On the observable spectrum of theories with a Brout-Englert-Higgs effect
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1 On the observable spectrum of theories with a Brout-Englert-Higgs effect René Sondenheimer FSU Jena & L. Egger, A. Maas arxiv: & A. Maas, P.Törek arxiv: , arxiv: Higgs Couplings 2017, Heidelberg 8th of November 2017
2 Gauge invariance 2
3 Gauge invariance Physical observable is gauge invariant! 2
4 Gauge invariance Physical observable is gauge invariant! QED: Dressing by Dirac phase factor 2
5 Gauge invariance Physical observable is gauge invariant! QED: Dressing by Dirac phase factor QCD: Confinement 2
6 Gauge invariance Physical observable is gauge invariant! QED: Dressing by Dirac phase factor QCD: Confinement Elementary fields: Quarks and Gluons L = 1 4 Giµ G i µ + q a i /D ab q b + m q q a q a 2
7 Gauge invariance Physical observable is gauge invariant! QED: Dressing by Dirac phase factor QCD: Confinement Elementary fields: Quarks and Gluons L = 1 4 Giµ G i µ + q a i /D ab q b + m q q a q a Observable states: hadrons q q q q q g g g q q q q q q q q q q q Mesons Baryons Glueballs? Hybrids? Tetraquarks? Pentaquarks? 2
8 Gauge invariance Physical observable is gauge invariant! QED: Dressing by Dirac phase factor QCD: Confinement Elementary fields: Quarks and Gluons L = 1 4 Giµ G i µ + q a i /D ab q b + m q q a q a Observable states: hadrons q q q q q g g g q q q q q q q q q q q Mesons Baryons Glueballs? Hybrids? Tetraquarks? Pentaquarks? Weak interaction? 2
9 Higgs-W Subsector 3
10 Higgs-W Subsector Elementary fields: Higgs and W L = 1 4 W iµ W i µ +(D µ ) a (D µ ) a U( a a ) 3
11 Higgs-W Subsector Elementary fields: Higgs and W L = 1 4 W iµ W i µ +(D µ ) a (D µ ) a U( a a ) U L Higgs potential: U = µ ( ) 2 f 3
12 Higgs-W Subsector Elementary fields: Higgs and W L = 1 4 W iµ W i µ +(D µ ) a (D µ ) a U( a a ) U L Higgs potential: U = µ ( ) 2 Expansion around vev: (x) = 1 ' p + (x) 2 v + h(x)+' 0 (x) f 3
13 Higgs-W Subsector Elementary fields: Higgs and W L = 1 4 W iµ W i µ +(D µ ) a (D µ ) a U( a a ) U L Higgs potential: U = µ ( ) 2 Expansion around vev: (x) = 1 ' p + (x) 2 v + h(x)+' 0 (x) f Mass for the W s from the Higgs kinetic term (D µ ) D µ = 1 2 g 2 v 2 4 W i µw iµ
14 Higgs-W Subsector BUT! Elementary states are not gauge invariant Cannot be observable Gauge-invariant states are composite e.g., Higgs-Higgs, W-W, Higgs-W,. W Bound states are not asymptotic states in perturbation theory Why does perturbation theory works at all? Higgs condensate exist only in some gauges Local symmetry breaking vs Elitzur s theorem Lee et al 72, Osterwalder&Seiler 77 Elitzur 81 4
15 Fröhlich-Morchio-Strocchi mechanism Fröhlich et al 80, 81 5
16 Fröhlich-Morchio-Strocchi mechanism Fröhlich et al 80, Construct a gauge-invariante operator O(x) =( )(x) 5
17 Fröhlich-Morchio-Strocchi mechanism Fröhlich et al 80, Construct a gauge-invariante operator O(x) =( )(x) 2. Expand Higgs field in correlator in fluctuations around the vev = v + ' ho(x)o(y)i = const. + v 2 hh(x)h(y)i + v 3 h'i + vh' 3 i + h' 4 i 5
18 Fröhlich-Morchio-Strocchi mechanism Fröhlich et al 80, Construct a gauge-invariante operator O(x) =( )(x) 2. Expand Higgs field in correlator in fluctuations around the vev = v + ' ho(x)o(y)i = const. + v 2 hh(x)h(y)i + v 3 h'i + vh' 3 i + h' 4 i 3. Perform standard perturbation theory on the right-hand side ho(x)o(y)i = v 2 hh(x)h(y)i tl + hh(x)h(y)i 2 tl + O(g 2, ) 5
