B mixing: introduction and the case of the B d. 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 = H 0 + H W.
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Universita’ di Roma “La Sapienza”
Universita’ di Roma3, 4/12/06
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
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
Stong interactions produce a B0 which in terms of Heff eigenstates is
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 systemSigns of mixing
If no way to measure time
Just count how many mixed events you see
Otherwise time dependence helps a lot!!!
P (B0phys B0) - P (B0phys B0)
P (B0phys B0) + P (B0phys B0)
= cos (Δm t)
area~ |Vij|2CKM Matrix
In 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:
In the Standard Model CP violation shows up as a complex phase in the CKM matrix
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.
isin(Dm t/2) exp(–2ib)exp(2iq)
isin(Dm t/2) exp(2ib)Mixing and CP in the Standard Model
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
Study the oscillation frequency in decay channels common to B0 and B0
The LEP adventure
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
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
Lint: 391 fb-1
Lint: 680 fb-1
WARNING : All future detector descriptions refer to BaBar
B Meson Reconstruction
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
B0 B0 or B0 B0
B0 B0 or B0 B0
Mistake tagging with probability w (=22% in figure)
Resolution on Dz, sDz(=170 mm in figure)
BUT : cascade events can mimic opposite tag
b quarks are tagged by negatively charged leptons.
e- or m-
e- or m-
anti-b quark (Q = +1/3)
anti-s quark (Q = +1/3)
b quark (Q = -1/3)
c quark (Q = +2/3)
TAG tracks, V0sVertexing Algorithm
If one of the two Bs is fully reco’d the full kinematics can be exploited:
* good resolution (sDz~180mm)
* limited bias from D lifetimes
Otherwise only one track per side is used (typically the two leptons)
* reasonable core resolution but …
* … very long tail from D lifetimes
Use BD(*)ln decay both to reconstruct and to tag
reconstruct only the charged lepton
Pros: extremely high stat
cons: high, irreducible backgrounds
lots of parameters in simultaneous fit
cascade, resolution, mistags, fractions,…
dependency on sDz and lack of control samples
Belle 32M BB~
Removing assumptions on CP(T) symmetries
CP symmetry p=q
CPT symmetry z=0
40% reduction in s(q/p)
80% reduction in s(Im(z))
First Measurement of Re(z)!
on New Physics from |q/p|
Look for BD*p or D*ln
Pros: very high stat
cons: relatively high background, particles leaking in tag side
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!!!
Neutral B Mesons
Pros: clean sample, efficient tagging
cons: low stat
Dominant sys: vertex reconstruction
Relative error on world average: 1%
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!