Rethinking Flavor Physics - PDF Free Download

Rethinking Flavor Physics René Sondenheimer FSU Jena & L. Egger, A. Maas arxiv:1701.02881 Cold Quantum Coffee, Heidelberg 30th of May 2017

LHC works remarkably well Higgs discovery completed SM 2

LHC works remarkably well Higgs discovery completed SM No direct signal of BSM physics 2

The Standard Model in a nutshell Ɣ 0 e -1 0.511 MeV Gauge theory: U(1) 3

The Standard Model in a nutshell u +2/3 g 2.3 MeV -1/3 d 4.8 MeV Ɣ 0 0 e -1 0.511 MeV Gauge theory: SU(3)C x U(1) 4

The Standard Model in a nutshell u +2/3 g 2.3 MeV -1/3 d 4.8 MeV Ɣ 0 0 e -1 W ±1 0.511 MeV 80.4 GeV ν e <2eV Z 91.2 GeV Gauge theory: SU(3)C x SU(2)L x U(1)Y 5

The Standard Model in a nutshell +2/3 +2/3 +2/3 u c t g 2.3 MeV 1.275 GeV 173.2 GeV -1/3-1/3-1/3 d s b 4.8 MeV 95 MeV 4.18 GeV Ɣ 0 0-1 -1 e μ τ -1 W ±1 0.511 MeV 105.7 MeV 1.78 GeV 80.4 GeV ν e ν μ ν τ Z <2eV <0.17 MeV <15.5 MeV 91.2 GeV Gauge theory: SU(3)C x SU(2)L x U(1)Y 6

The Standard Model in a nutshell +2/3 +2/3 +2/3 u c t g 2.3 MeV 1.275 GeV 173.2 GeV -1/3-1/3-1/3 d s b 4.8 MeV 95 MeV 4.18 GeV Ɣ 0 0-1 0.511 MeV 105.7 MeV 1.78 GeV -1 e μ τ -1 W 80.4 GeV ±1 H ν e ν μ ν τ Z 125 GeV <2eV <0.17 MeV <15.5 MeV 91.2 GeV Gauge theory: SU(3)C x SU(2)L x U(1)Y 7

Quantum ChromoDynamics 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 8

Quantum ChromoDynamics 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? 8

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 ) 9

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 + 2 ( ) 2 f 9

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 + 2 ( ) 2 Expansion around vev: (x) = 1 ' p + (x) 2 v + h(x)+' 0 (x) f 9

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 + 2 ( ) 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 +... 9

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 Elitzur 81 Lee et al 72, Osterwalder&Seiler 77 10

Outline Introduction FMS mechanism Implications for Fermions Generations (FMS beyond the standard model) Summary 11

Fröhlich-Morchio-Strocchi mechanism Fröhlich et al 80, 81 12

Fröhlich-Morchio-Strocchi mechanism Fröhlich et al 80, 81 1. Construct a gauge-invariante operator 12

Fröhlich-Morchio-Strocchi mechanism Fröhlich et al 80, 81 1. Construct a gauge-invariante operator O(x) =( )(x) 12

Fröhlich-Morchio-Strocchi mechanism Fröhlich et al 80, 81 1. Construct a gauge-invariante operator O(x) =( )(x) 2. Expand Higgs field in correlator in fluctuations around the vev 12

Fröhlich-Morchio-Strocchi mechanism Fröhlich et al 80, 81 1. 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, ) 12

Fröhlich-Morchio-Strocchi mechanism 13

Fröhlich-Morchio-Strocchi mechanism W-Higgs sector of the standard model L = 1 4 W µ W i iµ +(D µ ) D µ U( ) Local SU(2) L Symmetry 13

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 13

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 13

Fröhlich-Morchio-Strocchi mechanism 14

Fröhlich-Morchio-Strocchi mechanism Full symmetry acting on the Higgs field: SU(2) L x SU(2)cust. 14

