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Scientific Report 2007-2009
Particle physics
P14. Measurement of the sides of the unitarity triangle
The weak force is responsible for the flavor transition
of quarks which allows unstable particles made of heavy
quarks and antiquarks to decay into lighter particles.
The rates of these decays are related to a set of measurables
called the Cabibbo-Kobayashi-Maskawa (CKM)
matrix and can be represented in a graphical form as a
triangle in the complex plane, called unitarity triangle
(see Fig.1). The area of this triangle is a measure of the
amount of charge-parity violation caused by the weak
force. To check the consistency of the Standard Model
it is important to determine not only the angles of the
triangle but also the length of its sides. The measurement
of the rate at which bottom quarks decay into up
and charm quarks allows to determine the two elements
of the CKM matrix called V ub and V cb .
The triangle’s right side is instead connected to the
mixing of neutral B mesons, i.e. the process where the
B 0 meson spontaneously turn into a ¯B 0 meson, its antiparticle.
The rate at which this transformation occurs
constrains the length of the right side of the triangle.
The BaBar Rome group has been actively involved
in the analyses aimed at determining both sides of the
triangle using the BaBar detector. In particular, in the
last three years important results have been achieved in
the determination of the V ub and V cb matrix elements.
The semileptonic B meson decays to charm and
charmless mesons (B → Xlν) are the primary tools for
measuring the CKM matrix elements V ub and V cb because
of their simple theoretical description at the quark
level and their relatively large decay rates. The measurement
proceeds as follows. A relatively pure sample
of B ¯B events where one of the two B mesons decays
semileptonically is identified by tagging a lepton and is
reconstructed in a limited range of the phase space. In
some analyses, to reduce the noise from B decays, additional
requirements are applied. For instance, the other
B meson produced in the event is fully reconstructed in
hadronic modes, thus constraining to the kinematics of
the whole event. The partial branching ratio is extracted
and converted in V ub and V cb via theoretical correction
factors. These factors introduce the largest systematic
uncertainty which can range between 5% and 20%, depending
on the analysis.
There are two main analysis methods which are complementary.
The exclusive analysis focuses on the identification
of a given final state, like B → πlν and
B → D ∗ lν [1,2]. This approach is very clean but with the
drawback of much larger theoretical uncertainties due
to the determination of the form factors. The inclusive
analysis, instead, integrates over all possible final state
[3,4]. For example, for the V ub extraction, the X meson
in the B → Xlν decay is required to be compatible with
a charmless state (π, ρ, ω, etc...). The charm contribution
is subtracted using fits to the X mass spectrum, as
shown in Fig.2. This approach is theoretically clean but
it suffers of much larger experimental uncertainties.
The resulting measurements of V ub and V cb constraint
the length of the left side of the triangle with an uncertainty
of ∼ 10%. It is consistent with the expectations,
confirming the success of the Standard Model. More
stringent tests can be expected if there will be a deeper
understanding of theory errors.
Figure 1: Unitarity triangle and CKM matrix elements.
Entries / bin
Entries / bin
3000
2000
1000
300
200
100
0
-100
0 1 2 3 4 5
2
(GeV/c
)
M X
Figure 2: Charmless meson (X) mass spectrum in B → Xlν.
Top: before subtraction of charm contribution (light blue and
black histograms). Bottom: after subtraction.
References
1. B. Aubert et al. Phys. Rev. Lett. 100, 171802 (2008).
2. B. Aubert et al. Phys. Rev. D 77, 032002 (2008).
3. B. Aubert et al. Phys. Rev. Lett. 100, 231803 (2008).
4. B. Aubert et al. Phys. Rev. Lett. 98, 091801 (2007).
Authors
E. Baracchini, F. Bellini, G. Cavoto 1 , D. del Re, E. Di
Marco, R. Faccini, F. Ferrarotto 1 , F. Ferroni, M. Gaspero,
P. D. Jackson 1 , L. Li Gioi, M. A. Mazzoni 1 , S. Morganti 1 ,
G. Piredda 1 , F. Polci, F. Renga, C. Voena 1
http://babar.roma1.infn.it/roma
Sapienza Università di Roma 121 Dipartimento di Fisica