[Paper Review] Elastic Cross-Section and Luminosity Measurement in ATLAS at LHC

I. Efthymiopoulos|ArXiv.org|Oct 31, 2005

Particle Detector Development and Performance1 references3 citations

TL;DR

This paper proposes using ultra-small-angle Roman Pot detectors at 240 m from the ATLAS interaction point to measure elastic proton scattering in the Coulomb-Nuclear Interference (CNI) region for absolute luminosity determination at the LHC. By fitting the differential cross-section to the CNI formula, the method enables luminosity measurement with ~2% statistical uncertainty, while also extracting total cross-section, ρ-parameter, and nuclear slope.

ABSTRACT

Recently the ATLAS experiment was complemented with a set of ultra-small-angle detectors located in ``Roman Pot'' inserts at 240m on either side of the interaction point, aiming at the absolute determination of the LHC luminosity by measuring the elastic scattering rate at the Coulomb Nuclear Interference region. Details of the proposed measurement the detector construction and the expected performance as well as the challenges involved are discussed here.

Motivation & Objective

• To enable absolute luminosity determination at the LHC using elastic proton scattering in the Coulomb-Nuclear Interference (CNI) region.
• To overcome ATLAS's limited forward coverage by accessing smaller angles than previously possible, reaching the theoretically calculable CNI regime.
• To achieve luminosity uncertainty below 2% using a fit to the CNI formula, minimizing reliance on inelastic rate measurements.
• To simultaneously extract fundamental parameters such as total cross-section, ρ-parameter, and nuclear slope from the same data.
• To support high-precision physics measurements in ATLAS, including Higgs boson rate and top quark pair production, by reducing luminosity uncertainty.

Proposed method

• Deploy ultra-small-angle detectors in 'Roman Pot' inserts at 240 m from the ATLAS interaction point to detect protons scattered at angles as small as 3.5 μrad.
• Use 'parallel-to-point' optics to focus scattered protons onto detectors, enabling precise reconstruction of momentum transfer t via y_det = θ*L_eff.
• Apply the CNI formula: dN/dt ≈ Lπ(f_C + f_N)^2, where f_C and f_N represent electromagnetic and strong amplitudes, to fit the differential cross-section.
• Utilize edge-less scintillating fiber tracker planes (0.5 mm fibers, 50 μm pitch) read out by multi-anode PMTs for high spatial resolution (<30 μm) and low acceptance loss.
• Implement a coincidence trigger using left-up/right-down hits and halo tracks for precise gap calibration and absolute t-scale determination.
• Perform statistical fits to simulated data in the CNI region (0.00055 ≤ |t| ≤ 0.03 GeV²) to extract luminosity and other parameters with minimal systematic bias.

Experimental results

Research questions

• RQ1 Can the luminosity at the LHC be determined absolutely with sub-2% uncertainty using elastic scattering in the CNI region?
• RQ2 To what extent can the CNI region be probed at LHC energies (7 TeV) with current detector and optics capabilities?
• RQ3 How accurately can the ρ-parameter, total cross-section, and nuclear slope be extracted from a fit to the CNI formula using real data?
• RQ4 What are the dominant systematic and background challenges in measuring small-angle elastic scattering near the beam pipe?
• RQ5 Can the luminosity measured via Roman Pot detectors be reliably transferred to high-luminosity running conditions using a calibrated luminometer like LUCID?

Key findings

• A statistical uncertainty of approximately 2% in luminosity was achieved in simulations using 5 million events, corresponding to ~90 hours of LHC running at 10²⁷ cm⁻²s⁻¹.
• The detector design achieves a spatial resolution of 20 μm with 95% efficiency, sufficient to resolve the required small-angle scattering at 3.5 μrad.
• The use of halo tracks in overlap detectors enables precise calibration of the inter-pot gap, ensuring accurate absolute t-scale determination.
• The method allows extraction of the ρ-parameter, total cross-section (σ_tot), and nuclear slope (b) as fit parameters, enhancing physics reach beyond luminosity.
• The expected background rate from beam halos is ~6 kHz, while the elastic signal rate is ~30 Hz at low-luminosity runs, providing a favorable signal-to-noise ratio.
• Theoretical and experimental results suggest that reaching the CNI region at |t| ≈ 6.5×10⁻⁴ GeV² is feasible with special optics and 10σ beam approach, maintaining emittance and beam stability.