Fröhlich-Morchio-Strocchi mechanism Full symmetry acting on the Higgs field: SU(2) L x SU(2)cust. X! U L XU cust 14

Fröhlich-Morchio-Strocchi mechanism Full symmetry acting on the Higgs field: SU(2) L x SU(2)cust. X! U L XU cust W mass: bound state operator in 1- channel 14

Fröhlich-Morchio-Strocchi mechanism Full symmetry acting on the Higgs field: SU(2) L x SU(2)cust. X! U L XU cust W mass: bound state operator in 1- channel Oĩµ =itr( ĩx D µ X) 14

Fröhlich-Morchio-Strocchi mechanism Full symmetry acting on the Higgs field: SU(2) L x SU(2)cust. X! U L XU cust W mass: bound state operator in 1- channel Expand Higgs field: Oĩµ =itr( ĩx D µ X) hoĩµ(x)o j (y)i = g 2 v 4 hw i µ(x)w j (y)i iĩ j j + O(' 2 ) 14

Fermions Fröhlich et al 80 Egger,Maas,RS 17 15

Fermions Fröhlich et al 80 Egger,Maas,RS 17 Flavor = weak gauge charge in a given generation 15

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 15

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 15

Fermions - Quarks Egger,Maas,RS 17 16

Fermions - Quarks O ud = X u d = 2u 1u + 1d 2d = v u d + O(') Egger,Maas,RS 17 16

Fermions - Quarks O ud = X u = d 2u 1d u 1u + = v + O(') 2d d Egger,Maas,RS 17 Quark sector different from lepton sector, bound in hadrons 16

Fermions - Quarks O ud = X u d = 2u 1u + 1d 2d Quark sector different from lepton sector, bound in hadrons Hadrons singlets of strong interaction, not necessarily of weak interaction = v u d + O(') Egger,Maas,RS 17 16

Fermions - Quarks O ud = X u d 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) = 2u 1u + 1d 2d = v u d + O(') Egger,Maas,RS 17 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 16

Fermions - Quarks O ud = X u d 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) = 2u 1u + 1d 2d = v u d + O(') Egger,Maas,RS 17 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 16

Fermions - Quarks O ud = X u d 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) = 2u 1u + 1d 2d = v u d + O(') Egger,Maas,RS 17 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., 16

Fermions - Quarks O ud = X u d 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) = 2u 1u + 1d 2d = v u d + O(') Egger,Maas,RS 17 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) 16

Fermions - Quarks O ud = X u d 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) = 2u 1u + 1d 2d = v u d + O(') Egger,Maas,RS 17 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 16

Fermions - Quarks O ud = X u d 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) = 2u 1u + 1d 2d = v u d + O(') Egger,Maas,RS 17 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 16 + : Ō ud 2 O ud 1 ( du)

Generations as excitation spectra (speculation!) Egger,Maas,RS 17 17

Generations as excitation spectra (speculation!) Egger,Maas,RS 17 Flavor identity from combination of generation and weak isospin 17

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 17

Gauge-invariant perturbation theory Egger,Maas,RS 17 Lepton collision as probing experiment of the bound state structure M = ho e 2 (p 1 )Ō e 2 (p 2 )O f (q 1 )Ōf (q 2 )i v 4 he + e ffi + he + e ihhh ffi +... Final state μ b t 1.00 dσ Full dσ Perturbative 0.99 0.98 0.97 0.96 0.95 200 400 600 800 1000 s 18

BSM - Grand Unified theories Maas,Törek 16 Maas,Törek,RS, in preparation 19

BSM - Grand Unified theories Maas,Törek 16 Maas,Törek,RS, in preparation SU(N) gauge theory + Higgs in fundamental representation Perturbative mass spectrum: 2N - 1 massive gauge bosons (N-1) 2-1 massless gauge bosons 1 massive scalar Higgs boson Local and global symmetry group do not match for N > 2 1 neutral bound state in 0+ channel = Higgs 19

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 BSM model building may be affected Same results in leading order for the standard model Verification requieres non-perturbative methods 20