Supersymmetry Breaking

Transcription

1 Supersymmetry Breaking LHC Search of SUSY: Part II Kai Wang Phenomenology Institute Department of Physics University of Wisconsin Madison Collider Phemonology

2 Gauge Hierarchy and Low Energy SUSY Gauge Hierarchy Problem Naturalness Problem M Pl M EW m 2 H = 3λ2 t 8π 2 Λ2 + O Low Energy SUSY

3 Gauge Couplings Unification b 3 = N g ; b 2 = N g n H; b 3 = 9 + 2N g b 2 = 6 + 2N g n H b 1 = 4 3 N g n H; b 1 = 0 + 2N g n H Matters belong to the GUT multiplates.

4 MSSM W MSSM = Qu c H u + Qd c H d + le c H d + µh u H d Superpotential is holomorphic. Anomaly cancelation H d = ( H 0 d H d ) H u = ( H + u H 0 u ) H d = ( vd 0 ) ( 0 H u = v u ) vectorial under U(1) Y v 2 u + v 2 d = v 2, v = 174 GeV, tan β = v u /v d

5 Symmetries SM gauge symmetries SU(3) c SU(2) L U(1) Y Q i u c i d c i l i e c i H u H d SU(3) C SU(2) L U(1) Y 1/6 2/3 1/3 1/2 1 1/2 1/2 R-parity: to distinguish L and H d PQ-symmetry: µ-term explicitly breaks PQ-symmetry R-symmetry: gaugino masses

6 SUSY must be broken Hamiltonian : H = ω 2 {Q a, Q a} 0 H 0 = a 0 Q 2 a 0 = 0 = a Q a 0 2 SUSY Limit : Q a 0 = 0 E = 0 Non-zero VEV may NOT Breaking SUSY Sufficient: Positive Vacuum Energy Witten Index Tr( 1) F = nb 0 n0 F, n: number of zero energy state

7 V = a F a 2 + g 2 2 D2 V 0 : F a 0 or D 0 F a = W / φ a ; D = ( a q a φ a 2 ) Moduli Space & Flatness F = 0 or D = 0: a field space solution:flat Direction Classical Potential: Flat direction Classical Moduli Space D-Flat: Parametrizing (Luty-Taylor, 1996) F-Flat: usual W linear in fields vanish at the origin & infinity at φ Run-away vacuum Non-renormalization Theorem: Flat at the first order Vanish up to All order perturbation Classical Flat directions can only be lifted by Non-perturbative effect

8 SUSY Breaking at Tree Level O Raifeartaigh Mechanism (F -term) ψ x : Goldstino W = m 2 X F = m 2 ; V = m 4 > 0 Fayet-Illiopoulos (D-term) d 4 θ[φ + egv Φ + 2kV ] a Shift of k in D-term

9 R-symmetry breaking Φ = φ + θψ + θ 2 F Φ See David Kaplan s Colloqium, Chiral Symmetry protects fermion mass Majorana Gaugino Masses Dirac Gaugino masses Soft scalar masses A-term & B-term

10 How to Mediate Breaking into Observable Sector SUGRA Mediated Gauge Mediated: extra matters Anomalous U(1) Mediated: both SM and hidden sector fields are charged Anomaly Mediated (suppressing the tree SUGRA contribution) Gaugino Mediated

11 Soft Breaking of SUSY No quadratic divergence L soft = m 2 Q Q 2 + m 2 ũ ũ 2 + m 2 d d 2 + m 2 L L 2 + m 2 ẽ ẽ 2 +m 2 ν ν 2 + m 2 H u H u 2 + m 2 H d H d 2 + A u Qũ c H u + A d Q d c H d + A l L e c H d + A ν L ν c H u + h.c. + B µ H u H d + h.c. W α M 1 B B M 2 M SUSY O(TeV) W α M G 3 a G a

12 SUSY Flavor Chiral Superfield Q = q + θq + θ 2 F q GIM mechanism in SM as well as Soft sector?

13 SUSY CP Phases in the soft SUSY breaking sector contribute to EDM. L eff i 2 d f ψσ µν γ 5 ψf µν

14 Proton Decay in Effective Theory New Physics in Low Energy Effective theory Non-renormalizable W NR = 1 Λ B QQQL + 1 Λ L LLH u H u L NR = 1 Λ 2 QQQL + 1 LLH u H u B Λ L L = W Φ 2

15 Proton Decay in SUSY GUTs p K + ν τ 1 p ( f 2 M Hc M SUSY ) 2 ( α ) 2 m 5 4π p

16 Constraint from K 0 K 0 Mixing sin 2 θ d ( m 2 d m 2 d ) 2 (30 ) TeV 2 1 (In mass eigenbasis) m 2 d: averaged squark mass, m 2 d: mass-squared difference; sin 2 θ d : mixing angle between d 1,2 m 0 universal 2 d sin θ d 0 alignment m d 30 TeV decoupling m d

17 Gauge Coupling Unification sin 2 θ W (M Z ) exp = ± Evidence of dark matter from WMAP Ω DM 23% No electric dipole moment d e < ecm No rare lepton decay Br(µ eγ) < K 0 K 0 mixing sin 2 θ d ( m2 d / m2 d )2 (30Tev/ m d )2 1 Low energy SUSY? SUSY breaking?

