Low Scale Flavor Gauge Symmetries

Low Scale Flavor Gauge Symmetries Michele Redi CERN in collaboration with Benjamin Grinstein and Giovanni Villadoro arxiv:1009.2049[hep-ph] Padova, 20 October

Outline Flavor Problem Gauging the Flavor Group The Model Experimental Bounds Two Examples

One of the most obscure aspects of the SM is the Yukawa sector m u m t = 10 5

One of the most obscure aspects of the SM is the Yukawa sector m u m t = 10 5 Very strong bounds from flavor physics. 4-fermion operators must be suppressed by high scale 1 Λ 2 ( d L γ µ d L ) 2 1 Λ 2 ( d R s L dl s R ) Λ LL > 10 3 10 4 TeV Λ LR > 10 4 10 5 TeV

One of the most obscure aspects of the SM is the Yukawa sector m u m t = 10 5 Very strong bounds from flavor physics. 4-fermion operators must be suppressed by high scale 1 Λ 2 ( d L γ µ d L ) 2 Λ LL > 10 3 10 4 TeV 1 Λ 2 ( d R s L dl s R ) Λ LR > 10 4 10 5 TeV Flavor physics seems very far. Major embarrassment for most BSM scenarios!

Without Yukawas SM (quark sector) has a flavor symmetry SU(3) QL U(3) UR U(3) DR Q L =(3, 1, 1) U R =(1, 3, 1) D R =(1, 1, 3)

Without Yukawas SM (quark sector) has a flavor symmetry SU(3) QL U(3) UR U(3) DR Q L =(3, 1, 1) U R =(1, 3, 1) D R =(1, 1, 3) Minimal Flavor Violation: Yukawas are the only sources of flavor violation. Higher dimensional operators must be built with positive powers of Yukawas q L y u y uγ µ q L dr y d y uy ud L dr y d y uy uy d γ µ d R With MFV new physics can lie around the TeV scale. But where is MFV coming from?

Can flavor be an exact symmetry of Nature?

Can flavor be an exact symmetry of Nature? Symmetry must be spontaneously broken. Most simply flavons with Yukawas quantum numbers: Y u =(3, 3, 1) Y d =(3, 1, 3) y u,d = <Y u,d > M u,d

Can flavor be an exact symmetry of Nature? Symmetry must be spontaneously broken. Most simply flavons with Yukawas quantum numbers: Global Y u =(3, 3, 1) Y d =(3, 1, 3) y u,d = <Y u,d > M u,d Massless Goldstone Bosons. Strong bounds from rare decays and astrophysics. f>10 12 GeV

L mass =Tr g U A U Y u g Q Y u A Q 2 +Tr g D A D Y d g Q Y d A Q 2 = 1 2 V Aa(M 2 V ) Aa,Bb V Bb, M 2 g 2 <Y 2 > Flavor gauge bosons mediate FCNC 1 8 (M 2 V ) 1 Aa,Bb λa ijλ b hk J ij,a µ J µhk,b J µij,a =(g Q Q i Lγ µ Q j L,g U U i Rγ µ U j R,g DD i Rγ µ D j R ) 1 M 2 ( qγµ q) 2 1 <Y 2 u,d >( qq)2 1 M 2 u,d y2 u,d ( qq) 2

But is y=<y>/m really? In a renormalizable theory this could originate from, L yuk = Q HΨ R + Ψ L M u Ψ R + Ψ L Y u U R

But is y=<y>/m really? In a renormalizable theory this could originate from, L yuk = Q HΨ R + Ψ L M u Ψ R + Ψ L Y u U R However functions of Y can transform as Y. We could imagine an inverted hierarchy, FCNC: y M Y 1 <Yu,d 2 >( qq)2 y2 u,d Mu,d 2 ( qq) 2

Anomalies Flavor gauge symmetries are anomalous: SU(3) 3 Q L SU(3) 3 U R SU(3) 3 D R U(1) Y SU(3) 2 Q L U(1) Y SU(3) 2 U R U(1) Y SU(3) 2 D R

Anomalies Flavor gauge symmetries are anomalous: SU(3) 3 Q L SU(3) 3 U R SU(3) 3 D R U(1) Y SU(3) 2 Q L U(1) Y SU(3) 2 U R U(1) Y SU(3) 2 D R New fermions need to be added, Ψ ur =(3, 1, 1) Ψ dr =(3, 1, 1) Ψ u =(1, 3, 1) Ψ d =(1, 1, 3)

