Proton-to-electron mass ratio

Proton-to-electron mass ratio

The proton-to-electron mass ratio, mu, is given simply by the proton mass divided by the electron mass. It is considered a fundamental quantity in physics, as it is dimensionless in all systems of units. It has a numerical value given by 1836.1526724718(80) (i.e. there is a 1 standard deviation uncertainty in the last two digits of ±80).

It turns out that the mass of the proton is composed primarily of gluons, and not of the individual quark masses (the up quark and down quark). In fact, in the chiral limit, the mass of the proton, m_p, is proportional to the QCD energy scale, Lambda_{QCD}. At a given energy scale, the strong coupling constant is related to the QCD scale (and thus mu) as

:alpha_s=-frac{2pi}{eta_0 ln(E/Lambda_{QCD})}

where eta_0 = -11 + 2n/3. n is the number of quark flavours.

References

* http://physics.nist.gov/cgi-bin/cuu/Value?mpsme (Current CODATA recommended value)

ee also

* proton
* quark
* electron
* QCD
* Coupling constant


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