The Natural Supersymmetry and its Collider Searches

Transcription

1 The Natural Supersymmetry and its Collider Searches Institute of Theoretical Physics, Chinese Academy of Sciences Topical Mini-Workshop of the new Physics at the Terascale T. D. Lee Institute, August 3-5, 2018

2 Outline

3 Outline

4 The Nature The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living. Jules H. Poincare

5 The Standard Model Gauge symmetry: SU(3) C SU(2) L U(1) Y Fermions: Q i, U c i, Dc i, L i, E c i Higgs: H The SM explains the existing experimental data very well, including electroweak precision measurements.

6 The New Physics beyond the SM New particles: scalars, fermions,... New gauge symmetries: U(1), SU(2), SU(N),... The particle physics model building: principle and motivations!!! Focus: the new physics can be tested at the LHC!

7 The convincing evidence for physics beyond the SM: Dark energy Dark matter Neutrino masses and mixings Baryon asymmetry Inflation The SM is incomplete!

8 Major Theoretical Problems in the SM Fine-tuning problems Aesthetic Problems

9 Fine-Tuning Problems: Cosmological constant problem Λ CC MPl 4. Gauge hierarchy problem M EW M Pl. Strong CP probelm θ < The SM fermion masses and mixings m electron 10 5 m top.

10 Aesthetic Problems: Interaction unification Fermion unification Charge quantization Gauge coupling unification The first three prolems can be solved when we embed the SM into the Grand Unified Theories (GUTs) and string models.

11 The Possible Hints The stability problem. The stability problem is solved in the SSMs. The muon anomolous magnetic moment. The B physics anomalies.

12 Outline

13 Theoretical motivations: Generalization of the Poincare Algebra Coleman-Madula Theorem (1967): no-go theorem. The most general symmetries of the S matrix are Poincare symmetry and internal symmetry: P µ, M µν, and A µ. Golfand and Likhtman (1971), extended the Poincare algebra by spinor generators Q α. Ramond, Neveu-Schwarz, Gervais, and Sakita (1971): supersymmetry in two dimensions (from string theory). Volkov and Akulov (1973): neutrinos as Goldstone particles (m = 0).

14 Theoretical motivations: Generalization of the Poincare Algebra Wess and Zumino (1974), supersymmetric field theories in four dimensions. The actual starting point in the systematic study of supersymmetry. Haag-Lopuszanski-Sohnius Theorem (1975): generalized Colemand-Mandula theorem including spinor generators Qα A with α = 1, 2 and A = 1, 2,..., N cooresponding to spin ( 1 2, 0) and QȦ α with spin (0, 1 2 ), but no further generators.

15 Supersymmetry A supersymmetry transformation turns a bosonic state into a fermionic state, and vice versa. Q Boson = Fermion, Q Fermion = Boson. Algebra: supersymmetry generator Q is a fermionic operator with spin-1/2. {Q, Q } = P µ, {Q, Q} = {Q, Q } = 0, [P µ, Q] = [P µ, Q ] = 0. Each supermultiplet contains an equal number of fermion and boson degrees of freedom.

16 Supersymmetry Supersymmetry partially solves the cosmological constant problem: M Pl M SUSY. Supersymmetry has a deep connection with the high-energy fundamental physics, such as the Grand Unified Theory and String Theory.

17 Gauge Hierarchy Problem L = λ f Hf f + λ S H 2 S 2. mh 2 = λ f 2 8π 2 Λ2 UV + λ S 16π 2 Λ2 UV.

18 Gauge Hierarchy Problem

19 Solutions Techicolor: the Higgs is a condensation of new fermions. Point: no fundamental scalar. Larger extra dimension(s): Arkani-Hamed-Dimopoulos-Dvali (ADD) and Randall-Sundrum (RS). Point: the high-dimensional Planck scale is close to the TeV. Supersymmetry. Little Higgs model, effective theories for compositeness, the string landscape with anthropic solution, etc.

20 Outline

21 The Supersymmetry Standard Model Four-dimesional N = 1 supersymmetry: Kähler potential, superpotential, gauge kinetic function. A chiral SM fermion has a complex scalar partner. Gauge bosons and Higgs fields have a spin 1/2 partner. Graviton has a spin 3/2 partner.

