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Register a new userPion magnetic polarisability using the background field method
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The magnetic polarisability is a fundamental property of hadrons, which provides insight into their structure in the low-energy regime. The pion magnetic polarisability is calculated using lattice QCD in the presence of background magnetic fields. The results presented are facilitated by the introduction of a new magnetic-field dependent quark-propagator eigenmode projector and the use of the background-field corrected clover fermion action. The magnetic polarisabilities are calculated in a relativistic formalism, and the excellent signal-to-noise property of pion correlation functions facilitates precise values.
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Background field methods provide an important nonperturbative formalism for the determination of hadronic properties which are complementary to matrix-element calculations. However, new challenges are encountered when utilising a fermion action exposed to additive mass renormalisations. In this case, the background field can induce an undesired field-dependent additive mass renormalisation that acts to change the quark mass as the background field is changed. For example, in a calculation utilising Wilson fermions in a uniform background magnetic field, the Wilson term introduced a field-dependent renormalisation to the quark mass which manifests itself in an unphysical increase of the neutral-pion mass for large magnetic fields. Herein, the clover fermion action is studied to determine the extent to which the removal of $mathcal{O}(a)$ discretisation errors suppresses the field-dependent changes to the quark mass. We illustrate how a careful treatment of nonperturbative improvement is necessary to resolve this artefact of the Wilson term. Using the $32^3 times 64$ dynamical-fermion lattices provided by the PACS-CS Collaboration we demonstrate how our technique suppresses the unphysical mass renormalisation over a broad range of magnetic field strengths.
Conventional hadron interpolating fields, which utilise gauge-covariant Gaussian smearing, are ineffective in isolating ground state nucleons in a uniform background magnetic field. There is evidence that residual Landau mode physics remains at the quark level, even when QCD interactions are present. In this work, quark-level projection operators are constructed from the $SU(3) times U(1)$ eigenmodes of the two-dimensional lattice Laplacian operator associated with Landau modes. These quark-level modes are formed from a periodic finite lattice where both the background field and strong interactions are present. Using these eigenmodes, quark-propagator projection operators provides the enhanced hadronic energy-eigenstate isolation necessary for calculation of nucleon energy shifts in a magnetic field. The magnetic polarisability of both the proton and neutron is calculated using this method on the $32^3 times 64$ dynamical QCD lattices provided by the PACS-CS Collaboration. A chiral effective-field theory analysis is used to connect the lattice QCD results to the physical regime, obtaining magnetic polarisabilities of $beta^p = 2.79(22)({}^{+13}_{-18}) times 10^{-4}$ fm$^3$ and $beta^n = 2.06(26)({}^{+15}_{-20}) times 10^{-4}$ fm$^3$, where the numbers in parantheses describe statistical and systematic uncertainties.
The COMPASS collaboration at CERN has investigated pion Compton scattering, $pi^-gammarightarrow pi^-gamma$, at centre-of-mass energy below 3.5 pion masses. The process is embedded in the reaction $pi^-mathrm{Ni}rightarrowpi^-gamma;mathrm{Ni}$, which is initiated by 190,GeV pions impinging on a nickel target. The exchange of quasi-real photons is selected by isolating the sharp Coulomb peak observed at smallest momentum transfers, $Q^2<0.0015$,(GeV/$c$)$^2$. From a sample of 63,000 events the pion electric polarisability is determined to be $alpha_pi = (,2.0 pm 0.6_{mbox{scriptsize stat}} pm 0.7_{mbox{scriptsize syst}},) times 10^{-4},mbox{fm}^3$ under the assumption $alpha_pi=-beta_pi$, which relates the electric and magnetic dipole polarisabilities. It is the most precise measurement of this fundamental low-energy parameter of strong interaction, that has been addressed since long by various methods with conflicting outcomes. While this result is in tension with previous dedicated measurements, it is found in agreement with the expectation from chiral perturbation theory. An additional measurement replacing pions by muons, for which the cross-section behavior is unambigiously known, was performed for an independent estimate of the systematic uncertainty.
The application of a uniform background magnetic field makes standard quark operators utilising gauge-covariant Gaussian smearing inefficient at isolating the ground state nucleon at nontrivial field strengths. In the absence of QCD interactions, Landau modes govern the quark energy levels. There is evidence that residual Landau mode effects remain when the strong interaction is turned on. Here we introduce novel quark operators constructed from the two-dimensional $U(1)$ Laplacian eigenmodes that describe the Landau levels of a charged particle on a periodic finite lattice. These eigenmode-projected quark operators provide enhanced precision for calculating nucleon energy shifts in a magnetic field. Using asymmetric source and sink operators, we are able to encapsulate the predominant effects of both the QCD and QED interactions in the interpolating fields for the neutron. The neutron magnetic polarizability is calculated using these techniques on the $32^3 times 64$ dynamical QCD lattices provided by the PACS-CS Collaboration. In conjunction with a chiral effective-field theory analysis, we obtain a neutron magnetic polarizability of $beta^n = 2.05(25)(19) times 10^{-4}$ fm$^3$, where the numbers in parentheses describe statistical and systematic uncertainties.
Recent experimental data on tau decays are used to reconstruct the difference in hadronic spectral densities with vector and axial-vector quantum numbers. The saturation of Das-Mathur-Okubo and Weinberg sum rules is studied. Two methods of improving convergence and decreasing errors are applied, and good agreement with the predictions of current algebra and chiral perturbation theory is observed. The resulting value of the pion polarisability is (2.64 +/- 0.36) 10^-4 fm^3.
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