Calculator inputs
Responsive 3 / 2 / 1 column formExample data table
| Scenario | Energy (GeV) | Distance (m) | Mode | Produced taus | Efficiency |
|---|---|---|---|---|---|
| Short tracker section | 5.0 | 0.002 | τ → e ν ν | 25,000 | 92% |
| Inner detector sweep | 10.0 | 0.005 | τ → μ ν ν | 100,000 | 90% |
| Hadronic benchmark | 25.0 | 0.020 | τ → h ν | 250,000 | 85% |
| Topology estimate | 45.6 | 0.050 | 1-prong topology | 1,000,000 | 88% |
Formula used
Lorentz factor: γ = E / mc²
Velocity factor: β = √(1 − 1/γ²)
Mean decay length: Lmean = βγcτ0
Survival probability to distance L: Psurvive = e−L/Lmean
Decay probability: Pdecay = 1 − Psurvive
Total decay width: Γ = ħ / τ0
Expected detected channel events: N = Nτ × Pdecay × BR × efficiency
This calculator treats the tau as a relativistic unstable particle with exponential decay in the lab frame. It converts lifetime into decay width, estimates mean flight distance, and uses the selected branching ratio to forecast observed channel counts.
The partial width equals the total width multiplied by the chosen branching fraction. Detector efficiency is applied only to the selected channel yield, so you can separate physical decay rates from practical reconstruction losses.
How to use this calculator
- Enter the tau mass and mean life, or keep the defaults for standard reference values.
- Set the tau total energy in GeV. Higher energy increases γ and the average flight distance.
- Add the detector travel distance you want to study, such as a tracker radius or decay-volume length.
- Choose the production count and detector efficiency to estimate realistic observed event totals.
- Select a standard decay mode or enter a custom branching ratio for a special channel study.
- Press Submit to place the result summary above the form, then export it as CSV or PDF.
Frequently asked questions
1. What does this calculator estimate?
It estimates relativistic tau behavior using energy, lifetime, distance, branching ratio, and efficiency. Outputs include decay width, lab lifetime, mean decay length, survival probability, and expected detected events.
2. Why does higher energy increase decay length?
Higher energy raises the Lorentz factor γ. That stretches the lifetime in the lab frame and increases βγcτ, so the tau travels farther on average before decaying.
3. What is the difference between survival and decay probability?
Survival probability is the chance a tau reaches the chosen distance without decaying. Decay probability is the complementary chance that it decays before reaching that same distance.
4. Why is the decay width useful?
Decay width is the inverse-timescale view of instability. It is often used in particle physics calculations, rate models, and cross-checks with lifetimes, branching fractions, and partial channel strengths.
5. What does the partial width represent?
The partial width is the share of the total decay width assigned to one decay channel. It equals total width multiplied by the channel branching fraction.
6. Can I use a custom branching ratio?
Yes. Choose the custom option, enter any percentage from 0 to 100, and the calculator will recompute partial width and expected detected event yield for that channel.
7. Does detector efficiency change the physics probabilities?
No. Efficiency does not change the survival or decay physics. It only scales the number of selected channel events you expect to reconstruct or identify experimentally.
8. Are the default inputs suitable for classroom and research use?
They are suitable for fast educational checks and early planning. For publication-grade analyses, replace defaults with the exact values, detector geometry, and channel assumptions used in your study.