The measurement: Λ⁰ → p π⁻

Last updated on 2026-09-30 | Edit this page

Overview

Questions

  • What is the p π⁻ invariant-mass observable, and its peak and background?
  • Which EDM4eic collections and units does it need?

Objectives

  • Compute m(p, π) by hand from the four momentum branches and the PDG masses.
  • Sketch the expected spectrum (peak position, width scale, background shape) before looking at data.

The Setup page covers the servers and the assistant. This episode describes the physics you reconstruct starting in Episode 3.

The decay

The Λ⁰ is the lightest strange baryon (uds, spin-parity ½⁺). It decays only weakly (a strangeness-changing ΔS = 1 transition), so it is long-lived: cτ ≈ 7.9 cm. Its dominant hadronic mode is

Λ⁰ → p + π⁻      (branching fraction ≈ 63.9%)

The centimeter-scale flight distance makes the decay a V0: two oppositely charged tracks from a vertex displaced from the primary interaction point.

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flowchart LR
    accTitle: {Lambda to proton pion V0 decay}
    accDescr: {Lambda to proton pion V0 decay}
    PV["primary vertex<br/>e + A collision"]:::vtx -. "Λ⁰: neutral, cτ ≈ 7.9 cm" .-> DV["displaced<br/>decay vertex"]:::vtx
    DV --> P["proton<br/>PDG 2212"]:::pos
    DV --> PI["pion<br/>PDG -211"]:::neg
    classDef vtx fill:#e7efff,stroke:#4c6ef5,stroke-width:1.5px,color:#10204a;
    classDef pos fill:#ffe3e3,stroke:#e03131,stroke-width:1.5px,color:#5c0a0a;
    classDef neg fill:#e7f5ff,stroke:#1971c2,stroke-width:1.5px,color:#0a3d62;

The observable

The Λ⁰ is neutral and not detected directly; we reconstruct it from its charged daughters. For a candidate proton \(p_1 = (E_1, \vec{p}_1)\) and candidate pion \(p_2 = (E_2, \vec{p}_2)\), the pair’s invariant mass is Lorentz invariant:

\[E_i = \sqrt{|\vec{p}_i|^2 + m_i^2}\]

with \(m_i\) the assigned proton or pion mass, and

\[m(p, \pi) = \sqrt{(E_1 + E_2)^2 - |\vec{p}_1 + \vec{p}_2|^2}\]

Assign the proton mass to one track and the pion mass to the other (using reconstructed particle ID). For true Λ⁰ decays this equals the parent mass; candidates accumulate in a peak at 1.115683 GeV.

Callout

Width: resolution, not lifetime

The Λ⁰ natural width (\(\Gamma = \hbar/\tau \approx 2.5 \times 10^{-6}\) eV) is far below any detector effect. The observed peak width, a few MeV, measures the detector momentum and angular resolution, not the particle.

Background

Most proton–pion pairs do not come from a Λ⁰ at all. These random (“combinatorial”) pairs do not peak; they form a smooth distribution under the signal. The analysis extracts a yield by fitting a Gaussian peak on top of a low-order polynomial background (Episode 5). The charge-conjugate mode Λ̄ → p̄ π⁺ is reconstructed identically with the antiparticles.

Callout

Reference values (PDG)

Quantity Value
m(Λ⁰) 1.115683 GeV
m(p) 0.9382720813 GeV
m(π±) 0.13957061 GeV
cτ(Λ⁰) 7.89 cm
BR(Λ⁰ → p π⁻) 63.9 %

Energies and momenta are in GeV (natural units, c = 1).

The data model

ePIC reconstruction output uses EDM4eic, an EIC extension of EDM4hep generated with PODIO. A file contains an events tree; each entry is one event, each branch a collection. We need one collection, the reconstructed charged tracks, and four members:

events  (tree; one entry per event)
    ReconstructedChargedParticles.PDG          reconstructed particle-ID hypothesis
    ReconstructedChargedParticles.momentum.x   p_x  [GeV]
    ReconstructedChargedParticles.momentum.y   p_y  [GeV]
    ReconstructedChargedParticles.momentum.z   p_z  [GeV]

PDG is the Particle Data Group code the reconstruction assigns each track. Select protons (2212) and π⁻ (-211) for Λ⁰, antiprotons (-2212) and π⁺ (211) for Λ̄.

You do not download a file. In Episode 3 the assistant uses the rucio tools to find a DIS dataset and xrootd to verify its files, then reads one of the dataset’s root:// URLs (e.g. root://epicxrd1.sdcc.bnl.gov:1095//...) in place with the uproot tools. It reads these branches without you writing any I/O code.

Key Points
  • The Λ⁰ shows up as a peak at 1.1157 GeV in the proton–pion invariant mass.
  • The peak width comes from detector resolution.