Transcript Comparison of y-scaling for Electrons and Hadrons

Comparison of y-scaling for electrons
and hadrons
R. J. (Jerry) Peterson
University of Colorado USA
Much has been learned from inclusive electron scattering from nuclei
at intermediate energies and momentum transfers. Scaling, with
several variables condensed into just one, has served to unify many
efforts. Electron-nuclear physics goes by a very well-known
reaction mechanism. Although the strong interaction complicates
analysis of inclusive hadron scattering at similar energied and
momentum transfers, there is much to be learned from the data
available.
Today—rules, constraints and a few examples for (p,px), (p,nx), (p,px),
(p,p0x) and (K+,K+x).
Assumptions:
One and only one elastic collision between the
beam particle and a bound nucleon, for “billiard
ball” kinematics. Thus, combine q and w data to a
single scaling variable=y today.
In-medium elastic cross sections are known from
free space scattering, with known off-shell effects.
The number of one-and-only-one collisions can be
computed with the eikonal Glauber model, which
depends upon in-medium total beam-nucleon
cross sections. Trivial for electrons.
Copy the lessons learned from electron scaling for
the hard case of hadron quasifree scattering.
This is interesting because we can
probe the interactions among
nucleons within the nucleus by
quasifree scattering from one of
them while it is interacting, but need
to match the quantum numbers of
the probe and the interaction.
Correlations are caused by forces that depend
on spin and isospin
Scaling of the Second Kind
For electron charge scattering, the response is
independent of A. Is this true for hadrons?
We need Aeff or Neff for computing F(y), so this is
a test of our Glauber method. We force this
scaling by changing the in-medium beam-nucleon
total cross section, with ratio b of in-medium/free
total cross sections =0.70-0.75
Superscaling, both first and second
kinds
• Include the expected nucleon Fermi
momentum by plotting
Y = y / kFermi
f(Y) = F(y) x kFermi
Is the beam energy high enough?
Scaling of the First Kind
The one-and-only-one scattering is
tested by being independent of
momentum transfer q, as found for
electron scattering, but not obvious
for hadrons.
Scattering of the Third Kind
Are the responses for carbon near
q=550 MeV/c the same for ALL
hadrons? Another test of the
Glauber method.
Scaling for Quality Control
Conclusions
• 1. Hadron scattering can meet the conditions for
quasifree scattering, and thus can sense in-medium
beam-hadron single-interactions, as shown by scaling of
the First Kind, best for light nuclei.
• 2. We can count the nucleons struck elastically once and
only once by the Glauber method, if smaller in-medium
total cross sections are used, giving scaling of the Second
and Third Kinds.
• 3. The isospin responses of nuclei can be separated with
hadrons, and are not the same.
• 4. At the special beam momentum of 750 MeV/c, pion
SCX can separate transverse spin responses.