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the basic goal of the ckm experiment  @xcite experiment  @xcite is to determine @xmath3 , contributing to test the standard model hypothesis that a single phase in the ckm matrix is the sole source of @xmath4 violation .
the idea is to over - constrain the predictions with measurements . to really falsify the hypothesis
, one needs a set of observables which can not only be measured sufficiently well , but also need to have controlled errors in the theoretical connection between the observable and the ckm matrix elements .
a short list of these clean measurements to be made in the near future includes : @xmath5 ( the golden mode at the @xmath6-factories ) , the ratio of the mixing parameters of @xmath7 and @xmath8 ( to be measured at the tevatron ) , @xmath9 and @xmath10 .
the standard model prediction for the branching ratio of @xmath9 is  @xcite @xmath11 $ ] , defining an ellipse in the @xmath12 plane .
the calculation  @xcite is done as a ratio to the branching ration of the decay @xmath13 , via weak isospin rotation . with current values
this leads to @xmath14 .
the theoretical uncertainty is estimated to be around @xmath15  @xcite , and dominated by the uncertainty in the charm quark mass .
we therefore aim at observing 100  events of that decay , giving a measurement of @xmath3 of @xmath1 including theoretical errors .
recently the brookhaven experiment  787 observed  @xcite two events of this decay after several years of running ; their branching ratio measurement is high but consistent with the prediction of the standard model .
a continuation of that stopped kaon experiment , e949 , hopes to see 5 - 10  events in the next couple of years .
the ckm ( charged kaons at the main injector ) collaboration the ckm ( charged kaons at the main injector )  @xcite collaboration plans to measure the branching ratio of @xmath9 to a statistical precision of @xmath1 by observing the decay _ in flight_. after a lengthy process  @xcite the experiment obtained stage  1 ( physics ) approval at fermilab in june  2001 .
the experiment plans to run in parallel to the collider run  2 .
protons from the fermilab main injector are used to produce an rf - separated beam , containing @xmath16 @xmath2 per second , with a total flux of @xmath17 .
a layout of the experiment is shown in fig .
[ layout ] .
the largest part of the experiment is a @xmath18 long vacuum decay volume , filled with photon counters to veto against ( under others ) the decay @xmath19 , one of the main backgrounds to suppress .
this system should give a @xmath20 rejection of @xmath21 , requiring an additional kinematic rejection of @xmath22 by redundant spectrometer systems : two conventional magnetic spectrometers and two velocity spectrometers based on rich detectors .
the kinematic rejection uses the fact that the main background modes are two - body decays , and , if calculating the invariant mass the @xmath23 recoils to ( @xmath24 ) , results within resolution a fixed value , whereas the signal mode is a three - body decay , leading to a distribution in @xmath24 .
the spectrometer systems have to measure the magnitude of the momenta of the @xmath2 and @xmath23 , as well as the decay angle between the @xmath2 and @xmath23 .
the velocity spectrometers consist of rich detectors , which will measure the vector velocity ( magnitude via the ring radius , track angles via the position of the ring center ) for the incoming @xmath2 and for the outgoing @xmath23 .
the detectors are modeled after the selex rich  @xcite , following the founding principle of the experiment that only proven detector technologies should be used to avoid surprises while searching for very rare decays .
the results from the selex rich are being used to study resolution effects and to tune the monte carlo simulation .    =    in fig .  [ radmom ]
we show , when operating the rich close to threshold , that one can obtain with a modest accuracy in ring radius an excellent measurement of momentum .
in addition , the curves for kaon and pion are widely separated , so particle identification comes nearly for free . that a rich can be operated in this regime
was shown by the selex rich  @xcite .    the experiment requires momentum and angular resolutions in the order of @xmath25 , which can easily be translated into required ring radius resolutions .
an even more important question is how gaussian is this resolution , e.g.  how will non - gaussian tails in the resolution function affect the overall performance when searching for rare decays .
=    in fig .
[ 06kpmg ] we show the result of a study with selex data , single track events with @xmath26 . to assign hits to a ring
, we used the standard selex algorithm , which uses the information of the tracking system to determine the ring center .
the average number of hits on a ring is @xmath27 , with a poisson distribution .
we fit a sum of gaussians to this distribution , where the width of the gaussians is scaled by @xmath28 ( @xmath29 being the number of hits on a ring ) , and the weight is given by how many events we observed for every given @xmath29 . as can be seen , the resolution function shows a gaussian behavior over more than 4 orders of magnitude .    for ckm we do not want to use information from the tracking system in order to keep the two spectrometer systems really independent and redundant .
we used the same selex sample as above , but this time performing a ring fit assigning _ all _ observed hits to the ring .
we calculated the pull ( deviation from mean divided by error ) for the radius , where we scaled again the error with @xmath28 . the result is shown in fig .  [ fig63 ] .
