Determination of the quark mass ratio $Q$ from $\eta \to 3 \pi$

Understand

The decay $\eta \to 3 \pi$ proceeds exclusively through isospin violating operators and is therefore an excellent probe to examine the strength of isospin breaking in the strong interaction.

• The latter can be expressed through the quark mass ratio $Q^2 = (m_s^2 - \hat{m}^2)/(m_d^2 - m_u^2)$.
• The main object of this thesis is to analyse the decay $\eta \to 3 \pi$ using dispersion relations in order to extract $Q$ as well as other physical quantities.
• The dispersion relations are a set of integral equations that lead to a representation of the decay amplitude in terms of four unknown subtraction constants.