arXiv subjects

Brian C. Tiburzi

Publications and source records attributed to Brian C. Tiburzi.

At least 37 records · Page 2Linked to original sources

arXiv2016

Massive photons: an infrared regularization scheme for lattice QCD+QED

Standard methods for including electromagnetic interactions in lattice quantum chromodynamics calculations result in power-law finite-volume corrections to physical quantities. Removing these by extrapolation requires costly computations at multiple volumes. We introduce a photon mass to alternatively regulate the infrared, and rely on effective field theory to remove its unphysical effects. Electromagnetic modifications to the hadron spectrum are reliably estimated with a precision and cost comparable to conventional approaches that utilize multiple larger volumes. A significant overall cost advantage emerges when accounting for ensemble generation. The proposed method may benefit lattice calculations involving multiple charged hadrons, as well as quantum many-body computations with long-range Coulomb interactions.

hep-lat↗

arXiv2016

Unitary Limit of Two-Nucleon Interactions in Strong Magnetic Fields

Two-nucleon systems are shown to exhibit large scattering lengths in strong magnetic fields at unphysical quark masses, and the trends toward the physical values indicate that such features may exist in nature. Lattice QCD calculations of the energies of one and two nucleons systems are performed at pion masses of $m_π\sim 450$ and 806 MeV in uniform, time-independent magnetic fields of strength {\bf B}| \sim 10^{19}$-$10^{20}$ Gauss to determine the response of these hadronic systems to large magnetic fields. Fields of this strength may exist inside magnetars and in peripheral relativistic heavy ion collisions, and the unitary behavior at large scattering lengths may have important consequences for these systems.

hep-lat↗

arXiv2016

Finite Volume Corrections to the Electromagnetic Mass of Composite Particles

The long-range electromagnetic interaction presents a challenge for numerical computations in QCD + QED. In addition to power-law finite volume effects, the standard lattice gauge theory approach introduces non-locality through removal of photon zero-momentum modes. The resulting finite volume effects must be quantitatively understood; and, to this end, non-relativistic effective field theories are an efficient tool, especially in the case of composite particles. Recently an oddity related to non-locality of the standard lattice approach was uncovered by the Budapest-Marseille-Wuppertal collaboration. Explicit contributions from antiparticles appear to be required so that finite volume QED results for a point-like fermion can be reproduced in the effective field theory description. We provide transparency for this argument by considering point-like scalars and spinors in finite volume QED using the method of regions. For the more germane case of composite particles, we determine that antiparticle modes contribute to the finite-volume electromagnetic mass of composite spinors through terms proportional to the squares of time-like form factors evaluated at threshold. We extend existing finite volume calculations to one order higher, which is particularly relevant for the electromagnetic mass of light nuclei. Additionally, we verify that the analogous finite volume contributions to the nucleon mass in chiral perturbation theory vanish in accordance with locality.

hep-lat↗

arXiv2015

Photon mass term as an IR regularization for QCD+QED on the lattice

Inclusion of QED in lattice QCD calculations can lead to power-law volume artifacts as a consequence of the long-range nature of the interaction. Such artifacts must be removed by extrapolation in order to attain reliable infinite volume estimates of observables and quantities derived from them. As an alternative to this methodology, we consider the use of a photon mass term as an infrared regulator for QCD+QED, and explore the viability of its use in determining hadron mass shifts and splittings.

hep-lat↗

arXiv2015

Low-Energy QCD in the Delta Regime

We investigate properties of low-energy QCD in a finite spatial volume, but with arbitrary temperature. In the limit of small temperature and small cube size compared to the pion Compton wavelength, Leutwyler has shown that the effective theory describing low-energy QCD reduces to that of quantum mechanics on the coset manifold, which is the so-called delta regime of chiral perturbation theory. We solve this quantum mechanics analytically for the case of a $U(1)_L \times U(1)_R$ subgroup of chiral symmetry, and numerically for the case of $SU(2)_L \times SU(2)_R$. We utilize the quantum mechanical spectrum to compute the mass gap and chiral condensate, and investigate symmetry restoration in a finite spatial volume as a function of temperature. Because we obtain the spectrum for non-zero values of the quark mass, we are able to interpolate between the rigid rotor limit, which emerges at vanishing quark mass, and the harmonic approximation, which is referred to as the p-regime. We find that the applicability of perturbation theory about the rotor limit largely requires lighter-than-physical quarks. As a stringent check of our results, we raise the temperature to that of the inverse cube size. When this condition is met, the quantum mechanics reduces to a matrix model. The condensate we obtain in this limit agrees with that determined analytically in the epsilon regime.

