arXiv subjects

Andrew D. Hanlon

Publications and source records attributed to Andrew D. Hanlon.

33 records · Page 2Linked to original sources

arXiv2022

Nucleon-nucleon scattering from distillation

We report an ongoing analysis of nucleon-nucleon scattering based on finite-volume spectroscopy. The calculation is performed using the distillation method on eight lattice ensembles at the SU(3)-symmetric point with $m_π=m_K\approx 420$ MeV generated by CLS, covering a range of lattice spacings and volumes and previously used to study the $H$ dibaryon. We obtain nonzero signals for $S$, $P$, $D$, and $F$ waves as well as the mixing between spin-1 $S$ and $D$ waves. For $S$ waves, lattice artifacts are significant and tend to strengthen baryon-baryon interactions. In the deuteron and dineutron $S$ waves, we find virtual bound states.

hep-lat↗

arXiv2022

Setting the Scale Using Baryon Masses with Isospin-Breaking Corrections

We present the status of an ongoing project aimed at the inclusion of isospin-breaking corrections arising from the non-degeneracy of the light quark masses and electromagnetic interactions in calculations of the low-lying octet and decuplet baryon masses. Our ultimate goal is to perform a precision determination of the lattice scale including isospin-breaking effects. We apply the perturbative formalism to isospin-symmetric $N_f=2+1$ CLS ensembles. We show results on baryon masses up to leading order in isospin-breaking corrections on two ensembles with $m_π\approx290\,\text{MeV}$ and $m_π\approx215\,\text{MeV}$ at a lattice spacing of $a\approx0.076\,\text{fm}$.

hep-lat↗

arXiv2022

Pion distribution amplitude at the physical point using the leading-twist expansion of the quasi-distribution-amplitude matrix element

We present a lattice QCD determination of the distribution amplitude (DA) of the pion and the first few Mellin moments from an analysis of the quasi-DA matrix element within the leading-twist framework. We perform our study on a HISQ ensemble with $a=0.076$ fm lattice spacing with the Wilson-Clover valence quark mass tuned to the physical point. We analyze the ratios of pion quasi-DA matrix elements at short distances using the leading-twist Mellin operator product expansion (OPE) at the next-to-leading order and the conformal OPE at the leading-logarithmic order. We find a robust result for the first non-vanishing Mellin moment $\langle x^2 \rangle = 0.287(6)(6)$ at a factorization scale $μ=2$ GeV. We also present different Ansätze-based reconstructions of the $x$-dependent DA, from which we determine the perturbative leading-twist expectations for the pion electromagnetic and gravitational form-factors at large momentum transfers.

hep-lat↗

arXiv2022

Lattice QCD Determination of the Bjorken-$x$ Dependence of Parton Distribution Functions at Next-to-next-to-leading Order

We report the first lattice QCD calculation of pion valence quark distribution with next-to-next-to-leading order perturbative matching correction, which is done using two fine lattices with spacings $a=0.04$ fm and $0.06$ fm and valence pion mass $m_π=300$ MeV, at boost momentum as large as $2.42$ GeV. As a crucial step to control the systematics, we renormalize the pion valence quasi distribution in the recently proposed hybrid scheme, which features a Wilson-line mass subtraction at large distances in coordinate space, and develop a procedure to match it to the $\overline{\rm MS}$ scheme. We demonstrate that the renormalization and the perturbative matching in Bjorken-$x$ space yield a reliable determination of the valence quark distribution for $0.03\lesssim x \lesssim 0.80$ with 5-20\% uncertainties.

hep-lat↗

arXiv2022

Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives

This is a collection of perspective pieces contributed by the participants of the Institute of Nuclear Theory's Program on Nuclear Physics for Precision Nuclear Physics which was held virtually from April 19 to May 7, 2021. The collection represents the reflections of a vibrant and engaged community of researchers on the status of theoretical research in low-energy nuclear physics, the challenges ahead, and new ideas and strategies to make progress in nuclear structure and reaction physics, effective field theory, lattice QCD, quantum information, and quantum computing. The contributed pieces solely reflect the perspectives of the respective authors and do not represent the viewpoints of the Institute for Nuclear theory or the organizers of the program.

