Theory of CP Violation
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- Charity Bridges
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1 Theory of CP Violation IPPP, Durham
2 CP as Natural Symmetry of Gauge Theories P and C alone are not natural symmetries: consider chiral gauge theory: L = 1 4 F µνf µν + ψ L i σdψ L (+ψ R iσ ψ R) p.1
3 CP as Natural Symmetry of Gauge Theories P and C alone are not natural symmetries: consider chiral gauge theory: L = 1 4 F µνf µν + ψ L i σdψ L (+ψ R iσ ψ R) L violates P: L violates C: L preserves CP: right-handed fermions do not couple to gauge bosons left-handed antifermions do not couple to gauge bosons both left-handed fermions and right-handed antifermions couple to gauge bosons Massless gauge theories are invariant under CP and T. p.1
4 CP as Natural Symmetry of Gauge Theories P and C alone are not natural symmetries: consider chiral gauge theory: L = 1 4 F µνf µν + ψ L i σdψ L (+ψ R iσ ψ R) p.1
5 But CP IS violated! CP violation in K decays known since 1964; observed in B decays in Origin in SM: Yukawa interactions: L SM = L G (ψ, W, φ) + L H (φ) + L Y (ψ, φ) }{{}}{{}}{{} kinetic Higgs potential Yukawa IA energy + spontaneous fermion gauge IA symmetry breaking masses } {{ } } {{ } gauge sector scalar sector p.2
6 But CP IS violated! CP violation in K decays known since 1964; observed in B decays in Origin in SM: Yukawa interactions: L Y = λ ij d Q i L Φdj R (λij d ) dj R Φ Q i L +... λ d : general, not necessarily symmetric or Hermitian matrices (Yukawa couplings), not constrained by gauge symmetry CP: λ d λ d (explicit) CP violation if λ d complex CP violation happens in the scalar sector! p.2
7 Experimental Status of the Scalar Sector CP is violated. Number, size and origin of CP phases unknown. p.3
8 Experimental Status of the Scalar Sector CP is violated. Number, size and origin of CP phases unknown. Fermion masses and masses of gauge bosons of weak interactions measured. p.3
9 Experimental Status of the Scalar Sector CP is violated. Number, size and origin of CP phases unknown. Fermion masses and masses of gauge bosons of weak interactions measured. No scalar particle observed. p.3
10 Experimental Status of the Scalar Sector CP is violated. Number, size and origin of CP phases unknown. Fermion masses and masses of gauge bosons of weak interactions measured. No scalar particle observed. Mechanism of SU(2) L U(1) symmetry breaking and mass generation not verified experimentally. p.3
11 Experimental Status of the Scalar Sector CP is violated. Number, size and origin of CP phases unknown. Fermion masses and masses of gauge bosons of weak interactions measured. No scalar particle observed. Mechanism of SU(2) L U(1) symmetry breaking and mass generation not verified experimentally. Mechanism of CP violation not identified. p.3
12 Experimental Status of the Scalar Sector CP is violated. Number, size and origin of CP phases unknown. Fermion masses and masses of gauge bosons of weak interactions measured. No scalar particle observed. Mechanism of SU(2) L U(1) symmetry breaking and mass generation not verified experimentally. Mechanism of CP violation not identified. Next generation of accelerators (LHC 2007/8): direct Higgs searches indirect effects: CP in B decays complementary tests of the scalar sector! p.3
13 CP Violation in the Standard Model diagonalise Yukawa matrices quark mass eigenstates p.4
14 CP Violation in the Standard Model diagonalise Yukawa matrices quark mass eigenstates mass eigenstates mix by virtue of weak interactions p.4
15 CP Violation in the Standard Model diagonalise Yukawa matrices quark mass eigenstates mass eigenstates mix by virtue of weak interactions mixing described by unitary Cabibbo-Kobayashi-Maskawa (CKM) matrix V p.4
