Supersymmetry V. Hitoshi Murayama (Berkeley) PiTP 05, IAS

Transcription

1 Supersymmetry V Hitoshi Murayama (Berkeley) PiTP 05, IAS

2 Plan Mon: Non-technical Overview what SUSY is supposed to give us Tue: From formalism to the MSSM Global SUSY formalism, Feynman rules, soft SUSY breaking, MSSM Wed: SUSY breaking how to break SUSY, mediation mechanisms Thu: SUSY at colliders basic reactions, signatures, and how do we know it is SUSY? Fri: SUSY as a telescope supersymmetry breaking, GUT, string

3 s-channel t-channel testing chirality of scalar bosons e + ~ l + R e + ~ e + R! /Z + 4 $ i=1 # ~ 0 i e - L/R l=e,!," ~ l - R e - R ~ e - R

4 Opening the door Once the hierarchy problem solved, we can get started to discuss physics at shorter distances and earlier universe. It opens the door to the next level: Hope to answer big questions The solution to the hierarchy problem itself, e.g., SUSY, provides additional probe to physics at short distances

5 accelerators recreate Big Bang neutrinos observatories reconstruct Big Bang quarks Big Bang inflation unification Dark Field string anti-matter Dark Energy CMB B-mode Dark Matter 10!10 sec 1sec 300Kyr CMB

6 Telescope to the Planck scale Imagine SUSY breaking originates from Planck-scale physics (but not anomaly mediation) Their low-energy values subject to all physics between the Planck and TeV scales boundary conditions at the Planck scale running due to extra particles above the GUT-scale effects due to other particles below M GUT

7 Grand Unification

8 Big Questions Vertical Why are there three unrelated gauge forces? Why is strong interaction strong? Charge quantization anomaly cancellation quantum numbers Is there a unified description of all forces? Why is mw MPl? (Hierarchy Problem) Q(3, 2, ), u(3, 1, +2 3 ), d(3, 1, 1 3 ), L(1, 2, 1 ), e(1, 1, 1) 2

9 Motivations for GUT Charge quantization, anomaly cancellation, bizarre hypercharge assignments in the Standard Model Three seemingly unrelated forces yet all gauge forces Einstein s dream towards a unified description of all forces Baryogenesis no longer a prime motivation

10 Quantum Numbers in the Standard Model I didn t become a physicist to memorize these weird numbers... u d ν l L L (3,2, 1 6 ) u R (3,1,+ 2 3 ) d R(3,1, 1 3 ) (1,2, 1 2 ) l R (1,1, 1)

11 Quantum Numbers in the Standard Model To treat them on equal footing, make all particles left-handed using CP u d ν l L L (3,2, 1 6 ) u L (3 *,1, 2 3 ) d L (3*,1, 1 3 ) (1,2, 1 2 ) l L (1,1,1)

12 SU(5) GUT SU(3) SU(2) U(1) SU(5) U(1) must be traceless: try 5*: 5 5 matrices d d d ν l 1 2 λa* 0 0 0! SU(3) SU(2) τ a! U(1) 1 3 I I 2

13 SU(5) GUT u d Then the rest belongs to 10 All quantum numbers work out this way (3,2, 1 6 ) ~ ν L l L (1,2, 1 2 ) d L (3*,1, 1 3 ) * 0 u u d u u 0 u d u u u 0 d u d d d 0 l u u u l 0 u L (3 *,1, 2 3 ) ~ [ d L (3*,1, 1 3 ) d L (3*,1, 1 3 ) ] * l L (1,1,1) ~ ν (1,2, 1 l 2 ) ν L l Anomaly cancellation: L (1,2, 1 2 ) * #10 #5 * = 0

14 gauge coupling unification U(1) U(1) MSSM i SU(2) i 1 30 SU(2) SU(3) Standard Model SU(3) (GeV) (GeV)

15 Fermion Mass Relation Down- and lepton-yukawa couplings come from the same SU(5) operator 10 5* H Fermion mass relation:! m b = m τ, m s = m µ, m d = m e Reality:!! m b = m τ, 3m s = m µ, m d = 3m e Not bad!