19 Fröhlich-Morchio-Strocchi mechanism Fröhlich et al 80, Construct a gauge-invariante operator O(x) =( )(x) 2. Expand Higgs field in correlator in fluctuations around the vev = v + ' ho(x)o(y)i = const. + v 2 hh(x)h(y)i + v 3 h'i + vh' 3 i + h' 4 i 3. Perform standard perturbation theory on the right-hand side ho(x)o(y)i = v 2 hh(x)h(y)i tl + hh(x)h(y)i 2 tl + O(g 2, ) 4. Compare poles on both sides 5
20 Fröhlich-Morchio-Strocchi mechanism Fröhlich et al 80, Construct a gauge-invariante operator O(x) =( )(x) 2. Expand Higgs field in correlator in fluctuations around the vev = v + ' ho(x)o(y)i = const. + v 2 hh(x)h(y)i + v 3 h'i + vh' 3 i + h' 4 i 3. Perform standard perturbation theory on the right-hand side ho(x)o(y)i = v 2 hh(x)h(y)i tl + hh(x)h(y)i 2 tl + O(g 2, ) 4. Compare poles on both sides Confirmed on the lattice for SU(2)-Higgs theory Maas 12 5
21 Fröhlich-Morchio-Strocchi mechanism 6
22 Fröhlich-Morchio-Strocchi mechanism W-Higgs sector of the standard model L = 1 4 W i µ W iµ +(D µ ) D µ U( ) Local SU(2)L Symmetry W µ! UW µ U 1 i g (@ µu)u 1,! U 6
23 Fröhlich-Morchio-Strocchi mechanism W-Higgs sector of the standard model L = 1 4 W i µ W iµ +(D µ ) D µ U( ) Local SU(2)L Symmetry W µ! UW µ U 1 i g (@ µu)u 1,! U Additional global SU(2)cust. symmetry W µ! W µ,! V + W 6
24 Fröhlich-Morchio-Strocchi mechanism W-Higgs sector of the standard model L = 1 4 W i µ W iµ +(D µ ) D µ U( ) Local SU(2)L Symmetry W µ! UW µ U 1 i g (@ µu)u 1,! U Additional global SU(2)cust. symmetry W µ! W µ,! V + W Convenient to rewrite Higgs-Lagrangian 6
25 Fröhlich-Morchio-Strocchi mechanism W-Higgs sector of the standard model L = 1 4 W i µ W iµ +(D µ ) D µ U( ) Local SU(2)L Symmetry W µ! UW µ U 1 i g (@ µu)u 1,! U Additional global SU(2)cust. symmetry W µ! W µ,! V + W Convenient to rewrite Higgs-Lagrangian L =Tr[@ µ µ X] U(TrX X) where X = = = v 0 0 v + O(')
26 Fröhlich-Morchio-Strocchi mechanism 7
27 Fröhlich-Morchio-Strocchi mechanism Full symmetry acting on the Higgs field: SU(2)L x SU(2)cust. X! U L XU cust X =
28 Fröhlich-Morchio-Strocchi mechanism Full symmetry acting on the Higgs field: SU(2)L x SU(2)cust. X! U L XU cust X = W mass: bound state operator in 1- channel Oĩµ =itr( ĩx D µ X) 7
29 Fröhlich-Morchio-Strocchi mechanism Full symmetry acting on the Higgs field: SU(2)L x SU(2)cust. X! U L XU cust X = W mass: bound state operator in 1- channel Oĩµ =itr( ĩx D µ X) Expand Higgs field: hoĩµ(x)o j (y)i = g 2 v 4 hw i µ(x)w j (y)i iĩ j j + O(' 2 ) 7
30 Fröhlich-Morchio-Strocchi mechanism Full symmetry acting on the Higgs field: SU(2)L x SU(2)cust. X! U L XU cust X = W mass: bound state operator in 1- channel Oĩµ =itr( ĩx D µ X) Expand Higgs field: hoĩµ(x)o j (y)i = g 2 v 4 hw i µ(x)w j (y)i iĩ j j + O(' 2 ) Pole of bound state the same as for the elementary fields 7
31 Fröhlich-Morchio-Strocchi mechanism Full symmetry acting on the Higgs field: SU(2)L x SU(2)cust. X! U L XU cust X = W mass: bound state operator in 1- channel Oĩµ =itr( ĩx D µ X) Expand Higgs field: hoĩµ(x)o j (y)i = g 2 v 4 hw i µ(x)w j (y)i iĩ j j + O(' 2 ) Pole of bound state the same as for the elementary fields Mapping of local to global multiplets 7
32 Fermions Fröhlich et al 80 Egger,Maas,RS 17 8
33 Fermions Fröhlich et al 80 Egger,Maas,RS 17 Flavor = weak gauge charge in a given generation 8
34 Fermions Fröhlich et al 80 Egger,Maas,RS 17 Flavor = weak gauge charge in a given generation Necessary to construct suitable gauge-invariant state which emulate elementary fermions 8
