## How are muon velocities measured so accurately in storage rings/hadron colliders?

How accurate are the muon velocity measurements in storage rings, for muons generated in hadron colliders like CERN. How is the velocity measured?

For example, Bailey et. al. confirmed SR mathematical predictions in their famous muon ring experiment (1977), which lists the velocity of muons as 0.9994c and corresponding γ as 29.3 with a very high level of accuracy/confidence.

Did they measure the velocity of muons though some "time of flight" mechanism independent of the γ value, or was it derived using the "relativistic velocity equation" from the measured γ (or the known muon energy level for that matter)?

The reason I ask about the accuracy is that the velocity in fact has to be an even more accurate 0.99942c (using SR time dilation equation 1/√(1-v2/c2)) to arrive at the measured γ of 29.3. Even 0.9994c or 0.9995c produces a hugely different γ at that level of velocity (28.87 and 31.62 respectively!).

Appreciate any answers from anyone who is knowledgeable in this area.
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 Blog Entries: 1 Recognitions: Science Advisor arindamsinha, They don't measure the muon's velocity, they measure its momentum, by observing the curvature of its trajectory in a strong magnetic field.
 Thanks Bill. Can you give some details how this is done, and how accurate it is?

Mentor

## How are muon velocities measured so accurately in storage rings/hadron colliders?

Doesn't the paper by Bailey et al. say anything about the methods used?
 Mentor Actually, in storage rings, what they measure is frequency - the frequency that matches the beam circulation time. Using something cheap and commercially available like a crystal oven gives you eight decimal places of accuracy on the velocity.
 jtbell, I tried that first, but the paper doesn't seem to be available online for free. One has to buy it from Nature or other websites for \$30+. Vanadium 50, that is very helpful. Is there are link where I can find more detail about the method you mentioned, even if not with respect to the Bailey experiment?
 Mentor You might google "BNL g-2 experiment" and see if there is a good description of the storage ring.
 Thanks. One other follow-up question - is there an explanation why the experiment didn't show any gravitational time dilation in spite of a very large acceleration?

 Tags accuracy, bailey, dilation, muon, relativity