arXiv subjects

Ben Hörz

Publications and source records attributed to Ben Hörz.

At least 19 recordsLinked to original sources

arXiv2026

Di-nucleons do not form bound states at heavy pion mass

We perform a high-statistics lattice QCD calculation of the low-energy two-nucleon scattering amplitudes. In order to address discrepancies in the literature, the calculation is performed at a heavy pion mass in the limit that the light quark masses are equal to the physical strange quark mass, $m_π= m_K \simeq 714 $ MeV. Using a state-of-the-art momentum space method, we rule out the presence of a bound di-nucleon in both the isospin 0 (deuteron) and 1 (di-neutron) channels, in contrast with many previous results that made use of compact hexaquark creation operators. In order to diagnose the discrepancy, we add such hexaquark interpolating operators to our basis and find that they do not affect the determination of the two-nucleon finite volume spectrum, and thus they do not couple to deeply bound di-nucleons that are missed by the momentum-space operators. Further, we perform a high-statistics calculation of the HAL QCD potential on the same gauge ensembles and find qualitative agreement with our main results. We conclude that di-nucleons do not form bound states at heavy pion masses and that previous identification of deeply bound di-nucleons must have arisen from a misidentification of the spectrum from off-diagonal elements of a correlation function.

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arXiv2025

Two- and three-meson scattering amplitudes with physical quark masses from lattice QCD

We study systems of two and three mesons composed of pions and kaons at maximal isospin using four CLS ensembles with $a\approx 0.063\;$fm, including one with approximately physical quark masses. Using the stochastic Laplacian-Heaviside method, we determine the energy spectrum of these systems including many levels in different momentum frames and irreducible representations. Using the relativistic two- and three-body finite-volume formalism, we constrain the two and three-meson K matrices, including not only the leading $s$ wave, but also $p$ and $d$ waves. By solving the three-body integral equations, we determine, for the first time, the physical-point scattering amplitudes for $3π^+$, $3K^+$, $π^+π^+ K^+$ and $K^+ K^+ π^+$ systems. These are determined for total angular momentum $J^P=0^-$, $1^+$, and $2^-$. We also obtain accurate results for $2π^+$, $π^+ K^+$, and $2K^+$ phase shifts. We compare our results to Chiral Perturbation Theory, and to phenomenological fits.

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arXiv2025

QCD predictions for physical multimeson scattering amplitudes

We use lattice QCD calculations of the finite-volume spectra of systems of two and three mesons to determine, for the first time, three-particle scattering amplitudes with physical quark masses. Our results are for combinations of $π^+$ and $K^+$, at a lattice spacing $a=0.063\;$fm, and in the isospin-symmetric limit. We also obtain accurate results for maximal-isospin two-meson amplitudes, with those for $π^+ K^+$ and $2K^+$ being the first determinations at the physical point. Dense lattice spectra are obtained using the stochastic Laplacian-Heaviside method, and the analysis leading to scattering amplitudes is done using the relativistic finite-volume formalism. Results are compared to chiral perturbation theory and to phenomenological fits to experimental data, finding good agreement.

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arXiv2024

Lattice QCD study of $πΣ-\bar{K}N$ scattering and the $Λ(1405)$ resonance

A lattice QCD computation of the coupled channel $πΣ-\bar{K}N$ scattering amplitudes in the $Λ(1405)$ region is detailed. Results are obtained using a single ensemble of gauge field configurations with $N_{\rm f} = 2+1$ dynamical quark flavors and $m_π \approx 200$ MeV and $m_K\approx487$ MeV. Hermitian correlation matrices using both single baryon and meson-baryon interpolating operators for a variety of different total momenta and irreducible representations are used. Several parametrizations of the two-channel scattering $K$-matrix are utilized to obtain the scattering amplitudes from the finite-volume spectrum. The amplitudes, continued to the complex energy plane, exhibit a virtual bound state below the $πΣ$ threshold and a resonance pole just below the $\bar{K}N$ threshold.

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arXiv2024

Two-pole nature of the $Λ(1405)$ from lattice QCD

This letter presents the first lattice QCD computation of the coupled channel $πΣ-\bar{K}N$ scattering amplitudes at energies near $1405\,{\rm MeV}$. These amplitudes contain the resonance $Λ(1405)$ with strangeness $S=-1$ and isospin, spin, and parity quantum numbers $I(J^P)=0(1/2^-)$. However, whether there is a single resonance or two nearby resonance poles in this region is controversial theoretically and experimentally. Using single-baryon and meson-baryon operators to extract the finite-volume stationary-state energies to obtain the scattering amplitudes at slightly unphysical quark masses corresponding to $m_π\approx200$ MeV and $m_K\approx487$ MeV, this study finds the amplitudes exhibit a virtual bound state below the $πΣ$ threshold in addition to the established resonance pole just below the $\bar{K}N$ threshold. Several parametrizations of the two-channel $K$-matrix are employed to fit the lattice QCD results, all of which support the two-pole picture suggested by $SU(3)$ chiral symmetry and unitarity.

