nucl-th digest · Oct 19, 2020

[Submitted on 15 Oct 2020] (cross-list from hep-ph)

Constraints on the two-pion contribution to hadronic vacuum polarization

Gilberto Colangelo🇨🇭 · Martin Hoferichter🇨🇭 · Peter Stoffer🇺🇸

At low energies hadronic vacuum polarization (HVP) is strongly dominated by two-pion intermediate states, which are responsible for about $70%$ of the HVP contribution to the anomalous magnetic moment of the muon, $a_{μ}^{HVP}$ . Lattice-QCD evaluations of the latter indicate that it might be larger than calculated dispersively on the basis of $e^{+} e^{-} \to hadrons$ data, at a level which would contest the long-standing discrepancy with the $a_{μ}$ measurement. In this Letter we study to which extent this $2 π$ contribution can be modified without, at the same time, producing a conflict elsewhere in low-energy hadron phenomenology. To this end we consider a dispersive representation of the $e^{+} e^{-} \to 2 π$ process and study the correlations which thereby emerge between $a_{μ}^{HVP}$ , the hadronic running of the fine-structure constant, the $P$ -wave $π π$ phase shift, and the charge radius of the pion. Inelastic effects play an important role, despite being constrained by the Eidelman-Lukaszuk bound. We identify scenarios in which $a_{μ}^{HVP}$ can be altered substantially, driven by changes in the phase shift and/or the inelastic contribution, and illustrate the ensuing changes in the $e^{+} e^{-} \to 2 π$ cross section. In the combined scenario, which minimizes the effect in the cross section, a uniform shift around $4%$ is required. At the same time both the analytic continuation into the space-like region and the pion charge radius are affected at a level that could be probed in future lattice-QCD calculations.

Comments:: 9 pages, 9 figures; version published in PLB
Subjects:: High Energy Physics — Phenomenology (hep-ph); High Energy Physics — Experiment (hep-ex); High Energy Physics — Lattice (hep-lat); Nuclear Theory (nucl-th)
arXiv:: 2010.07943 [pdf]

PLB(2021)·162 citations

Neutron star crust in Voigt approximation: general symmetry of the stress-strain tensor and an universal estimate for the effective shear modulus

I discuss elastic properties of neutron star crust in the framework of static Coulomb solid model when atomic nuclei are treated as non-vibrating point charges; electron screening is neglected. The results are also applicable for solidified white dwarf cores and other materials, which can be modeled as Coulomb solids (dusty plasma, trapped ions, etc.). I demonstrate that the Coulomb part of the stress-strain tensor has additional symmetry: contraction

B_{ij i l} = 0

. It does not depend on the structure (crystalline or amorphous) and composition. I show as a result of this symmetry the effective (Voigt averaged) shear modulus of the polycrystalline or amorphous matter to be equal to

- 2/15

of the Coulomb (Madelung) energy density at undeformed state. This result is general and exact within the model applied. Since the linear mixing rule and the ion sphere model are used, I can suggest a simple universal estimate for the effective shear modulus:

\sum_{Z} 0.12 n_{Z} Z^{5/3} e^{2} / a_{e}

. Here summation is taken over ion species,

n_{Z}

is number density of ions with charge

Z e

. Finally

a_{e} = (4 π n_{e} /3)^{- 1/3}

is electron sphere radius. Quasineutrality condition

n_{e} = \sum_{Z} Z n_{Z}

is assumed.

Comments:: 5 pages, accepted for publication in MNRAS:Letters
Subjects:: High Energy Astrophysical Phenomena (astro-ph.HE); Solar and Stellar Astrophysics (astro-ph.SR); cond-mat.mtrl-sci (cond-mat.mtrl-sci); Nuclear Theory (nucl-th); Plasma Physics (physics.plasm-ph)
arXiv:: 2010.08398 [pdf]

MNRAS(2020)·15 citations

Monday·October 19, 2020

Constraints on the two-pion contribution to hadronic vacuum polarization

Neutron star crust in Voigt approximation: general symmetry of the stress-strain tensor and an universal estimate for the effective shear modulus

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