A SUSY SO(10) GUT with 2 Intermediate Scales

Transcription

1 A SUSY SO(10) GUT with 2 Intermediate Scales Manuel Drees Bonn University & Bethe Center for Theoretical Physics SUSY SO(10) p. 1/25

2 Contents 1 Motivation: SO(10), intermediate scales SUSY SO(10) p. 2/25

3 Contents 1 Motivation: SO(10), intermediate scales 2 The Model SUSY SO(10) p. 2/25

4 Contents 1 Motivation: SO(10), intermediate scales 2 The Model 3 Neutralino Dark Matter SUSY SO(10) p. 2/25

5 Contents 1 Motivation: SO(10), intermediate scales 2 The Model 3 Neutralino Dark Matter 4 LHC Phenomenology SUSY SO(10) p. 2/25

6 Contents 1 Motivation: SO(10), intermediate scales 2 The Model 3 Neutralino Dark Matter 4 LHC Phenomenology 5 Summary SUSY SO(10) p. 2/25

7 Contents 1 Motivation: SO(10), intermediate scales 2 The Model 3 Neutralino Dark Matter 4 LHC Phenomenology 5 Summary Based on: MD, Ju Min Kim, arxiv: v1 (JHEP); MD, Ju Min Kim, Eun-Kyung Park, to appear very soon SUSY SO(10) p. 2/25

8 Introduction: Why SO(10)? 3 gauge couplings of SM unify quite nicely in MSSM SUSY SO(10) p. 3/25

9 Introduction: Why SO(10)? 3 gauge couplings of SM unify quite nicely in MSSM Minimal unified group has rank 4: SU(5). SUSY SO(10) p. 3/25

10 Introduction: Why SO(10)? 3 gauge couplings of SM unify quite nicely in MSSM Minimal unified group has rank 4: SU(5). In SU(5), ν R would have to be gauge singlet. SUSY SO(10) p. 3/25

11 Introduction: Why SO(10)? 3 gauge couplings of SM unify quite nicely in MSSM Minimal unified group has rank 4: SU(5). In SU(5), ν R would have to be gauge singlet. Instead, in SO(10): ν R required to fill 16 with matter (s)fermions! SUSY SO(10) p. 3/25

12 Introduction: Why SO(10)? 3 gauge couplings of SM unify quite nicely in MSSM Minimal unified group has rank 4: SU(5). In SU(5), ν R would have to be gauge singlet. Instead, in SO(10): ν R required to fill 16 with matter (s)fermions! Naturally allows to implement see saw mechanism! SUSY SO(10) p. 3/25

13 Introduction: Why intermediate scales? SO(10) has rank 5 SUSY SO(10) p. 4/25

14 Introduction: Why intermediate scales? SO(10) has rank 5 Usually need several Higgs reps to break it to SM gauge group SUSY SO(10) p. 4/25

15 Introduction: Why intermediate scales? SO(10) has rank 5 Usually need several Higgs reps to break it to SM gauge group No reason why the corresponding vevs should be the same SUSY SO(10) p. 4/25

16 Introduction: Why intermediate scales? SO(10) has rank 5 Usually need several Higgs reps to break it to SM gauge group No reason why the corresponding vevs should be the same See saw: m ν = m2 ν D M νr < 3 mev, if m νd m t = 170 GeV, M νr M X GeV! SUSY SO(10) p. 4/25

17 Introduction: Why intermediate scales? SO(10) has rank 5 Usually need several Higgs reps to break it to SM gauge group No reason why the corresponding vevs should be the same See saw: m ν = m2 ν D M νr < 3 mev, if m νd m t = 170 GeV, M νr M X GeV! Need m ν3 > 50 mev! SUSY SO(10) p. 4/25

18 Introduction: Why intermediate scales? SO(10) has rank 5 Usually need several Higgs reps to break it to SM gauge group No reason why the corresponding vevs should be the same See saw: m ν = m2 ν D M νr < 3 mev, if m νd m t = 170 GeV, M νr M X GeV! Need m ν3 > 50 mev! = need M νr GeV! SUSY SO(10) p. 4/25

