Effect of initial state interaction in proton-antiproton annihilation

Nuclear Physics B (Proc. Suppl ) 8 (1989) 215-217 North-Holland, Amsterdam

215

EFFECT OF INITIAL STATE INTERACTION IN PROTON-ANTIPROTON ANNIHILATION

G. IHLE, J. CARBONELL and J.M. RICHARD Institut des Sciences Nucl6aires, Uni. Grenoble, 53 av. des Martyrs, F-38026 Grenoble Cedex We use different optical potenuals to compare the initial state distortion for nucleon-antinucleon (NN-I) annihilation from protonium and scattering states. We further examine the influence of neutron-antineutron admixture in the protonium wavefunction on selected two meson branching ratios.

INTRODUCTION: Proton-antiproton (pl5) physics near threshold is very rich: there exist Coulomb bound states (protonium) with a Bohr radius of 57 fm; between 1 and 3 fm the system feels the strong interaction, most economically described by the G-parity transformed NN-forces; the extended hadrons annihilate for pO separations less than about 1 fm; this annihilation leads to ordinary mesons or, posssibly, to exotic states such as baryonium or gluonium. The physics of stopped antiprotons may thus improve our understanding of quark-gluon dynamics in the nonperturbative domain. Unfortunately, this hope is facing some problems. On the experimental side, the analysis of all possible final channels is far from being complete even for annihilation at rest. Channels with several neutrals are not yet reconstructed and there is a lack of data on the annihilation of antineutrons or of polarized anunucleons. On the theoretical side, the unsolved confinement problem of QCD requires phenomenological descriptions of annihilation, whmh per se do not establish an hierarchy of possible quarkline processes and effective qcl annihilation or creation vertices. Once fixed upon a microscopic model for annihilation, there remains the uncertainty on how to match it to the longe range meson exchange potential. The results turn out to be sensitive to both the genuine quark dynamics of annihilation and the long range initial state interaction. MODELING THE INITIAL STATE INTERACTION: As proposed by Kaufmann and Pxlkuhn 1, we use the p~-nfi particle basis to calculate the protonium energies and widths. Thus we couple properly the p~ and nfi channels and take into account the n-p mass difference. The strong interaction and the annihilation are parametrized either by the Dover-Richard 2 or the more recent Kohno-Weise 3 potentials. These contain the Paris or Ueda-Green meson exchanges with cut off at 0.8 and 1.0 fm respectively. They are completed by Woods-Saxon forms having annihilation radii between 0 and 0.8 fm and depths from 20 to 0.5 GeV. Despite these differences in parameters all three potentials give very similar values for the complex protonium energies (see ref. 4 for a more detailed analysis and presentation of our calculations) and moreover lead to results which are compatible with the available experimental data: a.) spin averaged s-wave protonium shifts and widths. The experimental values in KeV from several 0920-5632/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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G Ihle et a l . / Effect of initial state interaction

groupP PS 174. -0.75+i0.9; PS 171: -0.5+1< 1.0; PS 175: -0.66+i 1.13 have to be confronted with the theoretical ones DRI: -0.71+10.93; DR2: -0.76+a0.95; KW: -0 71+11 03, b.) p-wave widths. Here experiment yaelds5 (40-45)+10 meV and theory gaves (31-35) meV, c ) asospm dependence of annihilation cross-sections at low momenta plab < 400MeV/c. Experimentally 6 as well as theoretically the isospm T=0 component dominates over T= 1. d.) even stronger lsospm dependence for p-wave anmhdauon from recent ~(3He,4He) measurements an ref. 6. An annihilauon cross-section ratio o(T=l)/~(ptS)---0.35 containing about 50% p-wave as reported, whereas our calculations give 0.70-0.76 for the p-wave average of this ratio. This may indicate the need of an energy and lsospin dependence of the phenomenological annihilation potentml. We have compared for various partial waves the ratio o(T=l)/g(T--0) of annihdation crosssection in fhght at plab ~ 0 and the ratio F(T=I)/I"(T=0) of anmhdation from protonium. They agree within 20%, although we have ormtted the n-p mass difference and the Coulomb correction in the scattering calculation. The extrapolation from E>0 to E<0 does not hold, however, for the relauve importance of L=J- 1 and L=J+ 1 waves in natural parity states 4. We now define the local anmhilation density as YTL(r) = -2 I UTL(r) 12 ImW(r), whose integral is the protomum width FTL = j YTL(r) dr. The examination of YTL(r) for the different potentmls shows that the annihilation densities are channel dependent (fig. 1) but their gross features are insensitive to the parameters o f W(r) 4. We find a remarkable asospin dependence of the p-wave annthilatmn range induced by the tensor force, being once attracuve, once repulsive, wath the corresponding values of 0 8 and 1.2 fro. There is no effect of cenmfugal bamer, so that p-wave anmhdation does not look more peripheral than the s-wave one.

