Neutron electric dipole moment using lattice QCD simulations at the physical point

TL;DR

This paper computes the neutron electric dipole moment using lattice QCD simulations at physical quark masses, comparing fermionic and gluonic topological charge definitions, and finds results consistent with zero.

Contribution

It introduces a lattice QCD method to extract the neutron EDM at the physical point, comparing topological charge definitions and providing a precise estimate.

Findings

Fermionic topological charge reduces errors by over two times.

Neutron EDM value is statistically consistent with zero.

Comparison of topological charge definitions enhances reliability.

Abstract

We extract the neutron electric dipole moment $\vert \vec{d}_N\vert$ within the lattice QCD formalism. We analyse one ensemble of $N_f=2+1+1$ twisted mass clover-improved fermions with lattice spacing of $a \simeq 0.08 \ {\rm fm}$ and physical values of the quark masses corresponding to a pion mass $m_{\pi} \simeq 139 \ {\rm MeV}$. The neutron electric dipole moment is extracted by computing the $CP$-odd electromagnetic form factor $F_3(Q^2 \to 0)$ through small $\theta$-expansion of the action. This approach requires the calculation of the topological charge for which we employ a fermionic definition by means of spectral projectors while we also provide a comparison with the gluonic definition accompanied by the gradient flow. We show that using the topological charge from spectral projectors leads to absolute errors that are more than two times smaller than those provided when the field theoretic definition is employed. We find a value of $\vert \vec{d}_N\vert = 0.0009(24) \ \theta \ e \cdot {\rm fm}$ when using the fermionic definition, which is statistically consistent with zero.