Crossed-channel lightest-breather exchange
= Crossed-channel lightest-breather exchange
{title2=$t(ia)=m_2^2+m_1^2-2m_2m_1\cos a=m_1^2$}
At the closest physical-strip <pole> of $S_{2,1}$, the difference of the analytically continued external momenta has squared <mass> $m_1^2$. Using $m_2=2m_1\cos a$ makes the identity immediate. Thus the exchanged <t-channel> one-particle state is the lightest <Sine-Gordon breather>, not a new member of the spectrum.