Extraordinary nature of the nucleon scalar charge and its densities as a signal of nontrivial vacuum structure of QCD

Abstract

It is widely known that the nucleon scalar charge is proportional to the pion-nucleon sigma term as one of the important low energy observables of QCD. Especially interesting to us is the physics of the nucleon scalar charge densities. This comes from the fact that the corresponding operator has the same quantum number as the physical vacuum. It indicates unusual behavior of the the nucleon scalar density as a function of the distance $r$ from the nucleon center. Namely, it would not be reduced down to zero at the spatial infinity but rather approaches some nonzero constant corresponding to the vacuum quark condensate. Naturally, this unique nature of the nucleon scalar density in the position space also affects the corresponding density in the momentum space, i.e. the corresponding parton distribution function (PDF) as a function of the Bjorken variable $x$. This PDF is known as the chiral-odd twist-3 PDF $e(x)$. We argue that $e(x)$ is likely to have a delta-function type singularity at $x=0$, and that the appearance of this singularity can be interpreted as a signal of the nontrivial vacuum structure of the QCD.

invited contribution to a Special Issue of Symmetry : "Chiral Symmetry, and Restoration in Nuclear Dense Matter"

References in corpus (7)

• Extraction of Spin-Dependent Parton Densities and Their Uncertainties
• The Deuteron Spin-dependent Structure Function g1d and its First Moment
• Nucleon axial, scalar, and tensor charges using lattice QCD at the physical pion mass
• On the role of isospin violation in the pion-nucleon $\sigma$-term
• Parton distribution function for the gluon condensate
• Extraction of the higher-twist parton distribution $e(x)$ from CLAS data
• On the new COMPASS measurement of the deuteron spin-dependent structure function $g_1^d$

Cited by in corpus (1)

• Chiral Solitons