19 The model Ref: al. et Senjanovic, Nucl. Phys B597 (2001) 89 SO(10) SU(4) SU(2) L SU(2) R D at M X using 54 SU(3) C U(1) B L SU(2) L SU(2) R at M C using 45 SU(3) C SU(2) L U(1) Y at M R using 126,126 D: Discrete symmetry, ensures parity (same L and R couplings) SUSY SO(10) p. 5/25

20 Higgs fields Most general renormalizable superpotential = light Higgs states: SUSY SO(10) p. 6/25

21 Higgs fields Most general renormalizable superpotential = light Higgs states: 54 = (1,1,1) (20,1,1) (1,3,3) (6,2,2); 45 = (15,1,1) (1,1,3) (1,3,1) (6,2,2); 126 = (10,1,3) (10,3,1) (15,2,2) (6,1,1); 126 = (10,1,3) (10,3,1) (15,2,2) (6,1,1). Decomposition under SU(4) SU(2) L SU(2) R ; components obtaining vev are written first. SUSY SO(10) p. 6/25

22 Higgs spectrum all of 54 State Mass all of 45, except (15,1,1) 45 all of 126 and 126, except 10, 10 of SU(4) M X (10,3,1) 126 and (10,3,1) 126 3, 6 of SU(3) C in (10,1,3) 126 and (10,1,3) 126 M C color triplets of (15,1,1) 45 (δ 0 δ 0 ), δ +, δ M R [ ] M 2 color octet and singlet of (15,1,1) A M 1 max R M C, M2 C M X (δ 0 + δ 0 ), δ ++, δ M2 M 2 R /M X δ = (1,1,3) 126 ; δ = (1,1,3) 126 SUSY SO(10) p. 7/25

23 Running gauge couplings Existence of states with mass < M R is crucial for allowing intermediate scales, given that single step unification works. SUSY SO(10) p. 8/25

24 Running gauge couplings Existence of states with mass < M R is crucial for allowing intermediate scales, given that single step unification works. From RGE: Can compute M C and M R for given M X (and given weak scale parameters): No prediction for M X or ratios of weak scale couplings. SUSY SO(10) p. 8/25

25 Running gauge couplings Existence of states with mass < M R is crucial for allowing intermediate scales, given that single step unification works. From RGE: Can compute M C and M R for given M X (and given weak scale parameters): No prediction for M X or ratios of weak scale couplings. In particular, M X = M C = M R remains possible: allows smooth transition to Grand Desert SUSY SO(10) p. 8/25

26 Running gauge couplings Existence of states with mass < M R is crucial for allowing intermediate scales, given that single step unification works. From RGE: Can compute M C and M R for given M X (and given weak scale parameters): No prediction for M X or ratios of weak scale couplings. In particular, M X = M C = M R remains possible: allows smooth transition to Grand Desert Introduce second pair of 10, 10 with mass M 2, to allow more realistic fermion masses (see below). SUSY SO(10) p. 8/25

27 Relation between scales log(q/gev) log(m X /GeV) log(m C /GeV) log(m R /GeV) /α U SUSY SO(10) p. 9/25

28 Superpotential above M C W = Y 1 F c FΦ Y N ( F c ΣR F c + F Σ L F ) F = (4, 2, 1): left handed matter fields F c = ( 4, 1, 2): right handed matter fields Φ 1,2 = (1, 2, 2): Higgs bi doublets Σ R = (10, 1, 3) of 126 Σ L = (10, 3, 1) of 126 SUSY SO(10) p. 10/25

29 Superpotential above M C W = Y 1 F c FΦ Y N ( F c ΣR F c + F Σ L F ) F = (4, 2, 1): left handed matter fields F c = ( 4, 1, 2): right handed matter fields Φ 1,2 = (1, 2, 2): Higgs bi doublets Σ R = (10, 1, 3) of 126 Σ L = (10, 3, 1) of 126 Have set coupling Y 2 of Φ 2 to zero: can always be done via field re definition SUSY SO(10) p. 10/25

