# Quenched & Unquenched Quark Model

1. Jul 21, 2015

### Naeem Anwar

Just started the study Exotic Hadrons (like mixing of Charmonium states with tetraquarks etc.) and got confused with quenched & unquenched quark model.

What are the major differences between these two models? What key factors I should keep in mind doing calculations with these models invidiously?

I will highly acknowledge literature recommendations.

2. Jul 21, 2015

### fzero

In terms of the path integral (PI) for QCD , since the fermions appear only quadratically, one can symbolically do the functional integral over them to find a highly nonlocal determinant
$$\int D\psi D\bar{\psi} \exp \left[ \bar{\psi} ( { \not{ \! \! D}} + m ) \psi \right] = \det (\not{\! \! D} + m ) .$$
Since the gauge bosons and consequently the gauge coupling appears in the covariant derivative, if we were doing perturbation theory, we could treat this beast order by order. In the quenched approximation to lattice QCD, this determinant is simply ignored for computational simplicity (its value is set equal to 1 in the PI). We could analogously call this an approximation with nondynamical fermions, i.e. fermions that we don't promote to fields that we have to integrate over in the PI.

I haven't really studied lattice QCD, so I am not up on references. The lecture notes http://arxiv.org/abs/hep-ph/0205181 discusses the qualitative aspects of the quenched approximation in one or two places. The notes http://www.itp.uni-hannover.de/saalburg/Lectures/wiese.pdf (hat-tip: atyy) are a discussion of ways to incorporate fully dynamically fermions, but I don't think he discusses the quenched approximation in any detail.

3. Jul 27, 2015

### Naeem Anwar

Although my background is not LQCD but still this material is at least giving me the spirit of my query. Thanks & looking forward some exact explanations in detail.

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