16 CP Violation in the Standard Model diagonalise Yukawa matrices quark mass eigenstates mass eigenstates mix by virtue of weak interactions mixing described by unitary Cabibbo-Kobayashi-Maskawa (CKM) matrix V parametrised by three angles and one complex phase: source of CP violation in SM p.4
17 CP Violation in the Standard Model diagonalise Yukawa matrices quark mass eigenstates mass eigenstates mix by virtue of weak interactions mixing described by unitary Cabibbo-Kobayashi-Maskawa (CKM) matrix V parametrised by three angles and one complex phase: source of CP violation in SM Im V ud Vub V cd Vcb (ρ,η) α V td Vtb V cd V cb Visualise unitarity relation Vdj V jb = 0 as triangle in complex plane: γ β 0 1 Re unitarity triangle (UT) p.4
18 Experimental Determination of UT 2 sin γ sin 2β sin γ sin 2β K + π + νν 1 m d ε, /ε K, K 0 π 0 νν η 0-1 ε K K 0 π 0 νν sin 2α V ub /V cb sin 2α K + π + νν ε K ρ The ideal... p.5
19 Experimental Determination of UT sin γ sin 2β sin γ excluded area has CL < 0.05 sin 2β K + π + νν 1 sin 2β m d 1 m d m s & m d 0.5 ε, /ε K, K 0 π 0 νν α B ρρ η 0 ε K η 0 ε K γ β K 0 π 0 νν V ub /V cb V ub /V cb sin 2α sin 2α ε K K + π + νν ρ ε K C K M f i t t e r Winter 2004 B ρρ The ideal... The reality... ρ p.5
20 UT from K Decays Experimentally favoured: ɛ K : th. uncertainty from B K, m t, V cb Theoretically favoured: B(K + π + ν ν), B(K L π 0 ν ν) hadronic matrix elements from K πlν SD dominated (W-box, Z-penguin) QCD corrections known to NLO: small residual scale-dependence BR O(10 11 ) complete determination of UT with strong dependence on V cb and (less strong) on m t! npqcd potentially more dangerous than in B decays (ɛ /ɛ etc.) p.6
21 The Case for B Physics large number of different decay channels, sensitive to different weak phases p.7
22 The Case for B Physics large number of different decay channels, sensitive to different weak phases expect sizeable CP asymmetries thanks to non-squashed unitarity triangles (in contrast to K decays) p.7
23 The Case for B Physics large number of different decay channels, sensitive to different weak phases expect sizeable CP asymmetries thanks to non-squashed unitarity triangles (in contrast to K decays) GIM-suppression largely relaxed thanks to m t m c, m u p.7
24 The Case for B Physics large number of different decay channels, sensitive to different weak phases expect sizeable CP asymmetries thanks to non-squashed unitarity triangles (in contrast to K decays) GIM-suppression largely relaxed thanks to m t m c, m u large and theoretically clean effects from B 0 B 0 mixing: B d W V jd q V 0 0 j i,j = u,c,t W * jb b B large penguin contributions: b V * ib q i V id d p.7
25 Manifestations of CP Violation CP violation in the decay (direct CP violation): A(B F ) A( B F ) p.8
26 Manifestations of CP Violation CP violation in the decay (direct CP violation): A(B F ) A( B F ) CP violation in mixing: mass eigenstates CP eigenstates p.8
27 Manifestations of CP Violation CP violation in the decay (direct CP violation): A(B F ) A( B F ) CP violation in mixing: mass eigenstates CP eigenstates CP violation in the interference of decays with and without mixing A(B F ) A( B F ) B 0 F B 0 p.8
28 Time-dependent CP Asymmetries Measure time-dependent CP asymmetry: Γ(B 0 q (t) F ) Γ( B 0 q (t) F ) Γ(Bq 0 (t) F ) + Γ( B q 0 (t) F ) { = A dir CP (B q F ) cos( M q t) + A mix } CP (B q F ) sin( M q t) p.9
29 Time-dependent CP Asymmetries Measure time-dependent CP asymmetry: Γ(B 0 q (t) F ) Γ( B 0 q (t) F ) Γ(Bq 0 (t) F ) + Γ( B q 0 (t) F ) { = A dir CP (B q F ) cos( M q t) + A mix } CP (B q F ) sin( M q t) In general A dir and Amix dependent on hadronic matrix elements. CP CP Special case: one single weak amplitude dominant: A mix ( ) CP = Im e iφ q gold-plated decay (e.g. B J/ψK S ) measure mixing phase φ q with small theoretical uncertainty p.9
