[Paper Review] Nucleon Electric Dipole Moments from QCD Sum Rules

Chuan-Tsung Chan, Ernest M. Henley+1 more|ArXiv.org|May 12, 1999

Quantum Chromodynamics and Particle Interactions1 references3 citations

TL;DR

This paper calculates nucleon electric dipole moments (NEDM) using QCD sum rules, deriving a functional dependence of NEDM on the QCD $θ$-bar parameter without perturbative assumptions. It finds $|\bar{\theta}| < 10^{-9}$, consistent with symmetry constraints and excluding dynamical CP suppression in QCD, in agreement with experimental nEDM bounds.

ABSTRACT

The electric dipole moments of nucleons (NEDM, d_N) are calculated using the method of QCD sum rules. Our calculations are based on the parity and time reversal violating parameter $ hetabar$ in QCD and establish a functional dependence of the NEDM on $ hetabar$, without assuming a perturbative expansion of this symmetry breaking parameter. The results obtained from the QCD sum rules approach are shown to be consistent with the general symmetry constraints on CP violations in QCD, including the necessity of: (1) finite quark masses, (2) spontaneous chiral symmetry breaking, and (3) the U_A(1) anomaly. Given the current experimental upper bound on the neutron electric dipole moment (nEDM), d_n &lt; 10^(-25) e-cm, we find | hetabar | &lt; 10^(-9). This result is compatible with previous calculations of nEDM using different techniques and excludes the possibility of solving the strong CP problem within QCD via a dynamical suppression mechanism.

Motivation & Objective

• To compute nucleon electric dipole moments (NEDM) using non-perturbative QCD methods.
• To establish a functional relationship between the NEDM and the QCD $\theta$-bar parameter without assuming perturbative expansions.
• To verify consistency with fundamental symmetry constraints: finite quark masses, spontaneous chiral symmetry breaking, and the U_A(1) anomaly.
• To constrain the value of $\bar{\theta}$ using the experimental upper bound on the neutron EDM.
• To assess the viability of dynamical CP violation mechanisms in resolving the strong CP problem.

Proposed method

• Employs the method of QCD sum rules to compute matrix elements of the electromagnetic current operator in the presence of $\theta$-violating interactions.
• Incorporates non-perturbative QCD effects such as quark condensates and gluon condensates in the sum rule formalism.
• Uses the operator product expansion (OPE) to systematically include higher-dimensional operators relevant to CP violation.
• Imposes constraints from chiral symmetry breaking and the U_A(1) anomaly to ensure consistency with QCD dynamics.
• Relies on the full QCD Lagrangian with the $\theta$-term to derive the NEDM in terms of $\bar{\theta}$.
• Performs a sum rule analysis on the correlation function of the electromagnetic current and the scalar current to extract the matrix element.

Experimental results

Research questions

• RQ1 What is the non-perturbative relation between the nucleon electric dipole moment and the QCD $\theta$-bar parameter?
• RQ2 How do the fundamental symmetries of QCD—finite quark masses, spontaneous chiral symmetry breaking, and the U_A(1) anomaly—affect the NEDM?
• RQ3 Can the QCD sum rules approach reproduce the known symmetry constraints on CP violation in QCD?
• RQ4 What is the upper bound on $\bar{\theta}$ implied by the current experimental limit on the neutron EDM?
• RQ5 Does the result exclude the possibility of dynamical CP violation mechanisms solving the strong CP problem?

Key findings

• The NEDM is found to depend non-perturbatively on the $\theta$-bar parameter, with no assumption of small $\theta$-bar.
• The calculation satisfies all required symmetry constraints: finite quark masses, spontaneous chiral symmetry breaking, and the U_A(1) anomaly.
• Given the experimental upper bound $d_n < 10^{-25}$ e-cm, the paper derives $|\bar{\theta}| < 10^{-9}$.
• This bound is consistent with previous calculations using different non-perturbative methods.
• The result rules out the possibility of solving the strong CP problem via a dynamical suppression mechanism within QCD.
• The functional dependence of NEDM on $\bar{\theta}$ is established without perturbative approximations.