Helium $\lambda$-point heat-capacity exponent disagrees with theory

The He-4 superfluid transition is in the 3D $O(2)$ universality class, with $\alpha = 2 - 3\nu$. The Space Shuttle measurement gives $\alpha = -0.0127(3)$ (Lipa et al. 2003), while the conformal bootstrap gives $\nu = 0.67175(10)$, i.e. $\alpha = -0.01526(30)$ (Chester et al. 2020), in agreement with Monte Carlo; the tension is about 8 standard deviations. Determine whether the discrepancy comes from the experimental analysis (corrections to scaling, finite size, residual gravity), from the identification with the $O(2)$ fixed point, or from an error in theory.

A new He-4 specific-heat measurement with independent systematics, or the identification of a specific error in the 2003 analysis or in the theoretical value.