Higgs Boson Decay Width Estimator

A partial decay width Gamma for a specific final state is the contribution that channel makes to the particle's total decay rate, measured in energy units (MeV here). Larger partial width means the Higgs decays to that fermion pair more often relative to other channels, the sum of all partial widths gives the total width, about 4.07 MeV for the Higgs boson.

The Higgs boson couples to fermions with a strength directly proportional to their mass, a direct consequence of the Higgs mechanism giving fermions their mass through this same coupling. Squaring that coupling in the decay rate formula gives the m_f squared scaling, which is also why the Higgs decays overwhelmingly to the heaviest kinematically accessible fermion, bottom quarks, rather than lighter ones.

This calculator computes only the leading order (tree-level) width, about 1.91 MeV for bb, while the measured Standard Model value is about 2.35 MeV. The gap comes from higher-order QCD radiative corrections, which are significant for colored quarks like bottom and charm but are completely absent for leptons. This tree-level number should not be read as matching the measured value directly.

Leptons carry no color charge, so they receive no QCD radiative corrections at all, the electroweak corrections that do apply are much smaller. That is why the tree-level formula used here gives about 0.259 MeV for tau (measured about 0.257 MeV) and about 0.918 keV for muon (measured about 0.887 keV), both within a few percent, while the quark channels undershoot by 15 to 20%.

A pole mass is the mass you would measure for a free, isolated particle, the everyday value used in most kinematics calculations. A running (MS-bar) mass instead depends on the energy scale at which it is evaluated, due to quantum corrections, and for quarks it is noticeably smaller than the pole mass at high energy scales. This calculator uses running masses evaluated at the Higgs mass scale (for example 2.79 GeV for the bottom quark, versus a pole mass closer to 4.8 GeV), which is why these values look smaller than the quark masses used elsewhere on this site.

125.25 GeV is the current measured Standard Model Higgs boson mass, a well established experimental result from ATLAS and CMS. Letting it vary would not represent a real physical scenario, so this calculator treats it as a constant and only lets the fermion mass, color factor, and fermion choice vary.

Bottom quark (mf=2.79 GeV, Nc=3), charm quark (mf=0.62 GeV, Nc=3), tau lepton (mf=1.77686 GeV, Nc=1), and muon (mf=0.1056584 GeV, Nc=1) are built in using MS-bar running masses at the Higgs scale, or you can enter a custom mass and color factor for any hypothetical fermion.

Nc counts the number of color states a fermion can carry. Quarks come in 3 colors (Nc=3), so each quark flavor contributes 3 times as much to the decay rate as a single lepton generation would at the same mass, since the Higgs can produce the fermion pair in any of the 3 color combinations. Leptons carry no color charge, so Nc=1 for tau and muon.

The top quark mass (about 173 GeV) is more than twice the Higgs mass (125.25 GeV), so there is not enough energy to create a top-antitop pair, this is why the (1 - 4mf squared/mH squared) term in the formula would become negative and the decay is kinematically forbidden. This calculator returns an error if you enter a custom mass above about 62.6 GeV for exactly this reason.

For leptons (tau, muon) it is accurate to within a few percent of the measured Standard Model value. For quarks (bottom, charm) it systematically undershoots by roughly 15 to 20%, since QCD radiative corrections, which this simplified calculator omits, meaningfully increase the true partial width for colored particles.

The Standard Model total Higgs decay width is about 4.07 MeV, with the bb channel alone making up roughly 58% of it (about 2.35 MeV), the single largest decay channel, precisely because the bottom quark is the heaviest fermion the Higgs can kinematically decay to in a fermion pair.