QCD Agenda
                                6/18/99
                                1 PM Pump Room
 
News/announcements
 
1. News/announcements/view from Les Houches
 
Preblessing
 
2.      Some additional MLLA studies of jet fragmentation       Alexei Safonov
 
Update
 
3.      Fitting event shapes in min bias                        Rick Field
 
 
1. News/announcements/view from Les Houches
 
The view from Les Houches was great (Joey and Andrey were connecting from
CERN, with Joey just returning from the workshop at Les Houches). There
will be a more detailed report on the QCD activities at Les Houches in
the near future.
 
Preblessing
 
2.      Some additional MLLA studies of jet fragmentation       Alexei Safonov
 
        Alexei presented a continuation of the jet fragmentation studies that he
and Andrey Korytov have been conducting, focussing on testing perturbative QCD
at its soft limit. The earlier results concentrated on  the dN/dln(1/x_p)
inclusive momentum distributions and average multiplicities.and can be
found in CDF notes 4886 and 4896. In this presentation
(summarized in CDF note 5041) three new sets of inclusive particle distributions
are discussed: dN_ch/dk_T, dN_ch/dln(p) and dN_ch/dx_p, as well as the analysis
of the track multiplicity flow araound the jet axis, dN_ch/dtheta.
 
        The dN_ch/dk_T, dN_ch/dln(p) and dN_ch/dtheta distributions all
accentuate the importance of the soft processes in jet fragmentation,
while dN_ch/dx_p is more relevant for hard gluon bremsstrahlung.
 
        QCD calculations of jet fragmentation can be expanded in terms of
alpha_s^n *ln^2n(E_jet/Q_cutoff) (Order(1) + Order(1/ln(E_jet/Q_cutoff) +
Order(1/ln^2(E_jet/Q_cutoff+...). The leading log approximation keeps track of
the expansion terms with the leading log precision (i.e. ignoring the last term
in the above expansion) while the modified leading logarithm
approximation (MLLA) accounts for the last term as well. MLLA calculations
result in analytical predictions for which the  analytical
predictions can be pushed down to Lambda_QCD. To relate the properties of
partons to observable hadrons, the concept of local parton-hadron
duality is invoked. The basic idea is that hadronization occurs at the
very last moment of the jet fragmentation and has a local nature.
One needs to introduce a normalization parameter that relates the
number of hadrons produced per parton. This approach is amazingly successful,
but has limitations as can be seen from this analysis.
 
        The event selection is described in the previous CDF notes.
Basically, the analysis is done in the center of mass frame of
the two jets for each of 9 dijet mass samples with tracks from one of five
cones around the dijet axis directions:
theta_cone=0.17,0.22, 0.28, 0.36, 0.47. CTC inefficiencies, backgrounds from
the underlying event, etc are all accounted for as described in the previous
notes.
 
        A plot of d^2N/dk_T dtheta indicates that tracks tend to pile up at
Very low kT (with respect to the jet axis) values. Below k_T values of
250 MeV*sin(theta), most of the tracks are being lost due to looping inside
the tracker and no efficiency corrections can be applied to recover for
such losses.
 
        Aside from the low k_T region, Herwig/QFL gives a very good description
of the  k_T distributions. Perturbative QCD by itself (with a k_T cutoff scale
of the order of 1 GeV/c) has little chance to describe jet fragmentation
features. Even if one accepts MLLA with LPHD, one should expect strong smearing
of kT's due to momentum transfers corresponding to the scale of
Lambda_QCD.
 
        The MLLA-motivated inclusive momentum distributions dN_ch/dln(1/x_p)
(where x_p=p/E_jet) were reported in the previous notes.  When plotted as
dN/dln(p), the MLLA predictions reveal an interesting feature: the multiplicity
of soft tracks in a jet is almost jet energy independent (in the limit that
quark and gluon jets have similar track multiplicities). This is a direct
consequence of color interference.  A result of color interference is the
angular ordering of the gluon emissions. Even if all emissions occur at
the minimum  k_T, emissions should occur at continually decreasing
angles, and thus at increasing momenta p. The increases in jet track
multiplicities observed  as a function of jet  E_T are due primarily to
a growth in higher momentum tracks.
 
