Particle Physics II – CP violation (also known as “Physics of Anti-matter”) Lecture 4 N. Tuning Niels Tuning (1)

Plan Mon 5 Feb: Anti-matter + SM Wed 7 Feb: CKM matrix + Unitarity Triangle Mon 26 Feb: Mixing + Master eqs. + B0J/ψKs Wed 28 Feb: CP violation in B(s) decays (I) Mon 12 Mar: CP violation in B(s) and K decays (II) Wed 14 Mar: Rare decays + Flavour Anomalies Wed 21 Mar: Exam Final Mark: if (mark > 5.5) mark = max(exam, 0.85*exam + 0.15*homework) else mark = exam In parallel: Lectures on Flavour Physics by prof.dr. R. Fleischer Niels Tuning (2)

Recap uI W dI u W d,s,b Diagonalize Yukawa matrix Yij Mass terms Quarks rotate Off diagonal terms in charged current couplings u d,s,b W Replace the derivative with the covariant derivative introducing the force carriers: gluons, weak vector bosons and photon. The constants g_s, g and g’ are the corresponding coupling constants of the gauge particles. Niels Tuning (4) 4

CKM-matrix: where are the phases? Possibility 1: simply 3 ‘rotations’, and put phase on smallest: Possibility 2: parameterize according to magnitude, in O(λ): u d,s,b W Niels Tuning (5)

This was theory, now comes experiment We already saw how the moduli |Vij| are determined Now we will work towards the measurement of the imaginary part Parameter: η Equivalent: angles α, β, γ . To measure this, we need the formalism of neutral meson oscillations… Niels Tuning (6)

Neutral Meson Oscillations (1) Start with Schrodinger equation: Find eigenvalue: Solve eigenstates: Eigenstates have diagonal Hamiltonian: mass eigenstates! (2-component state in P0 and P0 subspace) Niels Tuning (7)

Neutral Meson Oscillations (2) Two mass eigenstates Time evolution: Probability for |P0>  |P0> ! Express in M=mH+mL and Δm=mH-mL  Δm dependence

Meson Decays Formalism of meson oscillations: Subsequent: decay Niels Tuning (9)

Notation: Define Af and λf Niels Tuning (10)

Some algebra for the decay P0  f Interference P0 f P0P0 f Niels Tuning (11)

Some algebra for the decay P0  f Niels Tuning (12)

The ‘master equations’ (‘direct’) Decay Interference Niels Tuning (13)

The ‘master equations’ (‘direct’) Decay Interference Niels Tuning (14)

Classification of CP Violating effects CP violation in decay CP violation in mixing CP violation in interference Niels Tuning (15)

Meson Decays Formalism of meson oscillations: Subsequent: decay P0 f Interference P0 f P0P0 f Interference (‘direct’) Decay

Classification of CP Violating effects CP violation in decay CP violation in mixing CP violation in interference Niels Tuning (17)

Now: Im( λf) CP violation in decay CP violation in mixing CP violation in interference We will investigate λf for various final states f

CP violation: type 3 Niels Tuning (19)

Classification of CP Violating effects - Nr. 3: Consider f=f : If one amplitude dominates the decay, then Af = Af CP violation in interference Niels Tuning (20)

CP violation: a famous example The golden decay B0→J/ΨKs DESY KEK SLAC Niels Tuning (21)

|λf|=1 Final state f : J/ΨKs Interference between B0→fCP and B0→B0→fCP For example: B0→J/ΨKs and B0→B0→ J/ΨKs Lets’ s simplify … For B0 we have: Since fCP =fCP we have: The amplitudes |A( B0→J/ψKs)| and |A(B0→J/ψKs)| are equal: |λf|=1 B0 d B0 Niels Tuning (22)

Relax: B0J/ΨKs simplifies… ΔΓ=0 Niels Tuning (23)

λf for B0 ® J/yK0S c J/y K0 B0 b s d b d s d |Vcs Vcd|^2 mc^2 = (1*lambda)^2 mc^2 vs. |Vts Vtd|^2 mt^2 = (lambda^2*lambda^3)^2 mt^2  suppressed by lambda^8, enhanced by (mt/mc)^2 << 1 s d Niels Tuning (24)

