# Presentation: 000315

## Exclusive ΦΦ in E690

- G. Gutierrez
- FNAL-E690 Collaboration

*Small-X and Diffraction Physics Conference*

*FERMILAB, Sep 2003*

## Introduction

- But this reaction should be suppressed by Okubo-Zweig-Iizuka (OZI) rule! (in strange particle production gluons should bridge the gap.)OZI forbidden **→** gluon bound states?  In this case, useful for understanding gluon dynamics.
- BNL-MPS search for ***ΦΦ*** resonant states:• 1203 events in '82, first PWA• 3650 events in '85, refined PWA, found three 2++ resonances• 6650 events in '88, 3 states, all with *I**G**J**PC*=0+2++ and *LS*=02, 20, 22.
*K*-matrix fit:
- 	*f**2**(2010): **	**m=2011 **±** 60 MeV **	**Γ**=202 **±** 60 MeV**	**f**2**(2300): **	**m=2297 **±** 28 MeV**	**Γ**=149 **±** 40 MeV**	**f**2**(2340): **	**m=2339 **±** 60 MeV**	**Γ**=202 **±** 70 MeV*       annihilation at rest :CERN JETSET '94 in ***      ******→ ****Φ**Ф*, antiproton beam at 1.4 GeV/c.• Preliminary PWA shows 2++ predominance.• BW behavior of the 2+D0 wave, with parameters M=2231±2 MeV, Γ=70±10 MeV.

**Introduction**

## The three BNL-MPS waves

**The three BNL-MPS waves**

- ’82 PWA, 1203 events

- ’88 PWA with 6652 events

- 

- 

*f**2**(2010): **	**m=2011 ± 60 MeV **	**Γ**=202 ± 60 MeV**f**2**(2300): **	**m=2297 ± 28 MeV**	**Γ**=149 ± 40 MeV**f**2**(2340): **	**m=2339 ± 60 MeV**	**Γ**=202 ± 70 MeV*

## E690 Spectrometer

**E690 Spectrometer**

- • Beam: 800 GeV protons,  Δp/p ≤ 1.5e4• Target: Liquid Hidrogen, (2% int. length)• Main Spectrometer• Forward Spectrometer• Cherenkov Counter• Time Of Flight System
- • Vetoes System

## E690 Collaboration

- Columbia University
- A.Gara, B.C.Knapp
- Fermi National Accelerator Laboratory
- D.Christian, G.Gutierrez, E.Gottschalk, A.Wehmann
- Lawrence Livermore National Laboratory
- E.P.Hartouni
- University of Guanajuato
- J.Felix, G.Moreno, M.A.Reyes
- University of Massachussetts
- M.C.Berisso, M.N.Kreisler, S.Lee, K.Markianos, M.H.L.S.Wang, D.Wesson

## Data Selection

**Data Selection**

- Reaction:

- • 1 primary vertex inside *H*2 target
- • 5 tracks assigned to primary vertex, 3+, 2–
- • Invariant mass 1.0124≤*m**KK*≤1.0264 GeV/c2
- • Use *E-P* conservation to find missing proton, |*MM*2–*m**p*2|≤2 GeV2/c4
- • At least one track Č-identified as *K*
- • Kinematical cut on momentum of *p**missing* to ensure it is out of detector:           *P**z*≤0.250 GeV/c  or  arctan(*P**t**/P**z*)≥45

## ΦΦ Invariant mass

***ΦΦ***** Invariant mass**

-  • (UL) Missing mass squared, minus proton mass squared
-  • (UR) K+K– , C1 vs. C2
-  • (LL) K+K– invariant mass opposite to *Φ*, for both pairs
* *• (LR)* **ΦΦ* invariant mass.  99.6% of events have only one combination per event in this plot.

## xF and rapidities

***x******F***** and rapidities**

- Plots of *x**F* and rapidity distributions for the slow proton (left), *X* system,
- and fast proton (right), show that the *X* system is centrally produced.

