[Paper Review] Electromagnetic Form Factors for the $\Lambda$(1405)

Benjamin J. Menadue, Waseem Kamleh+3 more|arXiv (Cornell University)|Nov 20, 2013

Quantum Chromodynamics and Particle Interactions7 references3 citations

TL;DR

This study presents the first lattice QCD calculation of electromagnetic form factors for the Λ(1405), using a variational method with multiple source and sink smearings to isolate the state. The results reveal a significant departure from flavor-singlet behavior as the u and d quark masses approach their physical values, providing strong evidence for a non-trivial K̄N molecular component in the Λ(1405) wavefunction.

ABSTRACT

Building on our successful technique to isolate the otherwise-elusive $\\Lambda$(1405) using correlation matrix techniques and multiple source and sink smearings, we present calculations of the quark sector contributions to the electric form factors of the $\\Lambda$(1405). Using the PACS-CS $(2+1)$-flavour full-QCD ensembles available through the ILDG, our calculations reveal behaviour consistent with the development of a non-trivial molecular $\\overline{K}N$ bound-state component as one approaches the physical values of the $u$ and $d$ quark masses.

Motivation & Objective

• To calculate the electromagnetic form factors of the Λ(1405) baryon using lattice QCD.
• To investigate the quark-sector contributions to the electric form factors of the Λ(1405) in the low-energy regime.
• To probe the internal structure of the Λ(1405), particularly the emergence of a K̄N molecular component as the u and d quark masses are tuned toward their physical values.
• To validate the use of variational methods with multiple smearings and interpolating fields for isolating exotic baryon states in lattice QCD.

Proposed method

• Employed a 6×6 correlation matrix of interpolating fields with varying smearing and Dirac structures to disentangle mixed octet and singlet states.
• Used multiple source and sink smearings (16 and 100 sweeps) to enhance overlap with the ground state and suppress excited-state contamination.
• Applied variational analysis to extract the lowest-lying state with high stability in Euclidean time, enabling reliable current insertion for form factor calculations.
• Calculated effective form factors using matrix elements of current insertions at t=21, with the fermion source at t=16, to ensure long-time stability.
• Used the dipole fit ansatz to correct for momentum transfer dependence and enable comparison across different pion masses.
• Performed simulations on PACS-CS (2+1)-flavor full-QCD ensembles with pion masses from 156 to 640 MeV, using the PACS-CS scale-setting scheme.

Experimental results

Research questions

• RQ1 How do the electric form factors of the Λ(1405) vary with pion mass, particularly in the light-quark regime?
• RQ2 To what extent do the individual quark sector contributions (u, d, s) deviate from flavor-singlet symmetry as the u and d quark masses are reduced?
• RQ3 What evidence exists for a K̄N molecular component in the Λ(1405) structure based on the form factor behavior?
• RQ4 How effective is the variational method with multiple smearings in isolating the Λ(1405) from nearby octet and singlet states?
• RQ5 How do the form factors of the Λ(1405) compare to those of the ground-state Λ across the pion mass range?

Key findings

• The electric form factor of the light quarks (u/d) in the Λ(1405) shows a significant departure from the flavor-singlet behavior as the pion mass approaches its physical value.
• The strange quark form factor is suppressed relative to the ground-state Λ, consistent with the influence of the K̄N component distributing the strange quark further out.
• The light quark form factor is enhanced compared to the ground state, indicating that the anti-strange quark in the K̄N component pushes the light quark distribution outward.
• The behavior of the form factors across the pion mass range is consistent with the development of a non-trivial K̄N bound-state component in the Λ(1405) wavefunction.
• The variational method successfully isolates the Λ(1405) with long-time stability, enabling reliable extraction of form factors despite the state's exotic nature.
• The form factor results are robust under scale-setting variations between the Sommer and PACS-CS schemes, confirming the qualitative reliability of the findings.