LHC Phenomenology of SUSY multi-step GUTs

0/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 LHC Phenomenology of SUSY multi-step GUTs Jürgen Reuter Albert-Ludwigs-Universität Freiburg W. Kilian, JR, PL B64 (006), 81; arxiv:0709.40; work in progress (with F. Braam, K. Mallot, D. Wiesler) PHENO 09, Madison, May 1, 009

1/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Motivation for (SUSY) Unification Incompleteness/Theoretical Dissatisfaction EWSB, H, m ν, DM, hierarchy,........., reducible representation: q (3, ) 1 3 l (1, ) 1 u c (3, 1) 4 3 d c (3, 1) 3 ec (1, 1) H (1, ) 1 Supersymmetry: consistent extrapolation to high scales unification quantitatively testable two Higgs doublets H u, H d TeV-scale SM-superpartners 60 50 40 30 0 Running of 1/α, MSSM, i.e. with 1 [H u H d ] 1/α 1 1/α 1/α 3 Bottom-Up Approach: just MSSM 0 3 6 9 1 µ [GeV] 15 18 Unification verification only with megatons? What about colliders? SPA: super precision accurately Look for chiral exotics Physics beyond MSSM provides handle to GUT scale

/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 The Doublet-Triplet Splitting Problem MSSM Higgses included in 5 H 5 H ( ) D 5 H = (3, 1) (1, ) 1 : 3 H u ( ) D c 5 H = (3, 1) (1, ) 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 0 GeV, m D 16 GeV) Welcome, since SU(5)-symmetric Higgs interactions would read 5 5 H = lh d e c + qɛh d d c + qɛld c + d c u c D c 5 H = 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

3/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Doublet-Triplet Splitting Possible scenarios: 1. Colored singlets are heavy (GUT scale) = doublet-triplet splitting enables exact unification near 16 GeV, excludes rapid proton decay Proton decay may still be too fast (depends on superpotential) Doublet-triplet splitting is not trivially available. Colored singlets are light (TeV scale) Simple unification no longer happens near 16 GeV, nor elsewhere 60 50 40 Running of 1/α, MSSM with 1 [(H u,d) (H d,d c )] 1/α 1 1/α 1/α 3 30 0 0 3 6 9 1 µ [GeV] 15 18 Proton-decay coupl. must be excluded: consistent with GUT symmetry?

4/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Further MSSM Issues ) µ problem: SUSY µ-term µh u H d, not related to soft breaking Why µ O(0 GeV), not O( 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 S in the NMSSM requires existence of vectorlike pair of chiral superfields for instance, D and D c (colored) with SDD c... as required by SU(5), if SH uh d is present, gives Dirac mass to D Without tree-level quartic coupl., the CW mechanism implies S 4πm soft, so S H. 3) Higgs-matter unification: Why only one family of Higgs matter? E 6 unifies Higgs fields with SM matter... Possible scenarios: 1. Omit one bi-triplet D, D c family doublet-triplet splitting. Add one extra MSSM Higgs family ESSM S.King et al., 005/6 3. Different unification pattern

5/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Running Couplings: PSSSM [Braam/JR/W.Kilian, 006/009] Additional particles spoil simple unification Gauge couling unification below Λ P lanck due to intermediate Pati-Salam SU(4) SU() L SU() R[ U(1) χ] symmetry at 16 GeV 60 50 40 Running of 1/α, MSSM with 3 [(H u,d) (H d,d c )] 1/α 1 1/α 1/α 3 30 0 0 3 6 9 1 µ [GeV] 15 18

5/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Running Couplings: PSSSM [Braam/JR/W.Kilian, 006/009] Additional particles spoil simple unification Gauge couling unification below Λ P lanck due to intermediate Pati-Salam SU(4) SU() L SU() R[ U(1) χ] symmetry at 16 GeV SM U 1 ' Pati Salam U 1 Χ E 6 60 50 40 Α i 1 30 U 1 U 1 Y SU L SU L R 0 U 1 Χ SU 3 SU 4 4 6 8 1 14 16 18 Μ GeV SU() R and SU() L: identical particle content Identical running Crossing of SU(4) and SU() L/R couplings determines E 6 breaking scale