## Reference Frames

**Reference Frames**

- We need 6 angles to define the spin and angular momentum of the *ΦΦ** *system, each *Φ* decaying to a *K**+**K**–* pair.
- Using the protons' momentum transfer measured in the *pp* CM system, the GJ angles for one of the *Φ*'s in the *X* rest system are defined with respect to the following axis:
*	**	*		beam momentum transfer
*	**	*
*	**	*
- The GJ angles for the *K**+* from *Φ**1* in the *Φ**1* rest system are defined with respect to the following axis:
*	**	*      	in       direction
*	**	*      	perpendicular to *      *       plane
*	**	*

## Waves in the reflectivity basis

- Base vectors for an allowable combination of:
-    *J**    **ΦΦ* total angular momentum   *L*    orbital angular momentum   *S*    spin   *M   *   *P*    parity   *η*    reflectivity
- are given by

*I=0* and *C=+* for the *ΦΦ* system.  Bose statistics require that *L+S=even*.There are 54 waves with *0**≤**J**≤**4, 0**≤**L ≤3, 0 ≤S ≤2, 0 ≤M ≤2*; 14 of these have *M=0*.We use maximum likelihood to find the wave amplitudes

## Partial Wave Analysis

**Partial Wave Analysis**

- We tried all 54 waves one by one to find the best fit.  Then, added a second and third wave and selected the best fit with waves following from bin to bin.The result of this procedure is that we need three waves to describe the data, all of them with *J**PC**LS*=2++02, with different total angular momentum projections, *M=*0,1.Two of these three waves have *η*=–1, and interfere with a phase of about –90°.  The wave with *M*=0 predominates at threshold, and the two *M*=1 waves have similar distributions.

## Comparison of results using the three BNL-MPS waves

**Comparison of results using the three BNL-MPS waves**

- For comparison, we tried the three BNL waves in the PWA.
- As one can see here, there is not continuity in amplitudes and phases, and the BNL solution turns out to be up to 80 **log ****L** units bigger than our preferred solution.

## Resonances from wave amplitudes:  One BW fit

**Resonances from wave amplitudes:****  ****One BW fit**

- We fitted the wave amplitudes following Morgan and Pennington's approach:• use Jost functions to parameterize the *S*-matrix,• assume two channel decays, *XX* and *ΦΦ*,• *X* is assumed to be a low mass scalar  – *π** *–  (*ρ*1 ~ 1),• BW: two *k*–poles in sheets II and III,• production amplitudes are real numbers.From a one BW fit we find:	**M****R****=2.249 ****±**** 0.015 GeV,****	****Γ****R****=0.340 ****±**** 0.027 GeV.**

## Two BW fit

**Two BW fit**

- Data needs another BW type pole below threshold to describe the *J**z*=0 wave amplitude.
- 	• for |*J**z*|≠0 production is only via *ΦΦ*,
- 	• for |*J**z*|=0 production is via *XX* and *ΦΦ*,
- A two BW fit gives, for the BW above threshold:
**           *****M******R*****= 2243 ****±**** 15 (*****stat*****) ****±**** 10 (*****syst*****) MeV,    *****Γ******R*****= 368 ****±**** 33 (*****stat*****) ****±**** 30 (*****syst*****) MeV**
- The BW pole would be *m**0*≈2.30 GeV.
- For the BW pole below threshold, our fit gives:
- 		*M**R *≈1.9 GeV,  	*Γ**R *≈300 MeV
- but we need data on other channel to fix its parameters.  (More channels?       ?)

## Conclusions

- We report on the analysis of the centrally produced *ΦΦ* system
- • PWA shows we need three waves, all of them 2++02 with
- |*J**z*|*η*= 0–, 1–, 1+, to describe the data
- • We only see one of the 2++ waves seen by BNL-MPS
- • A fit to the wave amplitudes *a la M&P* shows a BW like structure
- above threshold with
*	**  **M**R* = 2243 ± 15 (*stat*) ± 10 (*syst*)  MeV
- 	   *Γ*R =   368 ± 33 (*stat*) ± 30 (*syst*)  MeV
- • The *J**z*=0 wave amplitude can be described only if there is another
- pole below threshold ...
- • ... but we need data on other channels to fix its parameters.