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measuring purely leptonic decays of heavy mesons allows the determination of meson decay constants , which connect measured quantities , such as the @xmath5 mixing ratio , to ckm matrix elements .
currently , it is not possible to determine @xmath6 experimentally from leptonic @xmath7 decays , so theoretical calculations of @xmath6 must be used .
the most promising of these calculations involves lattice qcd @xcite , though there are other methods @xcite .
measurements of pseudoscalar decay constants such as @xmath8 provide checks on these calculations and help discriminate among different models .
= 3.0 in    the decay diagram for @xmath9 is shown in fig .
[ dptomunu ] .
the decay rate is given by @xcite @xmath10 where @xmath11 is the @xmath12 mass , @xmath13 is the mass of the final state lepton , @xmath14 is a ckm matrix element equal to 0.224 @xcite , and @xmath15 is the fermi coupling constant . various theoretical predictions of @xmath8 range from 190 mev to 350 mev @xcite . because of helicity suppression , the electron mode @xmath16 has a very small rate in the standard model @xcite . the relative widths are @xmath17 for the @xmath18 , @xmath19 and @xmath20 final states , respectively .
unfortunately the mode with the largest branching fraction , @xmath21 , has at least two neutrinos in the final state and is difficult to detect .
the cleo - c detector is equipped to measure the momenta and direction of charged particles , identify charged hadrons , detect photons , and determine with good precision their directions and energies .
muons above 1.1 gev can also be identified .
the detector is almost cylindrically symmetric with everything but the muon detector inside a superconducting magnet coil run at a current that produces an almost uniform 1.0 t field .
the detector consists of a six - layer wire drift chamber at small radius that is low mass , suitable for these relatively low energies .
it is followed by a 47-layer drift chamber ; both chambers use a gas mixture of 60% helium and 40% propane .
these two devices measure charged track three - momenta with excellent accuracy .
the drift chamber also measures energy loss , de / dx , that is used to identify charged tracks below about 0.7 gev @xcite .
after the drift chamber there is a ring imaging cherenkov detector ( rich ) @xcite , that identifies charged particles over most of their momentum range .
the rich is surrounded by a thallium doped csi crystal array consisting of about 8000 tapered crystals , 30 cm long and about 5x5 @xmath22 at the front @xcite .
in this study we use 60 pb@xmath0 of cleo - c data produced in @xmath23 collisions and recorded at the @xmath24 resonance ( 3.770 gev ) . at this energy ,
the events consist of a mixture of pure @xmath25 , @xmath26 and three - flavor continuum events , resulting from the production of @xmath27 , @xmath28 or @xmath29 quark pairs .
there also may be small amounts of @xmath30 pairs and two - photon events .
we examine all the recorded events and retain those containing at least one charged @xmath31 candidate in the modes listed in table  [ tab : drecon ] .
the selection criteria are described in detail in what follows .
we then use this sample to look for cases where we have only a single muon candidate whose four - momentum is consistent with a two - body @xmath31 decay into a muon and a neutrino and no other charged tracks or excess neutral energy are present .
all acceptable track candidates must have a helical trajectory that approaches the event origin within a distance of 5 mm in the azimuthal projection and 5 cm in the polar view , where the azimuthal projection is in the bend view of the solenoidal magnet .
each track must possess at least 50% of the hits expected to be on a track , and it must be within the fiducial volume of the drift chambers , @xmath32 , where @xmath33 is the polar angle with respect to the beam direction .
we use both charged particle ionization loss in the drift chamber ( de / dx ) and rich information to identify kaons and pions used to fully reconstruct @xmath31 mesons .
the rich is used for momenta larger than 0.55 gev .
information on the angle of detected cherenkov photons is translated into a likelihood of a given photon being due to a particular particle .
contributions from all photons associated with a particular track are then summed to form an overall likelihood denoted as @xmath34 for each particle hypothesis . to differentiate between pion and kaon candidates , we use the difference : @xmath35 ) .
usually this cut is set at zero except for muon candidates where the difference @xmath36 ) is required to be less than 10 , to ensure a high , well understood efficiency . to utilize the de / dx information
we calculate @xmath37 as the difference between the expected ionization loss for a pion and the measured loss divided by the measurement error .
similarly , @xmath38 is defined in the same manner using the expected ionization for a kaon .
we use both the rich and de / dx information for @xmath39 meson tag candidate tracks in the following manner : ( a ) if neither the rich nor de / dx information is available , then the track is accepted as both a pion and a kaon candidate .
