Unification without Doublet-Triplet Splitting SUSY Exotics at the - PowerPoint PPT Presentation

J. Reuter Unification without Doublet-Triplet Splitting MSU, East Lansing, 20.3.2007 Unification without Doublet-Triplet Splitting — SUSY Exotics at the LHC Jürgen Reuter Carleton University, Ottawa University of Freiburg − → W. Kilian, J. Reuter, PLB B642 (2006), 81, and work in progress (with F . Deppisch) MSU, East Lansing, March 20, 2007

J. Reuter Unification without Doublet-Triplet Splitting MSU, East Lansing, 20.3.2007 The Standard Model (SM) – Theorist’s View Renormalizable Quantum Field Theory (only with Higgs!) based on SU (3) c × SU (2) L × U (1) Y non-simple gauge group M H [GeV] Reducible representation: 750 500 q ( 3 , 2 ) 1 3 ⊕ ℓ ( 1 , 2 ) − 1 ⊕ u c ( 3 , 1 ) − 4 d c ( 3 , 1 ) 2 3 ⊕ 250 3 ⊕ e c ( 1 , 1 ) ⊕ H ( 1 , 2 ) 1 Λ[GeV] 10 3 10 6 10 9 10 12 10 15 10 18 Incompleteness Theoretical Dissatisfaction ◮ Electroweak Symmetry Breaking ◮ 28 free parameters ◮ Higgs boson ◮ “strange” fractional ◮ Origin of neutrino masses U (1) quantum numbers ◮ Dark Matter: m DM ∼ 100 GeV ◮ Hierarchy problem

J. Reuter Unification without Doublet-Triplet Splitting MSU, East Lansing, 20.3.2007 Conventional and MSSM Unification 1971–74 Supersymmetry: consistent extrapolation to high scales Running of 1/ α , MSSM, i.e. with 1 × [H u ⊕ H d ] ⇒ unification quantitatively testable 60 1/ α 1 (assuming a given spectrum) 50 1/ α 2 1/ α 3 ⇒ two Higgs doublets H u , H d 40 30 ⇒ superpartners for all SM particles, 20 presumably in the TeV range 10 0 Bottom-Up Approach: just MSSM 10 3 10 6 10 9 10 12 10 15 10 18 µ [GeV] 1973 Unification of leptons and quarks by Pati/Salam: G SM ⊂ G PS = SU (4) c × SU (2) L × SU (2) R × Z 2 Each matter family in irreducible rep. (incl. ν R , 2nd Higgs doublet): 1974 Unification of gauge couplings by Georgi/Glashow: G SM ⊂ G GG = SU (5) Matter representation for SU (5) is reducible (classically) Simple-group unification: partial unification of leptons/quarks

J. Reuter Unification without Doublet-Triplet Splitting MSU, East Lansing, 20.3.2007 The prime example: (SUSY) SU (5) SU (5) − M X SU (3) c × SU (2) w × U (1) Y − → M Z SU (3) c × U (1) em → SU (5) has 5 2 − 1 = 24 generators: 24 → ( 8 , 1 ) 0 ⊕ ( 1 , 3 ) 0 ⊕ ( 1 , 1 ) 0 ⊕ ( 3 , 2 ) 5 ⊕ ( 3 , 2 ) − 5 3 3 � �� � � �� � � �� � � �� � � �� � G β W B X, ¯ ¯ X,Y Y α √ 2 G a λ a   ( ¯ X, ¯ GM gA a λ a Y ) g g 2 2 = √  − √ B diag( − 2 , − 2 , − 2 , 3 , 3)  √ 2 W a σ 2 2 15 ( X, Y ) T 2 SU (5) breaking: Higgs Σ in adjoint 24 rep. 5 � Σ � = w × diag(1 , 1 , 1 , − 3 2 , − 3 2 ) M X = M Y = √ g w 2 2 other breaking mechanisms possible (e.g. orbifold)