22 The Minimal Supersymmetry Standard Model (MSSM) Two Higgs doublets: holomorphic superpotential and anomaly cancellation. Unlike the SM, proton can decay at the renormalizable level in the SSMs. To forbid the proton decay operaors, we introduce a Z 2 R symmetry: R = ( 1) 3B L+2s. The SM particle are even while the supersymmetric particles are odd. Dark matter: neutralino, sneutrino, gravitino, etc. Other solutions: R symmetry is violated while U(1) B or U(1) L is preserved. No missing energy at the LHC.

23 Names spin 0 spin 1/2 SU(3) C, SU(2) L, U(1) Y squarks Q (ũ L dl ) (u L d L ) ( 3, 2, 1 6 ) quarks u ũr u R ( 3, 1, 2 3 ) d d R d R ( 3, 1, 1 3 ) sleptons L ( ν ẽ L ) (ν e L ) ( 1, 2, 1 2 ) leptons e ẽr e R ( 1, 1, 1) Higgs H u (H u + Hu) 0 ( H u + H u) 0 ( 1, 2, ) Higgsinos H d (Hd 0 H d ) ( H d 0 H d ) ( 1, 2, 1 2 ) Table : Chiral supermultiplets in the Minimal Supersymmetric Standard Model. The spin-0 fields are complex scalars, and the spin-1/2 fields are left-handed two-component Weyl fermions.

24 Names spin 1/2 spin 1 SU(3) C, SU(2) 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 B0 B 0 ( 1, 1, 0) Table : Gauge supermultiplets in the Minimal Supersymmetric Standard Model. Neutralinos: neutral Higgsinos, Wino and Bino. Chargino: charged Higgsinos and Wino.

25 Gauge Coupling Unification for the SM and MSSM

26 The Supersymmetric Standard Models Solving the gauge hierarchy problem Gauge coupling unification Radiatively electroweak symmetry breaking Natural dark matter candidates Electroweak baryogenesis Electroweak precision: R parity

27 Problems in the MSSM: µ problem: µh u H d Little hierarchy problem CP violation and EDMs FCNC Dimension-5 proton decays

28 µ Problem: The next-to-mssm (NMSM): an SM singlet S, and Z 3 symmetry to forbid the µh d H u term where ω 3 = 1. φ ωφ, W = λsh d H u. The supersymmetric U(1) model Giudice-Masiero mechanism in gravity mediation!

29 Supersymmetry Breaking and Mediation: The supersymmetry breaking is broken in the hidden sector via F -term and/or D-term. The supersymmetry breaking mediations: gravity mediation, gauge mediation, anomaly mediation, Yukawa mediation, and hybrid mediations, etc.

30 Dark Matter Constraints from the LUX, PANDAX, and XENON1T Experiments: (I) The lightest neutralino as dark matter candidate Coannihilation scenarios: χ ± 1 /χ0 2, sleptons (light stau), squarks (light stop). Higgs funnel/resonance (two LSPs annihilate via a resonant gauge or Higgs field): Z, h, H, A. Higgsino LSP and Wino LSP: very small density. Hybrid scenario. (II) The other dark matter candidates: sneutrino, gravitino, axino, etc.

31 The Grand Unified Theories: SU(5), and SO(10) Unification of the gauge interactions, and unifications of the SM fermions Charge quantization Gauge coupling unification in the MSSM, and Yukawa unification Radiative electroweak symmetry breaking due to the large top quark Yukawa coupling Weak mixing angle at weak scale M Z Neutrino masses and mixings by seesaw mechanism

32 Problems: Gauge symmetry breaking Doublet-triplet splitting problem Proton decay problem Fermion mass problem: m e /m µ = m d /m s

33 String Models: Calabi-Yau compactification of heterotic string theory Orbifold compactification of heterotic string theory Grand Unified Theory (GUT) can be realized naturally through the elegant E 8 breaking chain: E 8 E 6 SO(10) SU(5) D-brane models on Type II orientifolds N stacks of D-branes gives us U(N) gauge symmetry: Pati-Salam Models Free fermionic string model builing Realistic models with clean particle spectra can only be constructed at the Kac-Moody level one: the Standard-like models, Pati-Salam models, and flipped SU(5) models.

