arXiv subjects

Stephen R. Sharpe

Publications and source records attributed to Stephen R. Sharpe.

At least 19 recordsLinked to original sources

arXiv2026

Accessing the Wess-Zumino-Witten term using Lattice QCD

The Wess-Zumino-Witten interaction in chiral perturbation theory is a manifestation of chiral anomalies. One of its consequences is the presence of a nonvanishing $K \overline K \to π^+ π^0 π^-$ amplitude. We derive the finite-volume formalism that allows one to access this, and related, amplitudes, using the spectra of two and three particles in finite volumes, spectra that can be calculated using lattice QCD. Specifically, we present the formalism for the systems $K \overline K + 3 π$ with $I=0$ and $πK + ππK$ with $I=1/2$ and $3/2$. In addition, we determine the threshold expansions for the $2\leftrightarrow 3$ and $3\leftrightarrow 3$ K matrices that enter the formalism, and calculate the leading order predictions from chiral perturbation theory for the coefficients that enter these expansions.

hep-lat↗

arXiv2026

Three-body study of the $T_{cc}(3875)^+$ from lattice QCD

We discuss an ongoing first lattice study of the doubly-charmed tetraquark $T_{cc}^+$(3875) via a three-body approach. We investigate the $DDπ$ system in the $I=0$, $C=2$ sector, where the $T_{cc}^+$ appears as a pole in the $J^P = 1^+$ $DDπ$ elastic scattering amplitude. The approach automatically incorporates two-body $DD^*$ and three-body $DDπ$ effects and treats left-hand cuts due to single $π$ exchanges. Two CLS ensembles, X252 and X253, with pion mass $M_π\approx 280$ MeV, are used, and an operator set comprised of two- and three-hadron and tetraquark operators is employed to extract finite-volume energies. Additional inputs are required for the three-body finite-volume analysis, in the form of amplitudes for the $I=1$ $DD$ and $I=1/2$ $Dπ$ two-body subsystems. We present preliminary results for these subchannels and perform exploratory three-body spectra determinations for simple choices of the three-particle K-matrix $\mathcal{K}_{\text{df}, 3}$, allowing a first comparison to the lattice spectrum.

hep-lat↗

arXiv2026

Implementing the three-neutron quantization condition

We describe in detail the implementation of the relativistic three-neutron finite-volume quantization condition derived in Ref. [1]. In particular, we show how the complications due to Wigner rotations acting on spins are included, and present concrete formulas for the case when the angular momenta within pairs is restricted to be less than 2. We describe the symmetries of the matrices appearing in the quantization condition, and decompose solutions into irreducible representations of the appropriate doubled finite-volume symmetry groups. We present an implementation of the three-particle K matrix, keeping the two lowest-order terms in the threshold expansion. We provide numerical predictions for the finite-volume spectrum for a setup with nearly physical parameters, including two-particle interactions that are based on experimental results. This exploratory study shows the how lattice QCD calculations of the three-neutron spectrum with sufficient precision can provide detailed information on both two- and three-particle interactions.

hep-lat↗

arXiv2026

Three-particle scattering amplitudes from lattice QCD

I review recent progress in calculating scattering amplitudes and resonance properties involving three particles using results from lattice QCD. The necessary input is the finite-volume spectrum, and the outputs -- via solutions of integral equations -- are scattering amplitudes that can be continued into the complex plane to search for resonance poles. I describe the outlook for future extensions and applications of this work.

hep-lat↗

arXiv2025

Comparison of integral equations used to study $T_{cc}^+$ for a stable $D^*$

We perform a detailed comparison between three formalisms used in recent studies of $DD^*$ scattering, which aim to understand the properties of the doubly-charmed tetraquark, $T_{cc}^+(3875)$. These methods are the three-particle relativistic field theory (RFT) formalism, the two-body Lippmann-Schwinger (LS) equation with chiral effective field theory potentials, and the two-particle relativistic framework proposed by Baiao Raposo and Hansen (BRH approach). In a simplified single-channel setting, we derive the conditions under which the infinite-volume integral equations from the RFT and BRH approaches reduce to the LS form. We present numerical examples showing that differences between these methods can be largely removed by adjusting short-range couplings. We also address a number of technical issues in the RFT approach.

nucl-th↗

arXiv2025

Finite-volume formalism for $Nππ$ at maximal isospin

We extend the relativistic field theoretic finite-volume formalism to $N ππ$ scattering states at maximal isospin, $I=5/2$. As in previous work using the relativistic field theory approach, we work to all orders in a generic low-energy effective theory, and determine the quantization condition that relates finite-volume energies to intermediate K matrices, and the integral equations connecting the latter to the physical scattering amplitudes. We discuss the parametrization of the K matrices, and explain in detail the new features that arise in implementing the quantization condition due to the spin of the nucleon in combination with the use of non-degenerate particles. As a concrete example, we provide a sample numerical application including the $Δ$ resonance in the $Nπ$ subchannel. The extension to the $I=3/2$ and $1/2$ channels is more involved, due to mixing with $Nπ$ states, and we do not provide a complete formalism for these cases. We explain why $Nπ$ states cannot be included by treating the nucleon as a pole in $p$-wave $Nπ$ scattering, an approach that has been successful in studying $D D^*$ scattering using the three-particle $DDπ$ formalism. We additionally provide results for all isospins under the assumption of no two-to-three mixing, thereby laying the groundwork for a follow-up paper in which all $Nππ\leftrightarrow Nπ$ systems are fully treated. Finally, we study the singularities in $Nππ$ amplitudes arising from $Nπππ$ intermediate states, and find that our subthreshold cutoff functions must be modified to avoid such singularities.