hep-lat↗

arXiv2015

Excited-state contamination in nucleon correlators from chiral perturbation theory

Techniques to compute hadron properties from lattice QCD rely upon the limit of long time separation. For baryons, the signal-to-noise problem often restricts one to time separations that are not ideally long, and for which couplings to excited states can obstruct the isolation of ground-state baryon properties. We consider excited-state contamination in nucleon two- and three-point functions. Using chiral perturbation theory, we determine couplings to pion-nucleon and pion-delta excited states. In two-point functions, these contributions are small, in accordance with general properties of the spectral weights on a torus. For the axial-current correlation function in the nucleon, the sign of excited-state contributions suggests overestimation of the nucleon axial charge. Thus contamination from pion-nucleon excited states will not likely explain the trend in lattice QCD data.

hep-lat↗

arXiv2015

The Magnetic Structure of Light Nuclei from Lattice QCD

Lattice QCD with background magnetic fields is used to calculate the magnetic moments and magnetic polarizabilities of the nucleons and of light nuclei with $A\le4$, along with the cross-section for the $M1$ transition $np\rightarrow dγ$, at the flavor SU(3)-symmetric point where the pion mass is $m_π\sim 806$ MeV. These magnetic properties are extracted from nucleon and nuclear energies in six uniform magnetic fields of varying strengths. The magnetic moments are presented in a recent Letter. For the charged states, the extraction of the polarizability requires careful treatment of Landau levels, which enter non-trivially in the method that is employed. The nucleon polarizabilities are found to be of similar magnitude to their physical values, with $β_p=5.22(+0.66/-0.45)(0.23) \times 10^{-4}$ fm$^3$ and $β_n=1.253(+0.056/-0.067)(0.055) \times 10^{-4}$ fm$^3$, exhibiting a significant isovector component. The dineutron is bound at these heavy quark masses and its magnetic polarizability, $β_{nn}=1.872(+0.121/-0.113)(0.082) \times 10^{-4}$ fm$^3$ differs significantly from twice that of the neutron. A linear combination of deuteron scalar and tensor polarizabilities is determined by the energies of the $j_z=\pm 1$ deuteron states, and is found to be $β_{d,\pm 1}=4.4(+1.6/-1.5)(0.2) \times 10^{-4}$ fm$^3$. The magnetic polarizabilities of the three-nucleon and four-nucleon systems are found to be positive and similar in size to those of the proton, $β_{^{3}\rm He}=5.4(+2.2/-2.1)(0.2) \times 10^{-4}$ fm$^3$, $β_{^{3}\rm H}=2.6(1.7)(0.1) \times 10^{-4}$ fm$^3$, $β_{^{4}\rm He}=3.4(+2.0/-1.9)(0.2) \times 10^{-4}$ fm$^3$. Mixing between the $j_z=0$ deuteron state and the spin-singlet $np$ state induced by the background magnetic field is used to extract the short-distance two-nucleon counterterm, ${\bar L}_1$, of the pionless effective theory for $NN$ systems (equivalent to the meson-exchange current contribution in nuclear potential models), that dictates the cross-section for the $np\to dγ$ process near threshold. Combined with previous determinations of NN scattering parameters, this enables an ab initio determination of the threshold cross-section at these unphysical masses.

hep-lat↗

arXiv2015

Ab initio calculation of the $np \to d γ$ radiative capture process

Lattice QCD calculations of two-nucleon systems are used to isolate the short-distance two-body electromagnetic contributions to the radiative capture process $np \to dγ$, and the photo-disintegration processes $γ^{(\ast)} d \to np$. In nuclear potential models, such contributions are described by phenomenological meson-exchange currents, while in the present work, they are determined directly from the quark and gluon interactions of QCD. Calculations of neutron-proton energy levels in multiple background magnetic fields are performed at two values of the quark masses, corresponding to pion masses of $m_π\sim 450$ and 806 MeV, and are combined with pionless nuclear effective field theory to determine these low-energy inelastic processes. Extrapolating to the physical pion mass, a cross section of $σ^{lqcd}(np\to dγ)=332.4({\tiny \begin{array}{l}+5.4 \\ - 4.7\end{array}})\ mb$ is obtained at an incident neutron speed of $v=2,200\ m/s$, consistent with the experimental value of $σ^{expt}(np \to dγ) = 334.2(0.5)\ mb$.

