Phenomenology of 5d supersymmetry p. 1 Phenomenology of 5d supersymmetry Gautam Bhattacharyya Saha Institute of Nuclear Physics, Kolkata G.B., Tirtha Sankar Ray, JHEP 05 (2010) 040, e-print:arxiv:1003.1276 [hep-ph]
Phenomenology of 5d supersymmetry p. 2 The plan In a constrained 4d MSSM, one starts with a common scalar mass (m 0 ) and a common gaugino mass (M 1/2 ) at high scale (e.g. GUT scale) and run them down to weak scale. We do exactly the same, except that MSSM is embedded in a higher dimension with inverse compactification radius around 1 TeV. In scenarios where TeV-size soft masses are generated at a low cutoff scale (18-20 TeV), our work provides a common ground for a general class of theories. Compared to the standard 4d thery, here the running is faster but on a shorter interval. We show the allowed/disallowed zone in the plane of the common scalar mass and common gaugino mass, and compare our observations with the usual 4d results.
Phenomenology of 5d supersymmetry p. 3 Why SUSY AND Extra-D? SUSY and Extra-D are two general classes of BSM theories. From top-down approach, string theory provides a rationale to link SUSY and Extra-D. String models intrinsically extra dimensional and often contain SUSY. A rigorous connection is still a long shot! Extra-D theories are nonrenormalizable and more fundamental theories containing supersymmetry often provide UV completion. Supersymmetrization stabilizes the scalar potential (even in Extra-D). Corollary: Upper limit m h < 135 GeV gets relaxed by a few tens of GeV. G.B., S.K. Majee, A. Raychaudhuri, NPB 793 (2008) 114 (Flat space); G.B., S.K. Majee, T.S. Ray, PRD 78 (2008) 071701, Rapid Comm (Warped space) SUSY breaking may be triggered by Extra-D mechanism. R 1 > 500 GeV (g 2 of muon, FCNC, Z b b, ρ parameter, b sγ) [Appelquist et al, Nath et al, Buras et al, Agashe et al, Haisch, Weiler,...]
Phenomenology of 5d supersymmetry p. 4 LHC reach of R 1 Bulk and orbifold corrections split KK masses. If R 1 = 500 GeV, M γ (1) 500 GeV, M V (1), m l (1) 550 GeV, m Q (1) 600 GeV, M g (1) 650 GeV. qg Q (1) V (1) 1 jet + n leptons + Missing energy. Most imp cuts: (i) leptons isolated from jet ( R > 0.7), (ii) 5σ signal: R 1 700 GeV with 100 fb 1 at LHC. M li l j M Z > 10 GeV. 1000 Integrated Luminosity (fb -1 ) 100 10 1 3-Lep 4-Lep 2-Lep(L) 2-Lep(U) - // _ s = 14 TeV 3-Lep 4-Lep 2-Lep(L) 2-Lep(U) - / / _ s = 10 TeV 0.1 300 400 500 600 700 800 300 400 500 600 700 R -1 (GeV) R -1 (GeV) [G.B., A. Datta, S.K. Majee, A. Raychaudhuri, NPB 821 (2009) 48]
Phenomenology of 5d supersymmetry p. 5 SUSY UED 5d flat space-time. Compactification: S 1 /Z 2 orbifold. Orbifolding generates zero mode chiral fermions. 5d N=1 4d N=2. Compactification breaks N=2 to N=1 at the fixed points. ««Aµ φ φl φ R Vector hyp : V, Matter hyp : Ψ λ ψ ψ L ψ R Aµ φl λ ««φ ψ ψ L φr ψ R ««V(x, y) = Φ(x, y) = F L (x, y) = F R (x, y) = 2 2πR V (0) (x) + 2 2πR X 2 X 2πR n=1 n=1 Φ (n) (x)sin ny R, 2 2πR F (0) L (x) + 2 2πR X 2 X 2πR n=1 F (n) R n=1 ny (x) sin R. V (n) (x)cos ny R, F (n) L ny (x) cos R, N=1 supersymmetry broken by some brane dynamics.