35 Fermions Fröhlich et al 80 Egger,Maas,RS 17 Flavor = weak gauge charge in a given generation Necessary to construct suitable gauge-invariant state which emulate elementary fermions O g (x) =X (x)f g (x) 8
36 Fermions Fröhlich et al 80 Egger,Maas,RS 17 Flavor = weak gauge charge in a given generation Necessary to construct suitable gauge-invariant state which emulate elementary fermions O g (x) =X (x)f g (x) State remains custodial doublet 8
37 Fermions Fröhlich et al 80 Egger,Maas,RS 17 Flavor = weak gauge charge in a given generation Necessary to construct suitable gauge-invariant state which emulate elementary fermions O g (x) =X (x)f g (x) State remains custodial doublet E.g., (left-handed) electron and neutrino 8
38 Fermions Fröhlich et al 80 Egger,Maas,RS 17 Flavor = weak gauge charge in a given generation Necessary to construct suitable gauge-invariant state which emulate elementary fermions O g (x) =X (x)f g (x) State remains custodial doublet E.g., (left-handed) electron and neutrino O e = X = e e 2e = v e + O(') 8
39 Fermions Fröhlich et al 80 Egger,Maas,RS 17 Flavor = weak gauge charge in a given generation Necessary to construct suitable gauge-invariant state which emulate elementary fermions O g (x) =X (x)f g (x) State remains custodial doublet E.g., (left-handed) electron and neutrino O e = X = e e 2e = v e + O(') Ordinary states remerge when applying FMS 8
40 Fermions Fröhlich et al 80 Egger,Maas,RS 17 Flavor = weak gauge charge in a given generation Necessary to construct suitable gauge-invariant state which emulate elementary fermions O g (x) =X (x)f g (x) State remains custodial doublet E.g., (left-handed) electron and neutrino O e = X = e e 2e = v e + O(') Ordinary states remerge when applying FMS Phenomenological consequences 8
41 Fermions - Quarks Egger,Maas,RS 17 9
42 Fermions - Quarks Egger,Maas,RS 17 O ud = X u d = 2u 1u + 1d 2d = v u d + O(') 9
43 Fermions - Quarks Egger,Maas,RS 17 O ud = X u d = 2u 1u + 1d 2d = v u d + O(') Quark sector different from lepton sector, bound in hadrons 9
44 Fermions - Quarks Egger,Maas,RS 17 O ud = X u d = 2u 1u + 1d 2d = v u d + O(') Quark sector different from lepton sector, bound in hadrons Hadrons singlets of strong interaction, not necessarily of weak interaction 9
45 Fermions - Quarks Egger,Maas,RS 17 O ud = X u d = 2u 1u + 1d 2d = v u d + O(') Quark sector different from lepton sector, bound in hadrons Hadrons singlets of strong interaction, not necessarily of weak interaction Obvious for baryons (strong indices suppressed) 9
46 Fermions - Quarks Egger,Maas,RS 17 O ud = X u d = 2u 1u + 1d 2d = v u d + O(') Quark sector different from lepton sector, bound in hadrons Hadrons singlets of strong interaction, not necessarily of weak interaction Obvious for baryons (strong indices suppressed) c ijkl q i q j q k X ĩl or q i q j q k X ĩi X jj X kk 9
47 Fermions - Quarks Egger,Maas,RS 17 O ud = X u d = 2u 1u + 1d 2d = v u d + O(') Quark sector different from lepton sector, bound in hadrons Hadrons singlets of strong interaction, not necessarily of weak interaction Obvious for baryons (strong indices suppressed) c ijkl q i q j q k X ĩl or q i q j q k X ĩi X jj X kk c ijkl = a 1 ij kl + a 2 ik jl + a 3 jk il and ĩ =1 9
48 Fermions - Quarks Egger,Maas,RS 17 O ud = X u d = 2u 1u + 1d 2d = v u d + O(') Quark sector different from lepton sector, bound in hadrons Hadrons singlets of strong interaction, not necessarily of weak interaction Obvious for baryons (strong indices suppressed) c ijkl q i q j q k X ĩl or q i q j q k X ĩi X jj X kk Proton: c ijkl = a 1 ij kl + a 2 ik jl + a 3 jk il and ĩ =1 9