Time-dependent CP asymmetry λf for B0 ® J/yK0S Time-dependent CP asymmetry Theoretically clean way to measure b Clean experimental signature Branching fraction: O(10-4) “Large” compared to other CP modes! |Vcs Vcd|^2 mc^2 = (1*lambda)^2 mc^2 vs. |Vts Vtd|^2 mt^2 = (lambda^2*lambda^3)^2 mt^2  suppressed by lambda^8, enhanced by (mt/mc)^2 << 1 Niels Tuning (25)

Remember: C and P eigenvalue C and P are good symmetries (not involving the weak interaction) Can associate a conserved value with them (Noether Theorem) Each hadron has a conserved P and C quantum number What are the values of the quantum numbers Evaluate the eigenvalue of the P and C operators on each hadron P|y> = p|y> What values of C and P are possible for hadrons? Symmetry operation squared gives unity so eigenvalue squared must be 1 Possible C and P values are +1 and -1. Meaning of P quantum number If P=1 then P|y> = +1|y> (wave function symmetric in space) if P=-1 then P|y> = -1 |y> (wave function anti-symmetric in space) Niels Tuning (26)

Remember: P eigenvalues for hadrons The p+ meson Quark and anti-quark composite: intrinsic P = (1)*(-1) = -1 Orbital ground state  no extra term P(p+)=-1 The neutron Three quark composite: intrinsic P = (1)*(1)*(1) = 1 P(n) = +1 The K1(1270) Quark anti-quark composite: intrinsic P = (1)*(-1) = -1 Orbital excitation with L=1  extra term (-1)1 P(K1) = +1 Meaning: P|p+> = -1|p+> Niels Tuning (27)

Intermezzo: CP eigenvalue Remember: P2 = 1 (x  -x  x) C2 = 1 (ψ  ψ  ψ )  CP2 =1 CP | f > =  | f > Knowing this we can evaluate the effect of CP on the K0 CP|K0> = -1|K0> CP| K0> = -1|K0 > K0 is not CP eigenstate, but flavour eigenstate (sd) ! Mass eigenstates: |KS> = p| K0> +q|K0> |KL> = p| K0> - q|K0> |Ks> (CP=+1) → p p (CP= (-1)(-1)(-1)l=0 =+1) |KL> (CP=-1) → p p p (CP = (-1)(-1)(-1)(-1)l=0 = -1) ( S(K)=0  L(ππ)=0 ) Niels Tuning (28)

CP eigenvalue of final state J/yK0S CP |J/y> = +1 |J/y> CP |K0S> = +1 |K0S> CP |J/yK0S> = (-1)l |J/yK0S> ( S(J/y)=1 ) ( S(B)=0  L(J/yK0S)=1 ) Relative minus-sign between state and CP-conjugated state: |Vcs Vcd|^2 mc^2 = (1*lambda)^2 mc^2 vs. |Vts Vtd|^2 mt^2 = (lambda^2*lambda^3)^2 mt^2  suppressed by lambda^8, enhanced by (mt/mc)^2 << 1 Niels Tuning (29)

Time dependent CP violation If final state is CP eigenstate then 2 amplitudes (w/o mixing): B0f and B0B0f B0 - B0 oscillation is periodic in time  CP violation time dependent Amplitude 1 Amplitude 2 + e-iφ (i=eiπ/2 δ=90o) (φ=2β) Niels Tuning (30)

Time dependent CP violation If final state is CP eigenstate then 2 amplitudes (w/o mixing): B0f and B0B0f B0 -B0 oscillation is periodic in time  CP violation time dependent 1 + e-iφ (i=eiπ/2 δ=90o) (φ=2β) Niels Tuning (31)

Sum of 2 amplitudes: sensitivity to phase What do we know about the relative phases of the diagrams? B0  f B0  B0  f f(strong)=f Decays are identical f(strong)=f K0 mixing exactly cancels Vcs f(weak)=0 f(weak)=2b f(mixing)=p/2 There is a phase difference of i between the B0 andB0 Niels Tuning (32)

