the spin-independent structure functions of lepton-deuteron scattering, T\_1(,Q\^2)&=&F\_1(,Q\^2)\
[Im]{}T\_2(,Q\^2)&=&F\_2(,Q\^2). Given the known high-energy behavior of the structure functions, the two amplitudes obey the following form of dispersion relation, T\_1(q\_0,Q\^2)&=&|T\_1(0,Q\^2)+[Re]{}T\_1\^[pole]{}(q\_0,Q\^2)\
&+&\_[\_[thr]{}]{}\^\
[Re]{}T\_2(q\_0,Q\^2)&=&[Re]{}T\_2\^[pole]{}(q\_0,Q\^2) +\_[\_[thr]{}]{}\^,where for $T_1$ the subtraction at $q_0=0$ was performed with $\bar T_1(0,Q^2)$ the respective subtraction function. Above, we explicitly extracted the contribution of the ground state leading to a pole, $T_{1,2}^{pole}$. This contribution is defined in terms of the deuteron’s electromagnetic vertex &&d(p’)|J\^(q)|d(p)=G\_2(Q\^2)\[[’\^\*]{}\^(q)-\^(’\^\* q)\]\
&&-(p+p’)\^, where $\xi^\mu({\xi'^*}^\mu)$ denote the polarization vector of the initial (final) deuteron with momenta $p(p')$, respectively, and $Q^2=-q^2$ stands for the four-momentum transfer. The form factors $G_{1,2,3}$ are related to the charge, magnetic and quadrupole deuteron form factors as G\_M&=&G\_2,\
G\_C&=&G\_1+\_dG\_Q,\
G\_Q&=&G\_1-G\_2+(1+\_d)G\_3, and $\tau_d=Q^2/(4M_d^2)$. The elastic contribution to the structure functions reads F\_1\^[el]{}&=&(1+\_d)G\_M\^2(1-x\_d),\
F\_2\^[el]{}&=&(1-x\_d),with the Bjorken variable $x_d=Q^2/(2M_d\nu)$.

Correspondingly, we distinguish three contributions, $\Delta E_{n0}=\Delta E_{n0}^{subt}+\Delta E_{n0}^{el}+\Delta E_{n0}^{inel}$ where E\_[n0]{}\^[subt]{}&=&\^2\_[n0]{}(0)\_0\^|T\_1(0,Q\^2),\[subtraction\] E\^[el]{}\_[n0]{}&=&\^2\_[n0]{}(0) \_0\^\[elastic\]\
&&{ G\_M\^2 (1+\_d)( -) .\
&&-. (-) }E\^[inel]{}\_[n0]{}&=&-\^2\_[n0]{}(0) \_0\^\_[\_[thr]{}]{}\^\[inelastic\]\
&&.Above, we denote $\tau=\nu^2/Q^2$, $\tau_l=Q^2/(4m^2)$, and the auxiliary functions are given by \_1()&=&(1-2)+2\^[3/2]{}\
\_2()&=&(1+)\^[3/2]{}-\^[3/2]{}-\
\_1(,\_l)&=&\
\_2(,\_l)&=& .

Evaluation and Data Fits
========================

Elastic contribution
--------------------

We start with the elastic contribution. It can be noted that the integral in Eq. (\[elastic\]) is IR divergent 