SU(5) GUT with Additional Generations of Higgs Bosons J. Evans 1 The University of Tokyo, IPMU Evans Z 2 Higgs Bosons
The Standard Model Higgs Boson The interactions of the SM are chiral Left and right handed leptons carry different charges Chiral theories like the SM cannot have fermion masses Massless fermions contradict experiment Gauge invariant operators necessitate additional fields L = y f ij ¯ f L i f R j h h → � h � A priori it appears SM violates flavor L = U † q L i u R j + U † q L i d R j + y L ij h ¯ il y d lm W mj h ∗ ¯ il y u lm V mj h ¯ L L i e R j Evans Z 2 Higgs Bosons
Flavor Mixing: CKM Matrix Flavor violating couplings arise from additional interactions Even minimal Higgs Boson sector gives flavor violation y N = 0 leads to no CKM like matrix for leptons CKM matrix from rotating u L i and d L i separately W bosons mix u L i and d L i giving L i γ µ A † u L i γ µ d L i → g 2 ¯ u ′ ik B kj d ′ L W = g 2 ¯ L j ( M CKM ) ij = A † ik B kj Evans Z 2 Higgs Bosons
Difficulties of Additional Higgs Bosons in the SM Generic addition of a Higgs Boson to the SM Doubles number of Yukawa couplings Gives no additional reparameterizations Runge basis for two Higgs doublets (Only one vev) Φ vev = v 1 v Φ 1 + v 2 v Φ 2 Φ ⊥ = v 2 v Φ 2 − v 1 v Φ 1 v 2 = v 2 1 + v 2 2 Lagrangian in this basis q L i d R i + y L i Φ vev ¯ vev ¯ q L i u R i + y d i Φ ∗ L L i e R i + y N i Φ ∗ y u i Φ vev ¯ vev ¯ L = L L i N q L i d R j + ξ L ij Φ ⊥ ¯ ⊥ ¯ q L i u R j + ξ d ij Φ ∗ L L i e R j + ξ N ij Φ ∗ ξ u ij Φ ⊥ ¯ ⊥ ¯ + L L i N R j Evans Z 2 Higgs Bosons
Constraints on Additional Yukawa Couplings Each ξ will give a diagram contributing to FV Meson mass mixing will constrain the ξ couplings ∆ M expt Meson (quarks) B F f F (GeV) (GeV) F K 0 (¯ ( 3 . 476 ± 0 . 006 ) × 10 − 15 sd ) 0.79 0.159 d (¯ B 0 ( 3 . 337 ± 0 . 033 ) × 10 − 13 bd ) 1.28 0.216 D 0 (¯ ( 0 . 95 ± 0 . 37 ) × 10 − 14 cu ) 0.82 0.165 Table: Data associated with the neutral mesons K 0 , B 0 d and D 0 . (borrowed from Gupta, Wells). Constraints on ξ form meson mass mixing ξ ds ≤ 1 × 10 − 5 ξ uc ≤ 3 × 10 − 5 ξ db ≤ 4 × 10 − 5 ξ sb ≤ 2 × 10 − Evans Z 2 Higgs Bosons
Z 2 odd Higgs Bosons in the SM Two ways to evaded constraints and avoid tuning Identical couplings for additional Higgs bosons 1 ij ¯ ij ¯ ij ¯ ∆ L f = y d Q i F u ( { Φ k } ) d jR + y u Q i F d ( { Φ k } ) u jR + y e L i F e ( { Φ k } ) e jR + Reparametrization of fermions identical to SM Symmetries forbid coupling of additional Higgs boson to 2 SM fermions L = L SM + L Hid (Φ ′ k , Φ k , f ′ i ) Additional Higgs bosons interact with SM through Higgs Or both of the above combined 3 Additional Z 2 symmetry SM fermions even or odd SM Higgs even Additional Higgs odd Evans Z 2 Higgs Bosons
Higgs bosons of Supersymmetry Higgs physics suggests SUSY (Stabilize Hierarchy) SUSY Higgs interactions falls under the 3rd Higgs interactions with SM constrained by Holomorphy Exact SUSY has acceptable small flavor violation (FV) SUSY breaking CAN introduce flavor violation MSSM plus Z 2 odd Higgs boson gives no new FV W odd = W MSSM + µ 22 H u 2 H d 2 Evans Z 2 Higgs Bosons
SUSY and Grand Unification Gauge coupling unification in SUSY 60 α 1 −1 50 40 −1 α 30 α 2 −1 20 10 α 3 −1 0 2 4 6 8 10 12 14 16 18 Log 10 (Q/1 GeV) Figure: From Martins Supersymmetry Primer Evans Z 2 Higgs Bosons
