# Neutron decay discrepancy

I have been reading the article Neutron Lifetime Puzzle Deepens, but No Dark Matter Seen on the present methods of measuring the life span of neutrons The bottle method measures a mean lifespan which is seconds shorter than the other the beam method. One explanation is that neutrons decay into dark matter, but it seems to me that this should be expected. We know that a faster particle like a neutron in a beam should, by special relativity, experience time slower than a particle that is moving slowly or standing still.

Is it possible that the difference between "bottle" and "beam" measurements of the neutron lifetime is due to relativity, since the "beam" neutrons are moving faster than the "bottle" neutrons? Or do these discrepancies persist when Relativity is taken into account and thus require another explanation?

An ensemble of "thermalized" neutrons has come into near-equilibrium with some moderator at some temperature, and each neutron has $$\frac12 mv^2 \approx kT$$. For room temperature, $$T=300\rm\,K$$, the typical neutron velocity is about $$2000\rm\,m/s$$. The relativistic factor for such neutrons, which sets the scale for time-dilation effects, is
\begin{align} \gamma &= \left(1-\frac{v^2}{c^2}\right)^{-1/2} \\ &\approx 1 + \frac12 \frac{v^2}{c^2} \\ & = 1 + \frac12\left(\frac{2\times10^3\rm\,m/s}{3\times10^8\rm\,m/s}\right)^2 \\ & \sim 1 + 10^{-10} \end{align}