Proton-proton
and proton-antiproton interactions at SMALL distances
Proton-proton and proton-antiproton
potentials
-
In potentials designed for practical purpose, the
short-range part of the NN interaction is described
empirically by cutting off meson exchanges at distances
R < 1Fm and adding a phenomenological core to account for
the observed repulsion. This is the basis of the
Paris ,
Bonn
and others semi-phenomenological potentials.
There are two major mechanisms for the core in nucleon-nucleon
interaction : the exclusion principle
between quarks and chromomagnetic interaction.
-
However, the theoretical ground is uncomfortably split
into two parts.
The Yukawa picture accounts for the long-range part in terms of
nucleons and mesons, while the short-range part is described
directly at the quark level. A synthesis is badly needed.
- In analogy with electron-positron annihilation to photons
proton-antiproton annihilation first was expected to be ~ 1/m = 0.1 Fm.
It proved to be about 1.0 Fm instead.
Fig. 1
In the language of atomic collisions, most of the transitions
from baryon-antibaryon to mesons are NOT
"annihilation" reaction, they are "rearrangements", with sometimes
partial annihilation.
The crucial parameter is the size of the mesons, e.i., their ability
to make a "bridge" to pickup a quark in a nucleon and antiquark
in an antinucleon. The size of the baryons governs the spatial spread
of the mesons in the final state. The processes
or
should be of shorter range ( see Fig.1 c)
Pontecorvo reaction and similar reactions
-
Pontecorvo reaction
is an example of proton-antiproton annihilation at very
short range (~0.2 Fm). It is regarded as a deep inelastic,
short-distance annihilation of bayons into small mass
meson system (and/or photons) deep below the threshold
of the free nucleon reaction.
-
Inverse Pontecorvo reaction
-
Generalized inverse Pontecorvo reaction:
three particles in the final state allows to study
the size of the emission region experimentally.
Two-proton correlation function at small
relative momenta
-
Two-particle correlation function behavior at small
relative momenta q is sensitive to the interaction
characteristics and the size of emission region.
Example
of two-proton correlation function behavior for different
emission region sizes.
-
How it works ?
Correlation functions for different sizes
of emission region.
-
For large sizes of interaction region ( > 1.5 Fm) the shape of
the correlation function ( CF ) is well-known.
Simple nucleon-nucleon potential
for square well approximation and more sofisticated potentials
result in the same CF and the short-range wave
function contribution is small.
However, for sizes smaller than the hadron size the shape of CF
( actually, the height of the peak at q=0.04 GeV/c ) is different for
potentials with and without core. On the
Fig. 2
you can see the CF enhancement for pion ( 0.5 Fm),
eta (0.3 Fm) and eta_prim (0.2 fm) exchange in simple Yamaguchi
potential (no core). In this case the smaller the range, - the higher is
the peak value, and 0.2 Fm or 0.3 Fm is about the same.
-
On the
Fig. 3
you can see same enhancement for Paris potential (with core).
The situation is qualitatively different, - smaller ranges have
smaller peak values because of core repulsion.
-
On the
Fig. 4
you can see the peak value as a function of the emission region range.
The values at ranges > 1.5 Fm are the same for different approaches,
and at small ranges this value depends strongly on the form of
the potential. So, by measuring the CF in the process,
where this region is well-defined and small, we will have the
information about proton-proton and proton-antiproton short-range
potential.
Searching of the baryonium and correlation function
at small q
-
The reaction
is also interesting for a possible
baryonium search.
( Diagramm d )
Possible existence of the narrow peak in proton-antiproton
effective mass
M = 2.02 GeV
or virtual meson with M < 2Mp
does not affect the fact, that the irregularity of CF
at small q (or effective mass) must exist for any particles.
The nature of this irregularity defers from resonance one, and
can be , in principle, be separated from possible meson states.
Proton-proton interaction is a strike example, - the shape of the
CF differ from those expected for a virtual state, its
max value depends of the size of the region etc.
Existing experimental data
and
reactions
(Belle collaboration.)
reaction
(BES collaboration.)
The curve on the figure - the
estimate , using the low-energy parameters of
nucleon-antinucleon interactions.