The Stueckelberg Extension and Extra Weak Dark Matter

Size: px

Start display at page:

Download "The Stueckelberg Extension and Extra Weak Dark Matter"

Ophelia Ward
5 years ago
Views:

1 The Stueckelberg Extension and Extra Weak Dark Matter PN Miami-2006 Conference with Boris Kors, Daniel Feldman, and Zuowei Liu

2 CDM Candidates Axion Right handed neutrino Neutralino Singlino Sneutrino KK - CDM (LKP in UED models) Self-interacting dark matter (Glueballs from hidden sector) Superheavy dark matter (Cryptons with masses GeV) Superweakly interacting dark matter Lightest conformality particle +... (LCP) (in AdS/CFT type models)

3 Extra Weakly Interacting Massive Particles (XWIMP) suppression via the connector sector WIMP Visible Sector SU(3) C X SU(2) L X U(1) Y Connector Sector!! (Q Y,Q X ) FI D Terms MSSM (B "," B, D B ) (C "," C, D C ) Stueckelberg Hidden Sector U(1) X XWIMP The Stueckelberg extension provides an explicit model for XWIMPS. B. Kors, P.N,. PLB 586, 366 (2004); JHEP,0412, 005(2004). D. Feldman, B. Kors and P.N., hep-ph/ (PRD to appear)

4 Outline Stueckelberg mechanism St extension of SM and MSSM Predictions of St extensions Extra-weakly interacting dark matter Conclusions/prospects

5 Vector boson mass without the Higgs mechanism 2D Abelian Schwinger model 3D Chern-Simon theory 4D Stueckelberg mechanism L = 1 4 F µνf µν 1 2 (ma µ + µ σ) 2 +ga µ J µ Invariant under δa µ µ ɛ, δσ mɛ E.C.G. Stueckelberg, Helv. Phys. Acta 11, 225(1938).

6 Stueckelberg in compactification of extra dimensions Compactification of a 5D theory on half-circle L 5 = 1 4 F ab(z)f ab (z). a = 0, 1, 2, 3, 5 L 4 = 1 4 n=0 F µν (x) (n) F µν(n) (x) n 1 2 M 2 n (A(n) µ + 1 µ φ (n) (x)) 2 M n The mass growth in 4D is via Stueckelberg mechanism

7 Stueckelberg in D-Brane Models Four Stack intersecting D-brane SM Q L g Baryonic Left W L U R D R Right Leptonic E R, N R U(3) U(2) U(1) 2 (via Stueckelberg) SU(3) SU(2) L U(1) Y D branes models start with a number of unitary group factors The U(n) s are then broken to the special unitary form by St couplings.

8 Early Attempts at model building with Stueckelberg There were early attempts to include the St mass term for the U(1) gauge field in SU(2) L U(1) Y model L B = m2 2 (B µ + 1 m µσ) 2 Here the photon develops a mass of size O(m). V.A. Kuzmin and D.G.C. McKeon, Mod. Phys. Lett.A, Vol. 16, Nov. 11 (2001)

9 Stueckelberg U(1) X extension of Standard Model L St = 1 4 C µνc µν + g X C µ J µ X 1 2 ( µσ + M 1 C µ + M 2 B µ ) 2 invariant under δ Y B µ = µ λ Y, δ Y σ = M 2 λ Y, U(1) Y δ X C µ = µ λ X, δ X σ = M 1 λ X. U(1) X The total Lagrangian L = L SM + L St B. Kors and PN, PLB 586, 2004.

10 Stueckelberg extension from String models Recent string constructions have successfully generated the axionichypercharge couplings present in the Stueckelberg extended models P. Anastasopoulos, T. P. T. Dijkstra, E. Kiritsis and A. N. Schellekens, Orientifolds, hypercharge embeddings and the standard model, Nucl. Phys. B 759, 83 (2006) [arxiv:hep-th/ ].

11 Neutral Vector Bosons in StSM Basis: C µ, B µ, A µ3 M 2 1 M 1 M 2 0 M 1 M 2 M g2 Y v2 1 4 g Y g 2 v g Y g 2 v g2 2 v2 Eigenmodes: γ, Z, Z 1 = 1 e 2 g ɛ2 g 2 Y, ɛ = M 2 M 1 Fit to LEP data constrains ɛ A very narrow Z resonance Irrational electric charge in the hidden sector

12 StSM Fit to Precision Electoweak Data Quantity Value (Exp.) StSM Pull Γ Z [GeV] ± ( ) (0.2, 0.6) σ had [nb] ± ( ) (-0.3, -0.9) R e ± ( ) (-0.1, -0.2) R µ ± ( ) (-0.1, -0.4) R τ ± ( ) (-0.1, -0.3) R b ± ( ) (0.0, 0.0) R c ± ( ) (0.0, 0.0) A (0,e) F B ± ( ) (-0.2, -0.5) A (0,µ) F B ± ( ) (-0.3, -0.9) A (0,τ) F B ± ( ) (-0.2, -0.7) A (0,b) F B ± ( ) (-0.8, -2.3) A (0,c) F B ± ( ) (-0.3, -0.8) A (0,s) F B ± ) (-0.1, -0.3) A e ± ( ) (-1.0, -2.8) A µ ± ( ) (-0.1, -0.4) A τ ± ( ) (-0.5, -1.3) A b ± ( ) (0.0, 0.0) A c ± ( ) (0.0, 0.1) A s ± ( ) (0.0, 0.0) Table 1: Results of the StSM fit to a standard set of electroweak observables at the Z pole for ɛ in the range ( ) for M 1 = 350 GeV. Pull = (SM StSM)/δExp and Pull(StSM)=Pull(SM)+ Pull. D.Feldman, Z. Liu, PN: PRL, 97, , 2006.

