f is charged under the gauge group r. 3 r=1 C r f ( αr 4π Λ G = NΛ S = NF/M 100 TeV ) Λ S (leading order in F/M) Only a few parameters determine the entire MSSM spectrum! Messenger scale: M SUSY breaking scale: F Messenger number: N

13 OGM Spectrum M r = α r 4π Λ G, m f = where C r f 0 only if f is charged under the gauge group r. 3 r=1 C r f ( αr 4π Λ G = NΛ S = NF/M 100 TeV ) Λ S (leading order in F/M) Only a few parameters determine the entire MSSM spectrum! Messenger scale: M SUSY breaking scale: F Messenger number: N In particular, spectrum is independent of the messenger couplings. So doublet/triplet splitting has no effect on the spectrum, W = λ 3 Xq q + λ Xl l λ i

14 OGM Spectrum M r = α r 4π Λ G, m f = 3 r=1 C r f ( αr 4π Λ G = NΛ S = NF/M 100 TeV ) Λ S (leading order in F/M)

15 OGM Spectrum M r = α r 4π Λ G, m f = Some features of the OGM spectrum: 3 r=1 C r f ( αr 4π Λ G = NΛ S = NF/M 100 TeV ) Λ S (leading order in F/M)

16 OGM Spectrum M r = α r 4π Λ G, m f = Some features of the OGM spectrum: 3 r=1 C r f Gravitino LSP: m(gravitino) ~ F/Mpl ~ ev ( αr 4π Λ G = NΛ S = NF/M 100 TeV ) Λ S (leading order in F/M)

17 OGM Spectrum M r = α r 4π Λ G, m f = Some features of the OGM spectrum: Gravitino LSP: m(gravitino) ~ F/Mpl ~ ev m(colored) >> m(uncolored), or more precisely, 3 r=1 C r f ( αr 4π Λ G = NΛ S = NF/M 100 TeV ) Λ S M 3 : M : M 1 m q : m ll : m lr α 3 : α : α 1 (leading order in F/M)

18 OGM Spectrum M r = α r 4π Λ G, m f = Some features of the OGM spectrum: Gravitino LSP: m(gravitino) ~ F/Mpl ~ ev m(colored) >> m(uncolored), or more precisely, 3 r=1 C r f m(gaugino)/m(sfermion) increases with N ( αr 4π Λ G = NΛ S = NF/M 100 TeV ) Λ S M 3 : M : M 1 m q : m ll : m lr α 3 : α : α 1 (leading order in F/M)

19 OGM Spectrum M r = α r 4π Λ G, m f = Some features of the OGM spectrum: Gravitino LSP: m(gravitino) ~ F/Mpl ~ ev m(colored) >> m(uncolored), or more precisely, 3 r=1 C r f m(gaugino)/m(sfermion) increases with N ( αr 4π Λ G = NΛ S = NF/M 100 TeV ) Λ S M 3 : M : M 1 m q : m ll : m lr α 3 : α : α 1 (leading order in F/M) heavy higgsinos: µ m t

20 Some features of the OGM spectrum: Gravitino LSP: m(gravitino) ~ F/Mpl ~ ev m(colored) >> m(uncolored), or more precisely, m(gaugino)/m(sfermion) increases with N heavy higgsinos: OGM Spectrum M r = α r 4π Λ G, m f = 3 r=1 C r f ( αr 4π Λ G = NΛ S = NF/M 100 TeV ) Λ S M 3 : M : M 1 m q : m ll : m lr α 3 : α : α 1 µ m t Bino or right-handed slepton NLSP! (leading order in F/M)

21 More on the NLSP The nature of the NLSP determines much of the collider phenomenology, since every sparticle decay chain passes through it In particular, promptly decaying bino NLSP have a very clean and distinctive collider signature: diphoton+met: O( ) fb 1 cross section at the LHC SM background virtually non-existent