J. Reuter Unification without Doublet-Triplet Splitting MSU, East Lansing, 20.3.2007 Quantum numbers q ◮ Hypercharge: λ 12 3 Y = 1 Y = 3 diag( − 2 , − 2 , 3 , 3 , 3) 2 5 2 Quantized hypercharges are fixed by non-Abelian generator ◮ Weak Isospin: T 1 , 2 , 3 = λ 9 , 10 , 11 / 2 Q = T 3 + Y/ 2 = diag( − 1 ◮ Electric Charge: 3 , − 1 3 , − 1 3 , 1 , 0) ◮ Prediction for the weak mixing angle (with RGE running): α − 1 ( M Z ) = 128 . 91(2) , α s ( M Z ) = 0 . 1176(20) , s 2 w ( M Z ) = 0 . 2312(3) non-SUSY: s 2 α ( M Z ) 23 109 w ( M Z ) = 134 + ≈ 0 . 207 α s ( M Z ) 201

J. Reuter Unification without Doublet-Triplet Splitting MSU, East Lansing, 20.3.2007 Quantum numbers q ◮ Hypercharge: λ 12 3 Y = 1 Y = 3 diag( − 2 , − 2 , 3 , 3 , 3) 2 5 2 Quantized hypercharges are fixed by non-Abelian generator ◮ Weak Isospin: T 1 , 2 , 3 = λ 9 , 10 , 11 / 2 Q = T 3 + Y/ 2 = diag( − 1 ◮ Electric Charge: 3 , − 1 3 , − 1 3 , 1 , 0) ◮ Prediction for the weak mixing angle (with RGE running): α − 1 ( M Z ) = 128 . 91(2) , α s ( M Z ) = 0 . 1176(20) , s 2 w ( M Z ) = 0 . 2312(3) non-SUSY: s 2 α ( M Z ) 23 109 w ( M Z ) = 134 + ≈ 0 . 207 α s ( M Z ) 201 SUSY: s 2 α ( M Z ) 1 7 w ( M Z ) = 5 + ≈ 0 . 231 α s ( M Z ) 15 New Gauge Bosons Two colored EW doublets: ( X, Y ) , ( ¯ X, ¯ Y ) with charges ± 4 3 , ± 1 3

J. Reuter Unification without Doublet-Triplet Splitting MSU, East Lansing, 20.3.2007 Fermions (Matter Superfields) The only possible way to group together the matter:     d c u c − u c 0 − u − d − u c u c  d c   0 − u − d      1    u c − u c  d c √ 5 = : 10 = : 0 − u − d     2     − e c ℓ u u u 0     e c − ν ℓ d d d 0 5 = ( 3 , 1 ) 2 3 ⊕ ( 1 , 2 ) − 1 10 = ( 3 , 2 ) 1 3 ⊕ ( 3 , 1 ) − 4 3 ⊕ ( 1 , 1 ) 2 Remarks ◮ 2 = = 2 , ( 5 ⊗ 5 ) a = 10 , ( 3 ⊗ 3 ) a = 3 , ( ⊗ ) a = ◮ Quarks and leptons in the same multiplet ◮ Fractional charges from tracelessness condition (color!) ◮ 5 and 10 have equal and opposite anomalies ◮ ν c must be SU (5) singlet

J. Reuter Unification without Doublet-Triplet Splitting MSU, East Lansing, 20.3.2007 The Doublet-Triplet Splitting Problem MSSM Higgses included in 5 H ⊕ 5 H � D � D c � � 5 H = ( 3 , 1 ) − 2 3 ⊕ ( 1 , 2 ) 1 : 5 H = ( 3 , 1 ) 2 3 ⊕ ( 1 , 2 ) − 1 : H u ǫH 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 ( m H ∼ 100 GeV , m D ∼ 10 16 GeV) ◮ Doublet-triplet splitting problem Welcome, since SU (5) -symmetric Higgs interactions would read 5 H = ℓH d e c + qǫH d d c + qǫℓD c + d c u c D c ¯ 5 10 ¯ 10 5 H 10 = ℓH d e c + qǫH u u c + Du c e c + Dqǫq Generating SM masses ⇒ leptoquark and diquark coupl. for D, D c ⇒ triggers rapid proton decay

