The importance of an earnest amplitude

• Alessandro Pilloni (Messina U. and INFN Catania)

Recent Results and Perspectives from the GlueX Experiment

• Sean Dobbs (Florida State University)

The GlueX experiment has collected the largest polarized photoproduction data set for meson spectroscopy in the world. These data also allow the study of a wide range of other topics in hadronic physics, from meson decays, to hyperon spectroscopy, and near-threshold charmonium production. I will report on the status and plans for the main goals of the GlueX experiment, the search for hybrid mesons, describe other interesting results from GlueX, and give an outlook for the future.

Machine learning for hadron spectroscopy

• Lukasz Bibrzycki (Pedagogical University of Cracow)

We discuss two applications of machine learning for hadron spectroscopy. The long-debated nature of the Pc(4312) pentaquark candidate has been elucidated using the neural network based classifier. Production of the Pc(4312) state involves two coupled channels p J/ψ and Σ+c D0 thus necessitating the consideration of a 4-sheeted complex energy Riemann surface. Of these four Riemann sheets only 2th and 4th are relevant due to their proximity to the physical region of interest. Combined with two possible physical interpretations considered in our analysis, namely the bound state and virtual state it resulted in four possible class assignments dubbed b|2, v|2, b|4, and v|4. The unitary coupled channel amplitude was considered in the scattering length approximation. By careful statistical analysis, we showed that the v|4 assignment is the most probable. Employing the Principal Component Analysis we showed that just 6 dominant eigenfeatures are sufficient to explain 99% of the signal variance. And projecting the experimental data on these dominant features we showed that they are well represented within the training dataset. Finally, we applied the SHAP (SHapley Additive exPlanations) to identify that near threshold bins are decisive for the class assignment, thus providing an ex-post justification of the scattering length approximation. A short account of the ongoing joint JPAC-(AI)DAPT analyses to exploit the generative models for data analysis will also be given.

Consistent Interpretation of the LHCb Pentaquark Signals

• Tim Burns
• Eric Swanson (Univ Pittsburgh)

A model of the LHCb pentaquark signals that incorporates relevant experimental results and theoretical constraints is presented. An application of a similar model to the Pcs(4338) is also made.

Resonant processes via lattice QCD: an overview

• Raul Briceno (Jefferson Lab)

In this talk, I review the status for studying few-body scattering amplitudes involving external electroweak probes via lattice QCD. I discuss existing lattice QCD calculations on this front, but I primarily discuss the formal challenges that have been recently addressed and discuss the outstanding ones.

Two-nucleon interactions in the continuum from lattice QCD

• Andrew Hanlon (Brookhaven National Laboratory)

There remains a decade-old controversy regarding two-nucleon interactions from lattice QCD at higher than physical pion masses. Initially this began as a disagreement between two entirely different methods (i.e. Lüscher’s two-particle quantization condition and the HAL QCD potential method). However, Lüscher’s quantization condition relies on the extraction of finite-volume energies, and recent improved energy determinations have called into question older results using the Lüscher method. In this talk, I will show calculations for two nucleon interactions utilizing the variational approach for extracting finite-volume energies reliably. This work includes six lattice spacings, allowing us to take a continuum limit which is found to be necessary for obtaining correct results.

What lineshapes of resonances teach us about their nature

• Christoph Hanhart (FZ-Juelich)

In this talk I will explain how lineshapes of near threshold states can be used to distinguish hadronic molecules from more compact objects.

Some phenomenological applications of Khuri-Treiman equations

• Sergi Gonzàlez-Solís (Indiana University)

One of the main issues posed by the presence of hadrons in any reaction is their final-state interactions, which are formally expressed in terms of the unitarity of the amplitude. In two-body scattering, unitarity is usually imposed in the direct channel only, as one is not sensitive to the details of the crossed channels. This is certainly not the case for a three-body decay, where the three possible two-hadron channels are physical, and one ideally wants to impose unitarity in all channels at once. The Khuri-Treiman formalism is a dispersive approach which indeed allows one to do so. In this talk I will introduce such formalism and study various important applications, e.g. V→3π (V=ω,ϕ,J/ψ).

