Unification without Doublet-Triplet Splitting SUSY Exotics at the LHC

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1 Unification without Doublet-Triplet Splitting SUSY Exotics at the LHC Jürgen Reuter Albert-Ludwigs-Universität Freiburg W. Kilian, JR, PLB B642 (2006), 81; and work in progress (with F. Deppisch, W. Kilian) SUSY 07, Karlsruhe, July 26, 2007

2 Motivation for (SUSY) Unification Incompleteness/Theoretical Dissatisfaction EWSB, H, m ν, DM, hierarchy, , reducible representation: q (3, 2) 1 3 l (1, 2) 1 u c (3, 1) 4 3 d c (3, 1) 2 3 ec (1, 1) H (1, 2) 1 Supersymmetry: consistent extrapolation to high scales unification quantitatively testable two Higgs doublets H u, H d TeV-scale SM-superpartners Running of 1/α, MSSM, i.e. with 1 [H u H d ] 1/α 1 1/α 2 1/α 3 Bottom-Up Approach: just MSSM µ [GeV] Pati/Salam: G PS = SU(4) c SU(2) L SU(2) R Z 2 Gauge coupling unification by Georgi/Glashow: G GG = SU(5) Unification verification only with megatons? What about colliders? SPA: super precision accurately Look for chiral exotics King et al., 2005/6 Physics beyond MSSM provides handle to GUT scale

3 The Doublet-Triplet Splitting Problem MSSM Higgses included in 5 H 5 H ( ) D 5 H = (3, 1) 2 (1, 2) 1 : 3 H u ( ) D c 5 H = (3, 1) 2 (1, 2) 1 : 3 ɛh d D, D c colored triplet Higgses with charges ± 1 3 (EW singlet) colored Dirac fermion D with charge 1/3 (EW singlet) Unification requires omitting colored part of SU(5) Higgs 5 H, 5 H 1) Doublet-triplet splitting problem (m H 100 GeV, m D GeV) Welcome, since SU(5)-symmetric Higgs interactions would read H = lh d e c + qɛh d d c + qɛld c + d c u c D c 10 5 H 10 = lh d e c + qɛh u u c + Du c e c + Dqɛq Generating SM masses leptoquark and diquark coupl. for D, D c triggers rapid proton decay

4 Interactions e u D e u u d D D u d ν d D D Leptoquark couplings (and SUSY vertices) Diquark couplings (and SUSY vertices) Vector bosons induce e.g. decay p e + π 0 experimentally: τ(p) > yrs u d D ū u e +

5 Doublet-Triplet Splitting Possible scenarios: 1. Colored singlets are heavy (GUT scale) = doublet-triplet splitting enables exact unification near GeV and excludes rapid proton decay Proton decay may still be too fast (depending on the superpotential) Doublet-triplet splitting is not trivially available 2. Colored singlets are light (TeV scale) Simple unification no longer happens near GeV, nor elsewhere Running of 1/α, MSSM with 1 [(H u,d) (H d,d c )] 1/α 1 1/α 2 1/α µ [GeV] Proton-decay coupl. must be excluded: consistent with GUT symmetry?

6 Further MSSM Issues 2) µ problem: SUSY µ-term µh u H d, not related to soft breaking Why µ O(100 GeV), not O(10 16 GeV)? Possible extension as a solution: singlet Higgs S with superpotential λsh uh d λ S H uh d = µh uh d NMSSM: S should be somehow related to soft-breaking Large top Yukawa coupl. drives effective H u mass squared negative: This mechanism may also be responsible for a S vev in the NMSSM requires the existence of a vectorlike pair of chiral superfields for instance, D and D c (colored) with coupling SDD c... as required by SU(5), if SH uh d is present, gives Dirac mass to D Without tree-level quartic coupling, the CW mechanism implies S 4πm soft, so S H. 3) Higgs-matter unification: Why only one family of Higgs matter? SU(5), G PS SO(10) unify Higgs fields with SM matter...