22 Gauge mediation = OGM? It is crucial to fully map out the phenomenology of gauge mediation, if we are to discover or rule it out at the LHC. Motivated by this, we studied the phenomenology of a large family of simple extensions of OGM, obtained by deforming the OGM superpotential by messenger mass terms W = λ ij Xφ i φj + m ij φ i φj In fact, this corresponds to the most general messenger superpotential allowed by gauge symmetry and renormalizability. (Extra)ordinary gauge mediation

23 EOGM why not? W = λ ij Xφ i φj + m ij φ i φj

24 EOGM why not? W = λ ij Xφ i φj + m ij φ i φj Surprisingly, these models have not been much explored. Why not?

25 EOGM why not? W = λ ij Xφ i φj + m ij φ i φj Surprisingly, these models have not been much explored. Why not? They have explicit mass parameters. This seems unnatural. These mass parameters are analogous to the mu term of the MSSM. If we allow for the latter, then there is no reason not to allow for former. Also, there are now many examples of strongly-coupled SUSY gauge theories where EOGM-type superpotentials are dynamically generated.

26 EOGM why not? W = λ ij Xφ i φj + m ij φ i φj Surprisingly, these models have not been much explored. Why not? They have explicit mass parameters. This seems unnatural. These mass parameters are analogous to the mu term of the MSSM. If we allow for the latter, then there is no reason not to allow for former. Also, there are now many examples of strongly-coupled SUSY gauge theories where EOGM-type superpotentials are dynamically generated. They have dangerous contributions to sfermion masses from hypercharge D- terms. These can be forbidden by global symmetries (e.g. generalized messenger parity). We will assume this is the case for the rest of today s talk.

27 EOGM why not? Surprisingly, these models have not been much explored. Why not? They have explicit mass parameters. This seems unnatural. These mass parameters are analogous to the mu term of the MSSM. If we allow for the latter, then there is no reason not to allow for former. Also, there are now many examples of strongly-coupled SUSY gauge theories where EOGM-type superpotentials are dynamically generated. They have dangerous contributions to sfermion masses from hypercharge D- terms. These can be forbidden by global symmetries (e.g. generalized messenger parity). We will assume this is the case for the rest of today s talk. They can t possibly give rise to phenomenology that is qualitatively different than OGM. Actually... W = λ ij Xφ i φj + m ij φ i φj

28 EOGM - why not? In today s talk, we will see that many of the classic features of OGM can be modified in this more general (but just as ordinary!) class of models. Thus, there is more to gauge mediation than just OGM! 1

29 R-symmetry W = λ ij Xφ i φj + m ij φ i φj

30 R-symmetry W = λ ij Xφ i φj + m ij φ i φj We will limit our study to models with a continuous U(1) R symmetry

31 R-symmetry We will limit our study to models with a continuous U(1) R symmetry Motivations: W = λ ij Xφ i φj + m ij φ i φj Imposing an R-symmetry cuts down the parameter space, simplifies analysis, and has interesting consequences. Need an R-symmetry for SUSY breaking (Nelson & Seiberg)

32 R-symmetry We will limit our study to models with a continuous U(1) R symmetry Motivations: W = λ ij Xφ i φj + m ij φ i φj Imposing an R-symmetry cuts down the parameter space, simplifies analysis, and has interesting consequences. Need an R-symmetry for SUSY breaking (Nelson & Seiberg) Example: R(X) =, R(φ i ) = i, R( φ i ) = i W = M ij (X)φ i φj = λ i Xφ i φi + m i φ i φi+1 ( ) λx m 0 λx m M =, M = 0 λx m 0 λx 0 0 λx, etc.

33 Determinant Identity Because of the R-symmetry, the messenger mass matrix satisfies an important identity: M λx + m det M = X n G(m, λ) This determinant identity, which follows directly from the R-symmetry, has a number of important consequences. E.g. in the previous example det M = λ N X N (note: independent of m!)

