Niels Tuning (1) CP violation Lecture 5 N. Tuning.

Niels Tuning (1)

CP violation

Lecture 5

N. Tuning

Diagonalize Yukawa matrix Yij

– Mass terms

– Quarks rotate

– Off diagonal terms in charged current couplings

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RecapSM Kinetic Higgs Yukawa L L L L

0( , ) ...I I

Yuk Li L Rjd Ij id dY u

L

...2 2

Kinetic Li LiI I I

Li LIi

g gu W d d W u

L

5 5*1 1 ...2 2

ij iCKM i j j j i

g gu W d d uV VW

L

, , , , ...d u

s cL L

b tR R

Mass

m d m u

d s b m s u c t m c

m b m t

L

I

ICKM

I

d d

s V s

b b

SM CKM Higgs Mass L L L L

uI

dI

W

u

d,s,b

W

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CKM-matrix: where are the phases?

u

d,s,b

W

• Possibility 1: simply 3 ‘rotations’, and put phase on smallest:

• Possibility 2: parameterize according to magnitude, in O(λ):

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…

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Some algebra for the decay P0 f

0 ( )P t

Interference

P0 f P0P0 f

Meson Decays

• Formalism of meson oscillations:

• Subsequent: decay

0 ( )P t

Interference(‘direct’) Decay

Recap osc + decays

Classification of CP Violating effects

1. CP violation in decay

2. CP violation in mixing

3. CP violation in interference

Recap CP violation

Im( λf)




We will investigate λf for various final states f

Recap CP violation

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CP eigenvalue of final state J/K0S

* * *

/ * * *s

tb td cb cs cs cdJ K

tb td cb cs cs cd

V V V V V V

V V V V V V

sin 2 ( ) sin( )CPA t mt

2ie

• CP |J/> = +1 |J/>

• CP |K0S> = +1 |K0

S>

• CP |J/K0S> = (-1)l

|J/K0S> ( S(B)=0 L(J/K0

S)=1 )

( ) ( )( ) Im( )sin

( ) ( )B fB f

CP fB fB f

t tA t mt

t t

Relative minus-sign between state and CP-conjugated state:

( S(J/)=1 )

λf contains information on final state f

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Recap CP in B

Investigated three final states f

• B0J/ψKs

• B0sJ/ψφ

• B0sDsK


λf contains information on final state f

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• B0sJ/ψφ


Recap CP in B

βs: Bs0 J/φ : Bs

0 analogue of B0 J/K0S

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Recap CP in B

Remember!

Necessary ingredients for CP violation:

1) Two (interfering) amplitudes

2) Phase difference between amplitudes– one CP conserving phase (‘strong’ phase)

– one CP violating phase (‘weak’ phase)

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Remember!

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Basics

The basics you know now!

1. CP violation from complex phase in CKM matrix

2. Need 2 interfering amplitudes (B-oscillations come in handy!)

3. Higher order diagrams sensitive to New Physics

Next:

• (Direct) CP violation in decay

• CP violation in mixing (we already saw this with the kaons: ε≠0, or |q/p|≠1)

• Penguins

• The unitarity triangle

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Next: γ

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CKM Angle measurements from Bd,u decays

• Sources of phases in Bd,u amplitudes*

• The standard techniques for the angles:

*In Wolfenstein phase convention.

Amplitude Rel. Magnitude Weak phase

bc Dominant 0

bu Suppressed γ

td (x2, mixing) Time dependent

2β

B0 mixing + single bc decay

B0 mixing + single bu decay

Interfere bc and bu in B± decay.

