Lightest U -parity Particle (LUP) dark matter in the R -parity violating SUSY model Hye-Sung Lee University of Florida HL, K. Matchev, T. Wang [0709.0763]; T. Hur, HL, S. Nasri [0710.2653]; HL, C. Luhn, K. Matchev [0712.3505]; HL [0802.0506]. PHENO 2008
Lightest U -parity Particle (LUP) dark matter in the R -parity violating SUSY model Hye-Sung Lee University of Florida HL, K. Matchev, T. Wang [0709.0763]; T. Hur, HL, S. Nasri [0710.2653]; HL, C. Luhn, K. Matchev [0712.3505]; HL [0802.0506]. PHENO 2008
Lightest U -parity Particle (LUP) dark matter Outline • Companion symmetry of SUSY - R -parity - TeV scale U (1) ′ gauge symmetry • R -parity violating, U (1) ′ -extended SUSY model - Proton stability - Dark matter candidate PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter Companion symmetry of SUSY PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter SUSY with R -parity W R p = µH u H d y E H d LE c + y D H d QD c + y U H u QU c + ( λLLE c + λ ′ LQD c + µ ′ LH u + λ ′′ U c D c D c ) + M QQQL + η 2 η 1 M U c U c D c E c + · · · + 1. µ -problem: µ ∼ O (EW) to avoid fine-tuning in the EWSB. (Kim, Nilles [1984]) 2. over-constraining of the R -parity: All renormalizable L violating and B violating terms (unnecessarily) are forbidden. 3. under-constraining of the R -parity: Dimension 5 L & B violating terms still mediate too fast proton decay. PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter Fast proton decay e + q q d q � η λ ′′ λ ′ � W M � d � l q l u u ¯ [Dim 4 L violation & Dim 4 B violation] [Dim 5 B & L violation] R -parity violating terms R -parity conserving terms PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter Look for an additional or alternative explanation (symmetry). → We will consider TeV scale Abelian gauge symmetry, U (1) ′ . PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter TeV scale U (1) ′ gauge symmetry Natural scale of U (1) ′ in SUSY models is TeV (linked to soft term scales). → provides a natural solution to the µ -problem. ( z [ F ] : U (1) ′ charge of F ) Two conditions to “ solve the µ -problem ”. • µH u H d : forbidden z [ H u ] + z [ H d ] � = 0 • hSH u H d : allowed z [ S ] + z [ H u ] + z [ H d ] = 0 S is a Higgs singlet that breaks the U (1) ′ spontaneously. µ eff = h � S � ∼ O (EW / TeV) PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter Goal Construct a stand-alone R p violating TeV scale SUSY model without 1. µ -problem: U (1) ′ 2. proton decay problem 3. dark matter problem (non-LSP dark matter) “ R -parity violating U (1) ′ model” as an alternative to the usual “ R -parity conserving model”. Use residual discrete symmetry of the U (1) ′ to address the issues. PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter Conditions to have U (1) → Z N U (1) have a residual discrete symmetry Z N if their charges satisfy (after normalization to integers): • z [ F i ] = q [ F i ] + n i N • z [ S ] = N ( z [ F i ] : U (1) charge, q [ F i ] : Z N charge) for each field F i . PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter Residual discrete symmetry of the RPV U (1) ′ model : Proton stability without R -parity HL, Matchev, Wang [arXiv:0709.0763] HL, Luhn, Matchev [arXiv:0712.3505] PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter Discrete symmetries in presence of exotics • There may be TeV scale exotic fields required to cancel chiral anomaly. • The MSSM discrete symmetries still hold among the MSSM fields. For a physics process which has only MSSM fields in its effective operators (such as proton decay), we can still discuss with Z MSSM . N p ψ 1 ψ 2 u u ψ 3 ...... d ψ n � 1 � m = [ F 1 F 2 F 3 F 4 F 5 · · · � ] operator[p-decay] � �� M MSSM fields only PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter Proton stability in the L violating case ( U (1) ′ → B 3 ) 1. Solve the µ -problem with U (1) ′ gauge symmetry. 2. Require L violating terms such as λ ′ LQD c . 3. Then B 3 (baryon triality) is invoked in the MSSM sector. 