CP Violation Patricia Ball

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Theory of CP Violation Patricia Ball

IPPP, Durham

Patricia Ball CP as Natural Symmetry of Gauge Theories

P and C alone are not natural symmetries: consider chiral gauge theory:

1 µν † † L = − 4 Fµν F + ψLiσ¯DψL (+ψRiσ∂ψR)

Patricia Ball O – p.1 CP as Natural Symmetry of Gauge Theories

P and C alone are not natural symmetries: consider chiral gauge theory:

1 µν † † L = − 4 Fµν F + ψLiσ¯DψL (+ψRiσ∂ψR)

L violates P: right-handed fermions do not couple to gauge bosons L violates C: left-handed antifermions do not couple to gauge bosons L preserves CP: both left-handed fermions and right-handed antifermions couple to gauge bosons

Massless gauge theories are invariant under CP and T.

Patricia Ball O – p.1 CP as Natural Symmetry of Gauge Theories

P and C alone are not natural symmetries: consider chiral gauge theory:

1 µν † † L = − 4 Fµν F + ψLiσ¯DψL (+ψRiσ∂ψR)

Patricia Ball – p.1 But CP IS violated!

CP violation in K decays known since 1964; observed in B decays in 1999.

Origin in SM: Yukawa interactions:

LSM = LG(ψ, W, φ) + LH (φ) + LY (ψ, φ)

kinetic Higgs potential Yukawa IA energy| {z +} → spontaneous| {z } |→{z fer}mion gauge IA symmetry masses breaking

gauge sector scalar sector | {z } | {z }

Patricia Ball O – p.2 But CP IS violated!

CP violation in K decays known since 1964; observed in B decays in 1999.

Origin in SM: Yukawa interactions:

ij ¯i j ij ∗ ¯j † i LY = −λd QL · ΦdR − (λd ) dRΦ · QL + . . .

λd: general, not necessarily symmetric or Hermitian matrices (Yukawa couplings), not constrained by gauge symmetry

∗ CP: λd ↔ λd ⇒ (explicit) CP violation if λd complex

CP violation happens in the scalar sector!

Patricia Ball – p.2 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 complementary tests indirect effects: CP in B decays  of the scalar sector!  

Experimental Status of the Scalar Sector

CP is violated. Number, size and origin of CP phases unknown.

Patricia Ball O – p.3 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 complementary tests indirect effects: CP in B decays  of the scalar sector!  

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.

Patricia Ball O – p.3 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 complementary tests indirect effects: CP in B decays  of the scalar sector!  

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.

Patricia Ball O – p.3 Mechanism of CP violation not identiﬁed.

Next generation of accelerators (LHC 2007/8): direct Higgs searches complementary tests indirect effects: CP in B decays  of the scalar sector!  

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.

Patricia Ball O – p.3 Next generation of accelerators (LHC 2007/8): direct Higgs searches complementary tests indirect effects: CP in B decays  of the scalar sector!  

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.

Patricia Ball O – p.3 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 complementary tests indirect effects: CP in B decays  of the scalar sector!  

Patricia Ball – p.3 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

Visualise unitarity relation Im (ρ,η) ∗ V V = 0 V V ∗ α dj jb ud ub ∗ V V V V ∗ td tb cd cb ∗ P VcdVcb as triangle in complex plane: γ β unitarity triangle (UT) 0 1 Re

CP Violation in the Standard Model

diagonalise Yukawa matrices quark mass eigenstates

Patricia Ball O – p.4 mixing described by unitary Cabibbo-Kobayashi-Maskawa (CKM) matrix V parametrised by three angles and one complex phase: source of CP violation in SM

Visualise unitarity relation Im (ρ,η) ∗ V V = 0 V V ∗ α dj jb ud ub ∗ V V V V ∗ td tb cd cb ∗ P VcdVcb as triangle in complex plane: γ β unitarity triangle (UT) 0 1 Re

CP Violation in the Standard Model

diagonalise Yukawa matrices quark mass eigenstates mass eigenstates mix by virtue of weak interactions

