Proton-to-electron mass ratio

In physics, the proton-to-electron mass ratio (symbol μ or β) is the rest mass of the proton (a baryon found in atoms) divided by that of the electron (a lepton found in atoms), a dimensionless quantity, namely:

μ = mp/⁠me = 1836.152673426(32).

The number in parentheses is the measurement uncertainty on the last two digits, corresponding to a relative standard uncertainty of 1.7×10−11.

Discussion

μ is an important fundamental physical constant because:

Baryonic matter consists of quarks and particles made from quarks, like protons and neutrons. Free neutrons have a half-life of 613.9 seconds. Electrons and protons appear to be stable, to the best of current knowledge. (Theories of proton decay predict that the proton has a half life on the order of at least 1032 years. To date, there is no experimental evidence of proton decay.);

Because they are stable, are components of all normal atoms, and determine their chemical properties, the proton is the most prevalent baryon, while the electron is the most prevalent lepton;

The proton mass mp is composed primarily of gluons, and of the quarks (the up quark and down quark) making up the proton. Hence mp, and therefore the ratio μ, are easily measurable consequences of the strong force. In fact, in the chiral limit, mp is proportional to the QCD energy scale, ΛQCD. At a given energy scale, the strong coupling constant αs is related to the QCD scale (and thus μ) as

α

s

=

−

2

π

β

0

ln

⁡

(

E

/

Λ

Q

C

D

)

{\displaystyle \alpha _{s}=-{\frac {2\pi }{\beta _{0}\ln(E/\Lambda _{\rm {QCD}})}}}

where β0 = −11 + 2n/3, with n being the number of flavors of quarks.

Variation of μ over time

Astrophysicists have tried to find evidence that μ has changed over the history of the universe.