16 SO(10) GUT SU(5) U(1) SO(10) 16 = (10, +1) + (5 *, 3) + (1, +5) Come with right-handed neutrinos! Certain uniqueness anomaly-free for any multiplets Smallest simple anomaly-free group with chiral fermions Smallest chiral representation contains all standard model fermions

17 Seesaw meachanism Once SO(10) broken to the standard model, right-handed neutrino Majorana mass becomes allowed by the gauge invariance!! M h M GUT

18 Seesaw Mechanism Why is neutrino mass so small? Need right-handed neutrinos to generate neutrino mass ( ) ν L ν R, but ν R SM neutral m D m D M ν L ν m R ν = m D 2 M << m D To obtain m 3 ~(Δm 2 atm) 1/2, m D ~m t, M 3 ~10 15 GeV (GUT!) Neutrinos are Majorana

19 Proton Decay Quarks and leptons in the same multiplet Gauge bosons can convert q to l Cause proton decay! Γ g2 M X 2 2 m p 5

20 Supersymmetric Proton Decay Γ g2 2 h s h c θ C (4π ) 2 M HC m SUSY 2 m p 5 Suppressed only by the second power of GUT scale vs fourth in X-boson exchange

21 Rest In Peace Minimal SUSY SU(5) GUT RGE analysis: use α 1 (m Z ), α 2 (m Z ), α 3 (m Z ) to extract α GUT, M Hc, M GUT =(M X2 M Σ ) 1/3 SuperK limit M Hc > GeV Even if 1st, 2nd generation scalars decoupled, 3rd generation contribution M Hc > GeV

22 Avoiding Proton Decay (Un)fortunately, proton decay rate/mode is highly model-dependent more threshold corrections (HM, Pierce) Some fine-tuning (Babu, Barr) GUT breaking by orbifolds (Kawamura; Hall, Nomura) Depends on the triplet-doublet splitting mechanism, Yukawa (non-)unification

23 Don t give up! Still, proton decay unique window to physics at >10 15 GeV Suppression by fine-tuning: p K + ν may be just around the corner Flipped SU(5): p e + π 0 possible Eventually with 1000kt detector

24 p e + π 0 SuperK: τ(p e + π 0 )> year! (90% CL) Minimal SUSY GUT:!! τ(p e + π 0 )= year (M V /10 16 GeV) 4!! M V > GeV Flipped SU(5): τ(p e + π 0 )= year (M V /10 16 GeV) 4!! M V > GeV 5-D orbifold GUT: τ(p e + π 0 ) year 24

25 Any other tests of GUTs? Yes! Once you have superparticles, we can learn a great deal from them.

26 Model-independent parameter determination e + e - L/R! /Z s-channel Chargino/neutralino mass matrices have four parameters M 1, M 2, μ, tanβ Can measure 2+4 masses can measure 10x2 neutralino cross sections σ L,R (e + e χ 0 i χ 0 j) σ L,R (e + e χ + i χ j ) can measure 3x2 chargino cross sections depend on masses of ν e, ẽ L, ẽ R input fit " ~ + e + " ~ M GeV 152 ±1.8 GeV + # ~ e µ 316 GeV 316 ±0.9 GeV "- tanβ 3 3 ±0.7 ~ 1 e - " ~ - R 1 M GeV 78.7 ±0.7 GeV t-channel

27 Superpartners as probe 500 Most exciting thing about superpartners beyond existence: They carry information of small-distance physics to something we can measure! Are forces unified? gaugino mass (GeV) LHC+LC M 3 M 2 M Energy (GeV)

28 cf. gauge coupling unification U(1) U(1) MSSM i SU(2) i 1 30 SU(2) SU(3) Standard Model SU(3) (GeV) (GeV)