34 Classifying models using the determinant identity det(m + λx) = X n G(m, λ)

35 Classifying models using the determinant identity det(m + λx) = X n G(m, λ) n = 0 : det(m + λx) = det m ( det λ = 0)

36 Classifying models using the determinant identity det(m + λx) = X n G(m, λ) n = 0 : det(m + λx) = det m ( det λ = 0) n = N : det(m + λx) = X N det λ ( det m = 0)

37 Classifying models using the determinant identity det(m + λx) = X n G(m, λ) n = 0 : det(m + λx) = det m ( det λ = 0) n = N : det(m + λx) = X N det λ ( det m = 0) 0 < n < N : det(m + λx) = X n G(m, λ) (det m, det λ 0)

38 Classifying models using the determinant identity det(m + λx) = X n G(m, λ) n = 0 : det(m + λx) = det m ( det λ = 0) n = N : det(m + λx) = X N det λ ( det m = 0) 0 < n < N : det(m + λx) = X n G(m, λ) (det m, det λ 0) These three categories of models have very different properties. Since OGM belongs to the second category, we will focus on this category in today s talk.

39 Phenomenology of (Extra)Ordinary Gauge Mediation

40 Soft masses

41 Soft masses M r = α r 4π Λ G, m f = 3 r=1 C r f ( αr 4π ) Λ S Straightforward to compute soft masses, using technique of analytic continuation in superspace (Giudice & Rattazzi).

42 Soft masses M r = α r 4π Λ G, m f = 3 r=1 C r f ( αr 4π ) Λ S Straightforward to compute soft masses, using technique of analytic continuation in superspace (Giudice & Rattazzi). Same general structure as OGM, but now scales G, S are given by different expressions: Λ G = F X log det M = nf X Λ S = 1 F XX N i=1 (log M i ) Using determinant identity det M X n

43 Soft masses, cont d Λ G = F X log det M = nf X Λ S = 1 F XX N i=1 (log M i )

44 Soft masses, cont d G Λ G = F X log det M = nf X Λ S = 1 F XX is always independent of the couplings! Consequence: gauginos always obey the GUT relations in these models. N i=1 (log M i )

45 Soft masses, cont d G Λ G = F X log det M = nf X Λ S = 1 F XX is always independent of the couplings! Consequence: gauginos always obey the GUT relations in these models. N i=1 (log M i ) M 1 : M : M 3 = α 1 : α : α 3 1 : : 7 A direct consequence of R-symmetry!

46 Soft masses, cont d G is always independent of the couplings! Consequence: gauginos always obey the GUT relations in these models. Λ S Λ G = F X log det M = nf X Λ S = 1 F XX in general depends on the messenger superpotential couplings. So, let us define the effective messenger number [ ] 1 N eff (X, m, λ) = Λ G 1 N Λ = S n X XX ( log Mi ) N i=1 (log M i ) M 1 : M : M 3 = α 1 : α : α 3 1 : : 7 i=1 A direct consequence of R-symmetry!

47 Soft masses, cont d G is always independent of the couplings! Consequence: gauginos always obey the GUT relations in these models. Λ S Λ G = F X log det M = nf X Λ S = 1 F XX in general depends on the messenger superpotential couplings. So, let us define the effective messenger number [ ] 1 N eff (X, m, λ) = Λ G 1 N Λ = S n X XX ( log Mi ) N i=1 (log M i ) M 1 : M : M 3 = α 1 : α : α 3 1 : : 7 i=1 A direct consequence of R-symmetry! Remember, in OGM one has Λ G = NF/X, Λ S = NF/X, N eff = N

48 Doublet/Triplet Splitting 5 (3, 1, 1 3 ) (1,, 1 ) W = (λ 3ij X + m 3ij )q i q j + (λ ij X + m ij )l i lj

49 Doublet/Triplet Splitting 5 (3, 1, 1 3 ) (1,, 1 ) W = (λ 3ij X + m 3ij )q i q j + (λ ij X + m ij )l i lj In OGM, the spectrum does not depend on the superpotential couplings, so doublet/triplet splitting has no effect.