nucl-th↗

arXiv2021

Isospin-breaking Effects in Octet and Decuplet Baryon Masses

We present work designed to compute baryon masses on $N_f = 2 + 1$ CLS ensembles including isospin-breaking effects due to non-degenerate light quark masses and electromagnetic interactions. These effects are determined at leading order via a perturbative expansion around the iso-symmetric theory. We furthermore apply a group-theoretical operator construction for the various interpolators describing the different members of the baryon octet and decuplet based on a classification by spin, parity, and flavor content.

hep-lat↗

arXiv2021

$I=1$ $π$-$π$ scattering at the physical point

We present a preliminary analysis of $I=1$ $π\,π$ scattering at the physical point. We make use of the stochastic variant of the distillation framework (also known as sLapH) to compute the relevant two-point correlation matrices using a basis of single and multihadron interpolating operators to estimate the low energy spectra. We perform the Lüscher analysis to determine the scattering phase shift which is finding good agreement with the experimentally obtained phase shifts.

hep-lat↗

arXiv2021

Toward a resolution of the NN controversy

Lattice QCD calculations of two-nucleon interactions have been underway for about a decade, but still haven't reached the pion mass regime necessary for matching onto effective field theories and extrapolating to the physical point. Furthermore, results from different methods, including the use of the Luscher formalism with different types of operators, as well as the HALQCD potential method, do not agree even qualitatively at very heavy pion mass. We investigate the role that different operators employed in the literature may play on the extraction of spectra for use within the Luscher method. We first explore expectations from Effective Field Theory solved within a finite volume, for which the exact spectrum may be computed given different physical scenarios. We then present preliminary lattice QCD results for two-nucleon spectra calculated using different operators on a common lattice ensemble.

hep-lat↗

arXiv2021

$H$ dibaryon away from the $SU(3)_f$ symmetric point

We present the current status of our efforts in search of $H$ dibaryon on $N_f$=2+1 CLS ensembles away from the $SU(3)$ flavor symmetric point. Utilizing the distillation framework (also known as LapH) in its exact and stochastic forms, we calculate two-point correlation matrices using large bases of bi-local two-baryon interpolators to reliably determine the low-energy spectra. We report the low lying spectrum on several moving frames for multiple ensembles with different lattice spacing and physical volumes. The status of finite-volume analysis to extract the scattering amplitudes is also discussed.

hep-lat↗

arXiv2021

Continuum limit of baryon-baryon scattering with SU(3) flavor symmetry

We report a study of the scattering of two octet baryons using lattice QCD. The baryon-baryon spectrum is computed using distillation on eight lattice ensembles spanning six lattice spacings and multiple volumes, all at the SU(3) flavor symmetric point with $m_π=m_K\approx 420$ MeV. Using finite-volume quantization conditions, we determine the scattering phase shift and the presence of bound states. Focusing on the $H$ dibaryon, our results show large discretization effects: in the continuum, the binding energy is $B_H=4.56\pm1.13\pm0.63$ MeV, whereas on our coarsest lattice spacing this is larger by a factor of about 7.5. We also present preliminary results for a $D$-wave phase shift and for the spectrum in the nucleon-nucleon ${}^1S_0$ channel.

hep-lat↗

arXiv2021

Progress on Meson-Baryon Scattering

Progress in computing various meson-baryon scattering amplitudes is presented on a single ensemble from the Coordinated Lattice Simulations (CLS) consortium with $m_π=200$ MeV and $N_f=2+1$ dynamical fermions. The finite-volume Lüscher approach is employed to determine the lowest few partial waves from ground- and excited-state energies computed from correlation matrices rotated in a single pivot using a generalized eigenvector solution. This analysis requires evaluating matrices of correlation functions between single- and two-hadron interpolating operators which are projected onto definite spatial momenta and finite-volume irreducible representations. The stochastic LapH method is used to estimate all needed quark propagators. Preliminary results are presented for $I=\frac{1}{2}, \frac{3}{2}$ $Nπ$ amplitudes including the $Δ(1232)$ resonance and the $I=0$ $S$-wave amplitude with unit strangeness relevant for the $Λ(1405)$.

