e+e- -> gamma* -> mu+mu-
(Perkins "Introduction to High Energy Physics Section 5.1)
When the effects of spin and mass are neglected,
the differential cross
via single-photon exchange is
d sigma / d Omega = alpha^2 / (4s)
Question :
Derive the differential cross section
d sigma / d Omega = [ alpha^2 / (4s) ] x (1 +
cos_theta^2)
when the effects of spin are included.
Question :
Calculate the total cross
4 pi alpha^2 / (3s)
in units of nb / s, where
nb = nano-barn, and s = the cm energy in GeV^2.
e- mu+ -> e- mu+
(Perkins "Introduction to High Energy Physics Section 5.3)
Question :
Using Mandelstam variables s, t, u defined in Eq. (5.11),
derive Eq.s (5.12) through (5.17).
Drell-Yan process
When two hadrons collide at high energies, the quarks in them
can collide and produce a lepton pair (e+e-, or mu+mu-).
This is called a "Drell-Yan" process.
Question :
Draw Feynman digram for the Drell-Yan process, starting with
hadrons A and B.
Question :
The cm energy of hadrons A and B is
s = (P_A + P_B)^2,
and the cm energy of the quarks involved in the Drell-Yan
process is
s-hat = (P_q + P_qbar)^2.
Question :
Show that
s-hat = x xbar s (approximately)
where x and xbar are the fractions of hadron momenta carried
by quark (q) and antiquark (qbar).
Question :
Explain why the cross section for this process is
approximately given by
sigma = Sum(over q, q-bar) Integral dx dxbar
f_q/A(x) f_qbar/B(xbar) sigma-hat(q qbar -> mu+mu-)
where sigma-hat is the constituent cross section.
Question :
Write the constituent cross section, sigma-hat
(approximation).
Consider two cases for A and B:
A = pi+, with valence quarks (u dbar), and
B = carbon
A = pi-, with valence quarks (ubar d), and
B = carbon.
The carbon nucleus is isoscalar, that is, it has equal numbers of
u and d quarks.
Question
Show that the ratio