49 Fermions - Quarks Egger,Maas,RS 17 O ud = X u d = 2u 1u + 1d 2d = v u d + O(') Quark sector different from lepton sector, bound in hadrons Hadrons singlets of strong interaction, not necessarily of weak interaction Obvious for baryons (strong indices suppressed) c ijkl q i q j q k X ĩl or q i q j q k X ĩi X jj X kk Proton: c ijkl = a 1 ij kl + a 2 ik jl + a 3 jk il and ĩ =1 Some mesons are weak-gauge singlets, e.g., 9
50 Fermions - Quarks Egger,Maas,RS 17 O ud = X u d = 2u 1u + 1d 2d = v u d + O(') Quark sector different from lepton sector, bound in hadrons Hadrons singlets of strong interaction, not necessarily of weak interaction Obvious for baryons (strong indices suppressed) c ijkl q i q j q k X ĩl or q i q j q k X ĩi X jj X kk Proton: c ijkl = a 1 ij kl + a 2 ik jl + a 3 jk il and ĩ =1 Some mesons are weak-gauge singlets, e.g.,! meson (ūu + dd) 9
51 Fermions - Quarks Egger,Maas,RS 17 O ud = X u d = 2u 1u + 1d 2d = v u d + O(') Quark sector different from lepton sector, bound in hadrons Hadrons singlets of strong interaction, not necessarily of weak interaction Obvious for baryons (strong indices suppressed) c ijkl q i q j q k X ĩl or q i q j q k X ĩi X jj X kk Proton: c ijkl = a 1 ij kl + a 2 ik jl + a 3 jk il and ĩ =1 Some mesons are weak-gauge singlets, e.g.,! meson (ūu + dd) Not true for all mesons, e.g., pions + : Ō ud 2 O ud 1 ( du) 9
52 Beyond the standard model Maas, Törek 16, Maas, RS, Törek 17 10
53 Beyond the standard model Maas, Törek 16, Maas, RS, Törek 17 SU(N) gauge theory + Higgs in fundamental representation 10
54 Beyond the standard model Maas, Törek 16, Maas, RS, Törek 17 SU(N) gauge theory + Higgs in fundamental representation Local and global symmetry group do not match for N > 2 10
55 Beyond the standard model Maas, Törek 16, Maas, RS, Törek 17 SU(N) gauge theory + Higgs in fundamental representation Local and global symmetry group do not match for N > 2 J P Field Mass Degeneracy Operator Mass Degeneracy 0 + h m h
56 Beyond the standard model Maas, Törek 16, Maas, RS, Törek 17 SU(N) gauge theory + Higgs in fundamental representation Local and global symmetry group do not match for N > 2 J P Field Mass Degeneracy 0 + h m h 1 Operator Mass Degeneracy m h
57 Beyond the standard model Maas, Törek 16, Maas, RS, Törek 17 SU(N) gauge theory + Higgs in fundamental representation Local and global symmetry group do not match for N > 2 J P Field Mass Degeneracy 0 + h m h 1 Operator Mass Degeneracy m h 1 1 A µ i 0 (N 1)
58 Beyond the standard model Maas, Törek 16, Maas, RS, Törek 17 SU(N) gauge theory + Higgs in fundamental representation Local and global symmetry group do not match for N > 2 J P Field Mass Degeneracy 0 + h m h 1 Operator Mass Degeneracy m h 1 1 A µ i 0 (N 1) 2 1 Ã µ i m A 2(N 1) 10
59 Beyond the standard model Maas, Törek 16, Maas, RS, Törek 17 SU(N) gauge theory + Higgs in fundamental representation Local and global symmetry group do not match for N > 2 J P Field Mass Degeneracy 0 + h m h 1 Operator Mass Degeneracy m h 1 1 A µ i 0 (N 1) 2 1 Ã µ i m A 2(N 1) Ā µ i r 2(N 1) N m A 1 10
60 Beyond the standard model Maas, Törek 16, Maas, RS, Törek 17 SU(N) gauge theory + Higgs in fundamental representation Local and global symmetry group do not match for N > 2 J P Field Mass Degeneracy 0 + h m h 1 Operator Mass Degeneracy m h 1 1 A µ i 0 (N 1) 2 1 i D µ r 2(N 1) N m A 1 Ã µ i m A 2(N 1) Ā µ i r 2(N 1) N m A 1 10
