arXiv subjects

B. C. Tiburzi

Publications and source records attributed to B. C. Tiburzi.

At least 19 recordsLinked to original sources

arXiv2018

Symmetries and Interactions from Lattice QCD

Precision experimental tests of the Standard Model of particle physics (SM) are one of our best hopes for discovering what new physics lies beyond the SM (BSM). Key in the search for new physics is the connection between theory and experiment. Forging this connection for searches involving low-energy hadronic or nuclear environments requires the use of a non-perturbative theoretical tool, lattice QCD. We present two recent lattice QCD calculations by the CalLat collaboration relevant for new physics searches: the nucleon axial coupling, $g_A$, whose precise value as predicted by the SM could help point to new physics contributions to the so-called "neutron lifetime puzzle", and hadronic matrix elements of short-ranged operators relevant for neutrinoless double beta decay searches.

hep-lat↗

arXiv2015

Magnetic moments of light nuclei from lattice quantum chromodynamics

We present the results of lattice QCD calculations of the magnetic moments of the lightest nuclei, the deuteron, the triton and ${}^3$He, along with those of the neutron and proton. These calculations, performed at quark masses corresponding to $m_π\sim 800$ MeV, reveal that the structure of these nuclei at unphysically heavy quark masses closely resembles that at the physical quark masses. In particular, we find that the magnetic moment of ${}^3$He differs only slightly from that of a free neutron, as is the case in nature, indicating that the shell-model configuration of two spin-paired protons and a valence neutron captures its dominant structure. Similarly a shell-model-like moment is found for the triton, $μ_{{}^3{\rm H}} \sim μ_p$. The deuteron magnetic moment is found to be equal to the nucleon isoscalar moment within the uncertainties of the calculations.

hep-lat↗

arXiv2013

Chiral Symmetry Restoration from a Boundary

The boundary of a manifold can alter the phase of a theory in the bulk. We explore the possibility of a boundary-induced phase transition for the chiral symmetry of QCD. In particular, we investigate the consequences of imposing homogeneous Dirichlet boundary conditions on the quark fields. Such boundary conditions are sometimes employed in lattice gauge theory computations, for example, when including external electromagnetic fields, or when computing quark propagators with a reduced temporal extent. Homogeneous Dirichlet boundary conditions force the chiral condensate to vanish at the boundary, and thereby obstruct the spontaneous breaking of chiral symmetry in the bulk. We show the restoration of chiral symmetry due to a boundary is a non-perturbative phenomenon depending upon the mechanism of spontaneous symmetry breaking, and utilize the sigma model to exemplify the issues. Within this model, we find that chiral symmetry is completely restored if the length of the compact direction is less than 2.0 fm. For lengths greater than about 4 fm, an approximately uniform chiral condensate forms centered about the midpoint of the compact direction. While the volume-averaged condensate approaches the infinite volume value as the compact direction becomes very long, the finite-size corrections are shown to be power law rather than exponential.

hep-lat↗

arXiv2013

A Method to Extract Charged Hadron Properties from Lattice QCD in Magnetic Fields

By analyzing the external field dependence of correlation functions, the magnetic properties of hadrons can be determined using lattice QCD in magnetic fields. To compute the magnetic moments and polarizabilities of charged hadrons, for example, one requires sufficiently weak magnetic fields. Such field strengths, however, lead to closely spaced Landau levels that are not straightforwardly resolved using standard lattice spectroscopy. Focusing on charged spinless hadrons, we introduce a simple projection technique that can be used to isolate the lowest Landau level. As the technique requires the explicit coordinate-space wave-function, we investigate the extent to which the continuum, infinite volume wave-function can be employed. We find that, in practice, the effects of discretization can be handled using a perturbative expansion about the continuum. Finite volume corrections are taken into account by using the discrete magnetic translational invariance of the torus. We show that quantized magnetic fields can lead to pernicious volume effects which depend on the magnetic flux quantum, rather than on the lattice volume.

hep-lat↗

arXiv2013

Lattice QCD Methods for Hadronic Polarizabilities

Chiral dynamics makes definitive predictions for the electromagnetic polarizabilities of hadrons near the chiral limit; but, agreement with experiment is tenuous in some cases. We provide an overview of lattice QCD methods to compute the electric and magnetic polarizabilities of hadrons. Central to these methods is the lattice simulation of quarks in uniform, classical electromagnetic fields. A long-term goal is the determination of polarizabilities directly from lattice computations, however, in the near term, one may need to rely on partially quenched chiral perturbation theory. Nonetheless the same striking predictions for the pion mass dependence of electric and magnetic polarizabilities can be made from chiral dynamics, and tested with lattice QCD. A particular focus is a novel new method to handle charged particle correlation functions in magnetic fields.

hep-lat↗

arXiv2012

Isotensor Hadronic Parity Violation

Weak interactions between quarks give rise to hadronic parity violation which can be observed in nuclear and few-nucleon systems. We study the QCD renormalization of the isotensor component of parity violation at next-to-leading order accuracy. The renormalization group is employed to evolve the interaction down to hadronic scales. As the results are renormalization scheme dependent, we compare various schemes, including 't Hooft-Veltman dimensional regularization, and several regularization independent-momentum subtraction schemes.

