Perspectives Flavor Physics beyond the Standard Model

Transcription

1 Perspectives Flavor Physics beyond the Standard Model Invited Talk at FLASY13 (Jul 2013) OTTO C. W. KONG Nat l Central U, Taiwan

2 Personal :- PhD. dissertation on horizontal/family symmetry Frampton & O.K. PRL75 (95), PRD53 (96), PRL77 (96) postdiction on mass hierarchy (learn much?) weak model-building idea 4321/3321 models, SUSY w/o R parity, extra-d, little Higgs, DSB flavor Vs family? strong conceptual principles

3 Philosophical :- Paul Feyerabend : Against Method the only principle that does not inhibit progress is anything goes don t censor scientific endeavour however, individuals should have personal perspectives discussions/debates necessary Educated guess Vs Shooting in the dark / Blindly f ollowing everyone is qualified to speak up intend to provoke discussions

4 Going beyond the SM modeling :- not (complementary) model independent constraint analyses has to be bottom-up (the energy scale) down to earth/the colliders (experimental reach) ALL THEORIES ARE EFFECTIVE THEORIES theory of everything = theory of anything (string theory is good mathematical physics) no sign that HEP and QG should be unified my preferred approach quantum relativity Das & OK PRD73 (06) OK PLB665 (08) SIMPLICITY and BEAUTY

5 Physics Beyond the Standard Model WHY? WHAT? WHERE? Theoretical hierarchy problem, couplings Experimental m ν, a µ, B physics, Higgs (?) Flavor Problems

6 Standard Model :- gauge symmetry anomaly free chiral fermion spectrum a Higgs multiplet for EW symmetry breaking accidental global symmetries The Gauge Symmetry :- dictates interactions, gauge bosons may dictate all fields (massless) + supersymmetry, may dictate all matter content scalar field problematic/arbitrary Flavor Problem(s) Why 3 families?!

7 gauge symmetry fixes spin 1 sector The Story of the spin 1 fermion sector 2 3 families of 15 spin 1 2 quantum fields (Weyl 2-spinors) under SU(3) C SU(2) L U(1) Y (3,2,1) : u u u d d d ( 3,1, 4) : ū ū ū (1,2, 3) : ν L e L (1,1,6) : e + R minimal chiral set free from all anomalies complete nontrivial cancellation (Vs vector-like pairing)

8 SM fermion field spectrum for one family :- minimal chiral set with completely nontrivial anomaly cancellation less than appreciated well enough Geng & Marshak (89) taking SU(3) C SU(2) L U(1) Y assuming a (3,2,1) multiplet SU(3) requires ( 3,1,a) and ( 3,1,b) SU(2) requires an extra (1,2,c) U(1) anomalies have no solution adding a (1,1,k) give the unique solution idea extended to derive the 3-family spectrum O.K. MPLA11, PRD55 (97)

9 Principle of Gauge-Chiral Fields Why there is what there is why the list? gauge symmetry / no anomaly = full Lagrangian massless (before symmetry breaking) if not at model cut-off scale / decoupled Georgi : survival hypothesis (79) chiral fermions + gauge bosons (dictated by symmetry) SM two problems needs EWSB Higgs (SUSY and/or NJL solution) the most fundamental mystery : Why Three Families?

10 Supersymmetric SM :- SUSY is a beautiful symmetry one compelling model for TeV scale R-parity Violation (bottom-up!) early days faith in baryon and lepton number conservation (global) discrete symmetry theorists pretence of elegance in discarding arbitrary admissible terms in an Lagrangian? given SUSY simplest, natural, way to have neutrino masses flavor problems more complicated µ-problem vector-like Higgs superfields! NJL as a solution (interesting viable SUSY version) O.K. et.al. PRD81 (10), JHEP01 (12), PRD87 (13)

11 SUSY (w/o R parity) Flavor Physics:- one Higgs from L 0 an extra lepton flavor O.K. et. al. PLB430 (98) clarifying the flavor basis issue = better formulation phenomenology from all RPV combinations : O.K. et. al. (98-13) e.g. fermion EDM at 1-loop, h µ ± τ Keum & O.K. PRL86 (01), Choi et. al. PRD63 (00) Arhrib, Cheng, & O.K. PRD87 (13), EPL101 (13) for λ ijk and λ ijk being key source of m ν = no hierarchy or anti-hierarchy down the families O.K. MPLA14 (99)? flavor structure among soft SUSY breaking terms

12 Extending SM (vertical) Gauge Symmetry :- adding quarks and leptons w/o extending symmetry essentially a no go extending EW symmetry interesting flavor physics, flavor family little Higgs as models of extended EW symmetries? interesting option of TeV scale effective field theory? flavor symmetry when flavor family

13 Anomaly Free Gauged SU(N) L U(1) X Models :- family non-universal SM embeddings : cancellation among them some in the literature Frampton PRL69 (92), Singer et.al. PRD22, Pisano & Pleitez PRD46, Foot et.al. PRD50 infinite number exist under simple construction rules! O.K. IJMPA20 (05) Compatible with little Higgs? works for simplest Higgs little type of models Kaplan & Schmaltz JHEP10 (03) one for N = 3, more for N = 4 O.K. PRD70 (04), IJMPA20 (05)