        The total track multiplicity can be written as:
 
        N_tot(xi)=constant*(N_gluon*frac_gluon(xi) + N_gluon(xi)*
        frac_quark/r)
 
        where N_gluon is the prediction for the multiplicity in a gluon
jet, frac_gluon is  the fraction of jets that are  gluon jets (and likewise for
frac_quark), xi is and r and is the ratio of track multiplicity in a gluon jet
to that in a quark jet.
 
        This expression can be simplified to: N_tot(xi)=K*N_gluon(xi)
 
where K is an energy dependent constant, fit to the data. In the future
the fraction of quark and gluon jets can be input from Herwig and one
might be able to get a handle on the different quark and gluon jet track
multiplicities by using additional processes (like direct photon
production) which has predominantly
 
        From the dijet mass sample of 80 GeV to 630 GeV, the  fraction
of quark jets changes from about  25% to about 75%. If the  ratio of
gluon jet to quark jet track multiplicity is 2.0, then the low momentum
end of the track multiplicity would change as the jet energy changes.
An examination of the dN/dln(p) distribution in the data indicates that
the low momentum region of the spectrum (p<1) is almost energy
independent. From the distributions, it is clear that  the  quark jets
must have lower multiplicity in comparison to the gluon jets and the
choice of r must  be somewhere  between 1.4 and 2.0.
 
        A comparison of the differential dN/dtheta distribution of
tracks in a jet between data and MLLA theory indicates signficant
disagreement at low theta, even when one accounts for the errors in
the determination of the jet direction. One possibility is that QFL does not
accurately reproduce the jet directions but Herwig/QFL agrees well
with the data. Another physical reason that might be responsible for
the additional angular smearing of tracks is hadronization. The low
momentum kT transfers between partons at the stage of
hadronization are quite possible. With the most probable track energy
at a few GeV, momentum transfers of the order of Lambda_QCD are
likely and would disperse tracks with respect to the original parton
direction by  the order of 250 MeV/3 GeV or approx 0.1 rad.
 
        A comparison of dN/dx distributions in data and Herwig gives
very good agreement, again once the normalization factor of 0.89 is
taken into account.
 
Update
 
3.      Fitting event shapes in min bias                        Rick Field
 
        Rick's idea is to study the CDF minbias data with the goal of
finding a Monte Carlo generator that will fit the data. He would like
to describe (approximately) all features of the entire inelastic cross
section, at both low and high pT. Many observables in the data are
compared to MBR, Herwig, Isajet, and four versions of Pythia, including
one that was adjusted to fit the underlying event in bbar production,
a la CDF note 4097. Rick's transparencies can be viewed at:
http://www.phys.ufl.edu/~rfield/cdf/QCD_talks3.html. There are many
transparencies here, far more than were shown at the meeting.
 
        For now, only charged particles with pT values greater than
0.5 GeV/c and with abs(eta)<1 are considered. Event shapes and
charged particle distributions with respect to the leading jet
direction (where the jet is defined as a circular region in
eta-phi space) are considered.
 
        The jet algorithm that Rick uses is fairly simplistic. Jets are
defined as a circular region in eta-phi space of radius 0.7 centered on
the highest pT charged particle not already included in a jet. There can
be many jets in the central region, including the possibility of jet
overlaps. There is no merging algorithm used for the case of overlaps.
The momentum of the jet is defined as the sum of all of the charged
particles inside the cone.
 
        Rick showed some plots of the number of charged particles inside a jet
as a function of the pT of the (lead) jet, from jet pT values from 0.5 GeV/c up
to 50 GeV/c. The min bias data is used up to 20 GeV/c or so with the Jet20 data
being used at higher pT values. The average particle multiplicity rises with
increasing jet pT with there being a "knee" at around 8 GeV/c and a  more
modest rise after that point. Comparisons were made with various version of
Pythia, Isajet, Herwig and MBR. Herwig and the standard Pythia seem to do a
reasonable job of describing the data; Pythia 4097 (named after the CDF note
predicts far too large of a particle multiplicity in the jet).
 
        Rick defined three regions in phi: toward the jet (within 60 degrees),
 away from the jet (120-240 degrees away from the jet) and transverse
(everything else).
He showed plots of the average charged particle multiplicity for the
three different regions as a function of the jet pT. As might have been
expected, the toward region has the greatest multiplicity, the away second
greatest and the transverse, the least. Again, the comparisons look reasonable
with respect to the standard Herwig and Pythia.
 
        Rick promises a note within the next few weeks.