Helium $\lambda$-point heat-capacity exponent disagrees with theory
In plain words
The heat capacity of liquid helium near its superfluid transition was measured in orbit with high precision. Its critical exponent disagrees with the theoretical value by many error bars.
Precise statement
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.
What would settle it
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.
Status in the literature
Unverified note
No new measurement as of 2025; resummation claims of agreement with experiment have not displaced the bootstrap and Monte Carlo value.