Calculator Inputs
Plotly Graph
The chart shows how the proxy differential cross section and expected signal events vary with scattering angle for your current input set.
Example Data Table
| Scenario | √s (GeV) | m₁ (GeV) | m₂ (GeV) | θ (deg) | geff | Λ (GeV) | L (fb⁻¹) | Efficiency |
|---|---|---|---|---|---|---|---|---|
| Baseline WW | 3000 | 80.379 | 80.379 | 45 | 0.65 | 2000 | 300 | 0.70 |
| High-energy scan | 5000 | 80.379 | 91.188 | 60 | 0.72 | 2500 | 1000 | 0.62 |
| Efficiency-limited | 2500 | 91.188 | 91.188 | 35 | 0.60 | 1800 | 140 | 0.48 |
Formula Used
This calculator uses a simplified effective-scattering model rather than a full electroweak Monte Carlo implementation. It is useful for rapid scenario screening.
Core definitions
- s = (√s)²
- β = √[1 - (m₁ + m₂)² / s]
- t = m₁² - ½s(1 - β cosθ)
- u = m₂² - ½s(1 + β cosθ)
Effective amplitude proxy
|M| = geff2 × P × (1 + cos²θ) × [1 / (1 + s / Λ²)] × [1 - ½(m₁² + m₂²)/s]
Differential cross section proxy
dσ/dΩ = β|M|² / (64π²s)
Integrated proxy cross section
σ ≈ K × β|M|² / (16πs)
Event yield and significance
Signal events = σ × L × 1000 × efficiency
Background events = σbkg × L × 1000 × efficiency
Significance ≈ S / √(S + B)
The conversion from GeV⁻² to pb uses 3.89379 × 10⁸ pb per GeV⁻².
How to Use This Calculator
- Enter the collider center-of-mass energy in GeV.
- Provide the two outgoing vector boson masses.
- Set the scattering angle for the differential estimate.
- Choose an effective coupling and unitarization scale.
- Add polarization weight, luminosity, efficiency, and K-factor.
- Optionally enter a background cross section for significance.
- Press the calculation button to show results above the form.
- Review the graph, export the table as CSV, or save PDF.
FAQs
1) What does this calculator estimate?
It estimates simplified vector boson scattering observables, including Mandelstam variables, a proxy differential cross section, integrated cross section, expected events, and approximate significance.
2) Is this a replacement for a full collider simulation?
No. It is a fast educational and planning tool. Precision studies still require full matrix-element generators, detector simulation, detailed cuts, and theory-systematics treatment.
3) Why is there an effective coupling input?
The effective coupling lets you scan interaction strength assumptions quickly. It helps compare scenarios without rebuilding a full electroweak model each time.
4) What is the unitarization scale doing?
The scale suppresses growth at high energy through a simple form factor. It keeps the proxy amplitude better behaved during rough scenario studies.
5) Why do event counts use luminosity times 1000?
Cross sections are reported in picobarns, while luminosity is entered in inverse femtobarns. Multiplying luminosity by 1000 converts fb⁻¹ to pb⁻¹.
6) What is the polarization weight?
It is a user-controlled factor that approximates polarization-channel emphasis. You can use it to compare stronger or weaker contributions from selected boson states.
7) Can I use this for WW, WZ, or ZZ scattering?
Yes. Enter the masses appropriate to your chosen final state and adjust the effective coupling, scale, efficiency, and background assumptions accordingly.
8) Why does the graph vary with angle?
The proxy amplitude contains an angular term, so the differential cross section changes with θ. That angular behavior also shifts the expected event yield curve.