A Partial Wave Analysis of Proton Antiproton Annihilation

A Partial Wave Analysis of Proton. Antiproton Annihilation Above Threshold For Two Phi Meson Production in the JETSET Experiment Jim Marie Advisor: Richard Jones University of Connecticut

JETSET Experiment The channel was investigated with high statistics using a hydrogen-cluster jet target. The incident 2. 0 Ge. V/c. momentum ranged from 1. 1 to This is just above threshold ( Ge. V/c).

Physics Motivation Investigate gluonic resonances. The reaction is OZI suppressed: glueball? These resonances may form in the s channel.

Yang-Mills Glueball Spectrum from Lattice QCD C. Morningstar and M. Peardon, Phys. Rev. D 60, 034509 (1999)

Partial Wave Analysis Original spin parity analysis yielded a 3 wave solution consisting of only 2++ waves. Changes in the relative phases and a peak in the total cross section pointed toward a Breit-Wigner resonance. A subsequent analysis with 6 waves resulted in a better fit with 2++ waves still dominant, however 4++ waves gained significance. The question remained of the sensitivity of these results to the way the background was treated.

Role of the Background Could interference between the resonant channel and background be present? The 2 K mass distribution showed an enhancement near threshold underneath the f. This enhancement may be due to the presence of the scaler channel which has a tail above threshold for 4 K.

PWA for ff + f 0 f 0 A new PWA has been carried out including coherent interference between the ff channel and the scaler background. The quantum amplitude becomes used in the PWA

phi Partial Waves For , all waves up to J=4 and L=4 in the final state are included: Wave Label Linitial Sinitial Jpc Lfinal Sfinal 1 0 0 1 1 2 0 0 1 1 3 0 0 1 1 4 1 1 . . . 5 1 . . . 23 . . 4 . . . 2

f 0 Partial Waves For the background channel , waves up to J=4 and L=4 in the final state are included: Wave Label Linitial Sinitial Jpc Lfinal Sfinal 24 1 1 0 0 25 1 1 2 0 26 3 1 2 0 27 3 1 4 0 28 5 1 4 0

PWA Method Data is divided into 12 sets according to momenta. A log-likelihood is calculated and maximized with respect to the real and imaginary components of the wave amplitudes for each momentum bin.

Essential Ambiguities Partial waves divide into even and odd parity sets each having a global phase (continuous invariance). Four discrete sign transformations leave the differential cross section invariant:

Statistical Ambiguities Topology of the parameter space gives rise to different local maxima in the likelihood. These discrete ambiguities are revealed by a systematic numerical search. The acceptance and statistics in this data set are sufficient to eliminate all distinct solutions which correspond to secondary minima.

Starting Point Perform fits with all waves free plus phase space (background). This provides a baseline for measuring the “goodness of the fit”. Amplitude errors are large and undefined. Search for a minimal wave set that provides an adequate description of all the data. The same set of waves are required at each momentum point. All possible 3 wave combinations (3276 combinations) for were fitted.

Results All three wave combinations plus background were fitted over all momentum points and the best combination that describes the data is Waves: 5, 19, 20 A 4++ component gains some significance however, the 2++ component is still dominant as seen in the partial wave cross sections.

Partial Wave Cross Sections For Waves 5, 19, 20 Ge. V/c 2+ wave is dominant Ge. V/c

Relative Phases radians Reference wave 5 Ge. V/c

Total Cross Section Ge. V/c

Goodness of Fit For a large number of events, the likelihood ratio test behaves as a chi-squared with n 0 -n degrees of freedom. Lo is the likelihood with the full parameter set unconstrained where L is the likelihood obtained for an unconstrained subset of parameters.

Goodness of Fit Comparison 3 -wave fit compared to: 28 -wave reference: • all 23 ff waves • all 5 f 0 f 0 waves • phase space 23 -wave reference: • all 23 ff waves • phase space

Assessment of Fit Relative to Presence of the f 0 in the Background Quality of fit at lower momenta improves and suggests that only three waves is a sufficient description of the data at these points. However at higher momenta, the quality of fit becomes poorer.

Adding a Single f 0 Wave Will the fit improve with the addition of a single f 0 wave? Is coherent interference with the background present? Find the best fit from combinations where each of the 5 f 0 waves are individually included with waves 5, 19, 20 over all momentum points. Check if the fit improves using the likelihood ratio test.

Three phi Waves Plus One f 0 Wave The f 0 wave 26 along with waves 5, 19, 20 emerges as the best fit combination over all momenta.

Partial Wave Cross Sections for Waves 5, 19, 20 4 -wave fit: 5, 19, 20, 26 plus background Ge. V/c 2+ component remains dominant Ge. V/c

Background and Partial Wave Cross Section for Wave 26 Ge. V/c

Total Resonant Cross Section Waves 5, 19, 20 Ge. V

Relative Phases Ge. V/c radians Reference wave 5 Ge. V/c

Quality of Fit

Goodness of Fit Comparison

Summary Overall fit quality improves when coherent interference with the scaler background is included. A spin component of J=2 is dominant, however a J=4 component is significant. A clear narrow structure is not observed in the resonant cross section for these waves. Some phase motion is observed in the 4+ waves.