[Paper Review] P and T odd effects in deuteron in the Reid potential

R. V. Korkin|ArXiv.org|Apr 27, 2005

Quantum, superfluid, helium dynamics3 citations

TL;DR

This paper calculates P and T odd electromagnetic moments—specifically the electric dipole moment (EDM) and photodisintegration cross section asymmetry—in the deuteron using the Reid nucleon-nucleon potential in the chiral limit (mπ → 0). It finds that the d-wave component of the deuteron wave function strongly influences the asymmetry, yielding A = 0.16 × 10⁻⁷, significantly lower than previous zero-range approximations, and confirms that vector meson contributions are negligible compared to pion exchange.

ABSTRACT

The $P$ and $T$ odd deuteron multipoles are calculated in the Reid nucleon-nucleon potential in the chiral limit $m_π o 0$. The contact current generated by the $π$-meson exchange does not contribute to the anapole moment. The contact current generated by the vector meson exchange is negligible in comparison with other contributions of vector mesons. The result for the deuteron electric dipole moment is of great interest because of the experiment on its measurement discussed in Brookhaven. The deuteron photodisintegration cross section asymmetry at the threshold is also calculated. It is shown that its value strongly depends on the tensor forces and d-wave contribution to the deuteron wave function.

Motivation & Objective

• To calculate the deuteron's electric dipole moment (EDM) and magnetic quadrupole moment (MQM) in the chiral limit using the Reid potential.
• To investigate the role of d-wave admixture and short-distance behavior of the deuteron wave function in P and T odd observables.
• To resolve discrepancies in theoretical predictions of the P-odd photodisintegration cross section asymmetry by using realistic wave functions.
• To assess the contributions of pion and vector meson exchanges to the anapole moment and EDM, particularly in the context of upcoming Brookhaven experiments.

Proposed method

• Solves the Schrödinger equation numerically for the deuteron's S- and D-wave components using the soft-core Reid potential.
• Derives perturbed wave functions including P and T odd weak interactions via weak PNC nucleon-nucleon potentials.
• Computes the electric dipole moment (EDM) and magnetic quadrupole moment (MQM) using matrix elements involving the wave functions and weak current operators.
• Calculates the photodisintegration cross section asymmetry A in γd → np at threshold using the full deuteron wave function and weak current matrix elements.
• Evaluates contributions from pion exchange (singular in mπ), vector mesons (ρ and ω), and nucleon anapole moments separately.
• Compares results with previous zero-range approximations and other realistic potentials (e.g., Argonne v18), focusing on d-wave dependence and short-distance sensitivity.

Experimental results

Research questions

• RQ1 How does the d-wave component of the deuteron wave function affect the P-odd photodisintegration cross section asymmetry in γd → np?
• RQ2 What is the relative contribution of pion exchange versus vector meson exchange to the deuteron's electric dipole moment (EDM) in the chiral limit?
• RQ3 Why do theoretical predictions for the deuteron's P-odd asymmetry vary so significantly between different models and potentials?
• RQ4 How do the short-distance behaviors of the deuteron wave function and weak current matrix elements influence the EDM and MQM?
• RQ5 To what extent do vector meson contributions to the anapole moment and EDM deviate from negligible values in realistic potentials?

Key findings

• The calculated photodisintegration cross section asymmetry at threshold is A = 0.16 × 10⁻⁷, significantly lower than previous zero-range approximations (e.g., ~1 × 10⁻⁷), due to strong d-wave dependence.
• The d-wave admixture (Pd = 6.5%) in the Reid potential has a dominant influence on the asymmetry, and removing it increases A to 0.74 × 10⁻⁷, highlighting its critical role.
• The pion-exchange contribution to the anapole moment is singular in the pion mass and dominates, while vector meson contributions are negligible in magnitude.
• The deuteron EDM is found to be consistent with previous results in the literature, with the g₀ term vanishing in this calculation, unlike in some earlier models.
• Vector meson contributions to the EDM and MQM are small and highly sensitive to short-distance wave function behavior, making them model-dependent and unreliable in this context.
• The discrepancy between this work and previous results (e.g., depl2, FT) is primarily attributed to differences in d-wave content and wave function behavior at small distances.