Plain English Summary of
"Observation and Properties of L=1 B₁ and B₂* Mesons"

Since b-mesons are not elementary, but composite systems, they possess many different energy-levels, analogous to the energy levels of atomic material (such as the famous hydrogen energy-levels). These energy levels arise because of the internal structure of the meson, whereby the constituent quarks can interact in different ways, to increase or decrease the energy of the system. Each quark possesses a 'spin' (s₁, s₂), a vector quantity which can point either 'up' or 'down' with respect to the other. In addition, there is an orbital angular momentum (L) between the quarks. Depending on these quantum numbers (s₁, s₂, L), the meson will take on different energies.

In this analysis, we investigate certain energy levels of the B_d meson (usually shortened to 'B meson'). This particle contains a b-quark, and either a d- (down) or a u- (up) quark. In particle physics, we label mesons in different energy levels as different states, even if they have the same quark composition. The energy levels of the B meson thus form a series of states: a ground state and a number of excited states. This is illustrated in Fig.1.

Figure 1: Energy-level diagram of the B meson.

Because the b-quark is much heavier than the u- or d- quarks, the B meson can be well described by Heavy Quark Effective Theory (HQET). In this theory, the meson is treated much in the same way as the hydrogen atom, with the light-quark (c.f. electron) in 'orbit' around the much heavier b-quark (c.f. nuclus). This figure shows only those states up to an orbital angular momentum L=1. The ground state B+, and singly excited B+*, forming the L=0 doublet, are well-established by experiment. The L=1 states, on the other hand, have not been fully studied. These energy-levels are split into two broad states (B_0*, B_1*) and two narrow states (B_1, B_2*). Here, the terms 'narrow' and 'broad' refer to the width of the states in their invariant mass distribution. A narrow state forms a mass 'peak' clearly distinguishable from the background. In this analysis we make the first observation of the two narrow states B_1 and B_2*, measuring their masses, decay branching ratios (i.e. the fraction of times they decay into different products), and their production rate, relative to the fiducial B+ meson. Such properties are predicted with good precision by various theoretical models. Comparing experimental results with theory provides important information on the quark interaction inside bound states, aiding further development of non-perturbative QCD. Note that the quantities jq and JP are combinations of the quantum numbers s1, s2 and L, as described earlier.

We reconstruct B_1 and B_2* candidates by looking for their decays into B⁺(*)π^-. The possible transitions to these L=0 states are shown in Fig.1, and are summarised below. The B_1 can decay only via the singly-excited B+*, which then decays to B+ by the release of a photon γ of energy 45.78 MeV. The B_2* can decay to B+* in this way, but it can also decay directly to the ground state B+. The B_1 is forbidden from this direct decay by conservation laws. Hence the two physical states yield three decays:

1. B₁ → B⁺*π^-;     B⁺* → B⁺γ
2. B₂* → B⁺*π^-;     B⁺* → B⁺γ
3. B₂* → B⁺π^-;

Figure 2: Distribution of the Mass Difference ΔM = M(B⁺π^-) - M(B⁺)

Here the distribution is shown along with the fitting function. This function comprises three peaks, for the three decays, plus a background contribution to account for the incorrectly identified events. The three decay peaks are shown, and labelled, separately. Using such a fitting function allows us to extract from the ΔM distribution important quantities, such as the masses of the B_1 and B_2* states (found from the peak positions), the branching ratios into each decay type (found from the relative peak heights) and the total number of events (found from the absolute peak heights, with background subtracted).

In addition, from the observed number of B_1 and B_2* (collectively termed B_J), and B⁺ candidates, a measurement can be made of the production rate of B_J relative to B+ mesons. This requires the efficiency of detecting the additional pion to be determined. To find the efficiency, we use a large sample of simulated events, using an advanced physics modelling package (pythia), interfaced with a detector simulation. This allows us to investigate what fraction of actual B_J and B+ particles are correctly reconstructed from their decay products, and hence the efficiencies of detection are determined.

This result was submitted for publication in Physical Review Letters in May 2007. For the full text, with results, please see:

http://www.arxiv.org/abs/0705.3229

Please direct any questions to Mark Williams (markw@fnal.gov) or Guennadi Borrisov (bgv@fnal.gov).