61 Beyond the standard model Maas, Törek 16, Maas, RS, Törek 17 SU(N) gauge theory + Higgs in fundamental representation Local and global symmetry group do not match for N > 2 J P Field Mass Degeneracy 0 + h m h 1 Operator Mass Degeneracy m h 1 1 A µ i 0 (N 1) 2 1 Ã µ i m A 2(N 1) i r D 2(N 1) µ m 1 N A O ±1 (N 1)m A 1/ 1 Ā µ i r 2(N 1) N m A 1 10
62 Beyond the standard model Maas, Törek 16, Maas, RS, Törek 17 SU(N) gauge theory + Higgs in fundamental representation Local and global symmetry group do not match for N > 2 J P Field Mass Degeneracy 0 + h m h 1 Operator Mass Degeneracy m h 1 O ±1 (N 1)m A 1/ 1 1 A µ i 0 (N 1) 2 1 Ã µ i m A 2(N 1) i r D 2(N 1) µ m 1 N A O ±1 (N 1)m A 1/ 1 Ā µ i r 2(N 1) N m A 1 10
63 Beyond the standard model Maas, Törek 16, Maas, RS, Törek 17 SU(N) gauge theory + Higgs in fundamental representation Local and global symmetry group do not match for N > 2 J P Field Mass Degeneracy 0 + h m h 1 Operator Mass Degeneracy m h 1 O ±1 (N 1)m A 1/ 1 1 A µ i 0 (N 1) 2 1 Ã µ i m A 2(N 1) i r D 2(N 1) µ m 1 N A O ±1 (N 1)m A 1/ 1 Ā µ i r 2(N 1) N m A 1 Nonperturbative check for N=3 10
64 Beyond the standard model - SU(5) GUT 11
65 Beyond the standard model - SU(5) GUT h i w h i v SU(5) SU(3)xSU(2)xU(1) U(1) w v 11
66 Beyond the standard model - SU(5) GUT h i w h i v SU(5) SU(3)xSU(2)xU(1) U(1) w v J P Field Mass Degeneracy Operator Mass Degeneracy 0 + h m h 1 ' a w 6 i w 8 i w 3 w 1 i 1 11
67 Beyond the standard model - SU(5) GUT h i w h i v SU(5) SU(3)xSU(2)xU(1) U(1) w v J P Field Mass Degeneracy Operator Mass Degeneracy 0 + h m h 1 ' a w 6 i w 8 i w 3 w 1 1 i A µ W ±µ Z µ X µ Y µ 0 m W m Z w w 1 1/
68 Beyond the standard model - SU(5) GUT h i w h i v SU(5) SU(3)xSU(2)xU(1) U(1) w v Global symmetry: U(1)xZ2 J P Field Mass Degeneracy Operator Mass Degeneracy 0 + h m h 1 ' a w 6 i w 8 i w 3 w 1 1 i A µ W ±µ Z µ X µ Y µ 0 m W m Z w w 1 1/
69 Beyond the standard model - SU(5) GUT h i w h i v SU(5) SU(3)xSU(2)xU(1) U(1) w v Global symmetry: U(1)xZ2 J P Field A µ W ±µ Z µ X µ Y µ Mass 0 m W m Z w w Degeneracy 0 + h m h 1 ' a w 6 i w 8 i w 3 w 1 1 i 1 1/ Operator O 0+ O 0 O ±1,+ O ±1, Mass m h m h w w Degeneracy 1 1 1/ 1 1/ 1 11
70 Beyond the standard model - SU(5) GUT h i w h i v SU(5) SU(3)xSU(2)xU(1) U(1) w v Global symmetry: U(1)xZ2 J P Field A µ W ±µ Z µ X µ Y µ Mass 0 m W m Z w w Degeneracy 0 + h m h 1 ' a w 6 i w 8 i w 3 w 1 1 i 1 1/ Operator O 0+ O 0 O ±1,+ O ±1, Mass m h m h w w 0 O 0+ O 0 0 O ±1,+ w O ±1,+ w Degeneracy 1 1 1/ 1 1/ / 1 1/ 1
71 Summary Observable spectrum must be gauge invariant Non-Abelian gauge theory: composite operator FMS mechanism provides a mapping of the local to the global multiplets Gauge-invariant perturbation theory as a tool Same results in leading order for the standard model BSM model building may be affected Verification requieres non-perturbative methods 12
72 Generations as excitation spectra (speculation!) Egger,Maas,RS 17 13
73 Generations as excitation spectra (speculation!) Egger,Maas,RS 17 Flavor identity from combination of generation and weak isospin 13
74 Generations as excitation spectra (speculation!) Egger,Maas,RS 17 Flavor identity from combination of generation and weak isospin Difference: Yukawa and weak interactions cannot be simultaneously diagonal in generation space 13
75 Generations as excitation spectra (speculation!) Egger,Maas,RS 17 Flavor identity from combination of generation and weak isospin Difference: Yukawa and weak interactions cannot be simultaneously diagonal in generation space Flavor distinguishes between inter- and intrageneration effects 13
