Neutral $B$-meson oscillations

I would have a question about an Equation in Mark Thomson’s book "Modern Particle Physics".

On page 397, Eq. (14.62), he arrives at

$$vert Bleft( tright)rangle = frac{1}{2}left[ theta_{+}vert B^{0}rangle + xitheta_{-}vertbar{B}^{0}rangleright].$$
He then writes in Eq. (14.65) that $$Pleft( B_{t = 0}^{0}rightarrow B^{0}right) = leftvert leftlangle Bleft( tright) vert B^{0} rightrangle rightvert^2 = frac{1}{4}e^{-Gamma t}left| theta_{+}right|^2.$$

Unfortunately, it is unclear to me how the factor $e^{-Gamma t}$ enters, isn’t $leftlangle B^{0}vert B^{0}rightrangle = 1$? Thank you.

Edit: $theta_{+}$ is given by $2e^{-Gamma t/2}e^{-iMt}cosfrac{Delta m_d t}{2}$.