Charm Semileptonic Decays

Jim Wiss

Department of Physics

University of Illinois

Urbana, IL,61801, USA

I discuss new data on charm semileptonic decay concentrating on two topics involving the decay . The first topic is the observation of interference in this decay by the FOCUS collaboration[1]. The second are new measurements of branching ratio of relative to from CLEO[2] and FOCUS. Fig. 1 shows the signals of these two groups.

## 1 Interference in

In our attempts to fit for the form factors controlling the decay , we discovered a large, unexpected asymmetry in the distribution shown in Fig. 2. This asymmetry was very strong for events with a mass below the pole and weak for events above the pole.

It was possible to understand the forward-backward asymmetry in using the simple model summarized by Eqn. 1. Using the notation of [3], we write the decay distribution (in the zero charged lepton mass limit) for in terms of the three helicity basis form factors: ) that interferes with the Breit-Wigner () in the one place allowed by angular momentum conservation. . We have taken the standard amplitude and added an interfering s-wave amplitude with a constant modulus and phase (

(1) |

Assuming the s-wave amplitude is small (or the effect would have been
discovered already) it will be primarily observable through three
interference terms:

,
, and
. Only the first of
these terms will survive averaging over the acoplanarity, .
This was the term responsible for creating the asymmetry
shown in Fig. 2 since it is proportional to .
If we further weight our wrong-sign subtracted, azimuthally averaged
data by , this is the only term that will survive
in the full decay amplitude (given our nearly uniform
angular acceptance). It will have a distinct dependence on the
mass: , as well as on
: ().

Figure 3 shows two -weighted, wrong sign subtracted distributions for . The left plot is the asymmetry weighted distribution which should resemble . For , is odd function of - , while for this form is even in - . The data strongly resembles the expected plot for . The right half of Fig. 3 is the asymmetry weighted distribution with masses in the region . It resembles the expected parabola in with some modulation due to acceptance and resolution.

In the absence of the s-wave interference, all acoplanarity dependent
terms in the decay intensity are functions of
and . The s-wave interference includes additional
acoplanarity dependent s-wave terms of the form:

which brings
in a dependence thereby breaking symmetry. Figure 4 shows the
wrong-sign subtracted distribution separately for and
events in the range
Initially we were surprised by the inconsistency between the
and acoplanarity until we realized that there is a sign
change in the convention between the particle and antiparticle.
After applying the correct convention, the and distributions
become consistent, and the odd contributions brought in
through the s-wave interference
become very evident.

Why has the s-wave interference in never been reported before, given that it has been a process studied for nearly twenty years by several experiments? One answer is that an amplitude of this strength and form creates a very minor modulation to the spectrum as shown in Figure 4. Another reason is that this effect is much more evident when one divides the data above and below the pole. Finally, the FOCUS data set has significantly more clean events than previously published data.

## 2 New Measurements of

The CLEO Collaboration has made a new measurement of

FOCUS is in the process of making a new measurement of using a Monte Carlo that includes the s-wave interference described above. Our preliminary number is

To summarize: I presented evidence for an s-wave interference with the dominant contribution to decay. This interference creates a strong () forward-backward asymmetry in the decay angular distribution, but creates very minimal distortion to the mass distribution. The dependence of the asymmetry on the suggests that it has a phase of near the pole and amplitude that is roughly 7% of the Breit-Wigner amplitude at the pole mass in the helicity contribution.

CLEO recently published branching ratio of relative to that was somewhat higher than the previous world average and would help resolve a discrepancy with theoretical predictions. A preliminary number from FOCUS with better precision than previously reported is 1.6 lower than this CLEO number.

We can look forward to new measurements of the form factors, the and their form factors, studies of the dependence of the form factor, and Cabibbo suppressed ratios such as and .

I am grateful to the FOCUS Collaboration and organizers of this excellent conference.

## References

- [1] FOCUS Collaboration (J.M. Link et al.). FERMILAB-PUB-02-054-E, Mar 2002. 14pp. e-Print Archive: hep-ex/0203031
- [2] CLEO Collaboration, Measurement of the Branching Fraction Mar 20, 2002 hep-ex/0203030
- [3] J.G. Korner and G.A. Schuler, Z. Phys. C 46 (1990) 93.
- [4] Particle Data Group, J. Bartels et al., Eur. Phys. J. C15 (2000) 490.