hep-ph↗

arXiv2012

Hadronic Parity Violation at Next-to-Leading Order

The flavor-conserving non-leptonic weak interaction can be studied experimentally through the observation of parity violation in nuclear and few-body systems. At hadronic scales, matrix elements of parity-violating four-quark operators ultimately give rise to the parity violating couplings between hadrons, and such matrix elements can be calculated non-perturbatively using lattice QCD. In this work, we investigate the running of isovector parity-violating operators from the weak scale down to hadronic scales using the renormalization group. We work at next-to-leading order in the QCD coupling, and include both neutral-current and charged-current interactions. At this order, results are renormalization scheme dependent, and we utilize 't Hooft-Veltman dimensional regularization. The evolution of Wilson coefficients at leading and next-to-leading order is compared. Next-to-leading order effects are shown to be non-negligible at hadronic scales.

hep-ph↗

arXiv2011

Lattice QCD with Classical and Quantum Electrodynamics

We are doubtlessly familiar with some edition of Jackson's tome on electrodynamics, and Schwinger's calculation of the anomalous magnetic moment of the electron in QED. From the perspective of strong interactions, however, electromagnetic effects usually amount to negligible contributions. Despite this fact, electromagnetic probes have always been a fundamental source for our knowledge of QCD experimentally. Elastic scattering of electrons off nucleons provides us a window to their distributions of charge and magnetism. To account for the spectrum of QCD at the percent level, moreover, we need isospin breaking introduced from both quark masses and electric charges. This overview concerns some of the prospects and progress of studying electromagnetic effects in QCD. Our focus is divided between classical and quantum effects. In classical electromagnetic fields, the dynamical response of QCD to external conditions can be investigated. The vacuum and hadrons alike should be viewed as media which respond to external fields: both magnetize and polarize in magnetic fields, for example. At the quantum level, electromagnetism and QCD renormalize each other. In the era of high precision lattice computations, both strong and electromagnetic contributions must be accounted for to make predictions at the percent level.

hep-lat↗

arXiv2011

Electromagnetic Polarizabilities: Lattice QCD in Background Fields

Chiral perturbation theory makes definitive predictions for the extrinsic behavior of hadrons in external electric and magnetic fields. Near the chiral limit, the electric and magnetic polarizabilities of pions, kaons, and nucleons are determined in terms of a few well-known parameters. In this limit, hadrons become quantum mechanically diffuse as polarizabilities scale with the inverse square-root of the quark mass. In some cases, however, such predictions from chiral perturbation theory have not compared well with experimental data. Ultimately we must turn to first principles numerical simulations of QCD to determine properties of hadrons, and confront the predictions of chiral perturbation theory. To address the electromagnetic polarizabilities, we utilize the background field technique. Restricting our attention to calculations in background electric fields, we demonstrate new techniques to determine electric polarizabilities and baryon magnetic moments for both charged and neutral states. As we can study the quark mass dependence of observables with lattice QCD, the lattice will provide a crucial test of our understanding of low-energy QCD, which will be timely in light of ongoing experiments, such as at COMPASS and HIγS.

hep-lat↗

arXiv2010

Axial and electromagnetic observables of hyperons in 2-flavor chiral perturbation theory

Two-flavor chiral expansions provide a useful perturbative framework to study hadron properties. Such expansions should exhibit marked improvement over the conventional three-flavor chiral expansion. Although in principle one can formulate two-flavor theories for the various hyperon multiplets, the nearness of kaon thresholds can seriously undermine the effectiveness of such two-flavor theories in practice. We investigate the importance of virtual kaon thresholds on hyperon properties, specifically their isovector axial charges and electromagnetic observables. In particular we uncover the underlying expansion parameter governing the description of virtual kaon thresholds. For spin-half hyperons, this expansion parameter is under theoretical control. As a result, the virtual kaon contributions are well described in the two-flavor theory by terms analytic in the pion mass-squared. For spin three-half hyperons, however, one is closer to the kaon production threshold, and the expansion parameter is not as small. Breakdown of $SU(2)$ chiral perturbation theory is shown to arise from a pole in the expansion parameter associated with the kaon threshold. We find that, despite the fact that higher-order corrections to the expansion parameter is necessary to ascertain whether the two-flavor theory of spin three-half hyperons remains perturbative, there is a useful perturbative expansion for isovector axial charges and magnetic moments of both spin-half and spin three-half hyperons.