β

-i

-i

γ1 1

1 1 1

1 1

e

e

bu

td

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Determining the angle

• From unitarity we have:

• Must interfere b u (cd) and b c(ud)

• Expect b u (cs) and b c(us) to have the same phase, with more interference (but less events)

* * *ub ud tb td cb cdV V V V V V

*ub udV V *

tb tdV V

*cb cdV V

* * * *arg argub ud cb cd ub ud cb cdV V V V V V V V 3 2

3 2

Measure γ: B0s Ds

K-/+ : both λf and λf

Niels Tuning (20)NB: In addition B s Ds

K-/+ : both λ f and λf

+Γ(Bf)=

+Γ(Bf )=

2

2

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Measure γ: Bs DsK-/+ --- first one f: Ds

+K-

s s

scsV

s s

s

*usV

* 2cb udV V * 4 i

ub cdV V e * 3cb usV V * 3 i

ub csV V e

• This time | Af||Af|, so |λ|1 !

• In fact, not only magnitude, but also phase difference:

Measure γ: Bs DsK-/+

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• Need B0s Ds

+K- to disentangle and :

• B0s Ds

-K+ has phase difference ( - ):

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0

0B KB KBBAABBARARBBAABBARAR

CP violation in Decay? (also known as: “direct CPV”)

HFAG:

0.133 0.030 0.009 CPA

hep-ex/0407057Phys.Rev.Lett.93:131801,2004

4.2

BBAABBARARBBAABBARAR

B fB fCP

B fB f

A

First observation of Direct CPV in B decays (2004):

ACP = -0.098 ± 0.012

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LHCbLHCbLHCbLHCb

CP violation in Decay? (also known as: “direct CPV”)

LHCb-CONF-2011-011LHCbLHCbLHCbLHCb

B fB fCP

B fB f

A

First observation of Direct CPV in B decays at LHC (2011):

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Direct CP violation: Γ( B0 f) ≠ Γ(B0f )

220 * * 4 2( ) i i iub us tb tsB K V V e V V e

2 20 * * 4 2( ) i i iub us tb tsB K V V e V V e

Only different if both δ and γ are ≠0 !

Γ( B0 f) ≠ Γ(B0f )

CP violation if Γ( B0 f) ≠ Γ(B0f )

But: need 2 amplitudes interference

220 * * 4 2( ) i i iub us tb tsB K V V e V V e * 4i i i

ub usV V e e

Amplitude 1

+

Amplitude 2

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Hint for new physics? B0Kπ and BKπ0

0 B K 0 B KAverage 0.049 0.040 CPA

3.6

0 B K 0 B KAverage 0.114 0.020 CPA

Redo the experiment with B instead of B0…

d or u spectator quark: what’s the difference ??B0Kπ

B+Kπ


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T (tree) C (color suppressed) P (penguin)

B0→K+π-

B+→K+π0

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CP violation in Mixing? (also known as: “indirect CPV”: ε≠0 in K-system)

0 0P B B

0 0P B B

0 0B B0 0B B0 0B B0 0B B

gVcb* W

c

d

0 bB

d

gVcb

W

c

d

0 bB

d

X X X

X

0 0B B

t=0 t

0 0 0 0B B BP P B ?

Look for like-sign lepton pairs:Decay

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(limit on) CP violation in B0 mixing

Look for a like-sign asymmetry:

4

4

1

1T

q pN t N tA t

N t N t q p

As expected, no asymmetry is observed…

1q

p

CP violation in Bs0 Mixing??

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D0 Coll., Phys.Rev.D82:032001,2010.arXiv:1005.2757

0 0P B B

0 0P B B

0 0B B0 0B B0 0B B0 0B B

X X X

X

0 0B B

b

s

s

b

“Box” diagram: ΔB=2

φsSM ~ 0.004

φsSM

M ~ 0.04

CP violation from Semi-leptonic decays

• SM: P(B0s→B0

s) = P(B0s←B0

s)

• DØ: P(B0s→B0

s) ≠ P(B0s←B0

s)

• 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→B0

s) = P(B0s←B0

s)

• DØ: P(B0s→B0

s) ≠ P(B0s←B0

s) ?

B0

s→

Ds±X

0μ

ν

More β…

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Niels Tuning (1) CP violation Lecture 5 N. Tuning.

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