Sum of 2 amplitudes: sensitivity to phase Now also look at CP-conjugate process Investigate situation at time t, such that |A1| = |A2| : Directly observable result (essentially just from counting) measure CKM phase b directly! N(B0  f)  |A|2  (1-cosf)2+sin2f = 1 -2cosf+cos2f+sin2f = 2-2cos(p/2-2b)  1-sin(2b) + = Γ(Bf)= sin(f) p/2+2b CP 1-cos(f) + = sin(f) Γ(Bf)= p/2-2b N(B0  f)  (1+cosf)2+sin2f = 2+2cos(p/2-2b)  1+sin(2b) 1+cos(f) Niels Tuning (33)

2 amplitudes 2 phases Remember! Necessary ingredients for CP violation: Two (interfering) amplitudes Phase difference between amplitudes one CP conserving phase (‘strong’ phase) one CP violating phase (‘weak’ phase) 2 amplitudes 2 phases Niels Tuning (34)

Remember! 2 amplitudes 2 phases Niels Tuning (35)

eiφ e-iφ What do we measure? Γ( B f) = |A1+A2ei(φ+δ)|2 We measure quark couplings There is a complex phase in couplings! Visible when there are 2 amplitudes: matter anti-matter Γ( B f) = |A1+A2ei(φ+δ)|2 Γ( B f) = |A1+A2ei(-φ+δ)|2 Proof of existence of complex numbers… Niels Tuning (36)

B0→J/ψKs B-system - Time-dependent CP asymmetry BaBar (2002) Niels Tuning (37) BaBar (2002)

Consistency with other measurements in (r,h) plane 4-fold ambiguity because we measure sin(2b), not b Prices measurement of sin(2β) agrees perfectly with other measurements and CKM model assumptions The CKM model of CP violation experimentally confirmed with high precision! 2 1 without sin(2b) h 3 4 r Method as in Höcker et al, Eur.Phys.J.C21:225-259,2001 Niels Tuning (38)

βs: Bs0 ® J/yφ : Bs0 analogue of B0 ® J/yK0S Replace spectator quark d  s Niels Tuning (39)

βs: Bs0 ® J/yφ : Bs0 analogue of B0 ® J/yK0S Niels Tuning (40)

Remember: The “Bs-triangle”: βs Replace d by s: Niels Tuning (41)

βs: Bs0 ® J/yφ : Bs0 analogue of B0 ® J/yK0S Differences: B0 B0s CKM Vtd Vts ΔΓ ~0 ~0.1 Final state (spin) K0 : s=0 φ: s=1 Final state (K) K0 mixing - Niels Tuning (42)

βs: Bs0 ® J/yφ A║ A┴ A0 B0 B0s CKM Vtd Vts ΔΓ ~0 ~0.1 Vts large, oscilations fast, need good vertex detector A║ A0 A┴ l=2 l=1 l=0 3 amplitudes B0 B0s CKM Vtd Vts ΔΓ ~0 ~0.1 Final state (spin) K0 : s=0 φ: s=1 Final state (K) K0 mixing - Niels Tuning (43)

“Recent” excitement (5 March 2008) Niels Tuning (44)

Bs  J/ψФ : Bs equivalent of B J/ψKs ! The mixing phase (Vtd): φd=2β B0  f B0  B0  f Wolfenstein parametrization to O(λ5): Niels Tuning (45)

Bs  J/ψФ : Bs equivalent of B J/ψKs ! The mixing phase (Vts): φs=-2βs B0  f B0  B0  f Vts - s Ф Bs Bs Ф s s s Vts Wolfenstein parametrization to O(λ5): Niels Tuning (46)

Bs  J/ψФ : Bs equivalent of B J/ψKs ! The mixing phase (Vts): φs=-2βs B0  f B0  B0  f Vts - s Ф Bs Bs Ф s s s Vts Niels Tuning (47)

Measure γ: B0s  DsK-/+ : both λf and λf 2 + Γ(Bf)= 2 + Γ(B f )= NB: In addition B s  DsK-/+ : both λ f and λf Niels Tuning (48)