Confinement and Coulomb Gauge Lattice QCD

• Wyatt Smith (Indiana University)

In Coulomb gauge QCD, there exists an instantaneous chromo-electric interaction between static heavy quark-antiquark pairs. Studying this interaction is an effective way to probe aspects of quark confinement, as the confining behavior of this ‘Coulomb potential’ is related to the confining behavior of the Wilson potential in non-gauge fixed QCD. A clearer picture of the mechanism of confinement would then allow us to better explain aspects of the meson spectrum. We present our attempts to understand this interaction via SU(2) and SU(3) Coulomb Gauge Lattice QCD simulations on anisotropic lattices.

The search for exotic matter in the light-meson sector

• Boris Grube (Jefferson Lab)

The question whether exotic forms of hadronic matter such as four-quark states, hybrid states with excited gluon fields, or glueballs exist is one of the major open questions of the Standard Model and has been driving experiments and theory since the development of the quark model. In the light-meson sector, the focus lies mainly on the search for spin-exotic states, which have $J^{PC}$ quantum-number combinations that are forbidden for $q\bar{q}$ states in the non-relativistic limit. To find these states we need to explore the light-meson spectrum in great detail. Since excited light mesons often have large widths and are overlapping, the mapping of their spectrum is challenging and requires large quantities of data, which need to be analyzed using partial-wave analysis (PWA) techniques. In addition, most excited meson states decay into multi-particle hadronic final states, for which the PWA requires extensive modeling of the dynamics of the final-state hadrons. In this talk, I will report on recent partial-wave analysis results that shed new light on possible candidates for spin-exotic states. I will also touch on novel analysis techniques and the prospects for future progress.

Few-Body Dynamics from QCD

• Andrew Jackura (Old Dominion University)

Accessing the hadron spectrum from Quantum ChromoDynamics (QCD) poses several challenges given its non-perturbative nature and the fact that most states couple to multi-particle decay modes. Although challenging, advances in both theoretical and numerical techniques have allowed us to determine few-body systems directly from QCD. A synergistic approach between lattice QCD and scattering theory offers a systematic pathway to numerically compute properties such as the hadron spectrum from first principles. I will present an overview of this program, and discuss developments in determining three-body scattering processes and electroweak transitions of multi-hadron systems. These techniques allow us to push the boundaries of resolving the few-body problem in spectroscopy, and gives us insight into the structure of hadrons as the emergent phenomena of QCD.

Analysis of rescattering effects in $3\pi$ final states

• Dominik Stamen (Bonn University)

We quantify the importance of rescattering effects beyond the simplest isobar model in three-pion finales states for different decay masses and angular-momentum quantum numbers. We provide the reconstruction theorems for four different decay processes, resonances with $J^{PC} = 0^{-+}$, $1^{--}$, $1^{-+}$, and $2^{++}$, all of which decay, in the simplest approximation, into $\pi\rho$ final states. Two-pion rescattering can be described rigorously in terms of Omnès functions, which incorporate the effects of the $\rho$-resonances. Inclusion of full rescattering effects is achieved solving the Khuri--Treiman integral equations. Using log-likelihood differences, we compute the minimum number of events necessary to unambiguously identify rescattering effects beyond two-body resonances in future Dalitz plot analyses. The variation of this sensitivity for a series of decay masses is interpreted in terms of kinematic effects for different quantum numbers.

On the semileptonic production of the $\rho$ resonance from B-mesons

• Luka Leskovec

The production mechanism of resonances varies between experiments. One way to produce the \rho resonance at LHCb and BelleII is through the semileptonic B-meson decay, B\to\rho\ell\nu. It's transition amplitude provides insight into how the resonances are made and helps determine one of the basic parameters of the standard model, the CKM matrix element V_{ub}. In this talk, we will present our progress towards a lattice QCD determination of B\to\rho (\to \pi\pi) \ell \nu transition amplitude, with N_f=2+1 clover fermions whose mass corresponding to m_\pi ~ 320 MeV and L=3.6 fm. We will briefly introduce the theoretical framework and discuss some preliminary results.