Model SU(3) QL SU(3) UR SU(3) DR SU(3) c SU(2) L U(1) Y Q L 3 1 1 3 2 1/6 U R 1 3 1 3 1 2/3 D R 1 1 3 3 1-1/3 Ψ ur 3 1 1 3 1 2/3 Ψ dr 3 1 1 3 1-1/3 Ψ u 1 3 1 3 1 2/3 Ψ d 1 1 3 3 1-1/3 Y u 3 3 1 1 1 0 Y d 3 1 3 1 1 0 H 1 1 1 1 2 1/2 L =L kin V (Y u,y d,h)+ λu Q L HΨuR + λ u Ψ u Y u Ψ ur + M u Ψ u U R + λ d Q L HΨ dr + λ d Ψ d Y d Ψ dr + M d Ψ d D R + h.c.,

Yukawas: y u = λ um u λ uy u <Y> >> M y t λ u <Yt> << M y d = λ dm d λ d Y d

Yukawas: y u = λ um u λ uy u <Y> >> M y t λ u <Yt> << M y d = λ dm d λ d Y d Inverted hierarchy! Flavor physics can appear at the TeV scale.

Yukawas: y u = λ um u λ uy u <Y> >> M y t λ u <Yt> << M y d = λ dm d λ d Y d Inverted hierarchy! Flavor physics can appear at the TeV scale. Exotic fermions: m u,d λ u,d <Y u,d > Flavon couplings highly suppressed M Ŷ i + δy i v q iq i 1 y i δy i m qi q i q i M

Remarks: Only two flavor violating structures as SM, Y d = Ŷd Y u = ŶdV However NOT MFV.

Remarks: Only two flavor violating structures as SM, Y d = Ŷd Y u = ŶdV However NOT MFV. Potential: With two flavon fields no renormalizable potential. Possible to construct potential with high cut-off. Adding several flavons: More flavor violating structures but still enough flavor suppression. Trivial extension to lepton. Different gaugings.

Phenomenology

Modified SM Couplings, u i R u i R L yuk = λ u Q L HΨuR + λ u Ψ u Y u Ψ ur + M u Ψ u U R +... After EWSB the mass eigenstates are = curi s uri s uri c uri U i R Ψ i ur, u i L u i L = culi s uli s uli c uli U i L Ψ i u, Natural parametrization x i M u, y i λ uv, m ui 2mui yi 2 s uli = 1 x 2 x 2 i y2 i 1 i s uri = 1 x 2 i y2 i 1

Modified SM Couplings, u i R u i R L yuk = λ u Q L HΨuR + λ u Ψ u Y u Ψ ur + M u Ψ u U R +... After EWSB the mass eigenstates are = curi s uri s uri c uri U i R Ψ i ur, u i L u i L = culi s uli s uli c uli U i L Ψ i u, Natural parametrization Decoupling: x i M u, y i λ uv, m ui 2mui yi 2 s uli = 1 x 2 x 2 i y2 i 1 i s uri = 1 x 2 i y2 i 1 or x i y i 1

Right handed fermions mix with exotic with equal charges so their couplings are the same as in the SM.

Right handed fermions mix with exotic with equal charges so their couplings are the same as in the SM. SM left-handed doublets mix with singlets. The couplings are modified. Charged currents: ū L (c ul Vc dl )γ µ d L +ū L (c ul Vs dl )γ µ d L +ū L(s ul Vc dl )γ µ d L +ū L(s ul Vs dl )γ µ d L Neutral currents: ū L (T u 3 c 2 u L s 2 wq u )γ µ u L +ū L (T u 3 c ul s ul )γ µ u L +ū L(T u 3 s ul c ul )γ µ u L +ū L(T u 3 s 2 u L s 2 wq u )γ µ u L +(u d), Higgs Couplings: 1 2 λ u h[ t L c ul s ur t R + t L c ul c ur t R t Ls ul s ur t R + t Ls ul c ur t R]+(u d)+h.c.

