The measurement: Λ⁰ → p π⁻

Overview

Questions

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

Objectives

• Write m(p, π) in terms of the four branches and the PDG masses.
• State the expected peak position, width scale, and background shape before looking at data.

The observable

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The Λ⁰ decays weakly to p π⁻ (branching fraction ≈ 63.9%, cτ ≈ 7.9 cm). It is neutral, so we reconstruct it from its charged daughters. Assign the proton mass to one track and the pion mass to the other, using the reconstructed particle ID:

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

True Λ⁰ decays accumulate in a peak at 1.115683 GeV. Its width, a few MeV, is the detector resolution; the natural width is negligible. Random proton–pion pairs form a smooth combinatorial background under the peak, so the yield comes from a fit: a Gaussian on a second-order polynomial (Episode 5). The charge-conjugate mode Λ̄ → p̄ π⁺ is reconstructed the same way.

Quantity	Value
m(Λ⁰)	1.115683 GeV
m(p)	0.9382720813 GeV
m(π±)	0.13957061 GeV

The data model

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ePIC reconstruction output uses EDM4eic. A file contains an events tree; each entry is one event, each branch a collection. We need one collection 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]

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.