Protonium annihilation in optical models

Abstract

We calculate the wave-functions, energy shifts and widths of low lying protonium states using different optical potentials (Dover-Richard, Kohno-Weise). The importance of tensor and isospin coupling is studied and the initial state distortion is compared for protonium annihilation and pp annihilation in flight at low energy. We study the range of distances at which annihilation actually occurs in protonium. We also analyse the effect of the initial state interaction on two meson branching ratios and underline that it may dramatically change the predictions of those microscopic models which are based only on phase space and simple quark diagrams.

Diquark model for protonium annihilation into two mesons

“…As a reasonable approximation, we just take the statistical weight for spin triplet and singlet population, i.e., w(3S1)/w(1So)= 3/1. For the high-lying s-states, the strong interaction distortion of initial states discussed in [16,17] is not expected to have a significant influence.…”

The $$\bar pp \to e^ + e^ - $$ reaction at rest and the hierarchy of the annihilation ranges

“…In addition, different experimental groups have proposed phenomenological fits to the low-energy cross sections leading to different zeroenergy limits [7]. The second point, namely the problem of I V (0) ]2, is that quark models of annihilation say that annihilation "range" depends on the process (see [8] for a recent discussion of the annihilation ranges), and therefore the use of the same value for I V (0) 12 in (2) and (3) is at best arbitrary. The correction due to P-wave annihilation is quite sizeable (see [9]) and we shall explicitly take it into account.…”

ϕmeson production inpp¯annihilation at rest

“…Note that we restricted the considerations of Ref. [14] to the pentaquark components with the uuds configurations [31] …”

“…In addition, the functions γ(I, J), depending on the initial-state interaction, are related to the probability for a protonium state to have isospin I and spin J with the normalization condition γ(0, J)+γ(1, J) = 1. Here we adopt for a protonium state the probability γ(I, J) and the total decay width Γ tot (J) obtained in an optical potential calculation [31], where explicit values are listed in [29]. In Table III we give the theoretical results for the branching ratios of Eq.…”

“…Nonrelativistic quark model calculations reveal that the strangeness magnetic moment µs and the strangeness contribution to the proton spin σs from the first two models are consistent with recent experimental data where µs and σs are negative. For the third model, the uuds subsystem with the configurations [31] With effective quark line diagrams incorporating the 3 P0 model we give estimates for the branching ratios of the annihilation reactions at rest pp → φX (X = π 0 , η, ρ 0 , ω). Results for the branching ratios of φX production from atomic pp s-wave states are for the first and third model found to be strongly channel dependent, in good agreement with measured rates.…”