=    the gaussian behavior found in this study is already sufficient for the experiment .
we are currently working on improving the pattern recognition algorithm .
in addition , the integration in selex was @xmath30 , and in ckm we expect a time resolution in the order of a few  nsec , which should help to reduce the noise contribution .
the pion rich will be a straight copy of the selex rich , with the only exception of doubling the vessel length from @xmath31 to @xmath32 , with a corresponding change in curvature of the mirrors to @xmath33 .
the radiator gas will be neon at atmospheric pressure .
monte carlo simulations showed that we should use @xmath34photomultipliers sensitive down to @xmath35 to obtain a momentum resolution in the @xmath25 range .
the resolution is balanced between the different contributions ( pm size , chromatic dispersion ) , and the @xmath36-@xmath37 separation is @xmath38 .
due to the beam characteristics ( about @xmath39 diameter , very small divergence ) only a small number of phototubes is needed to cover the focal plane of the kaon rich .
due to space restrictions and rate problems , we will double - fold the light path in a @xmath40 long vessel , filled either with n@xmath41 at atmospheric pressure or with cf@xmath42 at about @xmath43 . the spherical mirror ( @xmath33 radius ) and
the second flat mirror will be outside the beam .
the mirror sizes are chosen so that only part of the cherenkov photons for the ( bigger ) pion ring are reflected , but the number of detected photons is still enough , as shown in fig .
[ kaonrich ] .
the rings from kaons and pions are nicely separated , a fact we will use in the experiment trigger . the rates per tube will be as high as @xmath44 . the resolution is limited by chromatic dispersion , and we will use @xmath34photomultipliers with a cutoff around @xmath45 .
we implemented both riches , together with all other detectors , into geant  @xcite .
we ran studies with up to @xmath46 @xmath19 events with full kinematic reconstruction to verify the performance of single detectors and of the experiment as a whole .
detailed results can be found in  @xcite .
a main result is that we have no correlations between the two spectrometer systems ( magnetic , riches ) . with the current design we should be able to reach the goal of the experiment .
the recently approved ckm experiment will measure the branching ratio of @xmath9 with 100  events , to obtain a @xmath47 measurement , including theoretical uncertainties , of the magnitude of @xmath48 .
we will employ two phototube rich detectors , modeled after the selex rich , as velocity spectrometers .
we can stand high rates , have a very low noise rate , good time resolution ( all intrinsic properties of photomultipliers ) , and we expect the non - gaussian tails of the resolution functions to be sufficiently small .
this work was supported in part by consejo nacional de ciencia y tecnologa ( mexico ) , fai - uaslp , and the us department of energy ( contract no .  de - ac02 - 76cho3000 and de - ac02 - 98ch10886 ) .
( contract no .
de - ac02 - 76cho3000 ) .
ckm collaboration : brookhaven national laboratory , fermi national accelerator laboratory , ihep ( protvino ) , inr ( troisk ) , universidad autnoma de san luis potos , university of michigan , university of south alabama , university of texas at austin , university of virgina , university of colorado .
+ welcome.html              ckm collaboration , r.  coleman et al . , _ ckm - charged kaons at the main injector - a proposal for a precision measurement of the decay @xmath49 and other rare @xmath2 processes at fermilab using the main injector_. proposal fermilab - p-0905 , april 1998 .
ckm collaboration , j.  frank et al .
, _ ckm - charged kaons at the main injector - a proposal for a precision measurement of the decay @xmath49 and other rare @xmath2 processes at fermilab using the main injector_. proposal ( 2nd edition ) fermilab - p-0921 , april 2001 .
we present the design of two velocity spectrometers , to be used in the recently approved ckm experiment . 
 ckm s main goal is the measurement of the branching ratio of @xmath0 with a precision of @xmath1 , via decays in flight of the @xmath2 . 
 the design of both rich detectors is based on the selex phototube rich . 
 we will discuss the design and the expected performance , based on studies with selex data and monte carlo simulations . 
 + _ keywords : _ rich detector , phototubes , rare kaon decay , ckm matrix + _ pacs : _ 29.40.ka , 85.60.ha , 13.20.eb , 12.15.hh