14 The Construction Rules :- (t,b) containing Q a as (3,N,X Q ) other quark doublets in (3, N,X Q ) because N f = N c SU(N) L anomaly cancels by 3 N s - 6 N s + 3 family universal leptonic (1,N,X L ) s [SU(N) L ] 2 U(1) X anomaly with correct doublet embeddings N c X Q + 2N c X Q + N f X L = 0 e.g. (with N = 4) Q = 1 2 λ3 + A 3 λ8 + B 6 λ15 + X condition : A + B + X Q = 1 6 etc. add singlets to keep QCD & QED spectra vectorlike

15 331 little Higgs Model :- there is a solution (existence not a priori clear) Gauge anomalies tx LLL LLX CCX X 3 (3 C,3 L, 1 3 ) (3 C, 3 L,0) (l C,3 L, 1 3 ) U(1) Y states 1 6 [Q] 2 3 (T) [Q] [L] 3 0(N) 4 ( 3 C,1 L, 2 3 ) (ū, c, t, T) 5 ( 3 C,1 L, 1 3 ) ( d, s, b, D, S) 3 (1 C,1 L,1) (e +, µ +, τ + ) Total (D, S) realistic little Higgs models = new picture on flavor physics (also neutrino physics) may need to go to SU(4) L U(1) X model (also fine)

16 SU(4) L U(1) X little Higgs Model 2nd example U(1) Y -states (3 C,4 L, 1 6 ) 1 6 [Q] 2 3 (T) 1 3 (B) 2 (3 C, 4 L, 1 6 ) [2 Q] (D,S) (U,C) 3 (l C,4 L, 1 2 ) [3 L] 3 0(3 N) 3-1(3 E ) 6 ( 3 C,1 L, 2 3 ) (ū, c, t, T) (Ū, C) 6 ( 3 C,1 L, 1 3 ) ( d, s, b, D, S) 1 3 ( B) 6 (1 C,1 L,1) 3 1 (e +,µ +,τ + ) 3 1(3 E + )

17 Flavor Structure of the 331-little Higgs Model(s) :- top Yukawa y 1 t a Φ 1 Q a + y 2 T a Φ 2 Q a y t th ( ) t bottom Yukawa no bφ i Qa but b Φ i Φ j Qa extra S and D may be relevant to B (b) physics b others from the gauge symmetry only u and c Yukawa 1 L Φ i Φ j 3 L d and s Yukawa 1 L Φ 3 i L family universal leptonic Yukawa l + Φ i Φ j L also extra singlet neutrinos

18 quark masses admit generic mass matrices note : L-handed quark mixings L top = λ t 1 t a Φ 1 Q a + λ t 2 T a Φ 2 Q a = f (λ t 1 t + λ t 2 T ) T + i 2 (λ t 1 t λ t 2 T ) h L Q = 1 M λu αj ū α Φ 1 Φ 2 Q j = i 2 f M λu αj ū α h ( t b ( ) u j d j + ) + L down = λ d1 βj d β Φ 1 Q j + λd2 βj d β Φ 2 Q j + 1 M λb β d β Φ 1 Φ 2 Q = f (λ d1 βj d β + λ d2 βj d β) D j + i 2 f M λb β d β h ( t b ) i 2 (λ d1 βj d β λ d2 βj d β) h ( + u j d j )

19 M q = mq 0 m Qq m Q M u M d SMALL PART OF THE STORY :- Z 0 boson couplings T 3 f Q f sin 2 θ W mixings of states with different T 3 f values CKM unitarity violation, FCNC,... = U f L = Kf S f R f T f e.g. S c 1 m T m T c g L (c) = 1 2 [ 1 Sc 2] 2 3 sin2 θ W g L (ūc) = 1 2 [ S us c ] hadronic Z-width gives < 0.014

20 3-family Models (with gauge-chiral fields?) :- construction of minimal (?) chiral (fermion) spectrum with extended (gauge) symmetry require consistent SM embedding 1 fully chiral spectrum + SSB = 3 SM families + vectorlike SM fermions note: extending embedding to kill all anomaly always possible spectrum may be huge (esthetic!) yielding new chiral SM fermion is phenomenologically fatal beyond 3N1 stories, N321 models O.K. MPLA430, PRD55 (97)

21 e.g. SU(4) A SU(3) C SU(2) L U(1) X multiplets X Gauge anomalies U(1) Y states t (4,3,2) (Q) -5(Q ) ( 4, 3,1) (ū) 2( d) ( 4, 1, 2) (L) 3( L) ( 4,1,1) (Ē) 0(N) (6,1,1) (E) 3 12(S) (1, 3,2) ( Q ) (1, 3,1) ( d) (1, 3,1) ( d) (1, 1, 2) (L) 3 (1,1,1) ( S) 3 (1,1,1) (E) Total

22 Back to Horizontal Symmetry SU(3) H SU(3) C SU(2) L U(1) Y Scheme I Scheme II U(1) Y -states U(1) Y -states (3,3,2) 3 1(Q) 3 1(Q) ( 3, 3,1) 3 2( d) 3-4(ū) ( 3, 1, 2, ) 3-3(L) 3-3(L) ( 3,1,1) 3-6(Ē) 3-12( S ) 3 (1, 3,1) 3-4(ū) 3 2( d) 3 (1,1,1) 3 6(E) 3 6(E) 3 (1,1,1) 3 6(E) 3 12(S ) simple gauge version of horizontal(/family) symmetry 3 SM families in one minimal chiral fermion spectrum

23 Concluding Remarks :- BSM flavor family how is quite model dependent Principle of gauge-chiral fields may works, however need SUSY and/or DSB (? NJL) need more imaginative ideas and deep thinking also experimental data (new particles)

24 THANK Y OU! well done Otto!