Measure γ: Bs  DsK-/+ --- first one f: Ds+K- This time | Af||Af|, so |λ|1 ! In fact, not only magnitude, but also phase difference: Niels Tuning (49)

Measure γ: Bs  DsK-/+ B0s  Ds-K+ has phase difference ( - ): Need B0s  Ds+K- to disentangle  and : Niels Tuning (50)

Next CP violation in decay CP violation in mixing CP violation in interference

γ B - → D0 K- (Time integrated) Bs0 → DsK+- (Time dependent) ( ) B - → D0 K- (Time integrated) Bs0 → DsK+- (Time dependent) Necessary ingredients for CP violation: Two (interfering) amplitudes Phase difference between amplitudes one CP conserving phase (‘strong’ phase) one CP violating phase (‘weak’ phase)

γ (GLW) D0K+ fCPK+ B+ GLW: CP eigenstate: D0→ K+K-(ππ) bc favoured Vub* Vcb* ( ) B- →D0K- Relative phase: γ B+ D0K+ fCPK+ bc favoured bu suppressed GLW: CP eigenstate: D0→ K+K-(ππ)

γ (GLW) D0K+ fCPK+ B+ GLW: CP eigenstate: D0→ K+K-(ππ) bc favoured Vub* Vcb* ( ) B- →D0K- Relative phase: γ B+ D0K+ fCPK+ bc favoured bu suppressed GLW: CP eigenstate: D0→ K+K-(ππ)

γ (GLW) D0K+ fCPK+ B+ GLW: CP eigenstate: D0→ K+K-(ππ) bc favoured bu suppressed GLW: CP eigenstate: D0→ K+K-(ππ)

γ (ADS) D0K+ B+ ADS: K-π+K+ B or D Cabibbo favoured: D0→ K+π- Vub* Vcb* ( ) B- →D0K- Relative phase: γ B+ D0K+ bc favoured bu suppressed K-π+K+ Cabibbo supp. Cabibbo allowed. ADS: B or D Cabibbo favoured: D0→ K+π-

γ (ADS) D0K+ B+ ADS: K-π+K+ B or D Cabibbo favoured: D0→ K+π- Vub* Vcb* ( ) B- →D0K- Relative phase: γ B+ D0K+ bc favoured bu suppressed K-π+K+ Cabibbo supp. Cabibbo allowed. ADS: B or D Cabibbo favoured: D0→ K+π- “Difference in suppression” “Average suppression”

γ (ADS) D0K+ B+ ADS: K-π+K+ B or D Cabibbo favoured: D0→ K+π- Suppressed mode for the B- is relatively more suppressed than for the B+… B+ D0K+ bc favoured K-π+K+ Cabibbo supp. Cabibbo allowed. bu suppressed ADS: B or D Cabibbo favoured: D0→ K+π- BR~ 2 x 10-7

CP violation in Decay? (also known as: “direct CPV”) First observation of Direct CPV in B decays (2004): BABAR hep-ex/0407057 Phys.Rev.Lett.93:131801,2004 4.2s BABAR HFAG: ACP = -0.098 ± 0.012 Niels Tuning (59)

CP violation in Decay? (also known as: “direct CPV”) First observation of Direct CPV in B decays at LHC (2011): LHCb LHCb-CONF-2011-011 LHCb Niels Tuning (60)

2 amplitudes 2 phases Remember! Necessary ingredients for CP violation: Two (interfering) amplitudes Phase difference between amplitudes one CP conserving phase (‘strong’ phase) one CP violating phase (‘weak’ phase) 2 amplitudes 2 phases Niels Tuning (61)

Direct CP violation: Γ( B0 f) ≠ Γ(B0f ) CP violation if Γ( B0 f) ≠ Γ(B0f ) But: need 2 amplitudes  interference Amplitude 1 Amplitude 2 + Only different if both δ and γ are ≠0 !  Γ( B0 f) ≠ Γ( B0f ) Niels Tuning (62)