34 F-Theory Model Building: The models are constructed locally, and then the gravity should decoupled, i.e., M GUT /M Pl is a small number. The SU(5) and SO(10) gauge symmetries can be broken by the U(1) Y and U(1) X /U(1) B L fluxes. Gauge mediated supersymmetry breaking can be realized via instanton effects. Gravity mediated supersymmetry breaking predicts the gaugino mass relation. All the SM fermion Yuakwa couplings can be generated in the SU(5) and SO(10) models. The doublet-triplet splitting problem, proton decay problem, µ problem as well as the SM fermion masses and mixing problem can be solved.

35 Supersymmetry The most promising new physics beyond the Standard Model. Gauge coupling unification strongly suggests the Grand Unified Theories (GUTs), and the SUSY GUTs can be constructed from superstring theory. Supersymmetry is a bridge between the low energy phenomenology and high-energy fundamental physics.

36 Outline

37 Higgs boson mass in the MSSM: The SM-like Higgs boson mass is around 125 GeV. The tree-level Higgs boson mass is smaller than M Z. The Higgs boson mass is enhanced by the top quarks/squarks loop corrections. The maximal stop mixing is needed to relax the fine-tuning. Problem: the SU(3) C U(1) EM symmetry breaking.

38 The LHC Supersymmetry Search Contraints: The first two-generation squark mass low bounds are around 1.6 TeV. The gluino mass low bound is around 2.0 TeV. The stop and sbottom mass low bounds are around 1 TeV, respectively. The SSMs are fine-tuned!!!

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42 Supersymmetry at the Current and Future Colliders Can we rule out supersymmetry at the LHC, VLHC, and SPPC? No! No!! No!!! Points: supersymmetry breaking soft mass scale can be pushed to be much higher than 1 TeV, for example, 100 TeV, while gauge coupling unification can still be realized due to threshold corrections around the GUT scale. Conclusion: supersymmetry will defintely not die in the near future!!! The interesting question: can we rule out the natural supersymmetry? Or can we solve the supersymmetry electroweak fine-tuning problem?

43 Fine-Tuning Definition I: Electroweak symmetry breaking condition µ M2 Z = m2 H d m 2 H u tan 2 β tan 2 β 1. Fine-tuning Definition I 1 : the quantitative measure FT for fine-tuning is the maximum of the logarithmic derivative of M Z with respect to all the fundamental parameters a i at the GUT scale FT = Max{ GUT i }, GUT i = ln(m Z ) ln(a GUT. i ) 1 J. R. Ellis, K. Enqvist, D. V. Nanopoulos and F. Zwirner, Mod. Phys. Lett. A 1, 57 (1986); R. Barbieri and G. F. Giudice, Nucl. Phys. B 306, 63 (1988).

44 Fine-Tuning Definition II Higgs potential: Higgs boson mass V = m 2 h h 2 + λ h 4 h 4. m 2 h = 2m2 h, m2 h µ 2 + m 2 H u tree + m 2 H u rad. The fine-tuning measure 2 : FT 2δm2 h m 2 h. 2 R. Kitano and Y. Nomura, Phys. Lett. B 631, 58 (2005) [hep-ph/ ]; Phys. Rev. D 73, (2006) [hep-ph/ ].

45 Fine-Tuning Definition II The µ term or effective µ term is smaller than 400 GeV. The squar root M t m 2 t + m 2 t of the sum of the two stop 1 2 mass squares is smaller than 1.2 TeV. The gluino mass is lighter than 1.5 TeV. Comment: these bounds can be relaxed a little bit if we do the precise calculations and consider low mediation scale.

46 Fine-Tuning Definition III The minimization condition for electroweak symmetry breaking MZ 2 2 = m2 H d + Σ d d (m2 H u + Σ u u) tan 2 β tan 2 µ 2. β 1 The fine-tuning measure 3 FT Max{ 2C i MZ 2 }. 3 H. Baer, V. Barger, P. Huang, D. Mickelson, A. Mustafayev and X. Tata, Phys. Rev. D 87, no. 11, (2013) [arxiv: [hep-ph]].