7 Higgs-Matter Unification Trinification: all IAs equally G Tri = SU(3) c SU(3) L SU(3) R Z 3 E 6 G Tri, SO(10) w/ add. gauge bosons X(3, 3, 3) + h.c. 78 irred. multiplet (27) unifies all matter, Higgs, singlets (for each family) contains NMSSM, allows for radiative SB for singlets + doublets Complete G Tri or E 6 multiplet: no unification Running of 1/α, MSSM with 3 [(H u,d) (H d,d c )] 1/α 1 1/α 2 1/α µ [GeV] Possible scenarios: 1. Omit one bi-triplet D, D c family doublet-triplet splitting 2. Add one extra MSSM Higgs family ESSM S.King et al., 2005/6 3. Different unification pattern

8 Running With Triplets Kilian/JR, 2006 Bottom-up approach: MSSM with one generation of triplets 60 Running of 1/α, MSSM with 1 [(Hu, D) (Hd, D c )] SU(3)c SU(2)L SU(2)R 40 1/α1 1/α2 20 1/α3 1/α log (µ [GeV]) GeV: crossing of SU(2) L and U(1) Y unification to LR symmetry SU(2) L SU(2) R, requires ν c R SU(3) c crosses at GeV: too high

9 Running With Triplets Kilian/JR, 2006 Bottom-up approach: MSSM with one generation of triplets 60 Running of 1/α, MSSM with 1 [(Hu, D) (Hd, D c )] SU(4)c SU(2)L SU(2)R 40 1/α1 1/α2 20 1/α3 1/α log (µ [GeV]) GeV: crossing of SU(2) L and U(1) Y unification to LR symmetry SU(2) L SU(2) R, requires ν c R SU(3) c crosses at GeV: too high extend to SU(4) C : unification possible at GeV

10 Running With Triplets Kilian/JR, 2006 Complete Model: Full SUSY E 6 /G Tri matter spectrum above 10 3 GeV, except ν c 60 Running of 1/α, MSSM with 3 [(Hu, D) (Hd, D c )] SU(4)c SU(2)L SU(2)R 40 1/α1 20 1/α2 1/α log (µ [GeV]) PS symmetry with ν R above GeV Q L = (Q, L) = (4, 2, 1) D = (D, D c ) = (6, 1, 1) Q R = ((u c, d c ), (ν c, l c )) = (4, 1, 2) S = (1, 1, 1) H = (H u, H d ) = (1, 2, 2) E 6 symmetry (and possibly extra fields) at GeV

11 Flavor Symmetry Proton decay? Once triplets are included, a PS-symmetric superpotential contains leptoquark and diquark couplings simultaneously: DQ R Q R = ɛ αβγ ɛ jk D α (Q R ) βj (Q R ) γk Possible solution: extra flavor symmetry SU(3) F (or SO(3) F ) D diquark coupling with SU(2) R, SU(3) c, SU(3) F : DQ R Q R = ɛ abc ɛ αβγ ɛ jk D a α(q R ) b βj(q R ) c γk Vanishes due to total antisymmetry no proton decay Analogous for ɛ abc ɛ αβγ ɛ jk (D c ) a α(q L ) b βj (Q L) c γk Leptoquark coupling of D not affected Eff. superpotential from (spontan.) breaking of LR and/or flavor symm.: Exclude spurions ɛ αβγ (color space) diquark couplings absent baryon number as low-energy symmetry, flavor symmetry not (necessarily)

12 Sample Implementation Toy Model (no dynamics!) Extend E 6 SU(3) F to E 8... by implementing N = 2 supersymmetry: We have: matter 273 and gauge Add: mirror matter 27 3 supersymmetrize by adding matter and gauge Decomposition of reps. in E 8 E 6 SU(3) F : 248 = Result: matter 248 and gauge 248 (fundamental = adjoint)

13 Sample Implementation Top Down 1. Somewhat below M Planck N = 2 1 breaking removes mirror matter: (273) a i (27 3) b j = δ ab δ j,i+1 Result: E6 zero mode of chiral matter 27 3, maybe adjoint matter 78 1 and 1 8 Flavor SU(3) on the zero modes (would be anomalous) is broken by colorless spurions, e.g., condensate 1 8. E6 is broken to G PS by colorless spurions, e.g., bilinear = Higgs µ term 1 2,21 2,2 in the mirror representation Additional allowed spurion = Singlet 1 1,1 = S (3. gen.) Note: all spurions so far break flavor as well PS symmetry all MSSM superpotential terms allowed, subject to PS symmetry/flavor constraints (no quark mixing): = 0 ( ), ( ), ( ), Flavor dynamics in higher-dim. superpotential due to 1 8 matter exchange