Hint for new physics? B0Kπ and BKπ0 Redo the experiment with B instead of B0… d or u spectator quark: what’s the difference ?? B0Kπ Average 3.6s ? B+Kπ Average Niels Tuning (63)

Hint for new physics? B0Kπ and BKπ0 Niels Tuning (64)

Hint for new physics? B0Kπ and BKπ0 T (tree) C (color suppressed) P (penguin) B0→K+π- B+→K+π0 Niels Tuning (65)

Next CP violation in decay CP violation in mixing CP violation in interference

CP violation in Mixing? (also known as: “indirect CPV”: ε≠0 in K-system) Look for like-sign lepton pairs: t=0 t Decay gVcb* gVcb Niels Tuning (67)

(limit on) CP violation in B0 mixing Look for a like-sign asymmetry: As expected, no asymmetry is observed… Niels Tuning (68)

2 amplitudes 2 phases Remember! Necessary ingredients for CP violation: Two (interfering) amplitudes Phase difference between amplitudes one CP conserving phase (‘strong’ phase) one CP violating phase (‘weak’ phase) 2 amplitudes 2 phases Niels Tuning (69)

CP violation in Bs0 Mixing?? D0 Coll., Phys.Rev.D82:032001,2010. arXiv:1005.2757 CP violation in Bs0 Mixing?? b s “Box” diagram: ΔB=2 φsSM ~ 0.004 φsSMM ~ 0.04 Niels Tuning (70)

CP violation from Semi-leptonic decays SM: P(B0s→B0s) = P(B0s←B0s) DØ: P(B0s→B0s) ≠ P(B0s←B0s) ? b→Xμ-ν, b→Xμ+ν b→b → Xμ+ν, b→ b → Xμ-ν Compare events with like-sign μμ Two methods: Measure asymmetry of events with 1 muon Measure asymmetry of events with 2 muons Switching magnet polarity helps in reducing systematics But…: Decays in flight, e.g. K→μ K+/K- asymmetry

CP violation from Semi-leptonic decays SM: P(B0s→B0s) = P(B0s←B0s) DØ: P(B0s→B0s) ≠ P(B0s←B0s) ? B0s→Ds±X0μν

More β… Niels Tuning (73)

Time? Niels Tuning (74)

Other ways of measuring sin2β Need interference of bc transition and B0 –B0 mixing Let’s look at other bc decays to CP eigenstates: All these decay amplitudes have the same phase (in the Wolfenstein parameterization) so they (should) measure the same CP violation Niels Tuning (75)

CP in interference with BφKs Same as B0J/ψKs : Interference between B0→fCP and B0→B0→fCP For example: B0→J/ΨKs and B0→B0→ J/ΨKs For example: B0→φKs and B0→B0→ φKs Amplitude 1 Amplitude 2 + e-iφ Niels Tuning (76)

CP in interference with BφKs: what is different?? Same as B0J/ψKs : Interference between B0→fCP and B0→B0→fCP For example: B0→J/ΨKs and B0→B0→ J/ΨKs For example: B0→φKs and B0→B0→ φKs Amplitude 1 Amplitude 2 + e-iφ Niels Tuning (77)

Penguin diagrams Nucl. Phys. B131:285 1977 Niels Tuning (78)

Penguins?? The original penguin: A real penguin: Our penguin: Niels Tuning (79)

Funny Flying Penguin Dead Penguin Penguin T-shirt: Super Penguin: Niels Tuning (80)

 The “b-s penguin” Asymmetry in SM B0J/ψKS B0φKS b s μ “Penguin” diagram: ΔB=1 … unless there is new physics! New particles (also heavy) can show up in loops: Can affect the branching ratio And can introduce additional phase and affect the asymmetry Niels Tuning (81)

? Hint for new physics?? B J/ψ Ks φ Ks B sin2β sin2βpeng g,b,…? ~~ d c s φ Ks B s b d t ? g,b,…? ~~ sin2βbccs = 0.68 ± 0.03 sin2βpeng = 0.52 ± 0.05 sin2β sin2βpeng Niels Tuning (82) S.T’Jampens, CKM fitter, Beauty2006