Down Sector Z->bb δg Z b b g Z b b = s 2 d L3 δγ Zb b Γ Zb b s dl3 = s 2 d L3 2+4s 2 wq d 1+4s 2 wq d +8s 4 wq 2 d m b M d s dl3 <.04 2.3 s 2 d L3,

Down Sector Z->bb δg Z b b g Z b b = s 2 d L3 Direct bounds δγ Zb b Γ Zb b s dl3 = s 2 d L3 2+4s 2 wq d 1+4s 2 wq d +8s 4 wq 2 d m b M d s dl3 <.04 2.3 s 2 d L3, m b > 268 GeV or < 100 GeV [b Zb, BR = 1] m b > 385 GeV [b Wt,BR = 1] (Tevatron) Our Model m b > 385 GeV allowed 45 GeV < m b < 385 GeV model dependent

Up Sector Oblique corrections S = 16πΠ 3Y (0), 4π T = s 2 wc 2 wmz 2 [Π 11 (0) Π 33 (0)], U = 16π [Π 11(0) Π 33(0)] W 3 W 3,B t, t,b (others irrelevant) T = 48π s 2 wc 2 wmz 2 [2s 2 u L3 Π LL (m t,m b, 0) + 2s 2 u L3 Π LL (m t,m b, 0) + (1 c 4 u L3 )Π LL (m t,m t, 0) s 4 u L3 Π LL (m t,m t, 0) 2s 2 u L3 c 2 u L3 Π LL (m t,m t, 0)] T = 3 s2 u L3 8π s 2 wc 2 w m 2 t MZ 2 c 2 u L3 m 2 t m 2 t m 2 t m 2 log t m 2 1 + s2 u L3 t 2 m 2 t m 2 t 1. S 0 U 0

Heavy Higgs A heavy Higgs can be naturally accommodated Correction to T is always positive while contribution to S is always negligible.

V tb Tevatron V CKM = c ul V c dl V tb c ul3 >.77 (single top production) b sγ A b sγ = f(m t )+s 2 u L3 (f(m t ) f(m t )) (always bigger than SM) Direct bounds m t > 335 GeV 45 GeV < m t < 335 GeV allowed model dependent

Examples We choose models with order 1 couplings. Always consistent with flavor bounds. Details of the spectrum model dependent but structure robust.

Examples We choose models with order 1 couplings. Always consistent with flavor bounds. Details of the spectrum model dependent but structure robust. SU(3) QL U(3) UR U(3) DR

spin 1 2 :.4, 1.8, 90 TeV spin 1 :.29, 1.9, 3.9, 80 TeV

Effective 4-Fermi operators from flavor gauge boson, Model Q q iq j 1 = q α jlγ µ q α il q β jl γµ q β il, Q q iq j 1 = q α jrγ µ q α ir q β jr γµ q β ir, Q q iq j 5 = q α jrq β il qβ jl qα ir. Bounds Safer than MFV!

SU(3) QL SU(3) UR SU(3) DR M u (GeV) M d (GeV) λ u λ u λ d λ d g Q g U g D 400 100 1 0.5 0.25 0.3 0.4 0.3 0.5 Y u Diag 1 10 5, 2 10 2, 8 10 2 V TeV, Y d Diag 5 10 3, 3 10 2, 6 TeV,

δr b R b = 1.0 10 3, S =0.00, T =0.01, U =0.00, V tb =1.00. spin 1 2 :.4, 1.8, 90 TeV spin 1 :2.8, 53, 53, 66 TeV

Signals b and t could be produced at LHC if allowed kinematically

Signals b and t could be produced at LHC if allowed kinematically b : Decay in Wt, Zb highly suppressed by small mixing, branching into Hb O(1) p p b b + X 2h +2b + X 6b + X

Signals b and t could be produced at LHC if allowed kinematically b : Decay in Wt, Zb highly suppressed by small mixing, branching into Hb O(1) p p b b + X 2h +2b + X 6b + X t : Possible larger mixing. Higgs coupling zero if <Yt>=0. SM decays forbidden up to mixing effects, t t t Flavor gauge boson: Non-universal lepto-phobic Z Mostly coupled to third generation. Drell-Yan production or gluon fusion.

Conclusions

Conclusions Flavor physics might not be as far in energy as previously expected.

Conclusions Flavor physics might not be as far in energy as previously expected. Simplest construction of flavor gauge symmetries in the SM realizes the inverted hierarchical structure. This allows flavor physics to be around the electro-weak scale. Interesting phenomenology: new vector like fermions, flavor gauge bosons, flavons. Possibility of a heavy Higgs. Details model dependent but structure robust.