13 GeV Γ(Z f f) ɛ π M Z g 2 Y O(MeV ) The Z is a very narrow resonance and would require care to discern.

14 10 0 Stueckelberg Z Signals D0 Run II 246!275 pb!1 CDF Run II 200 pb!1 StSM $ constrained by EW StSM $ =.05 StSM $ =.04 StSM $ =.03 StSM $ =.02 CDF µ + µ! 95% C.L. CDF e + e! 95% C.L. CDF l + l! 95% C.L. D0 µ + µ! 95% C.L. D0 (e + e! + % %) 95% C.L.! "Br(Z # l + l! ) [pb] 10!1 10!2 10! StSM Z Mass [GeV] D.Feldman, Z. Liu, PN: PRL, 97, , 2006.

15 Stueckelberg extension of MSSM dθ 2 d θ 2 (M 1 C + M 2 B + S + S) Invariant under U(1) Y and U(1) X gauge transformations δ Y B = Λ Y + Λ Y, δ X C = Λ X + Λ X, δ Y S = M 2 Λ Y δ X S = M 1 Λ X Components B : B µ, λ B, D B ; C : C µ, λ C, D C ; S : ρ + iσ, χ, F s Two additional Majorana spinors beyond MSSM ( ) ( ) χα λcα ψ S = χ α, λ X = λ α C

16 The neutralino sector of StMSSM Basis states: ψ S, λ X, λ Y, λ 3, h 1, h 2 0 M 1 M M 1 m X M 2 0 m s s m 0 0 m s s m 0 0 m s s m 0 0 m s s m Mass eigenstates: ξ 0 1, ξ0 2, χ0 1, χ0 2, χ0 3, χ0 4 m ξ 0 1 < m χ 0 1 case: Dark matter is composed of XWIMPS

17 XWIMP Relic Density Case: ξ 0 1 is the XWIMP (m ξ 0 1 < m χ 0 1 ) XWIMPs can coannihilate with WIMPS, if the WIMPS mass lies close to the XWIMP mass. σ eff (XW IMP ) σeff msugra ( Q 1+Q ) Q depends on the mass gap Q (1 + ) 3/2 e x f, = (m ξ 0 1 m χ 0 1 )/m χ 0 1 Typically Q O(1) and the XWIMP relic density can lie in the WMAP region. D. Feldman, B. Kors and P.N., hep-ph/ (PRD to appear)

18 Most recent top value: m t = ± 2.1 GeV D. Feldman, B. Kors and P.N., hep-ph/ (PRD to appear)

21 D. Feldman, B. Kors and P.N., hep-ph/ (PRD to appear)

22 XWIMPs in models with kinetic mixing L kin = δ 2 Cµν B µν iδ( λ C σ µ µ λ B + λ B σ µ µ λ C ) + δd B D C L St = dθ 2 d θ 2 (MC + S + S) The kinetic energy can be diagonalized by a GL(2) transformation ( B = C) 1 δ ( ) 1 δ 2 B 0 C 1 1 δ 2 The neutralino mass matrix is again 6 6 and δ is constrained to be small by LEP data. The model can lead to XWIMPS.

23 XWIMPS without Stueckelberg mechanism Visible sector: MSSM Hidden sector: U(1) X gauge multiplet Connector sector: φ ± chiral multiplet Add a Fayet-Illiopoulos D-term: L = ξ X D C + ξ Y D Y The scalar potential V = g2 X 2 (Q X φ + 2 Q X φ 2 + ξ X ) 2 + g2 Y 2 (Y φ φ + 2 Y φ φ 2 + ξ Y ) 2 Minimization: < φ + >= 0, < φ > 0 M 1 = g X Q X < φ >, M 2 = g Y Y φ < φ > LEP data constrains ɛ = M 2 /M 1 and we can have XWIMPs.

24 Extra Weakly Interacting Massive Particles (XWIMP) suppression via the connector sector WIMP Visible Sector SU(3) C X SU(2) L X U(1) Y Connector Sector!! (Q Y,Q X ) FI D Terms MSSM (B "," B, D B ) (C "," C, D C ) Stueckelberg Hidden Sector U(1) X XWIMP B. Kors, P.N,. PLB 586, 366 (2004); JHEP,0412, 005(2004). D. Feldman, B. Kors and P.N., hep-ph/ (PRD to appear)

25 Conclusions/Prospects The Stueckelberg extensions of SM and of MSSM do not rely on the Higgs mechanism to break the U(1) gauge symmetry. Thus one does not need to construct scalar potentials or minimize them. Some interesting phenomena arise A sharp Z with a width in the MeV regin. It can be distinguished from the narrow RS graviton. A new unit of electric charge with which the hidden sector couples to the photon. XWIMPs arise in Stueckelberg extensions but the class of models where XWIMPS arise could be much larger. Recent work indicates that Stueckelberg extension of the type discussed can arise from string theory.

Kaluza-Klein Theories - basic idea. Fig. from B. Greene, 00

Kaluza-Klein Theories - basic idea Fig. from B. Greene, 00 Kaluza-Klein Theories - basic idea mued mass spectrum Figure 3.2: (Taken from [46]). The full spectrum of the UED model at the first KK level,