Grand Unification in Supersymmetry If SUSY, Grand Unification likely Superpotential of SU(5) Grand Unification 1 3 Tr Σ 3 + 1 2 fV Tr Σ 2 + λ ¯ H β (Σ β α + 3 V δ β α ) H α W MSSM = √ + 1 j H ǫ + 4 h ij ǫ αβγδǫ ψ αβ ψ γδ 2 f ij ψ αβ φ j α ¯ H β . i i vev breaking SU(5) give doublet triplet splitting 2 0 0 0 0 0 2 0 0 0 � Σ � = 0 0 2 0 0 0 0 0 − 3 0 0 0 0 0 − 3 Doublet Triplet splitting important for proton stability H 3 ∼ 10 16 GeV) Triplet Higgs must be very heavy ( m 2 Evans Z 2 Higgs Bosons
The Higgs bosons of a SUSY SU ( 5 ) × Z 2 GUT Low scale Higgs superpotential of SUSY SU ( 5 ) × Z 2 H 3 − µ ′ H ′ ¯ W Z 2 = − µ H 3 ¯ H ′ Two problems with this Z 2 symmetry gives domain wall problem Additional Higgs will be very hard to detect (aka boring) Fixed by adding explicit breaking of Z 2 H ′ + H ′ ¯ / = ǫ ( H ¯ W Z 2 H ) Evans Z 2 Higgs Bosons
EWSB and the Higgs Triplet Masses of additional triplet and doublet identical Doublet Higgs constrained by EWSB Triplet Higgs constrained by absence of CCB EWSB requires at least one Higgs mass be negative ǫ 2 − m 2 3 − m 3 µ ′ < 0 for ǫ 2 > m 2 3 3 − ǫ 2 − m 3 µ ′ < 0 for ǫ 2 < m 2 m 2 3 No CCB requires all Triplet Higgs mass be positive µ ′ 2 − m 2 3 > 0 Evans Z 2 Higgs Bosons
Z 2 Odd Triplet Higgs Z 2 odd triplet Higgs bosons mix with SM triplet Higgs For µ GUT ≫ µ ′ , ǫ mixing small √ √ √ √ 2 2 2 ǫ 2 ǫ ¯ ¯ H ∗ H ∗ = 2 H 1 + 1 − H 2 − H 2 2 2 µ GUT 2 µ GUT √ √ √ √ 2 2 2 ǫ 2 ǫ ¯ ¯ ¯ 2 H ∗ H ∗ H = − 1 + H 1 − 2 + H 2 . 2 2 µ GUT 2 µ GUT But, µ GUT ≫ µ ′ , ǫ lead to light triplet Higgs m 2 µ 2 GUT + m 2 3 + 2 ǫ 2 = H 1 m 2 µ 2 GUT − m 2 3 + 2 ǫ 2 = ¯ H 1 µ ′ 2 + m 2 m 2 = H 2 3 µ ′ 2 − m 2 m 2 = 3 ¯ H 2 Evans Z 2 Higgs Bosons
Proton Decay From Z 2 Odd Higgs Bosons S-channel decay through odd Higgs bosons A ′ ǫ 2 i = 2 m 2 A SM H i Enhanced if 2 m 2 H i < ǫ 2 Dimension 5 operators are always suppressed A ′ ǫ ǫ i = A SM m H i µ GUT This contribution will be suppressed unless we fine tune Evans Z 2 Higgs Bosons
Parameter Space Constraints From Proton Decay The parameter space is only minimally constrained p−−> µ K 0 45 40 Proton Lifetime (log 10 (Years)) 35 30 =10 15 GeV m H 25 2 =10 14 GeV m H 2 =10 13 GeV m H 20 2 =10 12 GeV m H 2 15 0 20 40 60 80 100 120 140 160 180 200 m H 2 Evans Z 2 Higgs Bosons
BBN Constraints on Triplet Higgs Boson Once Z 2 is broken the odd Higgs bosons will decay Decay only through mixing and will be quite suppressed Strongly interacting and can mess up BBN Must decay before BBN ǫ 2 Γ( H → ¯ f i f j ) ∝ | y i | 2 m H µ 2 GUT 1 Γ ≤ 1 s Evans Z 2 Higgs Bosons
BBN Constraints on Parameter Space Very small values of m H and ǫ forbidden by BBN constraints 2000 1800 1600 1400 1200 GeV 1000 τ H > 1 s 2 m H τ H <1 s for m H <10 16 800 C τ H <1 s for m H < 2 X 10 16 GeV C 600 τ H <1 s for m H < 4X10 16 GeV C < 8X10 16 GeV τ H <1 s for m H 400 C 200 0 0 500 1000 1500 2000 2500 B GeV Evans Z 2 Higgs Bosons
Conclusions Additional Higgs bosons require symmetries to forbid FV Z 2 odd Higgs bosons will not introduce FV EWSB for SU(2) Higgs bosons and no CCB for SU(3) constrain the Z 2 breaking to be of EW scale EW scale Z 2 breaking can evade BBN/proton decay constraints Supersymmetric GUT with additional Z 2 odd Higgs boson will have an EW scale triplet Further analysis Collider phenomenology of light Triplet Higgs boson Possible motivations for this type of Higgs sector Evans Z 2 Higgs Bosons
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