30 Superpotential above M C W = Y 1 F c FΦ Y N ( F c ΣR F c + F Σ L F ) F = (4, 2, 1): left handed matter fields F c = ( 4, 1, 2): right handed matter fields Φ 1,2 = (1, 2, 2): Higgs bi doublets Σ R = (10, 1, 3) of 126 Σ L = (10, 3, 1) of 126 Have set coupling Y 2 of Φ 2 to zero: can always be done via field re definition Y N generates ν R mass! SUSY SO(10) p. 10/25

31 Superpotential between M R and M C W = Y q1 Q c QΦ 1 + Y l1 L c LΦ Y NL c δl c Q c = ( 3, 1, 2, 1/3): right handed quarks Q = (3, 2, 1, 1/3): left handed quarks L c = (1, 1, 2, 1): right handed leptons L = (1, 2, 1, 1): left handed leptons δ = (1, 1, 3, 2): breaks SU(2) R U(1) B L U(1) Y. SUSY SO(10) p. 11/25

32 Superpotential between M R and M C W = Y q1 Q c QΦ 1 + Y l1 L c LΦ Y NL c δl c Q c = ( 3, 1, 2, 1/3): right handed quarks Q = (3, 2, 1, 1/3): left handed quarks L c = (1, 1, 2, 1): right handed leptons L = (1, 2, 1, 1): left handed leptons δ = (1, 1, 3, 2): breaks SU(2) R U(1) B L U(1) Y. Matching condition at E = M C : Y q1 = Y l1 = Y 1 SUSY SO(10) p. 11/25

33 Superpotential between M R and M 2 W = Y u1 U c QH u1 + Y d1 D c QH d1 + Y l1 E c LH d Y NE c δ E c SUSY SO(10) p. 12/25

34 Superpotential between M R and M 2 W = Y u1 U c QH u1 + Y d1 D c QH d1 + Y l1 E c LH d Y NE c δ E c Matching condition at E = M R : Y u1 = Y d1 = Y q1 SUSY SO(10) p. 12/25

35 Superpotential below M 2 As in MSSM: W = Y u U c QH u + Y d D c H d + Y l E c LH d SUSY SO(10) p. 13/25

36 Superpotential below M 2 As in MSSM: W = Y u U c QH u + Y d D c H d + Y l E c LH d Matching: H u,d = cosϕ u,d H (u,d)1 +sin ϕ u,d H (u,d)2 = Y u,d = Y (u,d)1 cosϕ u,d SUSY SO(10) p. 13/25

37 Superpotential below M 2 As in MSSM: W = Y u U c QH u + Y d D c H d + Y l E c LH d Matching: H u,d = cosϕ u,d H (u,d)1 +sin ϕ u,d H (u,d)2 = Y u,d = Y (u,d)1 cosϕ u,d = need cos ϕ u 1, since Y t already near maximal SUSY SO(10) p. 13/25

38 Superpotential below M 2 As in MSSM: W = Y u U c QH u + Y d D c H d + Y l E c LH d Matching: H u,d = cosϕ u,d H (u,d)1 +sin ϕ u,d H (u,d)2 = Y u,d = Y (u,d)1 cosϕ u,d = need cos ϕ u 1, since Y t already near maximal = cosϕ d = Y d(m 2 ) Y u (M R ) [ g 2 1 (M R ) g 2 1 (M 2) ] 1/60 = Y d1 Y u,1 : always in large tanβ scenario for E M 2! SUSY SO(10) p. 13/25

39 Gaugino masses Assume unified boundary conditions: scalar mass m 0, gaugino mass M 1/2, single parameter A 0. SUSY SO(10) p. 14/25

40 Gaugino masses Assume unified boundary conditions: scalar mass m 0, gaugino mass M 1/2, single parameter A 0. Gauge β functions increase for E > M 2 = ratios M i /M 1/2 decrease (M i, i = 1, 2, 3: weak scale gaugino masses) SUSY SO(10) p. 14/25

41 Gaugino masses Assume unified boundary conditions: scalar mass m 0, gaugino mass M 1/2, single parameter A 0. Gauge β functions increase for E > M 2 = ratios M i /M 1/2 decrease (M i, i = 1, 2, 3: weak scale gaugino masses) E.g. for M X = GeV (minimal value): M 1 = 0.23M 1/2 M 2 = 0.46M 1/2 M 3 = 1.4M 1/2 Coefficients nearly two times smaller than in msugra. SUSY SO(10) p. 14/25

