# Determination of Charm Hadronic Branching Fractions at CLEO-c

###### Abstract

Recent results from CLEO-c on measurements of absolute hadronic branching fractions of , , and mesons are presented.

## I Introduction

Precise measurements of absolute hadronic branching fractions for , , and meson decays are important as they serve to normalize most and decays as well as many charm decays.

Results from the CLEO-c experiment at the Cornell Electron Positron Storage Ring based on 281 pb recorded at the are presented here for studies of and decays. In addition, CLEO-c has analyzed 298 pb of annihilation data near MeV for studies of decays. These samples provide very clean environments for studying decays of and mesons. The , produced in the annihilation, decays to pairs of mesons, either or . In particular, the produced mesons can not be accompanied by any additional pions. At MeV mesons are primarily produced as and pairs.

First, I will discuss the determination of the absolute hadronic , , and branching fractions. Then I will present CLEO-c measurements of inclusive , , and decays; the doubly Cabibbo suppressed decay ; studies of and ; decays to two pseudoscalars; and two-body and decays to pairs of kaons.

## Ii Absolute and hadronic branching fractions

This analysis dhadprd () makes use of a ’double tag’ technique initially used by Mark III markiii (). In this technique the yields of single tags, where one meson is reconstructed, and double tags, where both mesons are reconstructed, are determined. The number of reconstructed single tags, separately for and decays, are given by and , respectively, where and are the efficiency and branching fraction for mode . Similarly, the number of double tags reconstructed are given by where and label the and mode used to reconstruct the event and is the efficiency for reconstructing the final state. Combining the equations above and solving for gives the number of produced events as

and the branching fractions

In this analysis we determine all the single tag and double tag yields in data, determine the efficiencies from Monte Carlo simulations of the detector response, and extract the branching fractions and yields from a combined fit brfrfitter () to all measured data yields.

This analysis uses three decay modes
(, , and )
and six decay modes
(, , , ,
, and ).
The single tag yields are shown in Fig. 1.
The combined double tag
yields are shown in Fig. 2
for charged and neutral modes separately.
The scale of the statistical errors on the branching fractions
are set by the number of double tags and
precisions of
and are obtained for the neutral and charged modes
respectively.
The branching fractions obtained are summarized in Table 1
^{1}^{1}1The result presented here represents the final results and are
slightly different from the results presented at the workshop..
For the branching fractions we quote three uncertainties. The first is the statistical
uncertainty, the second is the systematic uncertainties excluding the uncertainty
in the modeling of final state radiation (FSR), and the third error is the FSR
uncertainty. For the mode the effect of the FSR is a 3.0% correction.
We have taken the uncertainty of the FSR correction to be about 30% of the
correction. This covers the difference between including or excluding the effect
of interference in simulating FSR in the decay .

Parameter | Fitted Value | Fractional Error | ||
---|---|---|---|---|

Stat.(%) | Syst.(%) | (%) | ||

## Iii Absolute branching fractions for hadronic decays

This analysis uses a sample of 298 pb of data recorded at a center-of-mas energy of 4170 MeV. At this energy mesons are produced, predominantly, as or pairs. We use the same tagging technique as for the hadronic branching fractions; we reconstruct samples of single tags and double tags and use this to extract the branching fractions.

In this study eight final states are used (, , , , , , , and ). The single tag event yields are shown in Fig. 3. The double tag yields are extracted by a cut-and-count procedure in the plot of the invariant mass of the vs. . This plot is shown in Fig. 4. Backgrounds are subtracted from the sidebands indicated in the plot and a total of double tag events are found.

Mode | Branching Fraction (%) | PDG 2006 fit (%) |
---|---|---|

From these yields we determine the preliminary branching fractions listed in Table 2. We do not quote branching fractions for as the signal is not well defined. In particular, the resonance interferes with the resonance. Instead we report preliminary results for partial branching fractions for in restricted invariant mass ranges of near the resonance. These partial branching fractions are summarized in Table 3.

range | Partial branching fraction() |
---|---|

MeV | |

MeV | |

MeV | |

MeV |

## Iv Inclusive measurements of , , and production in and decays

Using samples of tagged and decays CLEO-c has measured the inclusive production of , , and mesons by looking at the recoil against the tag cleoc_inclusive (). The results are summarized in Table 4. The knowledge of inclusive measurements before this CLEO-c measurement was poor, besides limits, only was measured. As expected the , , and rates are much higher in decays.

Decay | (%) |
---|---|

## V The doubly Cabibbo suppressed decay

CLEO-c cleoc_dcsd () has reconstructed candidates in the 281 pb sample of data recorded at the . We find the branching fraction , which is in good agreement with the recent BABAR measurement babar_dcsd () .

## Vi Modes with or in the final states

It has commonly been assumed that . However, as pointed out by Bigi and Yamamoto bigi () this is not generally true as for many decays there are contributions from Cabibbo favored and Cabibbo suppressed decays that interfere and contributes differently to final states with and . As an example consider . Contributions to these final states involve the Cabibbo favored decay as well as the Cabibbo suppressed decay . However, we don’t observe the and the but rather the and the . As these two amplitudes interfere constructively to form the final state we will see a rate asymmetry. Based on factorization Bigi and Yamamoto predicted

Using tagged mesons CLEO-c has measured cleoc_klks () this asymmetry and obtained

which is in good agreement with the prediction.

Similarly, CLEO-c has also measured the corresponding asymmetry in charged mesons and obtained

Prediction of the asymmetry in charged decays is more involved. D.-N. Gao gao () predicts this asymmetry to be in the range 0.035 to 0.044, which is consistent with the observed asymmetry.

## Vii decays to two pseudoscalars

CLEO-c has performed a study of decays to a pair of pseudoscalars. These final states consists of either a or a and one of , , , or . In the analysis presented here the following final states are studied: , , , and . The final state violates isospin and is expected to be small. The details of the analysis can be found in Ref. dstoPP (). The signals are observed in the invariant mass distribution as peaks at the mass. Significant signals are observed in all modes except . The observed mass distributions are shown in Fig. 5. We measure the ratio of the branching fractions of the Cabibbo suppressed modes with respect to the Cabibbo favored modes. The results are summarized in Table 5. The observed ratios of branching fractions are consistent with the naive expectation of . In addition, we have looked for a asymmetry in rate for and decays. No evidence for any asymmetry was found; the results are summarized in Table 6.

Mode | (%) |
---|---|

Mode | (%) |
---|---|

## Viii and decays to two kaons

CLEO-c has studied Cabibbo suppressed two-body decays of and mesons to a pair of kaons. In particular, the decays , , and have been analyzed. In addition to being Cabibbo suppressed, the mode is strongly suppressed due to destructive interference in the SU(3) limit between the two dominating exchange amplitudes for this decay. Figure 6 shows the observed yields in the three channels studied in this analysis.

The preliminary branching fractions are summarized in Table 7. For and there is good agreement with previous measurements. However, for our new measurement is lower than previous measurements.

Our Measurement () | PDG 2007 () | |
---|---|---|

## Ix Summary

I have presented results based on 281 pb of annihilation data recorded at the resonance for studies of and decays. Among the results presented here were the final results for the absolute and branching fractions. CLEO-c has also analyzed 298 pb of annihilation data recorded at the center-of-mass energy of 4170 MeV. Here we have studied the absolute hadronic branching fractions of mesons. CLEO-c has recorded more than 800 pb of data at the and are planing to double the data sample recorded at MeV, so there are still many interesting results to come from the CLEO-c data sample.

## Acknowledgments

This work was supported by the National Science Foundation grant PHY-0202078 and by the Alfred P. Sloan foundation.

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