Note on four-particle form factors of operators $T_{2n}T_{-2n}$ in sinh-Gordon model

The diagonal matrix elements $\langle\theta_1,\theta_2|T_{2n}T_{-2n}|\theta_1,\theta_2\rangle$ between two-particle states in the sinh-Gordon model are computed analytically for all integers $n>0$. This confirms the proposal by F. Smirnov and A. Zamolodchikov for these matrix elements and demonstrates effectiveness of the algebraic approach to form factors.