18 Solutions Gauge Mediated: Universal Exotic Matter Giudice & Rattazzi, 1998 String Dilaton Mediated: Universal Stabilization of Dilation Potential Arkani-Hamed et al, 1998 Anomalous U(1) mediated and flavor symmetry: Decoupled Gaugino mass (How to suppress SUGRA) Binetruy & Dudas, 1996; Dvali & Pomarol,1997; Mohapatra & Ritto, 1997 Negative squark mass (potentially breaks SU(3) C ) Arkani-Hamed & Murayama, 1997

19 String Dilaton 1 g 2 W 1 gw 2 d 2 θ k a TrWαW a aα + h.c. a 1 = S ıθ or in string : gst 2 = S + S 2 d 2 θ S k a TrW a 4 αw aα + h.c. a Chiral field S as a background field and has zero mass dimension Universal sfermions mass (gauge coupling) Gaugino Mass Question: How to Stabilize the Dilaton potential

20 Anomalous U(1) A Mediated SUSY Breaking Dvali & Pomarol, 1996; Mohapatra & Riotto, 1997 Hidden sector and observable sector are both charged under Anomalous U(1). Only φ is negatively charged. W = µ φ + φ + W MSSM F φ+ = µ φ ; F φ = µ φ + ; D = ( i q i Q i 2 + φ + 2 φ 2 + ξ) where ξ = g 2 TrQ i 192π 2 M2 Pl

21 V = i F i 2 + g 2 2 D2 = (µ 2 ξg 2 ) φ 2 + g 2 2 φ 4 + (µ 2 + ξg 2 ) φ g 2 φ = ξ µ 2 /g 2 ɛm Pl φ + = 0 Fφ+ = µ φ = µ ξ µ 2 /g 2 = µ ɛm Pl Fφ = µ φ + = 0 D = µ 2 /g 2 2 φ + 4 ɛ 0.2

22 Anomalous U(1) A vs SUGRA Soft scalar mass from F φ+ d 4 θ φ + φ +Q Q M 2 Pl F φ 2 + Q Q MPl 2 m 2 Q ɛ2 µ 2 Gaugino d 2 θw α W α φ +φ M 2 Pl ɛ 2 µ

23 D-term contribution: sfermion mass splitting m 2 Q i = q i µ 2 m 2 Q: qµ 2 ɛ 2 µ 2 D-term Dominate (F -term of the dilaton S depends on stabilization of dilaton potential.) Naturally Split!! m λ m SUSY ɛ2 q 10 3 Babu, et al, 2005

24 D-term contribution: sfermion mass splitting m 2 Q i = q i µ 2 m 2 Q: qµ 2 ɛ 2 µ 2 D-term Dominate (F -term of the dilaton S depends on stabilization of dilaton potential.) Naturally Split!! m λ m SUSY ɛ2 q 10 3 Babu, et al, 2005

25 Split Supersymmetry A phenomenological viable theory from bottom-up approach SUSY gauge unification Dark matter candidate Suppressed FCNC Suppressed large CP violation Well motivated from string theory Fine-tuning may bring in new theoretical interests. How to realize a split spectrum?

26 Outline Motivations Threshold correction in the split SUSY limit A explicit gauge mediated model U(1) B L U(1) R Model Other phenomenological feature Implications

27 A 3 = 3α + 3 (2(q α) + (u α) + (d α)) 2 = 3α 3 2 (h u + h d ) q + u + h u = 2α, q + d + h d = 2α

28 Induce mixed QCD anomaly A [SU(3)C ] 2 G The symmetry that ensures the absence of bare µ-term in the superpotential carries mixed QCD anomaly and is broken explicitly by anomaly thus a Goldstone induced. To address the µ-term problem from a gauge symmetry model Cancel mixed QCD anomaly by adding exotic quarks? Cancel the mixed QCD anomaly via Green-Schwarz Mechanism?

29 Induce mixed QCD anomaly A [SU(3)C ] 2 G The symmetry that ensures the absence of bare µ-term in the superpotential carries mixed QCD anomaly and is broken explicitly by anomaly thus a Goldstone induced. To address the µ-term problem from a gauge symmetry model Cancel mixed QCD anomaly by adding exotic quarks? Cancel the mixed QCD anomaly via Green-Schwarz Mechanism?

30 Threshold Corrections from Heavy Exotic Quarks!!! Possible Solution SUSY DSFZ axion+ Anomalous U(1) A Dynamical Generated M PQ

31 SUSY Breaking W = Sδ δ, Λ S = F S S [ M 2 F 2 xf 2 M λ = α B L α R Λ S 4π ( αb L 4π ) 2 Λ 2 S + y 2 F ( αr ) ] 2 Λ 2 4π S

32 SM Gaugino Masses A-term and B L gaugino induced Gluino Mass A t = α ( ) M ( α ) ( ) 2 F M 4π M λ log = M λ 4π M log M λ ( ) α i α t M M i = 2C i (4π) 2 A t log M f

33 Muon g 2 a µ L eff = a µ 2m µ ψσ µν ψf µν δa µ α 2 8π m 2 µ M 2 SUSY tan β Light L? Unification?