Physical Constants

Speed of light in vacuum: c = 299 792 458 ms −1

Gravitational constant: GN = 6. 67428(67) × 10 −11 m3 kg −1s−2

= 6. 70881(67) × 10 −39 ħc (GeVc−2) −2

Planck's constant: h = 6. 62606896(33) × 10 −34 J s

(Planck's constant)/2π: ħ = 1. 054571628(53) × 10 −34 J s

= 6. 58211899(16) × 10 −22 MeV s

Reduced Planck mass: MPl = (8πGN/ħc) −1/2

= 2. 43 × 1018GeVc2

Fine structure constant: α = e2/ħc = 1/137. 035

Fermi constant: GF/(ħc)3 = 1. 16637(1) × 10 −5 GeV −2

Boltzmann constant: kB = 1. 3806504(24) × 10 −23 JK −1

= 8. 617343(15) × 10 −5 eVK −1

Electron mass: me = 0. 51099 MeV

Proton mass: mp = 938. 2720 MeV

W−boson mass: MW = (80. 399 ± 0. 023) GeV

Z − boson mass: MZ = (91. 1876 ± 0. 0021) GeV

Strong coupling constant: αs (MZ) = 0. 1184(7)

Electron electric dipole moment: de < (7 ± 7) × 10 −28 ecm

Neutron electric dipole moment: dn < 0. 29 × 10 −25 ecm,

confidence limit (CL) = 90%

Some useful conversions are

The values of the physical constants listed are from K. A. Olive et al. (Particle Data Group), “Review of Particle Physics,” Chin. Phys. C 38, 090001 (2014).

Natural Units

Often, it is convenient to use units where the natural physical constants assume unit values. For instance, if we assume units so that

then in these units energy can be expressed as inverse length since L = ħc/E = 1/E, which gives

One may also assume as fundamental units the Boltzmann constant and Newton's constant so that

Equations (23.1) and (23.2) taken together are often referred to as Planck natural units.