Subatomic Physics

164 Structure of Subatomic Particles
6.9 Deep Inelastic Electron Scattering
The Thomson model of the atom, in vogue before 1911, assumed that the positive
and negative charges were distributed uniformly throughout the atom. Rutherford’s
scattering experiment (1) proved that one charge is concentrated in the nucleus; this
discovery profoundly affected atomic physics and founded nuclear physics. Highly
inelastic electron scattering has had a similar impact on particle physics and we
consequently discuss the most surprising results of these experiments here.
In deep inelastic scattering, usually only the energies and momenta of the initial
and final electron are observed, but not the particles produced from the target.
These measurements result in what is often called inclusive cross sections. Nevertheless
some kinematical information about the final hadronic state can be gleaned.
Energy and momentum conservation give for the energy E ′ h and momentum p′ h of
the final hadrons in the laboratory system (see Fig. 6.15)
E ′ h = ν + mc2 , p ′ h = p − p′ , (6.53)
where m is the mass of the struck particle. In terms of E ′ h and p′ h ,orq and ν one
can define the relativistically invariant effective mass, W , of all the hadrons in the
final state
W 2 = E ′2
h − (p ′ hc) 2 = m 2 c 4 + q 2 c 2 +2νmc 2 . (6.54)
Since q2 and W 2 are relativistic scalars or invariants, Eq. (6.54) makes it clear that
ν is also a Lorentz invariant, and therefore has the same value in any frame of
reference. Indeed, we can write ν in terms of the target particle’s energy Eh and
momentum p (32)
h
ν = ph · q
m =
�
Ehq0
mc2 − p �
h · q
, (6.55)
m
which makes its Lorentz invariance manifest.
At different scattering angles, what energies E ′ should be selected? The answer
can be obtained from elastic scattering and inelastic scattering to resonances: elastic
scattering corresponds to looking at a final state with W = mc 2 ; observation of a
resonance means selecting a final state with W = mresc 2 ,wheremres is the mass of
the resonance. W characterizes the total mass of the hadrons in the final state here
also, and the cross section d 2 σ/dE ′ dΩ for the continuum is consequently determined
as a function of q 2 for a fixed value of W .
Inelastic electron–proton scattering into the continuum has been studied both
at medium energies (E ∼ 0.5−4 GeV) on nuclei and with high energy electrons and
positrons. (45) At SLAC the primary electron energy was varied between about 4.5
and 24 GeV; ν reachedvaluesashighas15GeVand|q 2 | over 20(GeV/c) 2 .Atthe
45 A. Abramowicz and A.C. Caldwell, Rev Mod. Phys. 71, 1275 (1999).