Patricia Ball O – p.4 parametrised by three angles and one complex phase: source of CP violation in SM

Visualise unitarity relation Im (ρ,η) ∗ V V = 0 V V ∗ α dj jb ud ub ∗ V V V V ∗ td tb cd cb ∗ P VcdVcb as triangle in complex plane: γ β unitarity triangle (UT) 0 1 Re

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

Patricia Ball O – p.4 Visualise unitarity relation Im (ρ,η) ∗ V V = 0 V V ∗ α dj jb ud ub ∗ V V V V ∗ td tb cd cb ∗ P VcdVcb as triangle in complex plane: γ β unitarity triangle (UT) 0 1 Re

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

Patricia Ball O – p.4 CP Violation in the Standard Model

one complex phase: source of CP violation in SM

Visualise unitarity relation Im (ρ,η) ∗ V V = 0 V V ∗ α dj jb ud ub ∗ V V V V ∗ td tb cd cb ∗ P VcdVcb as triangle in complex plane: γ β unitarity triangle (UT) 0 1 Re

Patricia Ball – p.4 The reality. . .

Experimental Determination of UT

2 sin γ sin 2β sin γ

+ + sin 2β K →π νν

1 ∆ md |ε, ε | 0→π0νν / K , K

|ε |

η 0 K K0→π0νν |V /V | ub cb sin 2α sin 2α -1 K+→π+νν

|ε | K -2 -2 -1 0 1 2 ρ The ideal. . .

Patricia Ball O – p.5 Experimental Determination of UT

2 1.5

sin γ sin 2β sin γ excluded area has CL < 0.05

C K M |ε | f i t t e r → ρρ K Winter 2004 B -2 -1.5 -2 -1 0 1 2 -1 -0.5 0 0.5 1 1.5 2 ρ ρ The ideal. . . The reality. . .

Patricia Ball – p.5 UT from K Decays

Experimentally favoured: K : th. uncertainty from BK , mt, |Vcb| + + 0 Theoretically favoured: B(K → π νν¯), B(KL → π νν¯)

hadronic matrix elements from K → π`ν 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 |Vcb| and (less strong) on mt

! npQCD potentially more dangerous than in B decays (0/ etc.)

Patricia Ball – p.6 expect sizeable CP asymmetries thanks to non-squashed unitarity triangles (in contrast to K decays)

GIM-suppression largely relaxed thanks to mt mc, mu → large and theoretically clean → large penguin contributions: 0 effects from B0–B¯ mixing:

* d Vjd qj Vjb b i,j = u,c,t B0 W W B0

* b Vib q i Vid d

The Case for B Physics

large number of different decay channels, sensitive to different weak phases

Patricia Ball O – p.7 GIM-suppression largely relaxed thanks to mt mc, mu → large and theoretically clean → large penguin contributions: 0 effects from B0–B¯ mixing:

* d Vjd qj Vjb b i,j = u,c,t B0 W W B0

* b Vib q i Vid d

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)

Patricia Ball O – p.7 → large and theoretically clean → large penguin contributions: 0 effects from B0–B¯ mixing:

* d Vjd qj Vjb b i,j = u,c,t B0 W W B0

* b Vib q i Vid d

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 mt mc, mu

Patricia Ball O – p.7 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 mt mc, mu → large and theoretically clean → large penguin contributions: 0 effects from B0–B¯ mixing:

* d Vjd qj Vjb b i,j = u,c,t B0 W W B0

* b Vib q i Vid d

Patricia Ball – p.7 CP violation in mixing: mass eigenstates 6= CP eigenstates

CP violation in the interference of decays with and without mixing

A(B → F ) 6= A(B¯ → F )

B0 F

Manifestations of CP Violation

CP violation in the decay (direct CP violation):

|A(B → F )| 6= |A(B¯ → F¯)|

Patricia Ball O – p.8 CP violation in the interference of decays with and without mixing

A(B → F ) 6= A(B¯ → F )