30 The Big Picture Alternative scenarios of CP violation Recall: CP violation happens in the scalar sector combination of several mechanisms: CP violation in Yukawa interactions (complex couplings) p.10
31 The Big Picture Alternative scenarios of CP violation Recall: CP violation happens in the scalar sector combination of several mechanisms: CP violation in Yukawa interactions (complex couplings) CP violation in Higgs potential (complex couplings) p.10
32 The Big Picture Alternative scenarios of CP violation Recall: CP violation happens in the scalar sector combination of several mechanisms: CP violation in Yukawa interactions (complex couplings) CP violation in Higgs potential (complex couplings) CP violation from spontaneous symmetry breaking p.10
33 The Big Picture Alternative scenarios of CP violation Recall: CP violation happens in the scalar sector combination of several mechanisms: CP violation in Yukawa interactions (complex couplings) CP violation in Higgs potential (complex couplings) CP violation from spontaneous symmetry breaking SU L (2) SU R (2) U(1) SU L (2) U(1) p.10
34 The Big Picture Alternative scenarios of CP violation Recall: CP violation happens in the scalar sector combination of several mechanisms: CP violation in Yukawa interactions (complex couplings) CP violation in Higgs potential (complex couplings) CP violation from spontaneous symmetry breaking SU L (2) SU R (2) U(1) SU L (2) U(1) Higgs bidoublet with complex VEV: Φ = ( v 0 0 w exp(iα) ) p.10
35 The Big Picture Alternative scenarios of CP violation Recall: CP violation happens in the scalar sector combination of several mechanisms: CP violation in Yukawa interactions (complex couplings) CP violation in Higgs potential (complex couplings) CP violation from spontaneous symmetry breaking SU L (2) SU R (2) U(1) SU L (2) U(1) Higgs bidoublet with complex VEV: Φ = ( v 0 0 w exp(iα) electric dipole moment of neutron problematic ) p.10
36 The Truly Big Picture Matter-antimatter asymmetry: p.11
37 The Truly Big Picture Matter-antimatter asymmetry: Sacharov s conditions p.11
38 The Truly Big Picture Matter-antimatter asymmetry: Sacharov s conditions Baryon number violation p.11
39 The Truly Big Picture Matter-antimatter asymmetry: Sacharov s conditions Baryon number violation Non-equilibrium processes p.11
40 The Truly Big Picture Matter-antimatter asymmetry: Sacharov s conditions Baryon number violation Non-equilibrium processes CP violation: distinguish baryons from antibaryons p.11
41 The Truly Big Picture Matter-antimatter asymmetry: Sacharov s conditions Baryon number violation Non-equilibrium processes CP violation: distinguish baryons from antibaryons GUT baryogenesis? p.11
42 The Truly Big Picture Matter-antimatter asymmetry: Sacharov s conditions Baryon number violation Non-equilibrium processes CP violation: distinguish baryons from antibaryons Leptogenesis? p.11
43 The Truly Big Picture Matter-antimatter asymmetry: Sacharov s conditions Baryon number violation Non-equilibrium processes CP violation: distinguish baryons from antibaryons Electroweak baryogenesis? p.11
44 Outlook CP violation related to scalar sector nonstandard sources of CP violation to show up as inconsistencies of measurements of parameters of UT extraction of UT angles α, β, γ from experiment often hampered by nonperturbative QCD QCD factorisation? (Beneke, Buchalla, Neubert, Sachrajda) Phenomenological methods? (Fleischer, Gronau) B/K physics to give indirect hints at new physics complementary to results of direct searches exciting times for theorists and experimentalists alike! p.12
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