4. Selection rule of B 3 prevents p-decay ( ∆ B = 1 ). B 3 (baryon triality): (Ibanez, Ross [1992]) U c D c E c N c Q L H u H d meaning of q B 3 −B + y/ 3 0 − 1 1 − 1 − 1 0 1 − 1 Selection rule of B 3 : (Castano, Martin [1994]) ∆ B = 3 × integer PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter Recap of the goal Construct a stand-alone R p violating TeV scale SUSY model without 1. µ -problem: U (1) ′ 2. proton decay problem: U (1) ′ → B 3 3. dark matter problem (non-LSP dark matter) A dark matter candidate without introducing an independent symmetry? PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter Residual discrete symmetry extended to hidden sector : LUP dark matter from hidden sector Hur, HL, Nasri [arXiv:0710.2653] HL [arXiv:0802.0506] PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter SM-singlet (hidden sector) fields SM-singlet exotics (hidden sector fields): often required for anomaly cancellations with U (1) ′ ([gravity] 2 − U (1) ′ , [ U (1) ′ ] 3 ) . We consider Majorana fields for simplicity. W hidden = ξ jk 2 SX j X k These hidden sector fields ( X ) are neutral and massive particles. → Potentially dark matter candidate if they are stable. PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter How to stabilize hidden sector field? Introduce “ U -parity” U p [MSSM] = even , U p [ X ] = odd • Lightest U -parity Particle (LUP): Lightest X � → stable � �� either fermion ( ψ X ) or scalar ( φ X ) component It can be invoked as a residual discrete symmetry of the U (1) ′ . Z hid = U 2 N U c D c E c N c Q L H u H d X meaning of q U 2 −U ( X number) 0 0 0 0 0 0 0 0 − 1 (Other exotics: assumed to be heavier than the lightest X .) PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter Discrete symmetries over the MSSM and the hidden sectors How consider U (1) ′ → Z 6 , which is Z 6 = B 3 × U 2 with q = 2 q B + 3 q U mod 6 . U c D c E c N c Q L H u H d X Z 6 = B 3 × U 2 0 − 2 2 − 2 − 2 0 2 − 2 − 3 (Other exotic fields: assumed to be heavier than proton and the LUP → not stable due to the discrete symmetry.) More generally, it is U (1) ′ → Z tot N , which is Z tot N = Z obs N 1 × Z hid N 2 (where N = N 1 N 2 ; N 1 and N 2 are coprime). PHENO 2008 Hye-Sung Lee
0 obs hid Lightest U -parity Particle (LUP) dark matter U (1) ! Z � Z N N 1 2 MSSM se tor Hidden se tor A unified picture of the stabilities in the observable and hidden sectors obs hid Z ( B ) Z ( U ) 3 2 N N 1 2 : stable proton : stable dark matter A single U (1) ′ gauge symmetry provides stabilities for proton (MSSM sector) and dark matter (hidden sector). PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter LUP dark matter • LUP is a neutral, massive and stable particle from hidden sector. • To be a viable dark matter candidate, it should satisfy the relic density and direct detection constraints, too. PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter Annihilation channels for the LUP dark matter For ψ X (fermionic) LUP , 1. ψ X ψ X → f ¯ f ( Z ′ mediated s -channel) 2. ψ X ψ X → � f � f ∗ ( S mediated s -channel, Z ′ mediated s -channel) 3. ψ X ψ X → SS , Z ′ Z ′ ( S mediated s -channel, ψ X mediated t -ch) 4. ψ X ψ X → SZ ′ ( Z ′ mediated s -channel, ψ X mediated t -channel) 5. ψ X ψ X → � S � S ( Z ′ mediated s -channel, φ X mediated t -channel) Z ′ � 6. ψ X ψ X → � Z ′ ( φ X mediated t -channel) 7. ψ X ψ X → � S � Z ′ ( S mediated s -channel, φ X mediated t -channel) and also similarly for φ X (scalar) LUP . PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter Predictions of relic density and direct detection cross-section (for φ X ) [Simulated with micrOMEGAs + newly constructed UMSSM model file] LUP dark matter can satisfy both the relic density and direct detection constraints. PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter Summary R -parity conserving model vs. R -parity violating U (1) ′ model U (1) ′ → B 3 × U p R p RPV signals impossible possible µ -problem solvable ( U (1) ′ ) not addressed unstable w/ dim 5 op. ( R p ) stable ( B 3 ) proton stable LSP ( R p ) stable LUP ( U p ) dark matter Conclusion: TeV scale U (1) ′ is an attractive alternative to R -parity. PHENO 2008 Hye-Sung Lee
Lightest U -parity Particle (LUP) dark matter Summary R -parity conserving model vs. R -parity violating U (1) ′ model U (1) ′ → B 3 × U p R p RPV signals impossible possible µ -problem solvable ( U (1) ′ ) not addressed unstable w/ dim 5 op. ( R p ) stable ( B 3 ) proton stable LSP ( R p ) stable LUP ( U p ) dark matter Conclusion: TeV scale U (1) ′ is an attractive alternative to R -parity. PHENO 2008 Hye-Sung Lee
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