The main log approximation to Quantum Chromodynamics is derived, including gluon spin effects. A model for hadron scattering, using the principal log approximation, and a separate model for hadron formation are described.
Introduction
The formation of hadrons from partons must be described by some phenomenological model. The thesis deals with an event generator that uses the QCD cluster model to describe the formation of hadrons.
The Leading Log Approximation to QCD
- Introduction
- Explicit formulae for the density matrices
- Quark helicities
- Use of leading log approximation in Monte Carlo programs
It is shown below that the leading parts of the closed nodes are indeed proportional to the parton masses and that the unphysical gluon helices separate in the leading logarithm approximation. The term in curly brackets is a contraction of two density matrices involving a virtual gluon.
Hadronization Models
Independent fragmentation-the Field Feynman model
The momentum of the gluon is divided between the quark and the antiquark according to some ad hoc distribution; there are currently several in popular use3.4. The FFM can be tuned to agree well with the data6, although some of the parameters appear to be energy dependent.
This means that the quarks created must have some non-zero energy; they have to compensate for the finite length of the string to save energy. Neighboring string breaks must be forced to correlate to leave remnants with meson mass with quark content in the remnant. The result, if each of the partons has enough energy in the frame of the center of mass, is.
These arise from the constraint that the breaks in the string are correlated to produce hadrons of proper mass. Because string breaking is in the continuum of multihadron states, there is no need to impose correlations between string breaks. In this thesis a version of the cluster model is used; this version is discussed in detail in Chapter 4.
The ideas of QCD dynamics incorporated in the model are used to describe cluster formation.
Event Generation in Hadron Hadron Scattering
Introduction and overview
Choosing the initial partons
The transverse momentum of the parton is then chosen according to the Gaussian distribution. Earlier work by Fox4 suggested that the exact nature of the cutoff used is not crucial. Two of the previously generated final partons with spatial momentum are chosen at random.
The momentum of the gluon is shared between the two quarks; the carried fraction is chosen uniformly. The predictions of the model are not sensitive to the distribution used for the momentum sharing, provided it is symmetric between the quark and the antiquark. The color 3 of the gluon is connected to the quark, as shown in the second part of the figure.
None of the observables monitored at NA5 was appreciably dependent on the post-spread evolution threshold.
The evolution to the scale Q 2
Hard scatter and cross section
The second parton and other partons associated with it are reflected through a plane normal to the beam axis and rotated by a random angle about the beam axis. Two finite partons of spatially similar quantity are combined; if the invariant mass of both is high enough to allow dispersion with the required kt. 1-f sf 1 is the fraction of attempts to generate an event in which either one of the partons with spatially similar momentum develops below the limit (Eq. 4.4) or the combination of both partons with spatially similar momentum after development has too low an invariant mass that undergoes a hard scattering.
Thus the factor W 1 W 2f 1 f s is the flux of the appropriate partons, in units of the hadronic flux. The decay chains are calculated according to the principal log approximation, so when we are done we have parton-level events distributed along the cross sections in the approximations discussed above, that is, of order a~ for the strong distribution and the principal log approximation everywhere. other. We assume that hadronization does not affect the cross section; each parton-level event hasronized with weight 1.
At high energies it is reasonable to expect that the hadronization does not have much effect on the cross section since hadronization effects are asymptotically suppressed by forces of the energy scale relative to the leading effect.
Parton evolution after the hard scatter
In e +e- annihilation to hadrons at high energy, the cross section5 is consistent with 'Nith parton level calculations within the experimental uncertainty, so there is also experimental support for this assumption.
Formation of the clusters
When the quark radiates a gluon, which carries the color of the quark, 3 and a 3, the 3 color of the gluon is related to the 3 not shown. If the gluon were to radiate another gluon, the result would be as shown in the third part of the figure; strings that were associated with the radiating gluon are now associated with daughter gluons, one for each daughter gluon. String concatenation is chosen randomly, each option is given equal weight.
The only strings that are not like that are those that connect the partons originally selected to the rest of the hadrons. The flavor of the soft hadron(s) and the remaining quark(s) is chosen by a procedure that depends on the flavor of the initial parton. The four solid lines coming in on the left are the valence quarks and the antiquark of the nonvalence quark.
Because most of the particles are produced by hadronization of the string, the jet remnants fragment like any other jet, consistent with experiment7.
Hadronization
Fox, Invited talk presented at the Europhysics Study Conference on Jet Dynamics in Quark and Lepton Interactions, Erice, Sicily, September Hilger, Invited talk given at the 5th International Conference, "Novel Results in Particle Physics," Vanderbilt Univ., Nashville, Tennessee, Able to.
Comparison of the Model with Experiment
At low energies, such as those studied here, the events not described by the simulation make up almost the entire cross section. These events tend to be those with high amounts of bremsstrahlung, or where either the beam or scattered beams are at the high end of the transverse momentum range. That the simulation agrees with the experimental measurement of the cross section for both 2rr and smaller calorimeters over a range of energies is a strong indication that both jet-like and non-jet-like events appear with the correct cross section in the simulation.
Various observable data regarding the shape of the events were studied at -.IS =24, 30 and 63 GeV. There is much evidence to suggest that the disagreement with the experiment is indeed caused by the treatment of the gluons. The results of this study indicate that in areas sensitive to hard gluons this method of reducing the influence of the soft gluons is insufficient.
Hard gluon events are more sensitive to the treatment of soft gluons, since hard gluons radiate many more gluons than soft gluons or quarks, hard or soft. If this is the case, more data on the structure of high-mass events at UAl will be needed to parameterize the jets at collider energies. F'is· 5.17: Circularity distribution for events depositing E between 8.5 GeV and 11 GeV on one wall of the AFS calorimeter, compared to simulation.
Discussion and conclusions
Areas of phenomenological concern
- The beam remnant
There would be a strong tendency for the string to break in the region of a hard gluon where it is significantly stretched. The jet remnant is governed by low transverse momentum physics; it is not well described by perturbative QCD. In the model described above, the two beams exchange some momentum, and their color is shielded from a rather soft gluon emitted by the active partons on their way to the hard scattering.
One idea that begins to address these issues, since soft gluons do not break the strings, is to treat the beam remnant as part of a baryonic string related to the rest of the event as dictated by evolution. When the string decays, perhaps near some strong radiation, the remnant beam would be left in a substring with softer radiation in a very massive substring, which would then be hasronized. Other times, the beam remnant may be separated from the beam by the first string break.
It may be necessary to force the residual beam and the carrier radiation to merge together, separated from the parts resulting from strong scattering or strong radiation.
Other concerns
- Cutoffs and a spacetime picture
Since in hadron-hadron scattering, hard radiation will most likely occur near the hard scattering (this is where the partons are farthest from the shell) it may be a good idea to treat the hard scattering as a 2-+n process in any order per - turbation theory has been calculated; the leading log approximation will describe the evolution of the partons entering and the partons emitted from the hard scattering. A space-time model would have some theoretical advantages in addition to giving a better picture of the intercepts. The hard partons have moved away from the region where the soft hadrons are formed, but the slowest among them may still be close enough to the region where the soft hadrons are formed, within the intrinsic size of the strings, that the partons and forming hadrons can interact.
The main library contains the main loop (in qcdmain), the routine to enter data, setup, a routine tree which takes the output from the parton shower, forms the initial clusters, and. The routines that a user is likely to want to modify are those in. When a version of the hadronizer with the proposed treatment of the gluons is available, it will be included on the tape.
The first nine entries on each line determine the x-distribution; they are three sets each of the form a1xa2(1-x)a3 added together.
