MARCELLA BONA - Particle Physics Research Centrepprc.qmul.ac.uk/~bona/ulpg/cpv/lecture2.pdf · M.Bona – CP violation – lecture 2 3 CKM matrix in the Standard Model (recap) Quarks

MARCELLA BONA

CP violation lectures

University of London Intercollegiate Postgraduate Course in Elementary Particle Physics

Lecture 2

M.Bona – CP violation – lecture 2 2

◈ brief recap of lecture 1◈ Unitarity Triangle◈ types of CP violation◈ angles of the unitarity triangle

Outline


CKM matrix in the Standard Model (recap)

◉ Quarks change type in weak interactions:

◉ We parameterise the couplings Vij in the CKM matrix:

V =

V , ,iq u c t

, ,jq d s b

W

ijV

where here I usethe Buras correction

to the Wolfestein parameterisation

= (1- 2/2) = (1-2/2)


Unitarity relations

i Vij V*ik = jk

j Vij V*kj = ik

column orthogonality

row orthogonality

multiply with its conjugate transposeVV† = V†V = 1


column orthogonality

Unitarity relations

Areas have to be the same → Jarlskog parameter


VidV*ib = 0 represents the orthogonality condition between the first and the third column of the CKM matrix (the orientation depends on the phase convention)

rescaled version where sides have been divided by |VcdV*cb|

In terms of the Wolfenstein parameterization, the coordinates of this triangle are (0, 0), (1, 0) and (r, h):the two sides are (r − ih) and (1 − r + ih).

Third unitarity relation


• We need to measure the angles and sides to overconstrain this triangle, and test that it closes.

• Need experiments to measure these quantities

* * * 0ud ub td tb cd cbV V V V V V The angles can be written in terms of CKM matrix elements as:

Probing the structure of the CKM mechanism



• Need experiments to measure these quantities!

* * * 0ud ub td tb cd cbV V V V V V


If there is CP violation, the triangle is not flat!



• Need experiments to measure these quantities!


Many different ways to measure the angles and sides.

B → DK

B0 →

B0 → J/K0


normalized: normalized:

many observablesfunctions of and:

overconstraining

Unitarity triangle


3 kinds of CP violation

1.Direct CP violation.

2. Indirect CP violation (CPV in mixing).

3.CPV in the interference between mixing and decay.

• Need more than one amplitude to have a nonzero CP violation: interference

Cartoon shows the decay of a B0 orB0 into a CP eigenstate fCP.

P( B0 f ) ≠P(B0 f )

P( B0 B0 ) ≠P(B0 B0 )

CPmixing

decay

f

t Af

Af

B0

B0

t

t=0


Time evolution and CP violation (case of the U(4S) decays)

◎ At U(4S), theBB pairs are produced in coherent P wave◎ Three interference effects can be observed:

◉ CP violation in the mixing ( | q/p | 1 )◉ (direct) CP violation in the decays ( |A/A | 1 ) ◉ CP violation in interference between mixing and decay ( Iml 0 )

◎ Time evolution of theBB system (assuming DG=0)

◉ direct CP violation C 0◉ CP violation in interference S 0

neutral B

both neutral and charged B


◉ Ingredients of a timedependent CP asymmetry measurement:◎ Isolate interesting signal B decay: BRECO.

◎ Identify the flavour of the nonsignal B meson (BTAG) at the time it decays.◎ Measure the spatial separation between the decay vertices of both B mesons:

convert to a proper time difference Dt = Dz / bgc; fit for S and C.

◉ The time evolution of BTAG =B0(B0) is

Timedependent CP asymmetries


◉ Construct an asymmetry as a function of Dt:

Dt (ps)Dt (ps)

f+(Dt)f-(Dt)

Experimental effects we need to include:◎ Detector resolution on Dt.◎ Dilution from flavour tagging

With detector resolution With detector resolution and dilution

Timedependent CP asymmetries


Angles of the Unitarity triangle


Theoretically clean (SM uncertainties ~102 to 103) tree dominated decays to Charmonium + K0 final states.


