Griffiths Introduction to Elementary Particles · Problem 5.22

The Feynman Calculus — David J. Griffiths

Physics — QFT · meson-masses

Problem

On the basis of equation (5.99), using the values of

m_u

m_d

m_s

, and

A

given in the text, calculate all the meson masses in Table 5.3. [Hint: For the

\eta

\phi

, and

\omega

, first find the mass for pure

u\bar{u}

, pure

d\bar{d}

, and pure

s\bar{s}

. Think of the

\eta

, for instance, as being

\frac{1}{6}u\bar{u}

\frac{1}{6}d\bar{d}

, and

\frac{2}{3}s\bar{s}

.] Also apply the formula to the

\eta'

, and note the disastrous result. [For commentary on the

\eta'

mass problem, see C. Quigg, Gauge Theories of the Strong, Weak, and Electromagnetic Interactions (New York: Benjamin, 1983), p. 252.]