hep-lat↗

arXiv2015

Chiral Corrections to Nucleon Two- and Three-Point Correlation Functions

We consider multi-particle contributions to nucleon two- and three-point functions from the perspective of chiral dynamics. Lattice nucleon interpolating operators, which have definite chiral transformation properties, can be mapped into chiral perturbation theory. Using the most common of such operators, we determine pion-nucleon and pion-delta couplings to nucleon two- and three-point correlation functions at leading order in the low-energy expansion. The couplings of pions to nucleons and deltas in two-point functions are consistent with simple phase-space considerations, in accordance with the Lehmann spectral representation. An argument based on available phase space on a torus is utilized to derive the scaling of multiple-pion couplings. While multi-pion states are indeed suppressed, this suppression scales differently with particle number compared to that in infinite volume. For nucleon three-point correlation functions, we investigate the axial-vector current at vanishing momentum transfer. The effect of pion-nucleon and pion-delta states on the extraction of the nucleon axial charge is assessed. We show that couplings to finite volume multi-particle states could potentially lead to overestimation of the axial charge. Hence pion-nucleon excited states cannot explain the trend seen in lattice QCD calculations of the nucleon axial charge.

hep-lat↗

arXiv2014

Background field method and nonrelativistic QED matching

We discuss the resolution of an inconsistency between lattice background field methods and nonrelativistic QED matching conditions. In particular, we show that lack of on-shell conditions in lattice QCD with time-dependent background fields generally requires that certain operators related by equations of motion should be retained in an effective field theory to correctly describe the behavior of Green's functions. The coefficients of such operators in a nonrelativistic hadronic theory are determined by performing a robust nonrelativistic expansion of QED for relativistic scalar and spin-half hadrons including nonminimal electromagnetic couplings. Provided that nonrelativistic QED is augmented with equation-of-motion operators, we find that the background field method can be reconciled with the nonrelativistic QED matching conditions without any inconsistency. We further investigate whether nonrelativistic QED can be employed in the analysis of lattice QCD correlation function in background fields, but we are confronted with difficulties. Instead, we argue that the most desirable approach is a hybrid one which relies on a relativistic hadronic theory with operators chosen based on their relevance in the nonrelativistic limit. Using this hybrid framework, we obtain practically useful forms of correlation functions for scalar and spin-half hadrons in uniform electric and magnetic fields.

hep-lat↗

arXiv2014

Reconciling the lattice background field method with nonrelativistic QED: Spinor case

We show that inconsistency between background field methods, which are relevant for lattice QCD spectroscopy, and effective field theory matching conditions, which are obtained from scattering amplitudes, can be resolved by augmenting nonrelativistic QED with operators related by the equations of motion. To determine the coefficients of such operators, we perform the nonrelativistic expansion of QED for a spin-half hadron including non-minimal electromagnetic couplings. As an effective field theory framework could provide a valuable tool to analyze lattice QCD correlation functions in external fields, we investigate whether nonrelativistic QED can be used to this end. We argue, however, that the most desirable approach is a hybrid one, which combines a relativistic hadron theory with operator selection based on nonrelativistic QED power counting. In this hybrid framework, new results are obtained for charged spin-half hadrons in uniform magnetic fields, including a proper treatment of Landau levels both in infinite volume and on a torus.

hep-lat↗

arXiv2014

Volume Effects on the Method of Extracting Form Factors at Zero Momentum

The Rome method allows one to extract form factors using lattice computations performed strictly at zero momentum. We investigate the size of finite volume effects resulting from this method. As a test case, we focus on the pion charge radius and show how to ascertain the finite volume effect with the aid of chiral perturbation theory. The framework developed can easily be generalized to account for modified infrared physics of other low-energy matrix elements extracted at zero momentum.

hep-lat↗

arXiv2014

Finite Volume Effects on the Extraction of Form Factors at Zero Momentum

Hadronic matrix elements that depend on momentum are required for numerous phenomenological applications. Probing the low-momentum regime is often problematic for lattice QCD computations on account of the restriction to periodic momentum modes. Recently a novel method has been proposed to compute matrix elements at zero momentum, for which straightforward evaluation of the matrix elements would otherwise yield a vanishing result. We clarify an assumption underlying this method, and thereby establish the theoretical framework required to address the associated finite volume effects. Using the pion electromagnetic form factor as an example, we show how the charge radius and two higher moments can be calculated at zero momentum transfer, and determine the corresponding finite volume effects. These computations are performed using chiral perturbation theory to account for modified infrared physics, and can be generalized to ascertain finite volume effects for other hadronic matrix elements extracted at zero momentum.