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arXiv2023

The $Λ(1405)$ from Lattice QCD: Determining the Finite-volume Spectra

This work presents technical details of determining the finite-volume energy spectra for the scattering amplitude of the coupled-channel $πΣ- \bar{K}N$ from lattice QCD data. The importance of reliably extracting such spectra lies in the crucial dependence of the hadronic scattering amplitudes analysis on the energy spectrum when using Lüscher's formalism. Results of the methods used are presented and the final finite-volume spectra are shown. The analysis of the scattering amplitude based on these results, exhibits a two-pole structure for the $Λ(1405)$, a virtual bound state below the $πΣ$ threshold and a resonance pole right below the $\bar{K}N$ threshold.

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arXiv2023

Lattice QCD studies of the $Δ$ baryon resonance and the $K_0^\ast(700)$ and $a_0(980)$ meson resonances: the role of exotic operators in determining the finite-volume spectrum

Studies of the $Δ$ baryon resonance and the $K_0^\ast(700)$ and $a_0(980)$ meson resonances using $N_f=2+1$ lattice QCD for pion masses near 200 MeV are presented. The $s$-wave scattering lengths for both the $I=1/2$ $N π$ and $I=3/2$ $N π$ channels and properties of the $Δ$ resonance are identified from the finite-volume energy levels of the lattice simulation. The importance of a three-quark $Δ$-operator in the $Nπ$ system and tetraquark operators in the mesonic systems is investigated.

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arXiv2023

Interactions of $πK$, $ππK$ and $KKπ$ systems at maximal isospin from lattice QCD

We study the interactions of systems of two and three nondegenerate mesons composed of pions and kaons at maximal isospin using lattice QCD, specifically $π^+K^+$, $π^+π^+K^+$ and $K^+K^+π^+$. Utilizing the stochastic LapH method, we determine the spectrum of these systems on two CLS $N_f=2+1$ ensembles with pion masses of $200$ MeV and $340$ MeV, and include many levels in different momentum frames. We constrain the K matrices describing two- and three-particle interactions by fitting the spectrum to the results predicted by the finite-volume formalism, including up to $p$ waves. This requires also results for the $π^+π^+$ and $K^+ K^+$ spectrum, which have been obtained previously on the same configurations. We explore different fitting strategies, comparing fits to energy shifts with fits to energies boosted to the rest frame, and also comparing simultaneous global fits to all relevant two- and three-particle channels to those where we first fit two-particle channels and then add in the three-particle information. We provide the first determination of the three-particle K matrix in $π^+π^+K^+$ and $K^+ K^+ π^+$ systems, finding statistically significant nonzero results in most cases. We include $s$ and $p$ waves in the K matrix for $π^+ K^+$ scattering, finding evidence for an attractive $p$-wave scattering length. We compare our results to Chiral Perturbation Theory, including an investigation of the impact of discretization errors, for which we provide the leading order predictions obtained using Wilson Chiral Perturbation Theory.

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arXiv2023

Elastic nucleon-pion scattering at $m_π = 200~{\rm MeV}$ from lattice QCD

Elastic nucleon-pion scattering amplitudes are computed using lattice QCD on a single ensemble of gauge field configurations with $N_{\rm f} = 2+1$ dynamical quark flavors and $m_π = 200~{\rm MeV}$. The $s$-wave scattering lengths with both total isospins $I=1/2$ and $I=3/2$ are inferred from the finite-volume spectrum below the inelastic threshold together with the $I=3/2$ $p$-wave containing the $Δ(1232)$ resonance. The amplitudes are well-described by the effective range expansion with parameters constrained by fits to the finite-volume energy levels enabling a determination of the $I=3/2$ scattering length with statistical errors below $5\%$, while the $I = 1/2$ is somewhat less precise. Systematic errors due to excited states and the influence of higher partial waves are controlled, providing a pathway for future computations down to the physical light quark masses with multiple lattice spacings and physical volumes.

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arXiv2022

Performance Optimization of Baryon-block Construction in the Stochastic LapH Method

Implementations of measurement kernels in high-level Lattice QCD frameworks enable rapid prototyping, but can leave hardware capabilities significantly underutilized. This is an acceptable tradeoff if the time spent in unoptimized routines is generally small. The computational cost of modern spectroscopy projects however can be comparable to or even exceed the cost of generating gauge configurations and computing solutions of the Dirac equation. One such key kernel in the stochastic LapH method is the computation of baryon blocks; we discuss several implementation strategies and achieve a 7.2x speedup over the current implementation on a system with Intel(R) Xeon(R) Platinum 8358 processors, formerly Ice Lake.