Phenomenology of 5d supersymmetry p. 6 RG evolution New contributions to β functions come from ΛR number of KK states. The contribution from a given KK mode does not depend on the KK label. We neglect zero mode masses, i.e. n th KK level is kicked into life when we cross the energy scale n/r. As we cross different KK thresholds, the beta functions also change. At an energy scale Q, where n < QR < (n + 1), X t = β X, where β X = β 0X + n β X. Gauge couplings and gaugino masses: β gi = g3 i 16π 2 [ b 0 i + n b i ], β Mi = g2 i M [ ] i b 0 16π 2 i + n b i. with b 0 i = (33/5, 1, 3), and b i = (26/5, 2, 2).
Phenomenology of 5d supersymmetry p. 7 Multiplets and renormalization If all generation matters access bulk, pert. gauge unification requires R 1 > 10 10 GeV. Third generation better be in bulk to drive EWSB. First two generations kept at brane. For R 1 = 1 TeV, pert. gauge coupl unification at around 30 TeV. Yukawa interaction confined at the brane, otherwise it will break N = 2 bulk SUSY. Yukawa couplings become non-perturbative near Λ 20 TeV. N = 2 yields a massive representation of SUSY. This mass is like central charge which is not renormalized. As a consequence, no wave-function renormalization of matter/higgs hypermultiplets from bulk interaction (Dienes, Dudas, Gherghetta 98, Barbieri, Ferrara, Maiani, Palumbo, Savoy 82). β 0 t = y» t 16π 2 6yt y t + yb y b 16 3 g2 3 3g2 2 13 15 g2 1, βt = βt 0 (g i 0) β 0 a t = 1 16π 2»a t 18y t y t + y b y b 16 3 g2 3 3g2 2 13 32 + y t 3 g2 3M 3 + 6g2M 2 2 + 26 «15 g2 1M 1 15 g2 1 «+ 2a b yb y t, βat = β 0 a t (a t g i 0).
Phenomenology of 5d supersymmetry p. 8 gauginos, scalars, radiative EWSB M 1, M 2, M 3 (0.4,0.8,3.0) M 1/2 (in 4d), (0.7,0.8,2.0) M 1/2 (in 5d) m 2 Q3 m 2 0 + 5.5M2 1/2 (in 4d), m2 0 + 3.5M2 1/2 (in 5d)
Phenomenology of 5d supersymmetry p. 9 m 0 M 1/2 plots 3 DM candidates: Ñ 1 (LSP), γ 1, γ 1. If KK parity is not conserved, then the usual LSP is the only candidate. 2.6 Br(b sγ) 10 4 4.5, 10.6 a new µ 10 10 43.6, 0.087 Ω DM h 2 0.138
Phenomenology of 5d supersymmetry p. 10 Summary Top-down: Fundamental theories at high scale are generally higher dimensional and often contain SUSY at lower scale. Bottom-up: Supersymmetry breaking may be triggered by extra-d. MSSM embedded in S 1 /Z 2. Orbifolding gives chiral fermions. Zero modes correspond to 4d MSSM. 5d N = 1 4d N = 2: (Q, Q c ). In the 5d bulk N = 2, but at the orbifold fixed points N = 1. How to break N = 1 brane SUSY? SS mechanism (Pomarol, Quiros, von Gersdorff,..),S 1 /(Z 2 Z 2) (Barbieri, Hall, Nomura), brane-bulk interface dynamics (Mirabelli, Peskin,...) distant source (Kaplan, Kribs, Schmaltz). We assume a common scalar mass (m 0 ), common gaugino mass (M 1/2 ), and vary them in the range c/r, with c = [0.1 1.0]. Run them down from Λ 20 TeV with power law scaling with KK thresholds. Confront with low energy observables (DM, b sγ, (g 2) µ,..).