hep-lat↗

arXiv2014

Neutron in a Strong Magnetic Field: Finite Volume Effects

We investigate the neutron's response to magnetic fields on a torus with the aid of chiral perturbation theory, and expose effects from non-vanishing holonomies. The determination of such effects necessitates non-perturbative treatment of the magnetic field; and, to this end, a strong-field power counting is employed. Using a novel coordinate-space method, we find the neutron propagates in a coordinate-dependent effective potential that we obtain by integrating out charged pions winding around the torus. Knowledge of these finite volume effects will aid in the extraction of neutron properties from lattice QCD computations in external magnetic fields. In particular, we obtain finite volume corrections to the neutron magnetic moment and magnetic polarizability. These quantities have not been computed correctly in the literature. In addition to effects from non-vanishing holonomies, finite volume corrections depend on the magnetic flux quantum through an Aharonov-Bohm effect. We make a number of observations that demonstrate the importance of non-perturbative effects from strong magnetic fields currently employed in lattice QCD calculations. These observations concern neutron physics in both finite and infinite volume.

hep-lat↗

arXiv2013

Background Electromagnetic Fields and NRQED Matching: Scalar Case

The low-energy structure of hadrons can be described systematically using effective field theory, and the parameters of the effective theory can be determined from lattice QCD computations. Recent work, however, points to inconsistencies between the background field method in lattice QCD and effective field theory matching conditions. We show that the background field problem necessitates inclusion of operators related by equations of motion. In the presence of time-dependent electromagnetic fields, for example, such operators modify Green's functions, thereby complicating the isolation of hadronic parameters which enter on-shell scattering amplitudes. The particularly simple case of a scalar hadron coupled to uniform electromagnetic fields is investigated in detail. At the level of the relativistic effective theory, operators related by equations of motion are demonstrated to be innocuous. The same result does not hold in the non-relativistic effective theory, and inconsistencies in matching are resolved by carefully treating operators related by equations of motion. As uniform external fields potentially allow for surface terms, the problem is additionally analyzed on a torus where such terms are absent. Finite-size corrections are derived for charged scalar correlation functions in uniform electric fields as a useful byproduct.

hep-ph↗

arXiv2013

Restoration of Chiral Symmetry from a Boundary

The imposition of Dirichlet boundary conditions in lattice computations obstructs the formation of a chiral condensate. We use chiral perturbation theory and meson models to address the effect of a Dirichlet boundary on chiral symmetry breaking. While pions are the longest-range modes in QCD, the restoration of chiral symmetry due to a boundary is shown not to depend upon the pion Compton wavelength but rather on that of the sigma meson. Power-law finite size corrections are exposed, and require prohibitively large lattices to overcome. We further speculate on the frustration of the chiral condensate for the case of confinement to the surface of a sphere.

hep-lat↗

arXiv2011

The Fermion Sign Problem at Finite Density, and Large Nc Orbifold Equivalence

The study of QCD at finite baryon density is severely hampered by the so-called fermion sign problem. As a result, we have no known first principles approach to study nuclear matter, or neutron stars from QCD. On the surface, the large Nc limit does not seem to simplify matters. In this limit, however, one can exploit dualities that exist between strongly coupled gauge theories. Our focus will be on some rather novel orbifold equivalences that have recently been discovered at finite density. These equivalences relate strongly coupled theories plagued by a sign problem, to strongly coupled theories free of sign problems. As a result, such dualities give deeper insight into the nature of the sign problem and possibly provide a way to simulate QCD at finite density in the large Nc limit.

hep-ph↗

arXiv2011

Orbifold equivalence for finite density QCD and effective field theory

In the large N_c limit, some apparently different gauge theories turn out to be equivalent due to large N_c orbifold equivalence. We use effective field theory techniques to explore orbifold equivalence, focusing on the specific case of a recently discovered relation between an SO(2N_c) gauge theory and QCD. The equivalence to QCD has been argued to hold at finite baryon chemical potential, μ_B, so long as one deforms the SO(2N_c) theory by certain "double-trace" terms. The deformed SO(2N_c) theory can be studied without a sign problem in the chiral limit, in contrast to SU(N_c) QCD at finite μ_B. The purpose of the double-trace deformation in the SO(2N_c) theory is to prevent baryon number symmetry from breaking spontaneously at finite density, which is necessary for the equivalence to large N_c QCD to be valid. The effective field theory analysis presented here clarifies the physical significance of double-trace deformations, and strongly supports the proposed equivalence between the deformed SO(2N_c) theory and large N_c QCD at finite density.

hep-th↗