Lecture_HJ_7

Quantum Chromodynamics (QCD)

The theory of strong interactions provides the forces that keep quarks and antiquarks together in mesons and three quarks con ned in baryons. It should also in the end explain the nuclear forces which make nucleons bound in nuclei. Please note the di erence between con nement and binding! Nucleons can be ejected out of nuclei and measured in a nearby detector. Quarks can only be traced in deep inelastic scattering by their accompanying hadronic jets. The quark forces are forces between colored objects (quarks, gluons). The nuclear forces are forces between color neutral forces namely nucleons. They are therefore much weaker, comparable to forces inside molecules between neutral atoms.

Peculiar properties:

g2

s = 4s

1.asymptotic freedom: s(p2 ! 1) ! 0.

(Nobel Prize 2004 for Gross, Wilczek and Politzer)

2.con nement: Vqq(r) r for large distances. Millenium Prize riddle (Ja e, Witten).

3.sel nteraction of gauge elds Gauge elds are colour charged.

The QCD-Lagrangian

Hadronic current:

X

j (x) = e Qq q(x) q(x) (1)

q

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Hadronic states are invariant under SU(3) transformations in colour space:

Compare to the generators of SU(2) a:

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Table 1: Quarks and some of their properties.

In table 1 the avours of quarks, their current masses and their charges are listed.

Bound states in color space!:

1.Mesons: qq

2.Baryons: qqq

e.g.:

u1d1 + u2d2 + u3d3

p " u u d

+ and p are gauge invariant.

[ a; b] = 2i fabc c

where fabc are structure constants.

SU(3):

[ta; tb] = i fabc tc

with

tc = 12 c

fabc is anti-symmetric:

and

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|{z}

4

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4-gluon vertex:

igs2[fabefcde(g g g g ) +

+facefbde(g g g g ) + +fadefcbe(g g g g )]

ghost-gluon vertex:

gs fabcr

quark propagator iSjk (p):

i (=p+m0) jk p2 m20+i"

gluon propagator iDab (q):

ghost propagator:

i ab

p2+i"

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