Three-body dynamics of the a1(1260) from lattice QCD

• Michael Doring (George Washington U and Jefferson Lab)

The pole position of the $a_1(1260)$ is determined from lattice QCD data; complementing calculations in the infinite volume help understand the properties of this three-body resonance.

Search for Exotic Hadrons in 𝜂(′)𝜋 at GlueX

• Malte Albrecht (Jefferson Lab)

The strong interaction between quarks and gluons, from which hadrons are built, is theoretically described by quantum chromodynamics. However, the role of gluons and how they affect the properties of hadrons is still unresolved. The discovery of several unexpected and possibly exotic hadrons in recent years highlights the need for precise spectroscopic measurements to understand the nature of the strong interaction. The status of the search for exotic contributions in photoproduction data from the GlueX experiment at Jefferson Lab in $\eta^{(\prime)} \pi$ systems will be presented. Specifically, results on the production of the $a_2(1320)$ meson in these key channels, which are first steps in the search for exotic quantum-number hybrid mesons, will be discussed. The application of a partial wave analysis exploiting the polarization of the photon beam available to the GlueX experiment, and implications for the measures needed to identify the hybrid will be discussed.

Double-Regge contribution to $\eta^{(')}\pi$ production

• Cesar Fernandez-Ramirez (UNED/ICN-UNAM)

The production of $\eta^{(\prime)}\pi$ pairs constitutes one of the golden channels to search for hybrid exotics, with explicit gluonic degrees of freedom. Understanding the dynamics and backgrounds associated to $\eta^{(\prime)}\pi$ production above the resonance region is required to impose additional constraints to the resonance extraction. We consider the reaction $\pi^-p\to \eta^{(\prime)} \pi^-\, p$ measured by COMPASS. We show that the data in $2.4 < m_{\eta^{(\prime)}\pi} < 3.0$ GeV can be described by amplitudes based on double-Regge exchanges. The angular distribution of the meson pairs, in particular in the $\eta' \pi$ channel, can be attributed to flavor singlet exchanges, suggesting the presence of a large gluon content that couples strongly to the produced mesons.

Molecular states with charm and strangeness

• Raquel Molina Peralta (UV-IFIC)

In the last years there has been interesting physics around the thresholds of a charmed meson and a strange one. The firsts of these states discovered were the $D_{s0}(2317)$, near the $DK$ threshold and the $D_{s1}(2460)$, close to the $D^*K$ mass. Recently, the LHCb has reported several states which are near the $D^*K^*$ energy region. These are the $T_{cs}(2900)$ and $T_{c\bar{s}}(2900)$. We recall the predictions made on these states from the hidden gauge approach. Several reactions are proposed in order to look for the spin partners of the $T_{cs}(2900)$. We also study the reactions $B^0\to\bar{D}^0D_s^+\pi^-$ and $B^+\to D^-D_s^+\pi^+$ where the $T_{c\bar{s}}(2900)$ has been seen. Our study suggest that this new state is indeed a threshold effect formed by the $D^*K^*$, $D^*_s\rho$ interaction. Finally, we also show results of a recent lattice data analysis of $DK$ scattering in the HM$\chi$PT framework, from where the quark mass dependence of the $D_{s0}(2317)$ has been extracted.

Applying Information Field Theory to Partial-Wave Analysis

• Florian Kaspar (Technical University of Munich)

Spectroscopic information from scattering experiments is typically extracted using partial-wave analysis methods. Such an analysis is performed in bins of the final-state mass. In a second step, the information from the different mass bins is then combined through fits based on physics models. The large number of free parameters in such analyses leads to fluctuations (noise) across the mass range, which may correlate among different waves. We present a new method, in which we assume continuity in the final-state mass of the underlying signal in order to reduce noise on the fits. We implemented this method using the NIFTy framework for Numerical Information Field Theory, originally conceived for analysis of astrophysical data. We will explain the underlying ideas and methods, present studies using simulated data and first application to data from the COMPASS experiment.