47 Comments on Fine-Tuning Fine-Tuning Definition III is weak. Fine-Tuning Definition II is smilar to III. Fine-Tuning Definition I is strong. Question: the Natural SSMs?

48 Supersymmetric SMs: Natural supersymmetry 4. Supersymmetric models with a TeV-scale squarks that can escape/relax the missing energy constraints: R parity violation 5 ; compressed supersymmetry 6 ; stealth supersymmetry 7 ; etc. 4 S. Dimopoulos and G. F. Giudice, Phys. Lett. B 357, 573 (1995) [hep-ph/ ]; A. G. Cohen, D. B. Kaplan and A. E. Nelson, Phys. Lett. B 388, 588 (1996) [hep-ph/ ]. 5 R. Barbier, C. Berat, M. Besancon, M. Chemtob, A. Deandrea, E. Dudas, P. Fayet and S. Lavignac et al., Phys. Rept. 420, 1 (2005) [hep-ph/ ]. 6 T. J. LeCompte and S. P. Martin, Phys. Rev. D 84, (2011) [arxiv: [hep-ph]]; Phys. Rev. D 85, (2012) [arxiv: [hep-ph]]. 7 J. Fan, M. Reece and J. T. Ruderman, JHEP 1111, 012 (2011) [arxiv: [hep-ph]]; arxiv: [hep-ph].

49 Supersymmetric SMs: Supersymmetric models with sub-tev squarks that decrease the cross sections: supersoft supersymmetry 8. Displaced Supersymmetry 9. Double Invisible Supersymmetry 10. Radiative Natural Supersymmetry G. D. Kribs and A. Martin, arxiv: [hep-ph], and references therein. 9 P. W. Graham, D. E. Kaplan, S. Rajendran and P. Saraswat, JHEP 1207, 149 (2012) [arxiv: [hep-ph]]. 10 J. Guo, Z. Kang, J. Li, T. Li and Y. Liu, arxiv: [hep-ph]; D. S. M. Alves, J. Liu and N. Weiner, arxiv: [hep-ph]. 11 H. Baer, V. Barger, P. Huang, D. Mickelson, A. Mustafayev and X. Tata, Phys. Rev. D 87, no. 11, (2013) [arxiv: [hep-ph]].

50 Supersymmetric SMs: Maximally Natural Supersymmetry 12. Super-Natural Supersymmetry 13. Folded Supersymmetry (neutral naturalness) 14. The top quark partner is charged under another SU(3) but not SU(3) C, so its production cross section is highly suppressed. 12 S. Dimopoulos, K. Howe and J. March-Russell, Phys. Rev. Lett. 113, (2014) [arxiv: [hep-ph]]. 13 T. Leggett, T. Li, J. A. Maxin, D. V. Nanopoulos and J. W. Walker, arxiv: [hep-ph]; Phys. Lett. B 740, 66 (2015) [arxiv: [hep-ph]]; G. Du, T. Li, D. V. Nanopoulos and S. Raza, Phys. Rev. D 92, no. 2, (2015) [arxiv: [hep-ph]]; T. Li, S. Raza and X. C. Wang, Phys. Rev. D 93, no. 11, (2016) [arxiv: [hep-ph]]. 14 G. Burdman, Z. Chacko, H. S. Goh and R. Harnik, JHEP 0702, 009 (2007) [hep-ph/ ]; N. Craig, S. Knapen and P. Longhi, Phys. Rev. Lett. 114, no. 6, (2015) [arxiv: [hep-ph]].

51 The Second Definition: Natural Supersymmetry 15. The first two generation squarks can be very heavy: no effects on fine-tuning! The gluino and stop are light, possible one sbottom. The Higgsino are light. The LHC searches: gluino, stop, light sbottom, and Higgsinos. 15 S. Dimopoulos and G. F. Giudice, Phys. Lett. B 357, 573 (1995) [hep-ph/ ]; A. G. Cohen, D. B. Kaplan and A. E. Nelson, Phys. Lett. B 388, 588 (1996) [hep-ph/ ].