76 Generations as excitation spectra (speculation!) Egger,Maas,RS 17 Flavor identity from combination of generation and weak isospin Difference: Yukawa and weak interactions cannot be simultaneously diagonal in generation space Flavor distinguishes between inter- and intrageneration effects Speculation(!): 3 generations could be internal excitations of a single generation 13
77 Generations as excitation spectra (speculation!) Egger,Maas,RS 17 Flavor identity from combination of generation and weak isospin Difference: Yukawa and weak interactions cannot be simultaneously diagonal in generation space Flavor distinguishes between inter- and intrageneration effects Speculation(!): 3 generations could be internal excitations of a single generation SM effective theory of excitation spectrum 13
78 Generations as excitation spectra (speculation!) Egger,Maas,RS 17 Flavor identity from combination of generation and weak isospin Difference: Yukawa and weak interactions cannot be simultaneously diagonal in generation space Flavor distinguishes between inter- and intrageneration effects Speculation(!): 3 generations could be internal excitations of a single generation SM effective theory of excitation spectrum X Q E = T T Q E Q E = 2u E 2d E + 1 d E 1u E 13
79 Generations as excitation spectra (speculation!) Egger,Maas,RS 17 Flavor identity from combination of generation and weak isospin Difference: Yukawa and weak interactions cannot be simultaneously diagonal in generation space Flavor distinguishes between inter- and intrageneration effects Speculation(!): 3 generations could be internal excitations of a single generation SM effective theory of excitation spectrum X Q E = T T Q E Q E = 2u E 2d E + 1 d E 1u E Ground state: 13
80 Generations as excitation spectra (speculation!) Egger,Maas,RS 17 Flavor identity from combination of generation and weak isospin Difference: Yukawa and weak interactions cannot be simultaneously diagonal in generation space Flavor distinguishes between inter- and intrageneration effects Speculation(!): 3 generations could be internal excitations of a single generation SM effective theory of excitation spectrum X Q E = T T Q E Q E = 2u E 2d E + 1 d E 1u E Ground state: d =( Q E ) g 13
81 Generations as excitation spectra (speculation!) Egger,Maas,RS 17 Flavor identity from combination of generation and weak isospin Difference: Yukawa and weak interactions cannot be simultaneously diagonal in generation space Flavor distinguishes between inter- and intrageneration effects Speculation(!): 3 generations could be internal excitations of a single generation SM effective theory of excitation spectrum X Q E = T T Q E Q E = 2u E 2d E + 1 d E 1u E Ground state: d =( Q E ) g higher excitations: 13
82 Generations as excitation spectra (speculation!) Egger,Maas,RS 17 Flavor identity from combination of generation and weak isospin Difference: Yukawa and weak interactions cannot be simultaneously diagonal in generation space Flavor distinguishes between inter- and intrageneration effects Speculation(!): 3 generations could be internal excitations of a single generation SM effective theory of excitation spectrum X Q E = T T Q E Q E = 2u E 2d E + 1 d E 1u E Ground state: higher excitations: d =( Q E ) g s =( Q E ), b =( Q E ) 13
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