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arXiv2022

The hyperon spectrum from lattice QCD

Hyperon decays present a promising alternative for extracting $\vert V_{us} \vert$ from lattice QCD combined with experimental measurements. Currently $\vert V_{us} \vert$ is determined from the kaon decay widths and a lattice calculation of the associated form factor. In this proceeding, I will present preliminary work on a lattice determination of the hyperon mass spectrum. I will additionally summarize future goals in which we will calculate the hyperon transition matrix elements, which will provide an alternative means for accessing $\vert V_{us} \vert$. This work is based on a particular formulation of SU(2) chiral perturbation theory for hyperons; determining the extent to which this effective field theory converges is instrumental in understanding the limits of its predictive power, especially since some hyperonic observables are difficult to calculate near the physical pion mass (e.g., hyperon-to-nucleon form factors), and thus the use of heavier than physical pion masses is likely to yield more precise results when combined with extrapolations to the physical point.}

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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.

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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.

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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 $Λ(1405)$.

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arXiv2021

Nucleon Axial Form Factor from Domain Wall on HISQ

The Deep Underground Neutrino Experiment (DUNE) is an upcoming neutrino oscillation experiment that is poised to answer key questions about the nature of neutrinos. Lattice QCD has the ability to make significant impact upon DUNE, beginning with computations of nucleon-neutrino interactions with weak currents. Nucleon amplitudes involving the axial form factor are part of the primary signal measurement process for DUNE, and precise calculations from LQCD can significantly reduce the uncertainty for inputs into Monte Carlo generators. Recent calculations of the nucleon axial charge have demonstrated that sub-percent precision is possible on this vital quantity. In these proceedings, we discuss preliminary results for the CalLat collaboration's calculation of the axial form factor of the nucleon. These computations are performed with Möbius domain wall valence quarks on HISQ sea quark ensembles generated by the MILC and CalLat collaborations. The results use a variety of ensembles including several at physical pion mass.

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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.

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arXiv2021

Scale setting the Möbius Domain Wall Fermion on gradient-flowed HISQ action using the omega baryon mass and the gradient-flow scales $t_0$ and $w_0$

We report on a sub-percent scale determination using the omega baryon mass and gradient-flow methods. The calculations are performed on 22 ensembles of $N_f=2+1+1$ highly improved, rooted staggered sea-quark configurations generated by the MILC and CalLat Collaborations. The valence quark action used is Möbius Domain-Wall fermions solved on these configurations after a gradient-flow smearing is applied with a flowtime of $t_{\rm gf}=1$ in lattice units. The ensembles span four lattice spacings in the range $0.06 \lesssim a \lesssim 0.15$ fm, six pion masses in the range $130 \lesssim m_π\lesssim 400$ MeV and multiple lattice volumes. On each ensemble, the gradient-flow scales $t_0/a^2$ and $w_0/a$ and the omega baryon mass $a m_Ω$ are computed. The dimensionless product of these quantities is then extrapolated to the continuum and infinite volume limits and interpolated to the physical light, strange and charm quark mass point in the isospin limit, resulting in the determination of $\sqrt{t_0}=0.1422(14)$ fm and $w_0 = 0.1709(11)$ fm with all sources of statistical and systematic uncertainty accounted for. The dominant uncertainty in this result is the stochastic uncertainty, providing a clear path for a few-per-mille uncertainty, as recently obtained by the Budapest-Marseille-Wuppertal Collaboration.

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arXiv2021

Two-nucleon S-wave interactions at the $SU(3)$ flavor-symmetric point with $m_{ud}\simeq m_s^{\rm phys}$: a first lattice QCD calculation with the stochastic Laplacian Heaviside method

We report on the first application of the stochastic Laplacian Heaviside method for computing multi-particle interactions with lattice QCD to the two-nucleon system. Like the Laplacian Heaviside method, this method allows for the construction of interpolating operators which can be used to construct a positive definite set of two-nucleon correlation functions, unlike nearly all other applications of lattice QCD to two nucleons in the literature. It also allows for a variational analysis in which optimal linear combinations of the interpolating operators are formed that couple predominantly to the eigenstates of the system. Utilizing such methods has become of paramount importance in order to help resolve the discrepancy in the literature on whether two nucleons in either isospin channel form a bound state at pion masses heavier than physical, with the discrepancy persisting even in the $SU(3)$-flavor symmetric point with all quark masses near the physical strange quark mass. This is the first in a series of papers aimed at resolving this discrepancy. In the present work, we employ the stochastic Laplacian Heaviside method without a hexaquark operator in the basis at a lattice spacing of $a\sim0.086$~fm, lattice volume of $L=48a\simeq4.1$~fm and pion mass $m_π\simeq714$ MeV. With this setup, the observed spectrum of two-nucleon energy levels strongly disfavors the presence of a bound state in either the deuteron or dineutron channel.

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