Measuring L = 1 D mesons at BaBar
Tom Plagge
Iowa State University REU Program
July 31, 2000
Abstract
I investigated the L = 1 mesons D2 (2460)0 and D1 (2420)0 using
data gathered by the BaBar detector at Pep-II. The decay process
of these particles is interesting because it could serve to conrm or
deny certain predictions made by HQET models. Thus far, the data
gathered rougly conforms with measurements made by the CLEO and
ARGUS collaborations. The data is still preliminary, however, and as
such this paper should be considered merely a summary of the work
done thus far.
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1 Introduction
1.1 The BaBar experiment
The BaBar detector at Pep-II was designed to study B mesons produced in asymmetric e+ e, collisions. \Asymmetric" refers to the fact
that the colliding electrons and positrons have dierent energies. This
gives the resulting particles momentum in the laboratory reference
frame, allowing their lifetimes to be measured even if they carry away
most of the collision energy. In the current run at Pep-II, electrons
are stored in one ring at 9 GeV and positrons in the other at 3.1 GeV.
This sets the collision energy right at the (4S ) resonance, a shortlived combination of a bottom quark and its antiquark. This decays
preferentially into a pair of mesons B and B |hence the name of the
detector.
Mesons are short-lived systems made up of a quark and an antiquark; B s are mesons in which one quark is a bottom (or an antibottom) and the other is a light quark (up, down, strange, or their
corresponding antiquarks). The BaBar detector is optimized to measure the decay process of these B 's as precisely as possible. It is hoped
that dierences between the B and the B decay processes will be uncovered and measured, which will lead to a better understanding of
CP symmetry violation.
\CP violation" describes an event that breaks the so-called Charge{
Parity symmetry. For a time, it was believed that if matter and antimatter were interchanged (hence, Charge) and if right and left were
reversed (Parity), systems would behave in an identical manner. This
symmetry has since been found to be broken in certain kaon decays,
and it is suspected that further violations will be discovered in B decays. Note that if time is reversed as well as charge and parity, then
the system will behave in an indentical manner; this is known as CPT
symmetry, and is required for Lorentz transformations. It is hoped
that learning more about events that violate the \broken" CP symmetry will shed some light on the relative scarcity of antimatter in the
universe.
But CP violating events are not the only interesting phenomena
observed at BaBar. The e+ e, interaction produces a cc pair with
almost the same probability as bb, which means precise measurements
of these \charmed" systems can also be made. There is a lot of physics
associated with these particles; we focused specically on two rare
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states of the D meson, which consists of a c and a lighter u, d, or s1 .
1.2 L = 1 states of D mesons
The strong nuclear force is fairly well understood in the context of the
Standard Model{the quantum eld theory associated with it, known as
quantum chromodynamics (QCD), is almost as well established as the
quantum electroweak eld theory (QED) upon which it is based. QCD
is especially eective in situations where one quark carries most of the
mass of the system. In this situation perturbation theory applies, and
leads to models such as Heavy Quark Eective Theory (HQET).
This model works by treating the mass of the heavy quark|the
b in a B meson|as having essentially an innite mass and then correcting for the dierence. The meson is thus treated in a manner
analogous to a hydrogen atom, with the light quark bound to the
heavy one much like an electron is bound to a nucleus. This gives rise
to some interesting meson states where the light quark is excited|
that is, where it has angular momentum L with respect to the heavy
quark. The model works well in B mesons, but since the innite mass
approximation is less accurate when applied to a c than to a b, larger
corrections must be made to D mesons systems. Measuring the L = 1
states of D mesons and determining their decays more precisely would
allow us to test predictions made by HQET models and to determine
whether these corrections are appropriate.
There are four L = 1 D states [1]: D0 , D2 , and two varieties of
D1 2 . These states are collectively known as DJ . Of the DJ s, the
D2 (2460)0 and the D1 (2420)0 are easiest to handle because of their
relatively narrow mass ranges. There are diculties that arise from
the similarity of the two masses, but these problems are considerably
easier to deal with than those associated with the other D1 and the
D0 states, both of which are expected to have unmanageably large
widths. My analysis focuses on identifying D2 (2460)0 and D1 (2420)0
events and using the data to make a precise t to the D1 and D2 mass.