29 Gaugino and scalars gaugino mass (GeV) Gaugino masses test unification itself independent of intermediate scales and extra complete SU(5) multiplets, also GMSB LHC+LC M 3 M 2 M 1! Scalar masses test beta functions at all scales, depend on the particle content (Kawamura, HM, Yamaguchi) mass squared [10 3 GeV 2 ] D E Q L testing matter unification U Energy [GeV] Energy (GeV) 29

30 grand desert LHC finds SUSY, LC establishes SUSY no more particles beyond the MSSM at TeV scale Gaugino masses unify (two more coincidences) Scalar masses unify for 1st, 2nd generations (two for 10, one for 5*, times two) Scalar masses unify for the 3rd generation 10 (two more coincidences) strong hint that there are no additional particles beyond the MSSM below M GUT except for gauge singlets. 30

31 seesaw mechanism 0νββ seen, neutrinos are Majorana lepton-flavor violation (µ e conversion, τ µγ) seen at the reasonable level expected in SUSY seesaw (even though I don t believe msugra) LBL oscillation finds θ 13 soon just below the CHOOZ limit Scalar masses unify for the 3rd generation 5* up to the neutrino Yukawa coupling y 3 1 above M 3 =y 32 v 2 /m 3 pretty much proves seesaw 31

32 cosmology The neutralino mass and its coupling to other SUSY particles are measured Calculate the neutralino annihilation cross section, agrees with the Ω M h 2 =0.14 Calculate the neutralino scattering cross section, agrees with the direct detection B-mode fluctuation in CMB is detected, with a reasonable inflationary scale strong hint that the cosmology has been normal since inflation (no extra D etc) 32

33 Normal cosmology cosmic abundance WMAP LHC ILC B-mode fluctuation mass of the Dark Matter Ω M = 0.756(n +1)x f n+1 g 1/ 2 σ ann M Pl 3 Annihilation cross section 3s 0 2 8πH α 2 /(TeV) 2 0 σ ann 33

34 Large θ 23 and quarks Large mixing between ν τ and ν µ Make it SU(5) GUT Then a large mixing between s R and b R Mixing among righthanded fields drop out from CKM matrix But mixing among superpartners physical 34 O(1) effects on b s transition possible! (Chang, Masiero, HM)! Expect CP violation in neutrino sector especially if leptogenesis

35 more indirect evidence Possible additional evidence, e.g.,: B d φ K S shows deviation from the SM consistent with large b R -s R mixing above M GUT LBL oscillation finds θ 13 soon just below the CHOOZ limit determines the normal hierarchy and finds CP violation Isocurvature fluctuation seen suggestive of N 1 coherent oscillation (curvaton), avoiding the gravitino problem 35

36 Consequences in B physics CP violation in B s mixing (B s J/ψ φ) Addt l CP violation in penguin b s (B d φ K s ) Indirect evidence for leptonquark unification 36

37 Testing string theory?

38 Dirty Little Secret about Supersymmetry R-parity is not enough to ensure longevity of matter! Once supersymmetry is there, with or without grand unification, Planck-scale physics can cause too-rapid proton decay Dangerous operators: h M Pl Q 1 Q 1 Q 2 L i h Q 1 Q 2 Q 2 L i M Pl Typically, h < , 10 7, respectively 38

39 But there are small numbers But remember that we actually do see small numbers in our daily life. neutrinos d s b u c t e µ! TeV GeV MeV kev ev mev 39

40 But there are small numbers But remember that we actually do see small numbers in our daily life. Yukawa couplings for 1st, 2nd generations are pretty small. Using λ θ C 0.22, h u /h t λ 8, h d /h b λ 4, h e /h t λ 5 Aren t they unnatural? Yes, of course! 40

