On Deuteron Spin Dependent Structure Function $ g_{2}(x)$ in Relativistic Model of Deuteron

The spin dependent deuteron structure functions are investigated in the relativistic model of deuteron. It is shown that the deuteron structure function $g_{2}(X)$ can be considered properly only in the infinite momentum frame where the virtual photon has pure transverse components ($q_{0}=-q_{3}\rightarrow 0$ at $P\rightarrow \infty$), whereas in the conventional Breit frame the impulse approximation for $g_{2}(X)$ may be violated due to $q\bar{q}$ pair creation by the virtual photon. It is shown that due to relativistic effects the deuteron structure function $g_{2}(X)$ has a nontrivial contribution determined by first derivative of the nucleon structure function $g_{1}(x)$. Such contribution is small but it increases when $X \rightarrow 1$. It may achieve about 10 \% at $X \sim 0.75$ and could be essentially larger for the transverse structure function $g_{\perp}(X).$