hep-lat↗

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.

hep-lat↗

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.

hep-lat↗

arXiv2025

Finite- and infinite-volume study of $DDπ$ scattering

We develop a comprehensive framework for extracting the pole position and properties of the doubly-charmed tetraquark $T_{\rm cc}^+(3875)$ from lattice QCD data using the relativistic three-particle formalism. This approach incorporates the effect of the one-pion exchange diagram in $DDπ$ and $DD^*$ scattering, making it applicable at energies coinciding with the left-hand cut in the partial-wave projected $DD^*$ amplitude. We present an example application of this framework to existing lattice QCD data at $m_π= 280$ MeV. We solve the integral equations describing the $DDπ$ reaction, use LSZ reduction to determine the corresponding $DD^*$ amplitude, and find the values of the infinite-volume two- and three-body $K$ matrices that lead to agreement with lattice $DD^*$ phase shifts within their uncertainties. Using these $K$ matrices in the three-particle quantization condition, we describe the finite-volume $DD^*$ spectrum and find good agreement with the lattice QCD energies. Our results suggest that, at this pion mass, the tetraquark appears as a pair of subthreshold complex poles whose precise location strongly depends on the value of the $DDπ$ three-particle $K$ matrix.

hep-lat↗

arXiv2024

Implementation of the three-neutron quantization condition

We present an implementation of the three-neutron quantization condition (QC) derived in previous work. We construct the matrices appearing in the QC and determine solutions numerically. The symmetries of the QC allow the projection onto irreducible representations of the appropriate little group (depending on frame momentum), restricting the size of the matrices and reducing computational complexity. In this initial study, we include only two-neutron interactions, which are modeled based on experimental data for $I=1$ scattering amplitudes. We show examples of the finite-volume spectrum in two frames and for a range of energies, illustrating the potential and also the challenges of using three-neutron spectroscopy to constrain the underlying interactions.

hep-lat↗

arXiv2024

Three-particle formalism for multiple channels: the $ηππ+ K \overline K π$ system in isosymmetric QCD

We generalize previous three-particle finite-volume formalisms to allow for multiple three-particle channels. For definiteness, we focus on the two-channel $ηππ$ and $K \overline K π$ system in isosymmetric QCD, considering the positive $G$ parity sector of the latter channel, and neglecting the coupling to modes with four or more particles. The formalism we obtain is thus appropriate to study the $b_1(1235)$ and $η(1295)$ resonances. The derivation is made in the generic relativistic field theory approach using the time-ordered perturbation theory method. We study how the resulting quantization condition reduces to that for a single three-particle channel when one drops below the upper ($K\overline K π$) threshold. We also present parametrizations of the three-particle K matrices that enter into the formalism.

hep-ph↗

arXiv2024

Incorporating $DDπ$ effects and left-hand cuts in lattice QCD studies of the $T_{cc}(3875)^+$

We generalize the relativistic field-theoretic three-particle finite-volume scattering formalism to describe generic $DDπ$ systems in the charm $C=2$ sector. This includes the isospin-0 channel, in which the recently discovered doubly-charmed tetraquark $T_{cc}(3875)^+$ is expected to manifest as a pole in the $DD π\to DD π$ scattering amplitude. The formalism presented here can also be applied to lattice QCD settings in which the $D^*$ is bound and, in particular, remains valid below the left-hand cut in $D D^*$ scattering, thus resolving an issue in previous analyses of lattice-determined finite-volume energies.

hep-lat↗

arXiv2024

The three-pion $K$-matrix at NLO in ChPT

The three-particle $K$-matrix, $\mathcal{K}_{\mathrm{df},3}$, is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we compute its value for systems of three pions in all isospin channels through next-to-leading order in Chiral Perturbation Theory, generalizing previous work done at maximum isospin. We obtain analytic expressions through quadratic order (or cubic order, in the case of zero isospin) in the expansion about the three-pion threshold.

hep-ph↗

arXiv2023

Three-pion scattering: From the chiral Lagrangian to the lattice

In recent years, detailed studies of three-pion systems have become possible in lattice QCD. This has in turn led to interest in 3-to-3 scattering of pions in the chiral perturbation theory framework. In addition to being an interesting study of multi-meson dynamics in its own right, it provides a valuable handle on finite-volume effects and the pion mass dependence, thus complementing the lattice results. I present our derivation of the next-to-leading order amplitude for this process, as well as its conversion into the three-particle K-matrix, which enables direct comparison to the lattice. Our results significantly improve the agreement between theory and lattice, which was poor when only leading-order effects were taken into account.

hep-ph↗

arXiv2023

Three relativistic neutrons in a finite volume

We generalize the relativistic field-theoretic (RFT) three-particle finite-volume formalism to systems of three identical, massive, spin-$1/2$ fermions, such as three neutrons. This allows, in principle, for the determination of the three-neutron interaction from the finite-volume spectrum of three-neutron states, which can be obtained from lattice QCD calculations.

hep-lat↗

arXiv2023

The isospin-3 three-particle $K$-matrix at NLO in ChPT

The three-particle $K$-matrix, $\mathcal{K}_{\mathrm{df},3}$, is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we compute its value for systems of three pions at maximal isospin through next-to-leading order (NLO) in Chiral Perturbation Theory (ChPT). We compare the values to existing lattice QCD results and find that the agreement between lattice QCD data and ChPT in the first two coefficients of the threshold expansion of $\mathcal{K}_{\mathrm{df},3}$ is significantly improved with respect to leading order once NLO effects are incorporated.

hep-ph↗

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.

hep-lat↗

arXiv2022

Lattice QCD and Particle Physics

Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021).

hep-lat↗