EFFECTIVE FIELD THEORIES FOR VECTOR PARTICLES AND ...

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QCD AND CHIRAL EFFECTIVE FIELD THEORY
In this chapter, the well-established quantum field theory describing
the strong interaction, quantum chromodynamics (QCD), is presented.
In the so-called chiral limit, it reveals symmetries which motivate an
effective field theory, chiral perturbation theory (ChPT). It can be extended
to a chiral effective field theory, which includes heavy degrees of
freedom, such as vector mesons. This introduction is loosely based on
[31, 32, 33].
2.1 quantum chromodynamics
As already mentioned, the strong interaction can be described by an
SU(3) gauge theory called quantum chromodynamics (QCD). The full
QCD Lagrangian is given by [34, 35]
where
L QCD =
6
∑ ¯q f (iγ µ D µ − m f )q f − 1
f =1
2 Tr(G µνG µν ) , (2.1)
q f ,1
⎛ ⎞
q f =
⎜q ⎟⎟ f ,2
⎝q f ,3
⎠
(2.2)
is the Dirac spinor quark field written down as a color triplet for each
of the six quark flavors f , usually denoted up (u), down (d), strange (s),
charm (c), bottom (b) and top (t). In addition, the quantity 1
A µ ≡ A a λ a
µ
2
(2.3)
represents the eight gluon gauge fields and its field strength tensor is
given by
G µν ≡ Gµν
a λ a
2 = (∂µ Aν a − ∂ ν A a µ − g f abc A b µAν) c λa
2 . (2.4)
1 See section A.1 on page 95 for the notation used.
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