hep-lat↗

arXiv2021

Weakly bound $H$ dibaryon from SU(3)-flavor-symmetric QCD

We present the first study of baryon-baryon interactions in the continuum limit of lattice QCD, finding unexpectedly large lattice artifacts. Specifically, we determine the binding energy of the $H$ dibaryon at a single quark-mass point. The calculation is performed at six values of the lattice spacing $a$, using O($a$)-improved Wilson fermions at the SU(3)-symmetric point with $m_π=m_K\approx 420$ MeV. Energy levels are extracted by applying a variational method to correlation matrices of bilocal two-baryon interpolating operators computed using the distillation technique. Our analysis employs Lüscher's finite-volume quantization condition to determine the scattering phase shifts from the spectrum and vice versa, both above and below the two-baryon threshold. We perform global fits to the lattice spectra using parametrizations of the phase shift, supplemented by terms describing discretization effects, then extrapolate the lattice spacing to zero. The phase shift and the binding energy determined from it are found to be strongly affected by lattice artifacts. Our estimate of the binding energy in the continuum limit of three-flavor QCD is $B_H^{\text{SU(3)}_{\rm f}}=4.56\pm1.13_{\rm stat}\pm0.63_{\rm syst}$ MeV.

hep-lat↗

arXiv2021

Interactions of two and three mesons including higher partial waves from lattice QCD

We study two- and three-meson systems composed either of pions or kaons at maximal isospin using Monte Carlo simulations of lattice QCD. Utilizing the stochastic LapH method, we are able to determine hundreds of two- and three-particle energy levels, in nine different momentum frames, with high precision. We fit these levels using the relativistic finite-volume formalism based on a generic effective field theory in order to determine the parameters of the two- and three-particle K-matrices. We find that the statistical precision of our spectra is sufficient to probe not only the dominant $s$-wave interactions, but also those in $d$ waves. In particular, we determine for the first time a term in the three-particle K-matrix that contains two-particle $d$ waves. We use three $N_f=2+1$ CLS ensembles with pion masses of $200$, $280$, and $340\;$MeV. This allows us to study the chiral dependence of the scattering observables, and compare to the expectations of chiral perturbation theory.

hep-lat↗

arXiv2014

Residual Symmetries Applied to Neutrino Oscillations at NO$ν$A and T2K

The results previously obtained from the model-independent application of a generalized hidden horizontal $\mathbb{Z}_2$ symmetry to the neutrino mass matrix are updated using the latest global fits for the neutrino oscillation parameters. The resulting prediction for the Dirac $CP$ phase $δ_D$ is in agreement with recent results from T2K. The distribution for the Jarlskog invariant $J_ν$ has become sharper and appears to be approaching a particular region. The approximate effects of matter on long baseline neutrino experiments are explored, and it is shown how the weak interactions between the neutrinos and the particles that make up the Earth can help to determine the mass hierarchy. A similar strategy is employed to show how NO$ν$A and T2K could determine the octant of $θ_a (\equiv θ_{23})$. Finally, the exact effects of matter are obtained numerically in order to make comparisons with the form of the approximate solutions. From this analysis there emerges some interesting features of the effective mass eigenvalues.

hep-ph↗

arXiv2013

Phenomenological Study of Residual Z^s_2 and Zbar^s_2 Symmetries

The phenomenological consequences of the residual Z^s_2 and Zbar^s_2 symmetries are explored in detail. With a precisely measured value of the reactor angle, these two residual symmetries predict distinct distributions for the Dirac CP phase and the atmospheric angle, which leads to the possibility of identifying them at neutrino experiments. For both symmetries, it is possible to resolve the neutrino mass hierarchy in most of the parameter space, and they can be distinguished from one another if the true residual symmetry is Z^s_2 and the atmospheric angle is non-maximal. These results are obtained using an equally split schedule: a 1.5-year run of neutrinos and a 1.5-year run of antineutrinos at NOvA together with a 2.5-year run of neutrinos and a 2.5-year run of antineutrinos at T2K. This schedule can significantly increase and stabilize the sensitivities to the mass hierarchy and the octant of the atmospheric angle with only a moderate compromise to the sensitivity of distinguishing Z^s_2 and Zbar^s_2.

hep-ph↗