hep-lat↗

arXiv2009

Two-Flavor Chiral Perturbation Theory for Hyperons

The three-flavor chiral expansion for octet baryons has well-known problems with convergence. We show that this three-flavor chiral expansion can be reorganized into a two-flavor expansion thereby eliminating large kaon and eta loop contributions. Issues of the underlying formulation are addressed by considering the effect of strangeness changing thresholds on hyperon masses. While the spin-3/2 hyperon resonances are considerably more sensitive to these thresholds compared to the spin-1/2 hyperons, we demonstrate that in both cases the essential physics can be captured in the two-flavor effective theory by terms that are analytic in the pion mass squared, but non-analytic in the strange quark mass. Using the two-flavor theory of hyperons, baryon masses and axial charges are investigated. Loop contributions in the two-flavor theory appear to be perturbatively under control. A natural application for our development is to study the pion mass dependence of lattice QCD data on hyperon properties.

nucl-th↗

arXiv2009

Time Dependence of Nucleon Correlation Functions in Chiral Perturbation Theory

We consider corrections to nucleon correlation functions arising from times that are far from the asymptotic limit. For such times, the single nucleon state is contaminated by the pion-nucleon and pion-delta continuum. We use heavy baryon chiral perturbation theory to derive the spectral representation of the nucleon two-point function. Finite time corrections to the axial current correlation function are also derived. Pion-nucleon excited state contributions drive the axial correlator upward, while contributions from the interference of pion-delta and pion-nucleon states drive the axial correlator downward. Our results can be compared qualitatively to optimized nucleon correlators calculated in lattice QCD, because the chiral corrections characterize only low-energy excitations above the ground state. We show that improved nucleon operators can lead to an underestimation of the nucleon axial charge.

hep-lat↗

arXiv2009

Connected Parts of Decuplet Electromagnetic Properties

We determine the electromagnetic properties of decuplet resonances using chiral perturbation theory at next-to-leading order. Utilizing a partially quenched charge matrix, we isolate and remove the quark disconnected contractions. This allows us to compare the physical meson loop contributions to the connected contributions, of which the latter are currently calculated using lattice QCD. Finally we determine linear combinations of decuplet resonance and hyperon electromagnetic properties that are exactly independent of disconnected contractions in the isospin limit.

hep-lat↗

arXiv2008

Flavor Twisted Boundary Conditions and the Nucleon Vector Current

Using flavor twisted boundary conditions, we study nucleon matrix elements of the vector current. We twist only the active quarks that couple to the current. Finite volume corrections due to twisted boundary conditions are determined using partially twisted, partially quenched, heavy baryon chiral perturbation theory, which we develop for the graded group SU(7|5). Asymptotically these corrections are exponentially small in the volume, but can become pronounced for small twist angles. Utilizing the Breit frame does not mitigate volume corrections to nucleon vector current matrix elements. The derived expressions will allow for better controlled extractions of the isovector magnetic moment and the electromagnetic radii from simulations at zero lattice momentum. Our formalism, moreover, can be applied to any nucleon matrix elements.

hep-lat↗

arXiv2007

External Momentum, Volume Effects, and the Nucleon Magnetic Moment

We analyze the determination of volume effects for correlation functions that depend on an external momentum. As a specific example, we consider finite volume nucleon current correlators, and focus on the nucleon magnetic moment. Because the multipole decomposition relies on SO(3) rotational invariance, the structure of such finite volume corrections is unrelated to infinite volume multipole form factors. One can deduce volume corrections to the magnetic moment only when a zero-mode photon coupling vanishes, as occurs at next-to-leading order in heavy baryon chiral perturbation theory. To deduce such finite volume corrections, however, one must assume continuous momentum transfer. In practice, volume corrections with momentum transfer dependence are required to address the extraction of the magnetic moment, or other observables that arise in momentum dependent correlation functions. Additionally we shed some light on a puzzle concerning differences in lattice form factor data at equal values of momentum transfer squared.

hep-lat↗

arXiv2006

Flavor Twisted Boundary Conditions, Pion Momentum, and the Pion Electromagnetic Form Factor

We investigate the utility of partially twisted boundary conditions in lattice calculations of meson observables. For dynamical simulations, we show that the pion dispersion relation is modified by volume effects. In the isospin limit, we demonstrate that the pion electromagnetic form factor can be computed on the lattice at continuous values of the momentum transfer. Furthermore, the finite volume effects are under theoretical control for extraction of the pion charge radius.

hep-lat↗

arXiv2006

Electromagnetic and spin polarisabilities in lattice QCD

We discuss the extraction of the electromagnetic and spin polarisabilities of nucleons from lattice QCD. We show that the external field method can be used to measure all the electromagnetic and spin polarisabilities including those of charged particles. We then turn to the extrapolations required to connect such calculations to experiment in the context of chiral perturbation theory, finding a strong dependence on the lattice volume and quark masses.

hep-lat↗

arXiv2006

Extrapolations of Lattice Meson Form Factors

We use chiral perturbation theory to study the extrapolations necessary to make physical predictions from lattice QCD data for the electromagnetic form factors of pseudoscalar mesons. We focus on the quark mass, momentum, lattice spacing, and volume dependence and apply our results to simulations employing mixed actions of Ginsparg-Wilson valence quarks and staggered sea quarks. To determine charge radii at quark masses on the lattices currently used, we find that all extrapolations except the one to infinite volume make significant contributions to the systematic error.

hep-lat↗