Split Supersymmetry A Model Building Approach Kai Wang Phenomenology Institute Department of Physics the University of Wisconsin Madison UC Riverside HEP Seminar In Collaboration with Ilia Gogoladze (Notre Dame) and Heather Logan (UW-Madison)
Gauge Hierarchy and Low Energy SUSY Gauge Hierarchy Problem Naturalness Problem M Pl M EW 10 17 m 2 H = 3λ2 t 8π 2 Λ2 + O Low Energy SUSY
SUSY Flavor GIM mechanism in SMSoft sector?
SUSY CP Phases in the soft SUSY breaking sector contribute to EDM. L eff i 2 d f ψσ µν γ 5 ψf µν
Proton Decay in SUSY GUTs p K + ν τ 1 p ( f 2 M Hc M SUSY ) 2 ( α ) 2 m 5 4π p
Till 13:00:00 June, 1 st, 2005 PDT Gauge Coupling Unification sin 2 θ W (M Z ) exp = 0.23018 ± 0.00005 Evidence of dark matter from WMAP Ω DM 23% No electric dipole moment d e < 2.1 10 27 ecm No rare lepton decay Br(µ eγ) < 1.2 10 11 K 0 K 0 mixing sin 2 θ d( m 2 d / m2 d )2 (30Tev/ m d) 2 1 Low energy SUSY? SUSY breaking?
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
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
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
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 + 2 + 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
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
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
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
Gauge Couplings Unification b 3 = 11 + 4 3 N g ; b 2 = 22 3 + 4 3 N g + 1 2 n H; b 3 = 9 + 2N g b 2 = 6 + 2N g + 1 2 n H b 1 = 4 3 N g + 1 10 n H; b 1 = 0 + 2N g + 3 10 n H Matters belong to the GUT multiplates.
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?
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
Threshold Correction at the Split SUSY Limit M λ2 = α [ 2 mh 2 µ sin 2β 4π µ 2 mh 2 ( ) µ 2 log mh 2 m2 h µ 2 m 2 h ( )] µ 2 log mh 2 m H >> mu >> m h M λ2 α ( 2 m 2 ) µ sin 2β log H 4π µ 2 Heavy vectorial matter: heavy fermions as well as heavy scalars
Solutions to the µ-term Problem µ-term: Another independent fine-tuning in split SUSY? 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
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?
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?
Threshold Corrections from Heavy Exotic Quarks!!! Possible Solution SUSY DSFZ axion+ Anomalous U(1) A Dynamical Generated M PQ
the GMSB Model Under SU(2) L U(1) R U(1) B L Mohapatra & Nandi, 1997 Q(2, 0, 1/3); L(2, 0, 1); u c (1, 1/2, 1/3) d c (1, 1/2, 1/3); e c (1, 1/2, 1); ν c (1, 1/2, 1) H u (2, 1/2, 0); H d (2, 1/2, 0) Higgs fields δ(1, 1, 2); δ(1, 1, 2); S(1, 0, 0)
Remarks W = Qu c H u + Qd c H d + Le c H d + Lν c H u + δν c ν c + µh u H d SO(10) GUT Seesaw mechanism for generation of small neutrino mass Z 2 subgroup of U(1) R as an Automatic discrete gauge R-parity
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
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
M M f d dt M a = 2g 2 a (16π 2 ) 2 g 2 1 B a M λ + B 1 = i o 4 nn G hn c 2zQY 2 Q 2 + zuy 2 U 2 + zdy 2 D 2 + 2zLY 2 L 2 + ze 2 YE 2 + z 2 Hu Y 2 Hu + z 2 Hd Y 2 Hd B 2 = i 2 hn G N czq 2 + zl 2 + z 2 Hu + z 2 Hd B 3 = 2N G 2z 2 Q + z 2 U + z 2 D z F = g R g B L I 3R g B L g R B L 2 B L, Y F = I 3R + 2
RGE Running Most of RGE Runnings locate between B L breaking scale and B L gaugino mass scale
Explicit Numeric Example F S 10 20 Gev 2 S 10 12 Gev M λ (B L/R) 10 7 Gev M f 10 7 Gev A t 10 5 Gev M i 10 2 Gev
SUGRA Contribution d 2 θw α W α S F S M Pl d 4 Q Q S S M 2 Pl ( FS M Pl M Pl ) 2
Longer lived Gluino A. Arvanitaki, C. Davis, P.W. Graham, A. Pierce, J.G. Wacker hep-ph/0504210
Implications Predictable SM gaugino masses spectrum: Distinguishable from other split SUSY models Bino LSP as dark matter candidate Gauge coupling unification by imposing SO(10) normalization No FCNC from GMSB (SUGRA contribution suppressed) Less CPV phase Longer lived gluinos...
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?