( b ) if de / dx is available and rich is not then we insist that pion candidates have @xmath40 , and kaon candidates have @xmath41 ( c ) if rich information is available and de / dx is not available , then we require that @xmath42 for pions and @xmath43 for kaons .
( d ) if both de / dx and rich information are available , we require that @xmath44 for pions and @xmath45 for kaons .
we reconstruct @xmath46 s by first selecting photon candidates from energy deposits in the crystals not matched to charged tracks that have deposition patterns consistent with that expected for electromagnetic showers .
pairs of photon candidates are kinematically fit to the known @xmath46 mass .
we require the pull , the difference between the raw and fit mass normalized by its uncertainty , to be less than three for acceptable @xmath46 candidates .
@xmath47 candidates are formed from a pair of charged pions which are constrained to come from a single vertex .
we also require that the invariant mass of the two pions be within 4.5 times the width of the @xmath47 mass peak , which has an r.m.s .
width of 4 mev .
tagging modes are fully reconstructed by first evaluating the difference in the energy , @xmath49 , of the decay products with the beam energy .
we then require the absolute value of this difference to be within 20 mev of zero , approximately twice the r.m.s .
width , and then look at the reconstructed @xmath39 beam - constrained mass defined as @xmath50 where @xmath51 runs over all the final state particles .
the beam - constrained mass has better resolution then merely calculating the invariant mass of the decay products since the beam has a small energy spread . besides using @xmath39 tags and searching for @xmath52
, we also use the charge - conjugate @xmath12 tags and search for @xmath53 ; in the rest of this paper we will not mention the charge - conjugate modes explicitly , but they are always used .
the @xmath54 distributions for all @xmath39 tagging modes considered in this data sample are shown in fig .
[ drecon ] and listed in table  [ tab : drecon ] along with the numbers of signal events and background events within @xmath553 r.m.s .
widths of the peak .
the event numbers are determined from fits of the @xmath54 distributions to gaussian signal functions plus a background shape .
we fit with two different background parametrizations : ( a ) a @xmath56 order polynomial , ( b ) a shape function analogous to one first used by the argus collaboration @xcite which has approximately the correct threshold behavior at large @xmath54 ; to use this function , we first fit it to the data selected by using @xmath49 sidebands , mode by mode , defined as 40 mev @xmath57 60 mev to fix the shape parameters in each mode allowing the normalization to float . for the @xmath58 , @xmath59 and @xmath60 modes we use a single gaussian to describe the signal
whose mass and width are allowed to float .
for the @xmath61 and @xmath62 modes , where we see a small tail on the higher mass side , we use the sum of two gaussian s for a signal function @xcite ; in this case both the means and widths of both gaussians are allowed to float .
.tagging modes and numbers of signal and background events determined from the fits shown in fig .
[ drecon ] . [ cols="<,^,^",options="header " , ]     the models generally predict @xmath63 to be 10 - 15% larger than @xmath8 .
cleo previously measured @xmath63 as ( @xmath64 mev @xcite , and we are consistent with these predictions as well .
we look forward to more data to improve the precision .
we gratefully acknowledge the effort of the cesr staff in providing us with excellent luminosity and running conditions .
this work was supported by the national science foundation and the u.s .
department of energy .
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the function is @xmath70 ^ 2\right)}$ ] . here
@xmath71 is the overall normalization and @xmath7 , @xmath72 and @xmath31 are parameters that govern the shape .
see h. albrecht _
et al . _  ( argus ) , phys .
b * 229 * , 304(1989 ) .
in 60 pb@xmath0 of data taken on the @xmath1 resonance with the cleo - c detector , we find 8 @xmath2 decay candidates that are mostly signal , containing only 1 estimated background . 
 using this statistically compelling sample , we measure a value of @xmath3 , and determine @xmath4 mev .