42 Gaugino masses Assume unified boundary conditions: scalar mass m 0, gaugino mass M 1/2, single parameter A 0. Gauge β functions increase for E > M 2 = ratios M i /M 1/2 decrease (M i, i = 1, 2, 3: weak scale gaugino masses) E.g. for M X = GeV (minimal value): M 1 = 0.23M 1/2 M 2 = 0.46M 1/2 M 3 = 1.4M 1/2 Coefficients nearly two times smaller than in msugra. Ratios M 1 : M 2 : M 3 same as in msugra! SUSY SO(10) p. 14/25

43 Sfermion masses (1 st generation) For fixed M i, get larger gaugino loop contributions to sfermion masses; partly cancels previous effect when expressed in terms of M 1/2 : SUSY SO(10) p. 15/25

44 Sfermion masses (1 st generation) For fixed M i, get larger gaugino loop contributions to sfermion masses; partly cancels previous effect when expressed in terms of M 1/2 : m 2 f(m SUSY ) = m c fm 2 1/2 cẽr = 0.15 (as in msugra); cẽl = 0.21 (smaller than in msugra); c q = 1.15 (smaller than in msugra). SUSY SO(10) p. 15/25

45 Sfermion masses (1 st generation) For fixed M i, get larger gaugino loop contributions to sfermion masses; partly cancels previous effect when expressed in terms of M 1/2 : m 2 f(m SUSY ) = m c fm 2 1/2 cẽr = 0.15 (as in msugra); cẽl = 0.21 (smaller than in msugra); c q = 1.15 (smaller than in msugra). mẽr 1.68 M 1 : No co annihilation of χ 0 1 with ẽ R, µ R! mẽl M 2 : No W l L decays! m q 0.75m g : Similar to msugra SUSY SO(10) p. 15/25

46 3 rd generation sfermions & Higgs Y N reduces m τl,r, m t L,R, m br SUSY SO(10) p. 16/25

47 3 rd generation sfermions & Higgs Y N reduces m τl,r, m t L,R, m br = increases m 2 H u (M SUSY ) (and hence m A ) SUSY SO(10) p. 16/25

48 3 rd generation sfermions & Higgs Y N reduces m τl,r, m t L,R, m br = increases m 2 H u (M SUSY ) (and hence m A ) = reduces µ(m SUSY ) via EWSB condition SUSY SO(10) p. 16/25

49 3 rd generation sfermions & Higgs Y N reduces m τl,r, m t L,R, m br = increases m 2 H u (M SUSY ) (and hence m A ) = reduces µ(m SUSY ) via EWSB condition m ν3 m2 t Y N M R = smaller m ν3 implies larger Y N! SUSY SO(10) p. 16/25

50 Effect on the spectrum 2e+06 (a) m 0 = 1500GeV, M 12 = 900GeV, A 0 = 0, tanb = (b) m 0 = 700GeV, A 0 = 0, tanb = 50, m ν = 0.4eV M 12 = 700GeV M 12 = 1400GeV m 2 sf (M S ) 1.5e+06 1e m A0 /2mχ m 2 t m 2 L τ m 2 L 0.9 t m 2 R τ R m ν (ev) log (M X /GeV) SUSY SO(10) p. 17/25

51 Survey of parameter space (a) tanb=40, A 0 =0, m ν =0.4eV (a) tanb=40, A 0 =0, m ν =0.2eV m 0 (GeV) 1000 m 0 (GeV) M 1/2 (GeV) M 1/2 (GeV) Grey: no ESWB or tachyonic sfermion; red: mass bounds; pink: b sγ excluded; blue: favored by g µ ; green: DM allowed; black: all ok SUSY SO(10) p. 18/25

52 Survey of parameter space (a) tanb=40, A 0 =0, m ν =0.4eV (a) tanb=40, A 0 =0, m ν =0.2eV m 0 (GeV) 1000 m 0 (GeV) M 1/2 (GeV) M 1/2 (GeV) Grey: no ESWB or tachyonic sfermion; red: mass bounds; pink: b sγ excluded; blue: favored by g µ ; green: DM allowed; black: all ok In msugra: don t find allowed region (DM & g µ ) with m 2 0 M2 1/2! SUSY SO(10) p. 18/25

