1 cp violation in the b → π π system mark allen sass 1-30-08

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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


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:


α

βγ

CKM Angles


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*


•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


•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!


B0 →π+ π-

B0

π+

π-

duud

bd

Vub

Vud*

Vtb Vtd*

B0B0

Mixing Tree decay


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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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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[M. Gronau and D. London, Phys Rev. Lett. 65, 3381 (1990)]

Isospin Analysis: B→ππ

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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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Four-fold ambiguity in measuring Δα × Two-fold trigonometric ambiguity (sin2α) =

8-fold ambiguity

Ambiguities

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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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Measuring α: Δα Confidence Level

Δα1

Δα2Use the distribution of theΔα solutions to calculate

Confidence Levels

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αeff 1 αeff 2

Δα2

Δα1

Do the same for α

Measuring α: α Confidence Level

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•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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|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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done

1 cp violation in the b → π π system mark allen sass 1-30-08

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