6/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 E 6 unification with intermediate Pati-Salam Symmetry The quantum numbers of the 7 under the Pati-Salam gauge group are Q R = ((u c, d c ), (ν c, e c )) = ( 4, 1, ) 1 Q L = ((Q, L)) = (4,, 1) 1 H = (H u, H d ) = (1,, ) 1 D = (D, D c ) = (6, 1, 1) 1 Lepton number becomes 4 th color T 15 SU(4) B L Y = B L + T 3 R Integrating out ν c appropriate breaking see-saw mechanism (i.e. naturally small neutrino masses) S = (1, 1, 1)

7/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Flavor Symmetry Proton decay? Triplets included: PS-symmetric superpotential contains leptoquark and diquark couplings 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() 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)

8/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 The LHC phenomenology 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) [Braam/JR/Wiesler] 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. ) 1 3 fermionic leptoquarkinos D are probably heavy as well, but somewhat lighter than scalars (because m = λ S + m 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

9/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 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) 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

/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Investigation Of The Parameter Space # free parameters O(0), additional assumptions: - Unified SSB-parameters - Flavor structur Limitation on 14 free parameters Constraints: (1) Experimental lower bounds on masses of new particles () Running parameters perturbative up to Λ E6 (3) Scalar (non-higgs) mass terms have to remain positive ( No unwanted symmetry breaking) 1 14-dim parameter space grid scanning 8 points Güte Investigation per point (RGE, Higgs potential minimization, calculation of masses) 5 s Sol: Monte-Carlo Markov-Chain through parameter space Effective search for sensible parameter tupels 0. 0.4 Y SD 0.6 0.8 40 30 0 0 tanβ 1 50

+ u + g e 11/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Predictions for Collider Experiments Collider phenomenology with event generator WHIZARD [Kilian/Ohl/JR] Implementation of leptoquark/leptoquarkino + Higgs/weak ino sector First analyses: BRs, cross sections for scalar leptoquarks, S/B In progress: leptoquarkino pheno X L Branching Ratio D 1-1 - -3 Decays of D L - e 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 D Yukawa Coupling Y 1 D L D L D L D L D L + u 0 χ + D ~ 1 ~ u L + ~ d L ~ u L + + ~ e L ν ~ e R CrossSection σ [fb] 1-1 - -3 PairProduction q + q D L g + g D L p + p D L * + D L * + D L * + D L Cross section σ [fb] 1-1 - Leptoquark Single Production u + g e - d + g ν + D L + D R + D R -4-5 -3-6 -4-7 -8-5 500 00 1500 000 500 3000 Leptoquarkmass M [GeV] LQ 500 00 1500 000 500 3000 Leptoquark mass M [GeV] LQ Cuts Background m D = 0.6 TeV m D = 0.8 TeV m D = 1.0 TeV p T M ll N BG N 1 S 1/ B N S / B N 3 S 3/ B 50 41374 64553 93 1483 3 4819 7 0 150 37 40749 194 891 9 3767 45 00 150 198 1986 113 5678 74 405 47

+ u + g e 11/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Predictions for Collider Experiments Collider phenomenology with event generator WHIZARD [Kilian/Ohl/JR] Implementation of leptoquark/leptoquarkino + Higgs/weak ino sector First analyses: BRs, cross sections for scalar leptoquarks, S/B In progress: leptoquarkino pheno X R Branching Ratio D 1-1 - -3 Decays of D R ν 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 D Yukawa Coupling Y 1 D R D R D R D R D R - e + d + u 0 χ + D ~ 1 ~ u R + ~ u R + ~ e L ~ e R CrossSection σ [fb] 1-1 - -3 PairProduction q + q D L g + g D L p + p D L * + D L * + D L * + D L Cross section σ [fb] 1-1 - Leptoquark Single Production u + g e - d + g ν + D L + D R + D R -4-5 -3-6 -4-7 -8-5 500 00 1500 000 500 3000 Leptoquarkmass M [GeV] LQ 500 00 1500 000 500 3000 Leptoquark mass M [GeV] LQ Cuts Background m D = 0.6 TeV m D = 0.8 TeV m D = 1.0 TeV p T M ll N BG N 1 S 1/ B N S / B N 3 S 3/ B 50 41374 64553 93 1483 3 4819 7 0 150 37 40749 194 891 9 3767 45 00 150 198 1986 113 5678 74 405 47

