Taming the pion cloud of the nucleon

The asymmetry of antimatter in the proton

The fundamental building blocks of the proton-quarks and gluons-have been known for decades. However, we still have an incomplete theoretical and experimental understanding of how these particles and their dynamics give rise to the quantum bound state of the proton and its physical properties, such as its spin¹. The two up quarks and the single down quark that comprise the proton in the simplest picture account only for a few per cent of the proton mass, the bulk of which is in the form of quark kinetic and potential energy and gluon energy from the strong force². An essential feature of this force, as described by quantum chromodynamics, is its ability to create matter-antimatter quark pairs inside the proton that exist only for a very short time. Their fleeting existence makes the antimatter quarks within protons difficult to study, but their existence is discernible in reactions in which a matter-antimatter quark pair annihilates. In this picture of quark-antiquark creation by the strong force, the probability distributions as a function of momentum for the presence of up and down antimatter quarks should be nearly identical, given that their masses are very similar and small compared to the mass of the proton³. Here we provide evidence from muon pair production measurements that these distributions are considerably different, with more abundant down antimatter quarks than up antimatter quarks over a wide range of momenta. These results are expected to revive interest in several proposed mechanisms for the origin of this antimatter asymmetry in the proton that had been disfavoured by previous results⁴, and point to future measurements that can distinguish between these mechanisms.

Confinement in Nuclei and the Expanding Proton

High-precision knowledge of electromagnetic form factors of nuclei is an important current activity in nuclear and atomic physics. Such precision mandates that effects of the nonzero spatial extent of the constituent nucleons be treated carefully. A series of simple, Poincaré-invariant, composite-proton models that respect the Ward-Takahashi identity and in which quarks are confined are used to study such effects. All of the models display a general theorem showing how the medium modification of proton structure must occur. Combining this result with lattice QCD calculations leads to a conclusion that a bound proton must be larger than a free one.

The sea of quarks and antiquarks in the nucleon

The quark and gluon structure of the proton has been under intense experimental and theoretical investigation for five decades. Even for the distributions of the well-studied valence quarks, challenges such as the value of the down quark to up quark ratio at high fractional momenta remain. Much of the sea of quark-antiquark pairs emerges from the splitting of gluons and is well described by perturbative evolution in quantum chromodynamics. However, experiments confirm that there is a non-perturbative component to the sea that is not well understood and hitherto has been difficult to calculate with ab initio non-perturbative methods. This non-perturbative structure shows up, perhaps most directly, in the flavor dependence of the sea antiquark distributions. While some of the general trends can be reproduced by models, there are features of the data that do not seem to be well described. This article discusses the experimental situation, the status of calculations and models, and the directions where these studies will progress in the near future.

(d¯)-(u¯) asymmetry in the proton in chiral effective theory

We compute the d[over ¯]-u[over ¯] asymmetry in the proton in chiral effective theory, including both nucleon and Δ degrees of freedom, within the relativistic and heavy baryon frameworks. In addition to the distribution at x>0, we compute the corrections to the asymmetry from zero momentum contributions from pion rainbow and bubble diagrams at x=0, which have not been accounted for in previous analyses. We find that the empirical x dependence of d[over ¯]-u[over ¯] as well as the integrated asymmetry can be well reproduced in terms of a transverse momentum cutoff parameter.