Post on 21-Dec-2015
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CP Violation in the B → π π system
Mark AllenSASS 1-30-08
2Mark T. Allen, SLAC Jan 30, 2008
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
3Mark T. Allen, SLAC Jan 30, 2008
CKM Matrix
d s b
u
c
tV =
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(λ4), with CP violating phases in Vub and Vtd .
For example:
4Mark T. Allen, SLAC Jan 30, 2008
α
βγ
CKM Angles
5Mark T. Allen, SLAC Jan 30, 2008
Spontaneous flavor switch:
(Similar to the Kaon system)
B0 not CP eigenstates
K: Δ Lifetime large, Δ mass splitting smallB: Δ Lifetime small, Δ mass splitting “large”
B Mixing
Vtb Vtd*
6Mark T. Allen, SLAC Jan 30, 2008
•In decay: •In mixing:
( no sign of this in B’s)
CP Violation
Γ(B0 →K+ π-) ≠ Γ(B0 →K- π+)
B0 →K+ π-
B0 →K- π+
Probability of B0 → B0 ≠ B0 → B0
Note this is the CP violation seen on Kaon decays
7Mark T. Allen, SLAC Jan 30, 2008
•In interference between mixing and decay:
B0
CP eigenstate( J/ψ Ks, π+ π- )
B0
CP Violation
This is where the magic happensVtd has a phase!
8Mark T. Allen, SLAC Jan 30, 2008
B0 →π+ π-
B0
π+
π-
duud
bd
Vub
Vud*
Vtb Vtd*
B0B0
Mixing Tree decay
9Mark T. Allen, SLAC Jan 30, 2008
Δt = proper time difference between pure B0 or B0
meson and decay
TDCP Asymmetries
•Things to note: λ = e2iα
•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)
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Mark T. Allen, SLAC Jan 30, 2008
Not so fast.....
What if there are multiple decay amplitudes?!?!
B0
π+ π- B0
Mixing
Tree
Penguin B0
π+
π-
duud
bd
Vub
Vud*
π-
π+
ud
du
bdB0
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Mark T. Allen, SLAC Jan 30, 2008
Penguin pollution
π- (ρ, a1)
π+(ρ, a1)π+(ρ, a1)
π- (ρ, a1)
GOAL: Disentangle tree and penguin contributions.
With Penguin Pollution:
Different amplitudes with different CKM phases!
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Mark T. Allen, SLAC Jan 30, 2008
[M. Gronau and D. London, Phys Rev. Lett. 65, 3381 (1990)]
Isospin Analysis: B→ππ
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Mark T. Allen, SLAC Jan 30, 2008
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, 2but I3 = +1,
so I = 2 but...
But gluons don’t carry isospin!
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Mark T. Allen, SLAC Jan 30, 2008
Four-fold ambiguity in measuring Δα × Two-fold trigonometric ambiguity (sin2α) =
8-fold ambiguity
Ambiguities
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Mark T. Allen, SLAC Jan 30, 2008
4 years of my life lost
Now go out and measure: A+- , A+- , A00, A00, A+0, A-0
Or Rather:•BR(B0 → π+ π-) = (|A+-| + |A+-|)/2•BR(B0 → π0 π0) = (|A00| + |A00|)/2•BR(B+ → π+ π0) = (|A+0| + |A-0|)/2•C(B0 → π+ π-) = (|A+-| - |A+-|)•C(B0 → π0 π0) = (|A00| - |A00|)•S(B0 → π+ π-) = sin2αeff
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Mark T. Allen, SLAC Jan. 30, 2008
• Use toy method
•Each measurement we generate gaussian distribution of experiments with width of stat. ⊕ syst errors.
•C+-, S+-, C00, BR(π+ π-), BR(π0 π0), BR(π+ π0)
•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+- )|A00|2 = BR(π0 π0) × (1 + C00 )|A00|2 = BR(π0 π0) × (1 - C00 )|A+0|2 = τ(B+)/τ(B0) × BR(π+ π0)
Measuring α: Method
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Mark T. Allen, SLAC Jan. 30, 2008
Measuring α: Δα Confidence Level
Δα1
Δα2Use the distribution of theΔα solutions to calculate
Confidence Levels
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Mark T. Allen, SLAC Jan. 30, 2008
αeff 1 αeff 2
Δα2
Δα1
Do the same for α
Measuring α: α Confidence Level
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Mark T. Allen, SLAC Jan. 30, 2008
•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(B0
s → K+ K-)= (24.4 ± 1.4 ± 4.6) × 10-6
≈ 1.1
We take |P| < 2.5
Measuring α: Penguin Amplitude
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Mark T. Allen, SLAC Jan. 30, 2008
|Δαππ | < 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
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Mark T. Allen, SLAC Jan. 30, 2008
done