50 Doublet/Triplet Splitting 5 (3, 1, 1 3 ) (1,, 1 ) W = (λ 3ij X + m 3ij )q i q j + (λ ij X + m ij )l i lj In OGM, the spectrum does not depend on the superpotential couplings, so doublet/triplet splitting has no effect. However, in EOGM, the sfermion masses do depend on the superpotential couplings, so now doublet/triplet splitting can have a big effect.

51 Doublet/Triplet Splitting 5 (3, 1, 1 3 ) (1,, 1 ) W = (λ 3ij X + m 3ij )q i q j + (λ ij X + m ij )l i lj In OGM, the spectrum does not depend on the superpotential couplings, so doublet/triplet splitting has no effect. However, in EOGM, the sfermion masses do depend on the superpotential couplings, so now doublet/triplet splitting can have a big effect. This sensitivity to doublet/triplet splitting is the main source of differences between OGM and EOGM.

52 Doublet/Triplet Splitting (cont d) Doublet/triplet splitting means there can be different numbers of effective doublet and triplet messengers: N eff, = N eff (X, m, λ ), N eff,3 = N eff (X, m 3, λ 3 ) 3 m f = r=1 C r f ( αr ) Λ G m q : m l 4π N eff,r α 3 Neff,3 : α Neff, This can alter the spectrum in various ways. For instance, it can change the relations between slepton and squark masses -- one no longer necessarily has m q : m l α 3 : α A less obvious, but also important consequence is a focussing effect in the running of the Higgs soft masses...

53 D/T Splitting and Focussing m H u m H u (M mess ) 3 4π y t m t log M mess m t α Λ G/N eff, α 3Λ G/N eff,3 In OGM, the first term is always smaller than the second, leading to m H u 3 4π y t m t log M mess m t (TeV) This implies that there must be at least 0.1-1% fine tuning in the mu parameter in order to achieve the observed EWSB: µ + m H u m Z Little hierarchy problem

54 D/T Splitting and Focussing m H u m H u (M mess ) 3 4π y t m t log M mess m t α Λ G/N eff, α 3Λ G/N eff,3 Agashe & Graesser pointed out that with different numbers of doublets and triplets, one can make the first and second terms comparable, leading to a smaller Higgs mass parameter and hence smaller mu. Thus with doublet/triplet splitting, one can get much smaller mu in EOGM than OGM! µ 1 TeV normally µ 1 TeV with focussing

55 Higgsino NLSPs Small mu in turn implies that the lightest neutralino is Higgsino like: mñ = M 1 0 c β s W m Z s β s W m Z (Bino, wino) 0 M c β c W m Z s β c W m Z c β s W m Z c β c W m Z 0 µ Higgsinos s β s W m Z s β c W m Z µ 0 So the NLSP can be the Higgsino, not the bino or the stau!! Because of the bias from OGM, this is not a well-studied scenario. It could have interesting implications at the LHC, e.g. ZZ, Zh, hh + MET instead of γγ + MET Could the LHC be a Higgs factory??

56 Unification? Doublet/triplet splitting can potentially spoil gauge coupling unification. However the R-symmetry improves the situation. To see this, let us begin by ordering the eigenvalues of the doublet and triplet messenger mass matrices. M r;0 m Z < M r;1 < M r; < < M r;n < M r;n+1 m GUT, (r =, 3) Running the gauge couplings up gives N b r i α r (M GUT ) = α r (m Z ) + π i=0 log M a,i+1 M a,i = α GUT ;MSSM 1 π (N log M GUT log det M r )

57 Unification? Doublet/triplet splitting can potentially spoil gauge coupling unification. However the R-symmetry improves the situation. To see this, let us begin by ordering the eigenvalues of the doublet and triplet messenger mass matrices. M r;0 m Z < M r;1 < M r; < < M r;n < M r;n+1 m GUT, (r =, 3) Running the gauge couplings up gives N b r i α r (M GUT ) = α r (m Z ) + π i=0 log M a,i+1 M a,i = α GUT ;MSSM 1 π (N log M GUT log det M r ) Only depends on the determinant!