◎ branching fraction: O (103) the coloursuppressed tree dominates

and the t penguin has the same weak phase of the tree

◉

◎ theoretical uncertainty:◉ modelindependent datadriven estimation from J/0 data: SJ/K0 = SJ/K0 – sin2 = 0.000 ± 0.012◉ modeldependent estimates of the u and c penguin biases SJ/K0 = SJ/K0 – sin2 ~ (103) SJ/K0 = SJ/K0 – sin2 ~ (104)

sin2 in golden b ccs modes

S ~ sin2 C ~ 0

H.Li, S.MishimaJHEP 0703:009 (2007)

H.Boos et al.Phys. Rev. D73, 036006 (2006)

V*cbVcs


• The ‘Golden Measurement’ of the B factories. The aims of this measurement were:

– Measure an angle of the Unitarity Triangle.– Discover CP violation in B meson decays.

Sine term has a nonzero coefficient

This tells us that there is CP violation in the interference between mixing and decay amplitudes inccs decays.

( ) sin( ) cos( )CP d dA t S m t C m t

S = sin 2 = 0.671 0.024

sin2b in golden b ccs modes


◎ Theoretically clean CP violation measurements consistent with the Standard Model for:

◉ Established technique for extracting S and C that can be used for other final states.◉ Measured S=sin2 provides a reference point to search for New Physics (NP).

CP violation:

◎ Four solutions exist in the plane as we compute arcsin(2).◎ Additional measurements provide cos(2) and help to resolve ambiguities.


b uud transitions with possible loop contributions. Extract using• SU(2) Isospin relations.• SU(3) flavour related processes.


:tdV

* :tdV

:ubV

0

sin(2 )hh

hh

C

S

◉ This scenario is equivalent to the measurement of sin2b in Charmonium decays … but nature is more complicated than this!

CP violation: a

◎ Interference between box and tree results in an asymmetry that is sensitive to a in B hh decays: h = p, r, …


:tdV

* :tdV

:ubV

◎ Interference between box and tree results in an asymmetry that is sensitive to a in B hh decays: h = p, r, …

◎ Loop corrections are not negligible for a

◎ Measure S aeff

◎ Need to determine da = aeff – a [P/T is different for each final state]

0

sin(2 )hh

hh

C

S

+ Loops (penguins)

2eff

sin( )

1 sin(2 )

hh

hh hh

P T

C

S C

ﾵ

CP violation: a

∞


What's in a name


Bounding penguins

◉ Several recipes describe how to bound penguins and measure a.◎ These are based on SU(2) [or SU(3)] symmetry.

SU(2)(Isospin analysis)

p+p and r+r

GronauLondonIsospin Triangles

pr

Lipkin (et al.)Isospin Pentagons

◎ Use charged and neutral B decays to the hh final state to constrain the penguin contribution and measure a.

◎ Use charged and neutral B decays to the rp final state to constrain the penguin contribution and measure a. Remove any overlapping regions in the Dalitz plot.

ppp0

SnyderQuinn (et al.)Fit Dalitz plot and extract parameters related to a

◎ Regions of the Dalitz plot with intersecting r bands are included in this analysis; this helps resolve ambiguities.


from aeff to a: isospin analysis

◉ B p+p , p+p0, p0p0 decays are connected from isospin relations◉ p p states can have I = 2 or I = 0⇨ the gluonic penguins contribute only to the I = 0 state (DI=1/2)⇨ p+p0 is a pure I = 2 state (DI = 3/2) and it gets contribution only

from the tree diagram⇨ triangular relations allow for the determination

of the phase difference induced on a:

Both BR(B0) and BR(B0) have to be measured in all the p p channels

a: collecting the ingredients

Isospin analysis


Isospin analysis

= eff-

00 0

00 0

1

21

2

A A A

A A A

Measuring S in h0h0 provides an additional constraint on this angle.

◎ There are SU(2) violating corrections to consider, for example electroweak penguins, but these are much smaller than current experimental accuracy and eventually they can be incorporated into the Isospin analysis.

◉ Consider the simplest case: B pp / rr decays.


Belle 00 0 taggedB

0 taggedB

B

◎ Easy to isolate signal for + and +0 as these modes are relatively clean and have large B ~ O(5106).

◎ Much harder to isolate 00: B ~ 1.5106

◉ No tracks in the final state to provide vertex info.•B0 00 has a large E resolution.

Belle p+p

Belle +

0 taggedB0 taggedB

▻ Possible to separate flavour tags to measure C00. This information completes the set of information required for an Isospin analysis.


