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We report the measurement of hyperfine splitting in the $7d$ $^{2}D_{3/2}$state of $^{133}$Cs using high resolution Doppler-free two-photon spectroscopyin a Cs vapor cell. We determine the hyperfine coupling constants $A =7.3509(9)$ MHz and $B = -0.041(8)$ MHz, which represent an order of magnitudeimprovement in the precision. We also obtain bounds on the magnitude of thenuclear magnetic octupole coupling constant $C$. Additionally, we measure theac Stark shift of the $6s$ $^{2}S_{1/2} \rightarrow 7d$ $^{2}D_{3/2}$transition at 767.8 nm to be $-49 \pm 5$ Hz/(W/cm$^2$), in agreement withtheoretical calculations. We further report the measurement of collisionalshift [$-32.6 \pm 2.0$ kHz/mTorr] and pressure broadening for the individualhyperfine levels of the $6s$ $^{2}S_{1/2} \rightarrow 7d$ $^{2}D_{3/2}$transition. These measurements provide valuable inputs for analysis ofsystematic effects in optical frequency standards based on the cesium $6s$$^{2}S_{1/2} \rightarrow 7d$ $^{2}D_{3/2}$ two-photon transition

High precision measurement of the hyperfine splitting and ac Stark shift of the $7d$ $^{2}D_{3/2}$ state in atomic cesium