Introduction to QCD slides - P.Hoyer.pdf - High Energy Physics Group

Unitarity (white):
σtot(s) = �
Paul Hoyer Mugla 2010
Some Theorems
X
�
Before QCD
E.g., Lorentz inv., unitarity and the optical theorem
SS † = 1
“something will happen”
note: includes “no” scattering
The Lagrangian of QCD
Optical Theorem
As a consequence of the unitarity of the scattering matrix:
the total cross section may be expressed in terms of the
Unitarity (white)
imaginary part of the forward elastic amplitude:
SS † =1
dΦX |MX| 2 = 8π
Optical Theorem (white) √ Im [Mel(θ = 0)]
s
σtot(s) =
µ
)( D µ)ij ψ j q− mq ¯ ψ i qψqi− 1
4 F a µνF aµν
The Lagrangian of QCD in white
µ
)( D µ)ij ψ j q− mq ¯ ψ i qψqi− 1
X ~ XX
2
X
10
4 F a µνF aµν
SS † = 1
Total = The Lagrangian that can of happen QCD
dΦX |M X | 2 = 8π
√ Im [M
s
el(θ = 0) ]
Sum over everything
“Square Root” of
nothing happening
L = ¯ ψ i q(iγ µ )( D µ)ij ψ j q− mq ¯ ψ i qψqi− 1
4 F a µνF aµν
The Lagrangian of QCD in white
L = ¯ ψ i q(iγ µ )( D µ)ij ψ j q− mq ¯ ψ i qψqi− 1
4 F a µνF aµν
The sum over all states X becomes a completeness sum on the rhs.
QED satisfies unitarity at each order of α.
=
47
P. Skands