14 Sample Implementation only potentially dangerous term for proton decay: , because inserting (colorless) condensates into , integrating out 78 1 color-triplet leptoquark self-coupling XXX = 0 (antisymmetry) 2. At GeV Condensate in adjoint matter representation: 78 1 = WR 23 + higher-dimensional terms ( ) 2 W 23 R W 32 R S S ν R Majorana mass PS symmetry broken to SM ν R ν R Leptoquark couplings possible for D, D c, but no diquark couplings

15 Sample Implementation 3. At 10 3 GeV Soft-breaking terms (hidden sector) induce radiative symmetry breaking S via D/D c loops µ D -term D c S D (Dirac masses) µ H -term H u S H d Z mass if the extra U(1) broken by S was gauged... with flavor mixing 4. At 10 2 GeV Soft-breaking + effective µ-term induce radiative symmetry breaking H u via t/t c loops H d due to Higgs superpotential + soft-breaking terms Dirac masses for all charged MSSM matter Majorana masses (see-saw) for ν L... again, with flavor mixing

16 Dark Matter MSSM Higgses: Hu f, H f d with f = 1, 2, 3 VEV selects single direction (taken as f = 3) in family space 1 gen. MSSM Higgses, 2 gen. unhiggses Ellis et al., 1985; Campbell et al., 1986 (2 bi-doublets = 8 charged and 8 neutral scalars + fermion superpartners) In gauge interactions, unhiggses are pair-produced, thus suppressed in precision data, but also Yukawa interactions 1) FCNC 2) resonant single production in q q or e + e annihilation Unhiggses very heavy or artificially aligned or suppressed (approximate?) H parity: odd for unhiggses, even otherwise And why not? Flavor symmetry removes the need for R parity anyway. If H parity is exact: lightest unhiggs: H parity protected dark matter Griest/Sher, 1989 Pair production of unhiggses/unhiggsinos, cascade decays... and R parity is exact: dark matter mix: interesting relic abundance (relaxes all neutralino bounds!)

17 A little bit of Pheno Next step: Provide a viable low-energy spectrum At LHC: 1) 1 3 pairs of scalar leptoquarks D L, D R. probably heavy 1 TeV (but hierarchy is possible) Deppisch/Kilian/JR pair-produced in gg fusion at LHC decay into lu and νd: generation-diagonal, or just third-generation: τt and νb or generation-crossed (flavor symmetry!): ec, eb, µd,te, tµ... gq Dl production enhanced or, if R-parity is violated, may mix with down-type squarks. 2) 1 3 fermionic leptoquarkinos D are probably heavy as well, but somewhat lighter than scalars (because m 2 = λ S 2 + m 2 soft) are also pair produced (maybe singly if R-parity is violated) decay into lj, or l q, or ν q rich signatures! spin measurement distinguishes from ordinary squarks

18 A little bit of Pheno 3) (non)"standard" MSSM Higgs Relaxed Higgs bounds (like in NMSSM) Possibly large invisible decay ratio ( χ 0, a) 4) 2 4 doublets of unhiggses probably only pair-produced: Drell-Yan, maybe Higgs decays (singlets involved) missing-energy signatures, unique identification could be difficult: ILC? 5) 1 3 singlet scalars + pseudoscalars masses, properties? 6) and all associated neutralinos ( 11) and charginos ( 4) large and complicated chargino/neutralino mixing matrices. Decay chains at LHC become difficult to understand. 7) Either heavy Z (gauged NMSSM) or light pseudo-axion(s) η corresponding to extra U(1) Conclusion: LHC phenomenology rich... and confusing

19 Summary 3 independent building blocks for exotic SUSY phenomenology Color-triplet leptoquark scalars/fermions are present in the low-energy spectrum leads to a different unification pattern favoring PS symmetry above the R-neutrino mass scale Flavor symmetry prohibits proton decay instead of (or in addition to) R parity Superpotential terms are due to GUT- and flavor-breaking therefore do not exhibit GUT relations Higgs sector is flavored Unhiggses (1st and 2nd generation) carry conserved quantum number Unhiggses dark matter candidates Ordinary MSSM stuff might decay via R-parity violation Confusing LHC pheno, but provides handle to GUT scale

20 Some Unification needs time