41 Broken Flavor Symmetry M u ~ Flavor quantum numbers (SU(5)-like): 10(Q, u R, e R ) (+4, +2, 0) 5*(L, d R ) (+2, +2, +2) Flavor symmetry broken by a VEV λ 0.22 λ 8 λ 6 λ 4 λ 6 λ 6 λ 6 λ 6 λ 4 λ 2 λ 6 λ 4 λ 2, M ~ λ 4 λ 2 1 d λ 4 λ 4 λ 4, M ~ λ 2 λ 2 λ 2 l λ 6 λ 4 λ 2 λ 6 λ 4 λ 2 m u :m c :m t m d2 :m s2 :m b2 m e2 :m µ2 :m 2 τ λ 8 : λ 4 :1 Neutrinos are anarchy (Hall, HM, Weiner; Haba, HM; de Gouvêa, HM) 41

42 Flavor Symmetry Suppresses Proton Decay, too! Once the quarks and leptons carry a new charge, it would forbid the dangerous proton decay operators. Proton decay may be suppressed because of the same reason why 1st and 2nd generation particles are light. (HM, D.B. Kaplan) h h Q 1 Q 1 Q 2 L i Q 1 Q 2 Q 2 L i M Pl M Pl Previous charge assignment gives 42

43 A Very Ambitious Model Use string-inspired anomalous U(1) for everything The only symmetry beyond SU(3) C SU(2) L U(1) Y Only two right-handed neutrinos No new mass scales except for M Pl and m SUSY Quark masses and CKM matrix Lepton masses Right-handed neutrino masses (no GUT-scale) Left-handed neutrino masses and MNS matrix R-parity as an unbroken subgroup of U(1) Adequate suppression of proton decay? (Dreiner, HM, Thormeier) 43

44 44 Harnik, Larson, HM, Thormeier

45 dilaton domination (Kaplunovsky, Louis; Brignole, Ibañez, Muñoz) In string theory, there are many moduli fields Once SUSY broken, they tend to acquire SUSY breaking F-terms If they couple universally to all three generations, you get universal scalar mass dilaton (but no model exists) overall modulus if all generations have the same modular weight (but then how do we understand the fermion mass hierarchy?)

46 parametrization (Binétruy, Gaillard, Nelson) Assume SUSY breaking due to F-terms of the dilaton and the overall modulus threshold corrections to the gauge couplings: α 1 i (M U )=α 1 (M String ) + α 1 i α 1 i = 1 4π (b i b GS )log η(t) 4 b 3=9 + b 2= i=1 b 1= (2n Qi + n Ui + n Di ) 3 (3n Qi + n Li ) + n H1 + n H2 i=1 3 (n Qi + 8n Ui + 2n Di + 3n Li + 6n Ei ) + 3 i=1 5 (n H 1 + n H2 )

47 parametrization (Binétruy, Gaillard, Nelson) Assume SUSY breaking due to F-terms of the dilaton and the overall modulus M i = g 2 i m 3/2 s 3sinθ + M i M i = g 2 i m 3/2 {b i + s 3sinθg 2 s [ + 2t cosθg 2 (t) ( M 2 j ( =m2 3/2 1 + n j cos 2 θ ) + M 2 j { M 2 j =m2 3/2 C i C j i j ) δ GS + b i 2 C j i (1 + n j) j γ j + 2t cosθg 2 (t) km [ +2 3ssinθ i γ km γ i jg 2 i 1 2s km ]} /16π 2 j (n j + n k + n m + 3) ]} γ km j

48 extracting string parameters

49 Data Precision measurements of supersymmetry parameters at LHC/ ILC fit the data to the string predictions (Blair, Porod, Zerwas) Parameter Ideal Reconstructed m 3/ ±0.4 S ±0.006 T ±0.2 sin 2 θ ±0.002 g 2 s ±0.002 δ GS 0 0.1±0.4 n L ±0.04 n E ±0.05 n Q ±0.02 n U ±0.02 n D ±0.04 n H ±0.06 n H ±0.02 tan β ±0.13

50 Conclusion Supersymmetry has been motivated as a way to stabilize (and explain) the hierarchy If it is true, we expect exciting time at the near-future collider experiments Once seen and studied, they may be our telescope to physics at GUT and Planck/ string scales