For the rest of this paper, it can be assumed that a statement such as this applies also
to the corresponding antiparticle.
2 The subscripts refer to the mesons' spin-parities.
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2 Data
2.1 Event selection
We began by reconstructing events in which the DJ decays to a D
and a pion. The D quickly decays into a D0 and another pion, and
the D0 goes to a kaon and 1, 2, or 3 pions. Greater precision was
achieved by, rather than plotting the DJ mass itself, reconstructing
the D (2007)0 rst and then plotting the mass dierence between the
DJ and the D .
Background events were kept to a minimum with a number of
cuts. The momentum of the DJ was required to use up greater than
65 percent of the beam energy remaining after DJ production. This
eliminated events in which the DJ was produced from a (4S ) and
was thus less energetic and more dicult to measure. The cosine of
the angle between the DJ and the pion it emits, , was required to be
greater than -0.8 in the DJ reference frame|reasonable because the
asymmetry of Pep-II should boost the decay products forward. Pions
moving the wrong way are likely to be of continuum origin. The cosine
of the angle between the D0 and the kaon, K , was required to be less
than 0.8 in the D reference frame because of a very large background
peak near 1. The probability of the kaon decay was also determined,
and was required to be greater than 0.05 in order to purify the sample.
The data could then be further cut by enforcing certain requirements on the helicity angle , dened as the angle between the pion
decay in DJ0 ! D+ , and the pion decay in D+ ! D0 + [2]. Requiring cos 0:8 supresses the D2 state and reduces the background.
This allows for a more accurate measurement of the prominent D1
state.
2.2 Mass t
The expected mass signal calculated using Monte Carlo simulation
data is shown in Figure 1. As previously noted, the graph shows the
mass dierence between D and DJ . The signal is in the shape of
two superimposed Breit-Wigner distributions. Notice also that the
D2 signal is signicantly smaller and slightly wider than the D1 .
Figure 2 shows some actual data for the decay process that ends
up with K , + , + . The t used was again two Breit-Wigner distributions, this time superimposed on a polynomial background t.
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This plot illustrates the problems associated with the measurements,
particularly the D2 . We are currently revising our event selection to
cut events based on other variables such as the shape of the event.
However, the D1 (2420) mass can be clearly discerned from this and
other plots.
3 Conclusions
Obviously, this analysis is far from complete. BaBar is still taking
data, and we are continuing to improve our event selection algorithms.
As Table I shows, our current estimates are very close to data collected
by CLEO II[2], ARGUS[3], and E687[4]. However, because of the large
number of events available at BaBar, our nal numbers will probably
have a signicantly higher level of accuracy.
Acknowledgments
Producing the data that I analyzed involved a lot of work, most of
which was done by Dr. Pierre-Alexandre Fischer at SLAC. I was
advised in Ames by Dr. James Cochran.
Note
Statistical uncertainties are not included in our data because the computer on which it is stored is currently unavailable due to a power
outage.
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References
[1] Particle Data Group, K. Hikasa et al., Phys. Rev. D 45 (1992).
[2] CLEO Collab., P. Avery et al., \Production and Decay of
D1 (2420)0 and D2 (2460)0 ", hep-ph/9403359.
[3] ARGUS Collab., H. Albrecht et al., Phys. Lett. B 232, 398
(1989).
[4] E687 Collab., P. L. Frabetti et al., Phys. Rev. Lett. 72, 324
(1994).
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Table 1: D1(2420) Mass and Width Measurements
Experiment Mass (M eV =c2 ) Width (M eV =c2)
BaBar
2412
15
+1+2
CLEO II
2421,2,2
20+6+3
,5,3
ARGUS
2414 2 5
13+6+10
,6,5
E687
2422 2 2
15 8 4
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Figures
FIG. 1. Mass signal predicted by Monte Carlo simulation
FIG. 2. Actual t of mass dierence
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