1/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Invariant mass of lepton and jet # Events/bin 5 4 Signal + Background for: h3 Entries 0 D Mean µ + uµ - µ + L/R 8.3 RMS 150. D τ + L/R uτ - τ + Invariant mass of lepton and jet # Events/bin 3 Signal + Background for: h3 D µ Entries + uµ - µ + L/R 0 Mean 359.7 RMS D τ + uτ - τ + 314. L/R 3 1 0 00 400 600 800 00 100 1400 M [GeV] lj 0 00 400 600 800 00 100 1400 M [GeV] lj p distribution of the lepton T # Events/bin 5 h3 SM Background after cuts (1) Entries 0 Mean 60.16 + + - Signal: µ D µ µ j 4 RMS 44.8 L/R 3 Processes: SM Background: µ + µ - Signal after cuts(1) j # Events/bin 5 4 3 p distribution of the lepton T D-l-q coupl. λ=0.31 0.5 < cuts: η <3.5 p >50 T R(ll) < 6 Process pp De + ue - e + m D = 600 hbg m Entries 0 D = 800 Mean 65.04 m RMS D = 00 40.13 m D = 100 m D = 1500 SM Bg: Zj/γj 1 0 00 400 600 800 00 100 1400 1600 1800 000 p [GeV] T 0 00 400 600 800 00 100 1400 p [GeV] T

13/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Dark Matter MSSM Higgses: Hu f, H f d with f = 1,, 3 VEV selects single direction (taken as f = 3) in family space 1 gen. MSSM Higgses, gen. unhiggses Ellis et al., 1985; Campbell et al., 1986 ( 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 ) 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 Pair production of unhiggses/unhiggsinos, cascade decays... and R parity is exact: dark matter mix: interesting relic abundance (relaxes all neutralino bounds!)

14/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Summary/Outlook 3 independent building blocks for exotic SUSY phenomenology Color-triplet leptoquark/inos are present in the low-energy spectrum multi-step unification (PSSSM: E 6 with PS symmetry) 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 nd generation) carry conserved quantum number Unhiggses dark matter candidates Ordinary MSSM stuff might decay via R-parity violation Investigation of the parameter space Input for WHIZARD Leptoquark phenomenology could hint toward GUT Further Studies: PS-symmetry breaking, U(1)-mixing, threshold corrections More LHC pheno (leptoquarkinos, Higgs, weak inos, Z...)

14/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009

14/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Backup: E 6 Particle Content Unifies Higgs and matter fields Contains SU(3) c SU() L U(1) Y [ U(1) ] additional Z Ansatz: all new particles in the spectrum at TeV scale SM U(1) quantum numbers of the fundamental 7: Notation: (SU(3), SU()) Y,Q Q L = (3, ) 1 6,Q Q u c = ( 3, 1) 3,Q u d c = ( 3, 1) 1 3,Q d L L = (1, ) 1,Q L ν c = (1, 1) 0,Q ν =0 e c = (1, 1) 1,Q e H u = (1, ) 1,Q H u H d = (1, ) 1,Q H d D = (3, 1) 1 3, Q D S = (1, 1) 0,Q S 0 D c = ( 3, 1) 1 3, Q D

14/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Backup: Sample Implementation Toy Model (no dynamics!) Extend E 6 SU(3) F to E 8... by implementing N = supersymmetry: We have: matter 73 and gauge 78 1 + 1 8. Add: mirror matter 7 3 supersymmetrize by adding matter 781 + 1 8 and gauge 7 3 + 7 3. Decomposition of reps. in E 8 E 6 SU(3) F : 48 = 7 3 7 3 78 1 1 8 Result: matter 48 and gauge 48 (fundamental = adjoint)

14/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Backup: Sample Implementation Top Down 1. Somewhat below M Planck N = 1 breaking removes mirror matter: (73) a i (7 3) b j = δ ab δ j,i+1 Result: E6 zero mode of chiral matter 7 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 1,1, in the 7 37 3 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): 7 3 7 3 7 3 = 0 (7 3 78 1 7 3), (78 1 78 1 78 1 ), (7 3 1 8 7 3), 1 8 1 8 1 8 Flavor dynamics in higher-dim. superpotential due to 1 8 matter exchange

14/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Backup: Sample Implementation only potentially dangerous term for proton decay: 78 1 78 1 78 1, because inserting (colorless) condensates into 7 3 78 1 7 3, integrating out 78 1 color-triplet leptoquark self-coupling XXX = 0 (antisymmetry). At 15 GeV Condensate in adjoint matter representation: 78 1 = WR 3 + higher-dimensional terms (7 78 7) W 3 R W 3 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

14/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Backup: Sample Implementation 3. At 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 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

14/14 J. Reuter LHC Phenomenology of SUSY multi-step GUTs PHENO 09, Madison, 1.5.009 Backup: 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) > 33 yrs u d D ū u e +