The W boson mass is exp(-4pi^2) of a Planck mass

[franoisbelfor]

Almost: the result is 85 GeV, the measured mass is 80.4 GeV.
Is there anybody who has ever looked at this coincidence?

François

 

[arivero]

there is a thread about this kind of coincidences, https://www.physicsforums.com/showthread.php?t=46055

For exponential times the Planck mass, there are usually renormalization group arguments: "one expects that Me*sqrt(G)*Exp(1/alpha or similar) to be of order unity, if G is the ultimate cutoff "

 

[franoisbelfor]

For exponential times the Planck mass, there are usually renormalization group arguments: "one expects that Me*sqrt(G)*Exp(1/alpha or similar) to be of order unity, if G is the ultimate cutoff "

Can you explain the symbols in the expression? Thank you already!

François

 

[Vanadium 50]

First, numerology is hardly the path to understanding science. It's beloved by crackpots who spend a great deal of time finding simple, or in some cases complex, wholly unmotivated relations between measured quantities. Indeed, in many cases even when better measurements show that these relationships are spurious, the proponents cling to their ideas.

Second, your calculation gives 87.381 +/- 0.004 GeV. The measurement is 80.398 +/- 0.025 GeV. That's 280 standard deviations away, hardly "almost". With such a large number of possible expressions, surely you could have done better than getting within 9% of the measured value. Why 4 pi^2? Why not (283/45)^2?

Third, electroweak radiative corrections, mostly due to the top quark, pull the mass of the W up. Without them, the W would weigh 77.5 GeV. That makes your numerology even worse.