1. 1 CP Violation in the B → π π system Mark Allen SASS 1-30-08

2. Mark T. Allen, SLACJan 30, 2008 2 What I will cover A little on B physics A little on CKM physics Focus on details of B → π π As example of CPV asymmetry Isospin analysis What I will not cover: Measurments

3. Mark T. Allen, SLACJan 30, 2008 3 CKM Matrix d s b uctuct V = The quark mass eigenstates are not identical to the Weak eigenstates. The two bases are related through the CKM matrix Is unitary up to O(λ 4 ), with CP violating phases in V ub and V td. For example:

4. Mark T. Allen, SLACJan 30, 2008 4 α βγ CKM Angles

5. Mark T. Allen, SLACJan 30, 2008 5 Spontaneous flavor switch: (Similar to the Kaon system) B 0 not CP eigenstates K: Δ Lifetime large, Δ mass splitting small B: Δ Lifetime small, Δ mass splitting “large” B Mixing V tb V td *

6. Mark T. Allen, SLACJan 30, 2008 6 In decay: In mixing: ( no sign of this in B’s) CP Violation Γ(B 0 →K + π - ) ≠ Γ(B 0 →K - π + ) B 0 →K + π - B 0 →K - π + Probability of B 0 → B 0 ≠ B 0 → B 0 Note this is the CP violation seen on Kaon decays

7. Mark T. Allen, SLACJan 30, 2008 7 In interference between mixing and decay: B0B0 CP eigenstate ( J/ψ Ks, π + π - ) B0B0 CP Violation This is where the magic happens V td has a phase!

8. Mark T. Allen, SLACJan 30, 2008 8 B 0 →π + π - B0B0 π+π+ π-π- dudu udud bdbd V ub V ud * V tb V td * B0B0 B0B0 Mixing Tree decay

9. Mark T. Allen, SLACJan 30, 2008 9 Δt = proper time difference between pure B 0 or B 0 meson and decay TDCP Asymmetries Things to note: λ = e 2iα Integrated over Δt, only sensitive to CPV in decay & mixing. First term sensitive to |λ| only (Direct CP Violation) Need to: Make a ton of B mesons Effectively tag B mesons, Measure Δt Im(λ) = sin(2α)

10. Mark T. Allen, SLACJan 30, 2008 10 Not so fast..... What if there are multiple decay amplitudes?!?! B0B0 π + π - B0B0 Mixing Tree Penguin B0B0 π+π+ π-π- dudu udud bdbd V ub V ud * π-π- π+π+ udud dudu bdbd B0B0

11. Mark T. Allen, SLACJan 30, 2008 11 Penguin pollution π - (ρ, a 1 ) π + (ρ, a 1 ) π - (ρ, a 1 ) GOAL: Disentangle tree and penguin contributions. With Penguin Pollution: Different amplitudes with different CKM phases!

12. Mark T. Allen, SLACJan 30, 2008 12 [M. Gronau and D. London, Phys Rev. Lett. 65, 3381 (1990)] Isospin Analysis: B→ππ

13. Mark T. Allen, SLACJan 30, 2008 13 Isospin Analysis: B→ππ I = 1/2 This amplitude doesn’t contribute. But there are two amplitudes that do (tree and color- suppressed tree), but these decays have the same CKM/Weak phase. I can be 0, 2 but I 3 = +1, so I = 2 but... But gluons don’t carry isospin!

14. Mark T. Allen, SLACJan 30, 2008 14 Four-fold ambiguity in measuring Δα × Two-fold trigonometric ambiguity (sin2α) = 8-fold ambiguity Ambiguities

15. Mark T. Allen, SLACJan 30, 2008 15 4 years of my life lost Now go out and measure: A +-, A +-, A 00, A 00, A +0, A -0 Or Rather: BR(B 0 → π + π - ) = (|A +- | + |A +- |)/2 BR(B 0 → π 0 π 0 ) = (|A 00 | + |A 00 |)/2 BR(B + → π + π 0 ) = (|A +0 | + |A -0 |)/2 C(B 0 → π + π - ) = (|A +- | - |A +- |) C(B 0 → π 0 π 0 ) = (|A 00 | - |A 00 |) S(B 0 → π + π - ) = sin2α eff

16. Mark T. Allen, SLACJan. 30, 2008 16 Use toy method Each measurement we generate gaussian distribution of experiments with width of stat. ⊕ syst errors. C +-, S +-, C 00, BR(π + π - ), BR(π 0 π 0 ), BR(π + π 0 ) Toss out unphysical trials |C| or |S| > 1, Triangle does not close For each trial calculate Δα and α Drawn to Scale! 2Δα |A +- | 2 = BR(π + π - ) × (1 + C +- ) |A +- | 2 = BR(π + π - ) × (1 - C +- ) |A 00 | 2 = BR(π 0 π 0 ) × (1 + C 00 ) |A 00 | 2 = BR(π 0 π 0 ) × (1 - C 00 ) |A +0 | 2 = τ(B + )/τ(B 0 ) × BR(π + π 0 ) Measuring α: Method

17. Mark T. Allen, SLACJan. 30, 2008 17 Measuring α: Δα Confidence Level Δα 1 Δα 2 Use the distribution of the Δα solutions to calculate Confidence Levels

18. Mark T. Allen, SLACJan. 30, 2008 18 α eff 1 α eff 2 Δα 2 Δα 1 Do the same for α Measuring α: α Confidence Level

19. Mark T. Allen, SLACJan. 30, 2008 19 Tree and Penguin amplitudes grow to be unphysically large when α ≈ 0, π. Remove trials (and solutions) with large Penguin amplitudes Approximate the size of the amplitudes using BR(B 0 s → K + K - )= (24.4 ± 1.4 ± 4.6) × 10 -6 ≈ 1.1 We take |P| < 2.5 Measuring α: Penguin Amplitude

20. Mark T. Allen, SLACJan. 30, 2008 20 |Δα ππ | < 41° @ 90% CL. Take the maximum value of (1-C.L.) among all solutions 25°< α < 66° excluded at 90% C.L. Blue line: Gronau & London method Grey shade: L&G after requirement on size of penguin amplitude. Preferred Solution: α = 96°. +10° - 6° Measuring α: Results

21. Mark T. Allen, SLACJan. 30, 2008 21 done