# Can we calculate three-point correlation in lattice qcd

Is it feasible to calculate a three-point correlation on the lattice? Say, I have two quark fields separated at z_1+z_2 and 0, and a gluon field inserted at z_2. Also I need two gauge links to make this expression gauge invariant:

\bar{\psi}(z_1+z_2) \Gamma(z_1+z_2; z_2) F^{\mu\nu}(z_2) \Gamma(z_2;0) \psi(0).

I have asked some lattice people and they told me that it's hard to do such a calculation. What do you guys think of this?

## Answers and Replies

It's perfectly possible in principle to measure three-point functions. For example, it is common to compute matrix elements like ##\langle \pi^0 | \bar{d} \gamma_\mu (1 - \gamma_5) s | K^+ \rangle## which is needed for the calculation of the decay rate ##K^+ \to \pi^0 e^+ \nu_e##. This matrix element is computed as the correlation function of three operators: the current, an operator that creates a kaon, and an operator that destroys a pion.

Whether the measurement of a given three-point function can be expected to have a good signal-to-noise ratio is another matter and I don't know enough myself to guess the answer for your case.