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Heavy quark effective theory (HQET) is an effective quantum field theory aiming to describe heavy quarks in hadronic bound states.

Derivation of HQET
We start from the QCD Lagrangian

In the following, the gauge field strength tensor is untouched. We define the projectors $$P_v = (1 + \not v)/2$$ and $$\bar{P}_v = (1-\not v)/2$$. The QCD quark field is decomposed into

We absorb an extra factor of $$ \exp{(im_Q v\cdot x)} $$ into the definition of the fields $$h_v$$ and $$H_v$$ The Lagrangian density of HQET is

SCET
The leading-power SCET Lagrangian is