B


Isospinrelated decays

◉ simultaneous ML fit to all hh modes with h being or K:◎B+ +, K+, K+K (and cc)◎B+ +0, K+0 (and cc)

K

KK


◉ Inputs from:

How do I read plots like this?

◎ 1CL = 1: central value reported from measurements, before considering uncertainties.

◎ 1CL = 0: Region excluded by experiment.

◎ If we think in terms of Gaussian errors, then 1CL = 0.317, 0.046, 0.003 correspond to regions allowed at 1, 2 and 3.

GronauLondon Isospin analysis

B


⇨ If we have measured CP violation in B +, does this tell us something about ?

▶ CP violation measured as a non zero value of S is related to via:

▶ S 0 means there is CP violation in this decay and sin(2eff) 0.

▶ If =0, then the unitarity triangle would be flat, so if S0 we must have 0.

▶ =0 is a singularity where the amplitudes have to go to inf▶ to remove this nonphysical behaviour we can use constraints on P from BsK+K to remove the solutions near =0 and 180. UTfit Collaboration

Phys.Rev.D76:014015(2007)

B


◉ VectorVector modes: angular analysis required to determine the CP content. L=0,1,2 partial waves:◎ longitudinal: CPeven state◎ transverse: mixed CP states

◉ +: two 0 in the final state◉ wide resonance

but◉ BR 5 times larger with respect to ◉ penguin pollution smaller than in ◉ are almost 100% polarized:

◎ almost a pure CPeven state

B

see backup forfull discussion


◎ Obtain a more stringent constraint on than from B decays. BaBar 00 paper

◉ Not including S00 and C00.◉ Include C00, but not S00.◉ Using all constraints.

Some features of this result:

◎ Two of the solutions overlap near 90 and 180.

◎ Using S00 and C00 we see that the solution at 80 is very slightly preferred over the other solutions.

◎ There are two regions for that are excluded:

45 130

B


B (+0 Dalitz Plot)

◉ dominant decay is not a CP eigenstate

◉ 5 amplitudes need to be considered: ◎ B0 +, +, 00 and B+ +0, 0+

◎ Isospin pentagon

◉ or timedependent dalitz analysis: extraction together with the strong phases exploiting the amplitude interference: ◎ interference at equal masses

squared give information on the strong phases between resonances see backup for

full discussion


CP violation:

aSM = (92 ± 7)°

bayesian analysis:the quantity plotted isnow the ProbabilityDensity Function (PDF)

pp

evidence of CP violation

no CP violationobserved

rr rp

◎ Combining all the modes to maximize our knowledge of a..


Extract using BD(*)K(*) final states using:• GLW: Use CP eigenstates of D0.• ADS: Interference between doubly suppressed decays.• GGSZ: Use the Dalitz structure of DKsh+h decays.

Measurements using neutral D mesons ignore D mixing.


and DK trees

Vcb (~2)

◎ D(*)K(*) decays: from BRs and BR ratios, no timedependent analysis, just rates◎ the phase is measured exploiting interferences: two amplitudes leading to the same final states◎ some rates can be really small: ~ 107

Vub=|Vub|e i (~3)

Theoretically clean (no penguins neglecting the D0 mixing)


Sensitivity to : the ratio rB

Vcb (~2)

Vub=|Vub|e i (~3)

rB = amplitude ratio

B = strong phase diff.

~0.36 hadronic contributionchanneldependent◈ in B+ D(*)0K+: rB is ~0.1

◈ while in B0 D(*)0K0 rB could be ~0.4◈ to be measured: rB(DK), r*B(D*K) and rs

B(DK*)


Three ways to make DK interfere

GLW(Gronau, London, Wyler) method: uses the CP eigenstates D(*)0

CP with final states: K+K, + - (CPeven), Ks0 (,) (CPodd)

ADS(Atwood, Dunietz, Soni) method: B0 andB0 in the same final state with D0 K+ (suppr.) andD0 K+ (fav.)