58 Unification (cont d) According to the determinant identity, In general, α r (M GUT ) = α GUT ;MSSM 1 π (N log M GUT log det M r ) G(m, λ) det M r = X n G(m r, λ r ) is independent of some of the couplings. Then these couplings can be split arbitrarily without spoiling unification. E.g., G(m, λ) = det λ independent of m. Then as long as gauge coupling unification can be preserved. G(λ ) = G(λ 3 )

59 An example Consider again the model W = M ij (X)φ i φj = λ i Xφ i φi + m i φ i φi+1 M = ( λx m 0 λx ), M = λx m 0 0 λx m 0 0 λx, etc. At large X, the model is equivalent to N messenger OGM. At small X, there is only one light messenger. Thus Neff interpolates between 1 and N.

60 Example: Neff 5 Neff N N 3 N 4 N x (x = λx/m)

61 Mass GeV Mass GeV Χ (Λ G = M TeV, tan 1 β = 0) t1 Χ 0 Χ ± 1 t U 1 Τ 1 Τ M Τ Χ 0 Example: spectra Χ 0 1 Τ N 1 N 5 N 1, N d mu X 1 and m 3 X 1 3 L u R g g t1 d L u t g 1 d L u R R V 1 N 13 N 14 t U 1 Χ ± 1 M 1 Τ 1 Τ V 1 M N 13 N 14 Χ 0 1 Χ 0 t Μ Χ ± 1 M 1 V 1 Τ 1 Τ M Τ N 13 N Log 10 M GeV Log 10 M GeV Log 10 M GeV Fig. 3: A plot of some of the MSSM soft parameters Squark and and sparticle masses at the scale Q = m Z, as a function of the messenger scale slepton M masses (which we take to squashed be the mass of the lightest messenger). The left (middle) column is OGM with N = 1 (N = 5). The right column is a model of the form (4.1)(4.) with N = 5, m /X =, and m 3 /X = 1/3. In all cases, Λ G =00 TeV.

62 (Λ G = 00 TeV, tan β = 0) Example: spectra 600. Μ Mass GeV Χ 0 1 Χ 0 Χ ± 1 M 1 M Τ Χ 0 1 Χ 0 Χ ± 1 M 1 M Τ Χ 0 1 Χ 0 Μ Χ ± 1 M 1 M Τ U U 1 V U 1 V 1 N 13 N 14 V 1 N 13 N 14 N 13 N Log 10 M GeV Log 10 M GeV Log 10 M GeV

63 (Λ G = 00 TeV, tan β = 0) Example: spectra 600. Μ Mass GeV Χ 0 1 Χ 0 Χ ± 1 M 1 M Τ Χ 0 1 Χ 0 Χ ± 1 M 1 M Τ Χ 0 1 Χ 0 Μ Χ ± 1 M 1 M Τ U U 1 V U 1 V 1 N 13 N 14 V 1 N 13 N 14 N 13 N Log 10 M GeV Log 10 M GeV mu is much smaller than in OGM... Log 10 M GeV

64 (Λ G = 00 TeV, tan β = 0) Example: spectra 600. Μ Mass GeV Χ 0 1 Χ 0 Χ ± 1 M 1 M Τ Χ 0 1 Χ 0 Χ ± 1 M 1 M Τ Χ 0 1 Χ 0 Μ Χ ± 1 M 1 M Τ U U 1 V U 1 V 1 N 13 N 14 V 1 N 13 N 14 N 13 N Log 10 M GeV Log 10 M GeV mu is much Log 10 M GeV smaller than in... so the Higgsino OGM... can be the NLSP

65 Example: unification R-symmetry guarantees that the heavy doublet messengers come in just right to fix up the running!

66 Minimal Completions

67 Minimal Completions = O R models

68 Minimal Completions = O R models So far we have treated the SUSY-breaking field X in these models as a spurion for the unspecified hidden sector.

69 Minimal Completions = O R models So far we have treated the SUSY-breaking field X in these models as a spurion for the unspecified hidden sector. Now let us go one step further and attempt to specify the hidden sector in this framework.

