[Paper Review] Flavor Decomposition of Nucleon Form Factors

B. Wojtsekhowski|arXiv (Cornell University)|Jan 7, 2020

High-Energy Particle Collisions Research4 citations

TL;DR

This paper proposes a high-precision measurement of the proton's strange form factor at large momentum transfer (Q² > 3 GeV²) using the Super BigBite Spectrometer at Jefferson Lab. By exploiting longitudinal electron beam asymmetry in elastic scattering, the method isolates the s-quark contribution via interference with u- and d-quark currents, aiming to reduce uncertainty in flavor-separated form factors by a factor of six and set the first experimental limit on Fₛᵖ at high Q².

ABSTRACT

The nucleon form factors provide fundamental knowledge about the strong interaction. We review the flavor composition of the nucleon form factors and focus on an analysis of the possible impact of the s-quark contribution. A future experiment is presented to measure the strange form factor at large momentum transfer.

Motivation & Objective

• To measure the strange form factor Fₛᵖ of the proton at large momentum transfer (Q² > 3 GeV²), where pQCD scaling is expected.
• To reduce the current uncertainty in flavor-separated nucleon form factors—particularly F₂ᵈ—by suppressing the dominant uncertainty from strangeness contributions.
• To test the role of quark correlations (e.g., u-u diquark correlations) by analyzing the Q² dependence of flavor-specific form factor ratios.
• To provide the first experimental limit on Fₛᵖ at high Q², which is critical for understanding the internal structure of the nucleon beyond the valence quark model.

Proposed method

• Use longitudinal electron beam asymmetry in elastic ep scattering to isolate the s-quark contribution via interference with u- and d-quark currents in the electromagnetic current matrix element.
• Apply the one-photon exchange approximation, where the hadronic current J_μ^ⁿᵘᶜ is decomposed into u, d, and s quark contributions: J_μ^ⁿᵘᶜ = (2/3)ūγₘu + (-1/3)đγₘd + (-1/3)ŝγₘs.
• Measure the parity-violating (PV) asymmetry, which is proportional to the interference term involving Gᴹˢ and Gᴱˢ, enabling extraction of the strange form factors.
• Utilize a detector setup with high solid angle (0.1 sr) and tight time/angle correlations between scattered electron and recoiled proton to suppress inelastic background.
• Leverage the SBS spectrometer's existing infrastructure, including segmented hadron and electromagnetic calorimeters, for efficient detection and background rejection.
• Achieve 3% relative accuracy in PV asymmetry within 30 days of data taking at 6.6 GeV beam energy, translating to ΔFₛᵖ ≈ 0.002 at Q² = 3 GeV².

Experimental results

Research questions

• RQ1 What is the momentum transfer dependence of the strange form factor Fₛᵖ at Q² > 3 GeV², and does it exhibit a maximum at higher Q² than the neutron electric form factor due to the s-quark mass?
• RQ2 How does the suppression of the d-quark contribution to F₂ᵖ at high Q² (by a factor of 3 from Q² = 1 to 3.4 GeV²) affect the interpretation of scaling violations in nucleon form factors?
• RQ3 To what extent does the uncertainty in the s-quark contribution limit the precision of flavor-separated form factors like F₂ᵈ, and can this be reduced experimentally?
• RQ4 Can the observed Q² dependence of F₂ᵖ/F₁ᵖ be explained without invoking quark orbital angular momentum, and what does this imply about diquark correlations?

Key findings

• The d-quark contribution to the proton's Pauli form factor F₂ᵖ is suppressed by a factor of three when Q² increases from 1 to 3.4 GeV², indicating strong flavor-dependent dynamics.
• The u-quark contribution to F₁ᵖ at Q² = 3.4 GeV² is three times larger than the d-quark contribution when corrected for charge and quark number, suggesting enhanced u-u correlations.
• The uncertainty in the strange form factor Gᴹˢ and Gᴱˢ contributes linearly to the uncertainty in flavor-separated form factors, with Δ(Q⁴F₂ᵈ) ≈ 0.35 at Q² = 3.4 GeV²—larger than the uncertainty from Gᴱⁿ.
• The proposed experiment can reduce the uncertainty in F₂ᵈ by a factor of six by measuring Fₛᵖ with ΔFₛᵖ ≈ 0.002 at Q² = 3 GeV².
• A 30-day run with 6.6 GeV beam can achieve 3% relative accuracy in the PV asymmetry, enabling the first experimental limit on Fₛᵖ at Q² > 3 GeV².
• The detector configuration with 0.1 sr solid angle and tight kinematic correlations limits event rate variation to a factor of 4, ensuring stable acceptance across the desired Q² range.