52 The Third Definition: Radiative Natural Supersymmetry 16. The first two generation squarks can be heavy. The gluino and stop can be heavy as well. The Higgsino are light. The LHC searches: Higgsinos. 16 H. Baer, V. Barger, P. Huang, D. Mickelson, A. Mustafayev and X. Tata, Phys. Rev. D 87, no. 11, (2013) [arxiv: [hep-ph]].

53 The First Definition: Non-Universal Gaugino Masses 17. Higgsino LSP. The right-handed sleptons are light. The Bino might be light as well. The LHC searches: Higgsinos, right-handed sleptons, and Bino. 17 S. Antusch, L. Calibbi, V. Maurer, M. Monaco and M. Spinrath, JHEP 1301, 187 (2013) [arxiv: [hep-ph]]; L. Calibbi, T. Li, A. Mustafayev and S. Raza, Phys. Rev. D 93, no. 11, (2016) [arxiv: [hep-ph]].

54 The First Definition: Super-Natural Supersymmetry 18. Bino LSP. The right-handed sleptons are light. The LHC searches: Bino and right-handed sleptons. 18 T. Leggett, T. Li, J. A. Maxin, D. V. Nanopoulos and J. W. Walker, arxiv: [hep-ph]; Phys. Lett. B 740, 66 (2015) [arxiv: [hep-ph]]; G. Du, T. Li, D. V. Nanopoulos and S. Raza, Phys. Rev. D 92, no. 2, (2015) [arxiv: [hep-ph]]; T. Li, S. Raza and X. C. Wang, Phys. Rev. D 93, no. 11, (2016) [arxiv: [hep-ph]].

55 Natural Solution to the Fine-Tuning Problem Fine-Tuning Definition: FT Natural Solution: = Max{ GUT i }, GUT i = M n Z = f n ( MZ M 1/2 ) M n 1/2. ln(m Z ) ln(a GUT. i ) ln(m n Z ) ln(m n 1/2 ) Mn 1/2 M n Z M n Z M n 1/2 1 f n f n O(1).

56 Supersymmetry Mediation Gravity mediation Gauge mediation Gravitino is the LSP, the NLSP can be Wino, Higgsino, Bino, sneutrino, slepton, and stop/sbottom in general. Anomaly mediation Wino can be the LSP, but its density should be smaller than the observed value.

57 The muon anomalous magnetic moment The well-known discrepancy between theory and experiment is a exp µ a SM µ = (2.68 ± 0.63 ± 0.43) The neutralino-smuon loop contribution a χ0 µ µ 1 192π 2 m 2 µ M 2 SUSY The chargino-sneutrino loop contribution ( sgn(µm1 )g1 2 sgn(µm 2)g2 2 ) tan β. aµ χ± ν sgn(µm 2 ) 1 mµ 2 g 2 32π 2 MSUSY 2 2 tan β.

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59 The muon anomalous magnetic moment a µ ( 100 GeV M SUSY ) 2 tan β for sgn(µm2 ) > 0. The 2σ bound on a µ can be achieved for tan β = 10 if four relevant sparticles are lighter than GeV. While for smaller tan β ( 3), the lighter sparticles ( 500 GeV) are needed.

60 B Physics Anomalies: R(K)/R(K ) and R(D)/R(D ) 19 The superpotential in the MSSM with R-parity violation W = µh d H u + y u ij Q i U c j H u + y d ij Q i D c j H d + y e ij L i E c j H d, W L=1 = 1 2 λ ijkl i L j E c k + λ ijk L iq j D c k + µ il i H u, W B=1 = λ ijk Uc i D c j D c k. It might be very difficult to explain both anomalies simultaneously. The constraints on sparticle masses: m d 1.1 TeV, mũ 1 TeV, and m ν 600 GeV for R(K)/R(K ), and m d 1 TeV for R(D)/R(D ). 19 N. G. Deshpande, Xiao-Gang He, Eur. Phys. J. C77 (2017) no. 2, 134, arxiv: [hep-ph], etc.

61 Natural Anomaly Mediation

62 Gauge Mediation with Multiple Messengers

63 Type IIA Intersecting D-Brane Model

64 GmSUGRA

65 PMSSM-11 Input Parameters

66 Experimental Constraints

67 LHC Constraints

68 Best Fit

69 PMSSM-11 Figures

70 Thank You Very Much for Your Attention!