J. Reuter Unification without Doublet-Triplet Splitting MSU, East Lansing, 20.3.2007 Interactions    e e ν    Leptoquark couplings   X Y Y  (and SUSY vertices)  u  d d        u u    Diquark couplings   X Y   (and SUSY vertices) u  d     e + u Y Vector bosons induce e.g. u decay p → e + π 0 d d

J. Reuter Unification without Doublet-Triplet Splitting MSU, East Lansing, 20.3.2007 Doublet-Triplet Splitting Possible scenarios: 1. Colored singlets are heavy (GUT scale) = doublet-triplet splitting ◮ enables exact unification near 10 16 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 10 16 GeV, nor elsewhere ,D c Running of 1/ α , MSSM with 1 × [(H u ,D) ⊕ (H d )] 60 1/ α 1 50 1/ α 2 1/ α 3 40 30 20 10 0 10 3 10 6 10 9 10 12 10 15 10 18 µ [GeV] ◮ Proton-decay coupl. must be excluded: consistent with GUT symmetry?

J. Reuter Unification without Doublet-Triplet Splitting MSU, East Lansing, 20.3.2007 Further MSSM Issues Even if doublet-triplet splitting is accepted, the MSSM Higgs sector appears ad-hoc: ◮ µ problem µ -term µH u H d is supersymmetric, in principle not related to soft-SUSY-breaking Lagrangian: Why is it O (100 GeV ) , not O (10 16 GeV ) ? ⇒ Possible extension as a solution: singlet Higgs S with superpotential λSH u H d → λ � S � H u H d = µH u H d (does not change the unification prediction) ⇒ NMSSM, where � S � should be somehow related to soft-breaking Lagrangian How?

J. Reuter Unification without Doublet-Triplet Splitting MSU, East Lansing, 20.3.2007 Radiative Symmetry Breaking MSSM with cutoff Λ ∼ 10 16 GeV: major contribution to Higgs potential comes through Coleman-Weinberg mechanism: = + + ⇒ Large top Yukawa coupl. drives effective H u mass squared negative: m 2 λ 2 (Λ 2 · 0) + m 2 t ,soft m 2 eff = ( m 2 H ,soft + µ 2 ) + 16 π 2 ln t ,soft Λ 2 Such a 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 u H d is present . . . . . . would simultaneously give a Dirac mass to D . ◮ Without tree-level quartic coupling, the CW mechanism implies � S � ∼ 4 πm soft , so � S � ≫ � H � .

J. Reuter Unification without Doublet-Triplet Splitting MSU, East Lansing, 20.3.2007 Further MSSM Issues Even if doublet-triplet splitting is accepted, the MSSM Higgs sector appears ad-hoc: ◮ Why is there only one family of Higgs matter? Neither SU (5) , nor G PS (nor SO (10) ) does unify Higgs fields with SM matter. . .

J. Reuter Unification without Doublet-Triplet Splitting MSU, East Lansing, 20.3.2007 Higgs-Matter Unification 1976: Trinification: Treat all interactions equally G Tri = SU (3) c × SU (3) L × SU (3) R × Z 3 Multiplets:     H + H 0 ν L u L u d L (1 , 3 , ¯  = Q L (3 , ¯ H 0 3) = H − e L d L 3 , 1)    u d e c ν c S D L R R � � Q R (¯ u c d c D c 3 , 1 , 3) = R R R 1976: E 6 as superset of trinification (and SO (10) ) with additional gauge bosons X (3 , 3 , 3) and ¯ X (¯ 3 , ¯ 3 , ¯ 3) ⇒ 78 ⇒ irreducible multiplet ( 27 ) unifies all matter, Higgs, colored and neutral singlets (within each family) ⇒ contains NMSSM, allows for radiative symmetry breaking in both singlet and doublet sectors