Structure Factors of Neutron Matter at Finite Temperature

We compute continuum and infinite volume limit extrapolations of the structure factors of neutron matter at finite temperature and density. Using a lattice formulation of leading-order pionless effective field theory, we compute the momentum dependence of the structure factors at finite temperature and at densities beyond the reach of the virial expansion. The Tan contact parameter is computed and the result agrees with the high momentum tail of the vector structure factor. All errors, statistical and systematic, are controlled for. This calculation is a first step towards a model-independent understanding of the linear response of neutron matter at finite temperature.

Figure 1

Continuum limit extrapolation: for $S_V$ and $S_A$ for $z=1.0$ and $q/q_T=0.45$ (top) and contact (bottom).

Figure 2

Continuum limits of the vector and axial structure factors at fixed temperature and $z=1.0$ and $z=1.5$. The bands correspond to the OPE asymptotic limits in Eq. (11) and the dotted lines to the free theory result.

Figure 3

Experimental data for the value of the contact of the unitary gas is shown in yellows and oranges (Swinburne [36], JILA [37], MIT [38]), while theoretical results are shown in blues and greens (bold diagramatic Monte Carlo [39], Jensen [40], Drut [41], Wingate [42]). The dashed gray curve is the third-order virial expansion for the unitary gas [43] and the brown dashed line shows the second-order results for $a=-18.9\mathrm{fm}$. The band around the virial curves incorporates an estimate of the next-order contribution.