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