c Physics at the Energy
Threshold
John Yelton
U. of Florida
CLEO experiment
A review of what we know, and what we do not
know, about the c , with an accent on what new
knowledge can be gained by running with e+e-
annihilations (just) above threshold.
What is a c ?
A c+ is a cud combination in an iso-singlet
configuration. The ground state is the lowest
mass charmed baryon. The higher c+,c0,
c+, c++ states, (10 found so far!) all
cascade down to the c via strong decays,
leaving the c to decay weakly. Thus it is
copiously produced in e+e- annihilation, but
most of the observed c baryons do not
originate from the primary interaction.
c Investigations
The PDG uses 52 papers in its compilation:
22 from e+e- at B factories (CLEO, ARGUS and
BELLE)
19 from electronic fixed target experiments
(FNAL and CERN)
6 from bubble chambers at CERN
4 from Serpukhov
1 from SLAC, e+e- at threshold
c Mass Measurements
The c was discovered in
1974. However, its
mass was not reliably
measured until Abrams
et al (1980), measured
it in an e+e- threshold
experiment. They got
it right!
c Mass Measurements
The c mass still not as accurately measured as mass
differences of charmed baryons. The most precise
measurement was by CLEO I and was systematically
limited by uncertainties in the energy loss of the
protons in particular. At threshold, a beam-
constrained mass can be calculated, minimizing
these uncertainties. Thus, a machine running at
threshold should be able to make the definitive
measurement.
c Decay Lifetime
Running at low energy e+e- is
not the right way to
measure the c lifetime.
This has been well
measured both by fixed
target experiments, and by
CLEO and cannot be
measured at threshold.
c Decay Mechanisms
The short lifetime is well
understood. Charmed
baryons can decay via W-
exchange diagrams, which
are not (unlike for mesons)
helicity suppressed. These
compete with conventional
spectator-type diagrams
Lifetime Hierarchy for Baryons
The lifetime hierarchy for charmed baryons was
predicted in 1986 by Guberina et al. They expected:
(c0) < (c0) < (c+) < (c+)
(based upon relative contributions of W-exchange,
spectator and interference effects).
These are now measured to be:
(6420 < 9819 < 2006 < 44226) x 10-15 s
c pK -+ Branching Fraction
The decay mode pK-+ has long been used as the
normalizing mode for c decays. This is because it is
a) The largest decay mode known
b) It generally has high efficiency
However, it is rather unfortunate that this is the “best”
a) It is theoretically a mess as it decays via many decay
mechanisms, and
b) It is a 3-body decay with resonant substructure, and
therefore its efficiency is difficult to determine.
Absolute Branching Fraction
Without knowing an absolute branching fraction,
we have no means of knowing how many
charmed baryons are being produced in a
reaction.
The absolute branching fraction is a vital
engineering number for studies of B mesons.
It limits the measurement of B branching
fractions (Bc is 6%?)
Absolute Branching Fraction
Also in the B region, parameters such as quark
masses and the QCD renormalization cut-off
scale depend upon the bc fraction.
At the Z0 higher order corrections can be tested
by measuring the number of charm quarks per
hadronic event.
c pK -+ Measurements
Previous methods have included:
a)measuring the increase in proton production as one
crosses c threshold
b) assuming that baryonic B decays all proceed via B c
(known to be incorrect!)
c) using the semi-leptonic b.f. together with a theoretical
model. More recent studies have concentrated on
correlations of charmed particles and protons.
PDG “estimate” is 5.01.3% (in 2000)
Coincidentally, CLEO measured 5.0 1.3% soon after!
BaBar (unpublished) measure 6.12 0.31 0.42%
c pK -+ at Threshold
The high luminosity of B-factories at SLAC and KEK
make it possible to imagine many possible methods
for measuring B(c pK-+) either in continuum or B-
decays. They will be systematically limited.
Uncertainties, particularly concerning c production
and decay, are difficult to overcome.
You can work very hard and still get the answer wrong!
If you run at c+ c- threshold you are free from these
uncertainties.
Threshold Running
It has been shown by MARK II at SPEAR that
running at Ecm just above 2 x 2.285 GeV
produces charmed baryon pairs. If you
reconstruct one c there must be another in
the event. So we reconstruct one c and look
at the other particles.
Threshold Running
How many do we expect?
MARK II found a .B(cpK-+) of
0.0370.012 nb
This implies, for each 1 fb-1 of luminosity,
37000 produced cpK-+ decays.
The efficiency is large! The particles are of a
momentum where they can be easily
identified, and yet most of them are above
p=100 MeV/c. Efficiency may be 50%.
Threshold Running
Some particles have
momenta below 100
MeV/c – low
momentum tracking,
as always, very
important.
Threshold Running
What energy to run at?
We don’t know where will be best cross-section.
Ideally: 4.57 GeV < E < 4.71 GeV
Only a c+c- and no other particles – however is
the cross-section big enough?
Next threshold is c at 4.94 GeV
pD threshold of 5.08 GeV must be avoided.
Threshold Running
Assuming 50% reconstruction efficiency (for
pK), and 1 fb-1 of data, can expect 500 fully
reconstructed, clean events with e+e- c+c-
(where each c pK).
By itself, this should get a statistical uncertainty
in the measurement of 4.5% of itself, and be
enough for easily the best measurement in the
world.
Threshold Running
Can other decay modes used for absolute b.f.?
Obvious ones are pK0s and + . Both require
detection of secondary particles. Need to make
sure that the particle detection system does not
overly rely on hits close to the beampipe.
These are actually better decays to use for
absolute b.f. because they are 2-body.
B Factory Measurement
Huge samples of charmed baryons are available
for study at the “B factories”. These can be
used for spectroscopy and also for
measurements of other exclusive hadronic
channels.
It makes little sense to compete in these fields.
Inclusive Decays
By tagging one c and looking at the rest of the
event, we can measure inclusive decay rates.
c pX, c X, c X, c X etc.
These are all very good “engineering” numbers.
c nX may be possible, using anti-neutron
signature.
Do they add to 100%? Is there something
missing?
Semi-Leptonic Studies
The decay cl- has been measured and
studied, including the rates, form factor
studies, and CP violation. It is particularly
important because it is theoretically simple (the
only pure spectator diagram decay!),
No studies done on semi-leptonic decay with
anything other than a . Almost impossible to
perform an investigation of these decays
except at threshold.
Conclusion
Even a modest run of 1 fb-1 running at E=4.6 GeV
Should yield the definitive studies of
a) The c mass
b) The c absolute branching fractions
c) The c inclusive decay fractions
d) The c semi-leptonic decay rates
This will enable us to understand the c to the
same degree as charmed mesons are
understood today.