53 Same for tanβ = 50 (a) tanb=50, A 0 =0, m ν =0.4eV (a) tanb=50, A 0 =0, m ν =0.2eV m 0 (GeV) 1000 m 0 (GeV) M 1/2 (GeV) M 1/2 (GeV) SUSY SO(10) p. 19/25

54 Same for tanβ = 50 (a) tanb=50, A 0 =0, m ν =0.4eV (a) tanb=50, A 0 =0, m ν =0.2eV m 0 (GeV) 1000 m 0 (GeV) M 1/2 (GeV) M 1/2 (GeV) In right frame, DM relic density too small everywhere SUSY SO(10) p. 19/25

55 Same for tanβ = 50 (a) tanb=50, A 0 =0, m ν =0.4eV (a) tanb=50, A 0 =0, m ν =0.2eV m 0 (GeV) 1000 m 0 (GeV) M 1/2 (GeV) M 1/2 (GeV) In right frame, DM relic density too small everywhere 50% of plane DM allowed for tan β = 49! SUSY SO(10) p. 19/25

56 Impact on DM searches For m 0 M 1/2 : ( focus point, but no focussing in this scenario!) Very similar to msugra, if m χ 0 1, Ω χ 0 1 are fixed. SUSY SO(10) p. 20/25

57 Impact on DM searches For m 0 M 1/2 : ( focus point, but no focussing in this scenario!) Very similar to msugra, if m χ 0 1, Ω χ 0 1 are fixed. τ 1 co annihilation region: More promising, due to reduced µ = more higgsino gaugino mixing = enhanced couplings of χ 0 1 to Higgs bosons and Z0! SUSY SO(10) p. 20/25

58 Impact on DM searches For m 0 M 1/2 : ( focus point, but no focussing in this scenario!) Very similar to msugra, if m χ 0 1, Ω χ 0 1 are fixed. τ 1 co annihilation region: More promising, due to reduced µ = more higgsino gaugino mixing = enhanced couplings of χ 0 1 to Higgs bosons and Z0! cross section[*10-36 cm 2 ] 1e-05 1e-06 1e-07 1e-08 1e-09 tanβ=40, A 0 =0, m ν =0.2eV, M 1/2 =1000GeV FP CO CDMS II XENON100 (projected) 1e log M X [GeV] SUSY SO(10) p. 20/25

59 LHC signals: large m 0 region In SO(10) model: can get large bino higgsino mixing for relatively modest m 0, where q can be produced at LHC. This is not possible in msugra. SUSY SO(10) p. 21/25

60 LHC signals: large m 0 region In SO(10) model: can get large bino higgsino mixing for relatively modest m 0, where q can be produced at LHC. This is not possible in msugra. To get correct DM density in msugra for same m q, m g : have to increase tan β quite a lot (to reach A funnel ) SUSY SO(10) p. 21/25

61 LHC signals: large m 0 region In SO(10) model: can get large bino higgsino mixing for relatively modest m 0, where q can be produced at LHC. This is not possible in msugra. To get correct DM density in msugra for same m q, m g : have to increase tan β quite a lot (to reach A funnel ) = msugra has much smaller heavy Higgs masses: can be detected in τ + τ channel! SUSY SO(10) p. 21/25

62 LHC signals: large m 0 region In SO(10) model: can get large bino higgsino mixing for relatively modest m 0, where q can be produced at LHC. This is not possible in msugra. To get correct DM density in msugra for same m q, m g : have to increase tan β quite a lot (to reach A funnel ) = msugra has much smaller heavy Higgs masses: can be detected in τ + τ channel! msugra has much larger µ :changes χ 0, χ ± spectrum; can be checked via l + l invariant mass distribution! SUSY SO(10) p. 21/25

63 M l + l distribution (m 0 M 1/2 ) SO(10) msugra Events/10 GeV/300fb Invariant mass (GeV) Only msugra has Z 0 peak; SO(10) model has softer spectrum SUSY SO(10) p. 22/25