70 Minimal Completions = O R models So far we have treated the SUSY-breaking field X in these models as a spurion for the unspecified hidden sector. Now let us go one step further and attempt to specify the hidden sector in this framework. Many choices for the hidden sector are possible, but one is especially minimal. Because of the R-symmetry, these EOGM models are one step away from being generalized O Raifeartaigh models. δw = fx

71 Pseudo-moduli space W = λ ij Xφ i φj + m ij φ i φj + fx F X = φ T λ φ + f, F φ = (λx + m) φ, F φ = φ T (λx + m

72 Pseudo-moduli space W = λ ij Xφ i φj + m ij φ i φj + fx FX = φ T λ φ + f, Fφ = (λx + m) φ, F φ = φ T (λx + m SUSY is broken along a pseudo-moduli space φ = φ = 0, X min < X < X max, V tree = f V V tree X

73 Pseudo-moduli space W = λ ij Xφ i φj + m ij φ i φj + fx FX = φ T λ φ + f, Fφ = (λx + m) φ, F φ = φ T (λx + m SUSY is broken along a pseudo-moduli space φ = φ = 0, X min < X < X max, V tree = f V V eff V tree X

74 Pseudo-moduli space W = λ ij Xφ i φj + m ij φ i φj + fx FX = φ T λ φ + f, Fφ = (λx + m) φ, F φ = φ T (λx + m SUSY is broken along a pseudo-moduli space φ = φ = 0, X min < X < X max, V tree = f V V eff V tree Need minimum at X 0 to break the R-symmetry X

75 R-charge Condition

76 R-charge Condition The simplest O R models do not have an R-breaking vacuum.

77 R-charge Condition The simplest O R models do not have an R-breaking vacuum. The existence of such a vacuum requires a field with R 0,. (DS)

78 R-charge Condition The simplest O R models do not have an R-breaking vacuum. The existence of such a vacuum requires a field with R 0,. (DS) Interestingly, all R-symmetric deformations of OGM have this property: det λ 0 R( φ i ) = R(φ i ) If m ij 0 R(φ i ) + R( φ j ) = So either R(φ i ), R( φ i ), R(φ j ), or R( φ j ) must be different from 0,. Thus, any R-symmetric deformation of OGM leads to a viable model of SUSY and R-symmetry breaking! These are possibly the simplest known models of direct gauge mediation.

79 Simplest example with spontaneous R

80 Simplest example with spontaneous R Perturb N= OGM with the only renormalizable interactions allowed by an R-symmetry: W = λx(φ 1 φ1 + φ φ ) + mφ 1 φ + fx

81 Simplest example with spontaneous R Perturb N= OGM with the only renormalizable interactions allowed by an R-symmetry: W = λx(φ 1 φ1 + φ φ ) + mφ 1 φ + fx Straightforward to find messenger masses, compute Coleman- Weinberg potential: V CW = Tr MB 4 log M B µ Tr M F 4 log M F µ

82 Simplest example with spontaneous R Perturb N= OGM with the only renormalizable interactions allowed by an R-symmetry: W = λx(φ 1 φ1 + φ φ ) + mφ 1 φ + fx Straightforward to find messenger masses, compute Coleman- Weinberg potential: V CW = Tr MB 4 log M B µ Tr M F 4 log M F µ An R-symmetry breaking minimum is generated at one-loop!

83 Conclusions, future directions We have argued that OGM is part of a much wider model space which is not forbidden by any symmetries. By exploring this model space, we have seen that many of the classic features of OGM can qualitatively change. higgsino-like neutralino NLSP small mu squashed slepton/squark spectrum Thus, gauge mediation, even in its simplest form, allows for richer phenomenological possibilities than previously thought.

84 Conclusions, cont d Some future directions/open questions are: Collider phenomenology of these models, esp. higgsino NLSP (work in progress) What happens if we give up R-symmetry altogether? Can these types of models be generated dynamically? Cosmological implications R-axion, (nearly) stable messengers? What do known solutions to the mu problem look like in this framework?