Branching Ratio Calculator
Compute the branching ratio BR = Γᵢ/Γ_total for up to 4 particle decay channels from their partial decay widths.
📊 What is the Branching Ratio Calculator?
This branching ratio calculator computes the branching ratio (also called branching fraction) for up to 4 particle decay channels, using BR_i = Γ_i / Γ_total, where Γ_i is a channel's partial decay width and Γ_total is the sum of every channel's partial width.
Particle physicists use branching ratios to describe how an unstable particle splits its decays across different final states. For example, the Z boson decays to hadrons about 69.9% of the time, to charged lepton pairs about 3.4% of the time each, and to neutrino pairs (invisible decays) about 20.0% of the time. The W boson decays to hadrons about 67.5% of the time and to each charged lepton plus neutrino pair about 10.8% of the time.
A common point of confusion is mixing up partial width and branching ratio: the partial width Γ_i is an energy-dimension quantity (measured in eV, MeV, or GeV) describing how fast one specific channel proceeds, while the branching ratio is the dimensionless fraction that channel represents out of all decays. Because branching ratio is a ratio, any consistent unit works for the inputs, the units cancel in the division.
This calculator is useful for particle physics students and researchers who have measured or looked up partial decay widths and want to quickly convert them into branching ratios, or who want to check that a set of measured branching fractions is internally consistent.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Z boson decay channels
Example 2 - W boson decay channels
Example 3 - Simple round-number breakdown
❓ Frequently Asked Questions
🔗 Related Calculators
What is a branching ratio in particle physics?
The branching ratio (or branching fraction) BR of a decay channel is the fraction of all decays of a particle that proceed through that specific channel: BR_i = Γ_i/Γ_total, where Γ_i is the channel's partial decay width and Γ_total is the sum of all partial widths.
What is the formula for branching ratio?
BR_i = Γ_i / Γ_total, where Γ_total = Γ_1 + Γ_2 + ... + Γ_n is the sum of the partial decay widths of every open decay channel. Multiply by 100 to express it as a percentage.
Do branching ratios always add up to 100%?
Yes, when every decay channel of a particle is included, the branching ratios sum to exactly 100% (1.0), since Γ_total is defined as the sum of all partial widths. If you only enter a subset of channels, their branching ratios will sum to less than 100%.
What units should I use for the partial decay width?
Any consistent energy unit works (eV, keV, MeV, or GeV), because branching ratio is a ratio and the units cancel. Just make sure every channel you enter uses the same unit.
What is the difference between partial width and total width?
The partial width Γ_i measures how quickly a particle decays through one specific channel alone. The total width Γ_total = Σ Γ_i measures how quickly it decays through all channels combined, and sets the particle's overall mean lifetime via τ = ħ/Γ_total.
What is a real example of branching ratios?
The Z boson decays to hadrons about 69.9% of the time, to each charged lepton pair (e, μ, τ) about 3.4% of the time each, and to neutrino pairs (invisible) about 20.0% of the time, based on measured partial widths of roughly 1.7444, 0.0840, and 0.4990 GeV.
Can a branching ratio be greater than 100%?
No. Since a partial width can never exceed the total width (Γ_i ≤ Γ_total by definition), a correctly computed branching ratio is always between 0% and 100%.
How is branching ratio measured experimentally?
Experimentally, branching ratio is usually measured as the number of observed decay events in a specific channel divided by the total number of observed decay events, which is equivalent to the ratio of partial widths once enough events have been collected to be statistically representative.
Why do some decay channels have a much higher branching ratio than others?
A channel's partial width, and therefore its branching ratio, depends on the coupling strength of the interaction involved and the available phase space (how much kinetic energy the decay products can carry away). Channels with stronger couplings and more phase space have larger partial widths and higher branching ratios.
Is branching ratio the same as decay probability?
Yes, for a single decay event, the branching ratio of a channel equals the probability that the particle decays through that specific channel rather than any other open channel.