• D0 Dalitz plot with the decays B D(*)0[KS+] K

three free parameters to extract: , rB and B

more sensitive to rB

the most sensitive way to


Interference of B D0K, D0 K*+

(suppressed) with B D0K,D0 K*+

~ ADS like

Interference of B D0K, D0 K0

S0

with B D0K,D0 K0

S0

~ GLW like

◎ neutral D mesons reconstructed in three body CPeigenstate final states (typically D0 KS+ )◎ the complete structure (amplitude and strong phases) of the D0 decay in the phase space is obtained on independent data sets and used as input to the analysis ◎ use of the cartesian coordinate:

◉ x± = rB cos ( ± )◉ y± = rB sin ( ± )

◎ , rB and B are obtained from a simultaneous fit of the KS+ Dalitz plot density for B+ and B

◎ need a model for the Dalitz amplitudes◎ 2fold ambiguity on

: GGSZ Method


CP violation:

◎ As with , several methods available.► Best results come from the GGSZ Dalitz method.► LHCb is producing more precise analyses of these decay modes

using all methodsand all final stateswe can get significant resultsfor all theparameters

UTfit

= (74 11)

r = 0.10 0.02 r* = 0.11 0.03


backup


◉ (simplified) angular analysis◉ Inputs from:

◉ fL ~ 1 for B decays: this helps simplify extracting .◉ Can measure S00 as well as C00 to help resolve ambiguities.◉ Finite width of the is ignored in the determination

• We define the fraction of longitudinally polarised events as:

B


B


◎ for the 00 decay:◉ small BR: penguins less

important in than in

but:◉ all charged particles final

state: the vertex can be reconstructed so the timedependent analysis feasible

B


B (+0 Dalitz Plot)

◎ Analyse a transformed Dalitz Plot to extract parameters related to .◎ Use the SnyderQuinn method.

◎ Fit the timedependence of the amplitudes in the Dalitz plot:

0

+

(m0=m+-)

(0=

+- h

elic

ity)


◉ The amplitudes are written in terms of Us and Is:

◉ Which are related to CP conserving and CP violating observables:

CP conservingobservables

CP violatingobservables

Some features of this result:

◎ No region is excluded at 3 significance.

◎ A high statistics measurement will help resolve ambiguities in the measured value of .

◎ Results from the Dalitz analysis, and the pentagon analysis (solid) are more stringent than using the Dalitz analysis alone.

Belle + paper

B (+0 Dalitz Plot)


: GLW Method

◉ GLW Method: Study B+ DCP0X+ and B+ DX++ cc (D0 K+ )

◉ X+ is a strangeness one meson e.g. a K+ or K*+.◉ DCP

0 is a CP eigenstate (use these to extract ):

◉ The precision on is strongly dependent on the value of rB.▻ rB~0.1 as this is a ratio of Cabibbo suppressed to Cabibbo allowed decays

and also includes a colour suppression factor for B+D(*)K(*) bu decays. ◉ Measurement has an 8fold ambiguity on .

Gronau, London, Wyler, PLB253 p483 (1991).

01

0 0 0 0 01

,

, ,

CP

CP S S S

D K K

D K K K

• 4 observables• 3 unknowns: rB, and


◉ ADS Method: Study B,0 D(*)0 K(*)

◉ Reconstruct doubly suppressed decays with common final states and extract through interference between these amplitudes:

◉ extracted using ratios of rates:

Attwood, Dunietz, Soni, PRL 78 3257 (1997)

Vcb

Vus

Vub

Vcs CKM and Color SuppressedCKM Favoured

◎ (*) = (*)B + D

◎ (*) is the sum of strong phase differences between the two B and D decay amplitudes.◎ rD and rB are measured in B and charm factories.◎ D is measured by CLEOc

u

d

CKM FavouredD(*)0 K+

p

W

c s

u u

Vcs

Vud

Doubly CKM Suppressed D(*)0 p

K+

W+

c d

u u

s

u

Vus

Vcd

: ADS Method

B D(*)0 K(*)B D(*)0 K(*)

D(*)0 K+D(*)0 K+


◉ GGSZ (“Dalitz”) Method: Study D(*)0K(*) using the D(*)0Ksh+h Dalitz structure to constrain . (h = , K)◎ Self tagging: use charge for B decays or K(*) flavour for B0 mesons.

where

◎ Need detailed model of the amplitudes in the D meson Dalitz plot.

◎ Use a control sample (CLEOc data or D*+D0+) to measure the Dalitz plot.

p+p K+K

Control sample plots from BaBar GGSZ paper

: GGSZ Method

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MARCELLA BONA - Particle Physics Research Centrepprc.qmul.ac.uk/~bona/ulpg/cpv/lecture2.pdf · M.Bona – CP violation – lecture 2 3 CKM matrix in the Standard Model (recap) Quarks