B0 F

Manifestations of CP Violation

CP violation in the decay (direct CP violation):

|A(B → F )| 6= |A(B¯ → F¯)|

CP violation in mixing:

mass eigenstates 6= CP eigenstates

Patricia Ball O – p.8 Manifestations of CP Violation

CP violation in the decay (direct CP violation):

|A(B → F )| 6= |A(B¯ → F¯)|

CP violation in mixing:

mass eigenstates 6= CP eigenstates

CP violation in the

interference of decays with and without mixing

A(B → F ) 6= A(B¯ → F )

B0 F

Patricia Ball – p.8 In general dir and mix dependent on hadronic matrix elements. ACP ACP Special case: one single weak amplitude dominant: mix −iφq ACP = Im ∓e −→ “gold-plated” decay (e.g. B → J/ψKS )

−→ measure mixingphase φq with small theoretical uncertainty

Time-dependent CP Asymmetries

Measure time-dependent CP asymmetry:

0 ¯0 Γ(Bq (t) → F ) − Γ(Bq (t) → F ) 0 ¯0 Γ(Bq (t) → F ) + Γ(Bq (t) → F ) dir = ACP(Bq → F ) cos(∆Mqt) n mix + ACP (Bq → F ) sin(∆Mqt) o

Patricia Ball O – p.9 Time-dependent CP Asymmetries

Measure time-dependent CP asymmetry:

0 ¯0 Γ(Bq (t) → F ) − Γ(Bq (t) → F ) 0 ¯0 Γ(Bq (t) → F ) + Γ(Bq (t) → F ) dir = ACP(Bq → F ) cos(∆Mqt) n mix + ACP (Bq → F ) sin(∆Mqt) o In general dir and mix dependent on hadronic matrix elements. ACP ACP Special case: one single weak amplitude dominant:

mix −iφq ACP = Im ∓e −→ “gold-plated” decay (e.g. B → J/ψKS )

−→ measure mixingphase φq with small theoretical uncertainty

Patricia Ball – p.9 CP violation in Higgs potential (complex couplings) CP violation from spontaneous symmetry breaking

SUL(2) × SUR(2) × U(1) → SUL(2) × U(1) Higgs bidoublet with complex VEV: v 0 hΦi = 0 w exp(iα) ! electric dipole moment of neutron problematic

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)

Patricia Ball O – p.10 CP violation from spontaneous symmetry breaking

SUL(2) × SUR(2) × U(1) → SUL(2) × U(1) Higgs bidoublet with complex VEV: v 0 hΦi = 0 w exp(iα) ! electric dipole moment of neutron problematic

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)

Patricia Ball O – p.10 SUL(2) × SUR(2) × U(1) → SUL(2) × U(1) Higgs bidoublet with complex VEV: v 0 hΦi = 0 w exp(iα) ! electric dipole moment of neutron problematic

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

Patricia Ball O – p.10 Higgs bidoublet with complex VEV: v 0 hΦi = 0 w exp(iα) ! electric dipole moment of neutron problematic

The Big Picture

Alternative scenarios of CP violation

SUL(2) × SUR(2) × U(1) → SUL(2) × U(1)

Patricia Ball O – p.10 electric dipole moment of neutron problematic

The Big Picture

Alternative scenarios of CP violation

SUL(2) × SUR(2) × U(1) → SUL(2) × U(1) Higgs bidoublet with complex VEV:

v 0 hΦi = 0 w exp(iα) !

Patricia Ball O – p.10 The Big Picture

Alternative scenarios of CP violation

SUL(2) × SUR(2) × U(1) → SUL(2) × U(1) Higgs bidoublet with complex VEV:

v 0 hΦi = 0 w exp(iα) !

electric dipole moment of neutron problematic

Patricia Ball – p.10 Sacharov’s conditions

Baryon number violation Non-equilibrium processes CP violation: distinguish baryons from antibaryons

The Truly Big Picture

Matter-antimatter asymmetry:

Patricia Ball O – p.11 Baryon number violation Non-equilibrium processes CP violation: distinguish baryons from antibaryons

The Truly Big Picture