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r (fm) FIGURE 1: Annihilation densmes for the Kohno-Welse model m the IS 0 3P 0 and 3Pa channels. INFLUENCE OF INITIAL STATE DISTORTION ON TWO MESON FINAL STATES: We finally want to study the effect of the initial state chstortaon on the two meson anmhilation yaelds, companng directly only final states obeying selection rules, which allow to distinguish the lsospin weights for given J,S. The schematic expression for NN annihilation into one of the final channels f as the

217

G. Ihle et al./EtTect of initial state interaction

following product of terms of different physical origin: FN~ l ~ f = D(T,S,J) I M(Nhl ~ f ) 12 PS(f) where D stands for the square of the spin-isospin dependent initial state protonmm wavefuncuon, averaged over the annihilation region; M denotes the matrix element describing the transition of NN t o f (to be calculated in some microscopic model) and PS is the available phase space in channelf. For given J,S we xdentify D(T=I)/D(T=0) = RD with F(T=I)/I"(T=0) of our protonium calculation and adopt for M the rearrangement (R) and annihilation (A) models with effective 3P0 vertex (numbers are taken from7) and the gluon annihilation model (G) of ref. 8. We compare the predictions of these models in table 1. The most dramatic effect is seen in the 3P0 channel. Without initial state distortion in both models (R) or (G) the rates for various final states should vary by more than an order of magnitude. Now, with the value D(T=I)/D(T=0) = .03 due to the long range interaction, all rates become comparable, in agreement with experiment.

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TABLE 1: Comparison of models (R), (A) and (G) for p~ annihilation from 3P0 protonium states with and without initial state interaction (normalised to ~0~0). CONCLUSION: In the present note we have reinforced the warning that imtial state interacuons, namely due to meson exchange, greatly influence the branching ratios of annthilation at rest or in flight. Interesting models have been elaborated where annihilation is tentatively descnbed m terms of quark diagrams. An important effort should be done on the transition region between quark-gluon dynamics and Yukawa forces. ACKNOWLEDGEMENT: G. Ihle would like to thank the Deutsche Forschungsgemeinschaft for the grant which enables this collaboration in Grenoble and acknowledges the warm hospitality in the theory group at the ISN. REFERENCES 1.) W. Kaufmann and H. Pilkuhn, Rhys. Rev. C17 (1978) 215 2.) C.B. Dover and J.M. Richard, Phys. Rev. C21 (1980) 1466 3.) M. Kohno and W. Weise, Nuel. Phys. A454 (1986) 429 4.) J. Carbonell, G. Ihle and J.M. Richard, to be published 5.) C.A. Baker et al., Nucl. Phys. A483 (1988) 631 6.) CERN EP / 88-92, CERN preprint Aug. 88 7.) S. Furui, Z. Phys. 325A (1986) 325 8.) E.M. Henley, T. Oka and J. Vergados, Phys. Lett. 166B (1986) 274