64 LHC signals: co annihilation region In msugra: either slightly change A 0 (option a) or slightly increase tanβ (option b) to match Ω χ 0 1 for fixed m q, m g. SUSY SO(10) p. 23/25

65 LHC signals: co annihilation region In msugra: either slightly change A 0 (option a) or slightly increase tanβ (option b) to match Ω χ 0 1 for fixed m q, m g. In SO(10): smaller m t 1,2, m b1 SUSY SO(10) p. 23/25

66 LHC signals: co annihilation region In msugra: either slightly change A 0 (option a) or slightly increase tanβ (option b) to match Ω χ 0 1 for fixed m q, m g. In SO(10): smaller m t 1,2, m b1 Smaller µ = smaller m χ 0 3,4, m χ ± 2 SUSY SO(10) p. 23/25

67 LHC signals: co annihilation region In msugra: either slightly change A 0 (option a) or slightly increase tanβ (option b) to match Ω χ 0 1 for fixed m q, m g. In SO(10): smaller m t 1,2, m b1 Smaller µ = smaller m χ 0 3,4, m χ ± 2 = more g χ 0 3,4, χ± 2 decays SUSY SO(10) p. 23/25

68 LHC signals: co annihilation region In msugra: either slightly change A 0 (option a) or slightly increase tanβ (option b) to match Ω χ 0 1 for fixed m q, m g. In SO(10): smaller m t 1,2, m b1 Smaller µ = smaller m χ 0 3,4, m χ ± 2 = more g χ 0 3,4, χ± 2 decays = more g Z 0 on shell in SO(10)! SUSY SO(10) p. 23/25

69 ubtracted M l + l distribution (m 0 M 1/2 ) Events/10 GeV/300fb SO(10) msugra 2b msugra 2a Invariant mass (GeV) SO(10) has significantly more pronounced Z 0 peak SUSY SO(10) p. 24/25

70 ubtracted M l + l distribution (m 0 M 1/2 ) Events/10 GeV/300fb SO(10) msugra 2b msugra 2a Invariant mass (GeV) SO(10) has significantly more pronounced Z 0 peak SO(10) model also has more like sign di lepton events: 492 vs. 422 (434). SUSY SO(10) p. 24/25

71 Summary and Outlook SO(10) model natural if ν R state! SUSY SO(10) p. 25/25

72 Summary and Outlook SO(10) model natural if ν R state! Allows intermediate scale; required for see saw. SUSY SO(10) p. 25/25

73 Summary and Outlook SO(10) model natural if ν R state! Allows intermediate scale; required for see saw. This modifies the RG running below M X. SUSY SO(10) p. 25/25

74 Summary and Outlook SO(10) model natural if ν R state! Allows intermediate scale; required for see saw. This modifies the RG running below M X. For fixed boundary condition at M X : reduced µ tends to make DM detection easier! SUSY SO(10) p. 25/25

75 Summary and Outlook SO(10) model natural if ν R state! Allows intermediate scale; required for see saw. This modifies the RG running below M X. For fixed boundary condition at M X : reduced µ tends to make DM detection easier! Points with same m q, m g, m χ 0 1, Ω χ 0 1 can be distinguished at LHC, using di lepton events and heavy Higgs searches SUSY SO(10) p. 25/25

76 Summary and Outlook SO(10) model natural if ν R state! Allows intermediate scale; required for see saw. This modifies the RG running below M X. For fixed boundary condition at M X : reduced µ tends to make DM detection easier! Points with same m q, m g, m χ 0 1, Ω χ 0 1 can be distinguished at LHC, using di lepton events and heavy Higgs searches Results should be qualitatively same in other models where M R < M X. SUSY SO(10) p. 25/25

77 Summary and Outlook SO(10) model natural if ν R state! Allows intermediate scale; required for see saw. This modifies the RG running below M X. For fixed boundary condition at M X : reduced µ tends to make DM detection easier! Points with same m q, m g, m χ 0 1, Ω χ 0 1 can be distinguished at LHC, using di lepton events and heavy Higgs searches Results should be qualitatively same in other models where M R < M X. To fix high scale physics: need to know m ν, proton lifetime! SUSY SO(10) p. 25/25