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B mixing: introduction and the case of the B dPowerPoint Presentation

B mixing: introduction and the case of the B d

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### B mixing: introduction and the case of the Bd

Riccardo Faccini

Universita’ di Roma “La Sapienza”

Universita’ di Roma3, 4/12/06

What is Mixing?

Mixing occurs every time the eigenstates of the hamiltonian are different from the eigenstates of the decay operator

H = H0 + HW

Eigenstates of the hamiltonian are a continuum of states

Decay final states

Undecayed/mixed states

Considering only the subspace with B0 and B0 the hamiltonian becomes

NO MORE HERMITIAN!

The eigenstates of Heff are

Of eigenvalues mL- i GL/2 and mH- i GH/2, respectively.

Let us assume the following parametrization

and remember the Shroedinger equation

Time evolution

Stong interactions produce a B0 which in terms of Heff eigenstates is

Analogously for

with the evolution of time

Interference between two amplitudes with different phase

If we can count the and meson present at a given time after the

production of a

Note: case of the Bd: GL=GH=G

Note: all applies also to the K0-K0 and the D0-D0 system

Signs of mixingIf no way to measure time

Just count how many mixed events you see

Otherwise time dependence helps a lot!!!

B0phys B0

B0phys B0

No mixing

RATES

t(ps)

t(ps)

ASYMMETRY

P (B0phys B0) - P (B0phys B0)

A(t) =

P (B0phys B0) + P (B0phys B0)

t(ps)

= cos (Δm t)

s

b

u

c

t

area~ |Vij|2

CKM MatrixIn the Standard Model the complex couplings of the LH quarks and RH antiquarks to the charged weak force carriers (W±) are usually represented in the unitary Cabibbo-Kobayashi-Maskawa (CKM) matrix:

Discrete symmetries:

Charge conjugation:

Parity :

Time reversal:

In the Standard Model CP violation shows up as a complex phase in the CKM matrix

NO

YES

C

q L

q L

W-

W+

Vqq´

q´R

q´R

P

q R

q R

W+

W-

V*qq´

q´L

q´L

NO

YES

“The” Unitarity triangle

The unitarity condition that gives the most open triangle is

Vub*Vud + Vcb*Vcd + Vtb*Vtd= 0

The first and last terms contain the most-off-diagonal elements Vub and Vtd, those with the most significant complex part.

It is convenient to divide each term by the middle term so that the base of the triangle has unit length.

(r,h)

Vtb*Vtd

Vcb*Vcd

Vub*Vud

Vcb*Vcd

a

b

g

(1,0)

(0,0)

cos(Dmt/2)

cos(Dmt/2) exp(–2iq)

fCP

fCP

B0

B0

B0

B0

isin(Dm t/2) exp(–2ib)exp(2iq)

isin(Dm t/2) exp(2ib)

Mixing and CP in the Standard Modelt

d

b

W

W

B

B

t

d

b

Vtd*

Vtb

The mixing diagram has a real part DMd which allows to measure Vtd and a phase (q/p) which probes CP violation

The interference between B mixing and decays into a CP eigenstate (accessible to both B0 and B0) provides the cleanest theoretical predictions:

with a CP-violating asymmetry sin 2(b–q).

The CKM angle b is associated with the mixing box diagram.

The CKM angle q depends on the final state fCP

CP in Oscillations+ Decay

Study the oscillation frequency in decay channels common to B0 and B0

(r,h)

a

g

b

(0,0)

(1,0)

Examples

History of mixing

The LEP adventure

e+e-Zbb

(1990-1995)

B0B0 oscillations

ARGUS (1987) confirmed by CLEO

Two B0D*-m+nm decays in the same event e+e-Y(4S)B0B0

Note: B mixing was expected to be a much rarer process because of a lower expected top mass

Relative error:

2.8%

The B Factories

B0

e+

e-

Y(4S)

B0

Since J(Y)=1 and J(B)=0 and the B0 mesons have to obey the bose-einstein statistics

Two B mesons with opposite flavour are produced in a coherent state

WARNING : All future detector descriptions refer to BaBar

B-Flavor Tagging

II

0

B

tag

D

III

B Meson Reconstruction

I

Accurate and unbiased measurement of the vertices

Allows time dependent analyses!!!

Several techniques to reconstruct a lot of B mesons: look for states that better discriminate between B0 and anti-B0

B meson reconstruction

- Identification of a lepton leptonic
- Identification of BD*ln, D*p (D*D0ps) via the reconstruction of the lepton/p and pspartial reconstruction
- Fully reconstructed BDX

purity

efficiency

tagging

Effect of tagging and resolution

B0 B0 or B0 B0

UNMIXED

B0 B0 or B0 B0

MIXED

Perfect reconstruction

Mistake tagging with probability w (=22% in figure)

Resolution on Dz, sDz(=170 mm in figure)

BUT : cascade events can mimic opposite tag

- Cleanest tag is to require a lepton
- Only 10% of events per lepton

- In case of clean reconstruction dirtier tags can be used

b quarks are tagged by negatively charged leptons.

e- or m-

e- or m-

W+

W-

anti-c quark

n

n

W-

anti-b quark (Q = +1/3)

anti-s quark (Q = +1/3)

b quark (Q = -1/3)

c quark (Q = +2/3)

Effective efficiency:

BREC direction

BREC Vertex

BREC daughters

Interaction Point

Beam spot

BTAG direction

TAG Vertex

TAG tracks, V0s

Vertexing AlgorithmIf one of the two Bs is fully reco’d the full kinematics can be exploited:

* good resolution (sDz~180mm)

* limited bias from D lifetimes

s~70 mm

~0.1 mm

s~180 mm

~1cm

Otherwise only one track per side is used (typically the two leptons)

* reasonable core resolution but …

* … very long tail from D lifetimes

larger systematics

Dilepton mixing

Use BD(*)ln decay both to reconstruct and to tag

reconstruct only the charged lepton

Pros: extremely high stat

cons: high, irreducible backgrounds

B+B-, continuum

lots of parameters in simultaneous fit

cascade, resolution, mistags, fractions,…

dependency on sDz and lack of control samples

Exploring fundamental symmetries

Removing assumptions on CP(T) symmetries

Define:

CP symmetry p=q

CPT symmetry z=0

T/CP/CPT in B0 mixing

BaBar hep-ex/0603053

40% reduction in s(q/p)

80% reduction in s(Im(z))

First Measurement of Re(z)!

after

before

NP ?

Constraints

on New Physics from |q/p|

SM

SM

Partially reconstructed B decays

Look for BD*p or D*ln

D*D0p

BaBar

Belle

Pros: very high stat

cons: relatively high background, particles leaking in tag side

DMd(ps-1)

Fully reconstructed semileptonic B decays

Reconstruct one of the Bs with the decay

Neutrino not reconstructed

Pion easy to identify (soft)

Pros: relatively clean sample and high stat

cons: same as pros …

Ideal size and purity for the first simultaneous fit to lifetime and DMd!!!

Higher due to simultaneous measurement of tB

DMd(ps-1)

Fully reconstructed hadronic B decays

hadronic decays

Neutral B Mesons

Belle

Pros: clean sample, efficient tagging

cons: low stat

Dominant sys: vertex reconstruction

Summary of results

Relative error on world average: 1%

Constraints on the Unitarity Triangle

Current knowledge of the unitarity triangle

Regardless of all exp efforts the constraint on the unitarity triangle is not very stringent …

… but mixing has been critical to constrain the angles!

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