Status and perspectives in hadron spectroscopy with CLAS12

• Raffaella De Vita (INFN - Genova)

Exotic hadron spectroscopy with functional methods

• Gernot Eichmann (University of Graz)

I will give a brief overview on the status of exotic hadron spectroscopy with Dyson-Schwinger and Bethe-Salpeter equations. I will talk about glueballs in Yang-Mills theory, tetraquarks in the light- and heavy-quark sector and their mixing with q-qbar states, first exploratory calculations for pentaquarks and hybrid mesons, and progress in determining QCD's n-point functions that enter in such calculations.

Application of p.w. dispersive techniques in the analysis of experimental and lattice data.

• Igor Danilkin (Johannes Gutenberg University of Mainz)

In my talk I will overview our recent applications of the partial-wave (p.w.) dispersion relations written for the direct and inverse amplitudes. The requirement that the amplitude should satisfy the dispersion relation significantly constrains its possible forms and allow for a more precise determination of the resonance parameters. In particular, I will focus on the $\pi\pi$ and $\pi K$ isoscalar channels (for physical and unphysical pion mass) where broad scalar resonances reside.

Determination of the f0(1370) from a novel dispersive analysis of meson-meson scattering data

• Jose Pelaez (Complutense University of Madrid)

We establish the existence of the long-debated $f_0​(1370)$ resonance in the dispersive analyses of meson-meson scattering data. For this, we present a novel approach using forward dispersion relations, valid for generic inelastic resonances. We find its pole at $(1245\pm40)−i (300−70+30)$ MeV in ππ->ππ scattering. We also provide the couplings as well as further checks extrapolating partial-wave dispersion relations or with other continuation methods. A pole at $(1380−60+70)−i (220−70+80)$ MeV also appears in the $ππ\to K\bar K$ data analysis with partial-wave dispersion relations. Despite settling its existence in meson-meson scattering, our model-independent dispersive and analytic methods still show a lingering tension between pole parameters from the $ππ\to ππ$ and $ππ\to K\bar K$ channels that should be attributed to data

Computing the polarimeter vector field of Λc⁺ using its dominant hadronic mode

• Remco de Boer (Ruhr University Bochum)

The _aligned polarimeter vector field $\vec\alpha$_ is as a model-independent representation of the decay rate for polarized decays. Using the recent amplitude analysis of the $\Lambda_c^+ \to p K^- \pi^+$ transition by LHCb, we have computed the distribution of this $\vec\alpha$-field in the space of Mandelstam variables of the decay process. The result will facilitate polarization measurements of the $\Lambda_c$ baryon and ease inclusion of the $\Lambda_c$ decay mode to hadronic amplitude analysis. The computations were performed with a new approach using methods from [the ComPWA project](https://compwa-org.rtfd.io). Amplitude models are implemented symbolically with a Computer Algebra System, so that the mathematics can be easily inspected. The symbolic model then serves as a template for fast, numerical back-ends like JAX and TensorFlow. This _symbolic approach_ makes it easy to formulate and fit amplitude models in a self-documenting workflow with high performance on large, multidimensional data samples.

Amplitude Analysis of Two-Pseudoscalar Meson Systems at GlueX

• Alexander Austregesilo (JLab)

The GlueX experiment at Jefferson Lab is studying the light meson spectrum with an emphasis on the search for hybrid mesons. Besides the focus on hybrid meson candidates with exotic quantum numbers, the identification of hybrid mesons with conventional quantum numbers will be essential to confirm the pattern of hybrid multiplets predicted by Lattice QCD calculations and to determine their nature. In this talk, we will focus on the vector meson sector, particularly on the ones decaying into two-pseudoscalar meson final states. Vector mesons contribute to a large fraction of the total photoproduction cross section of the linearly-polarized photon beam at GlueX. The vector meson ground states $\rho$, $\omega$ and $\phi$ are currently studied with unprecedented precision for valuable input to models of the production process. Beyond that, the GlueX high-precision data set will shed light into the spectrum of excited vector mesons where existing information is limited. This knowledge is necessary to be able to identify potential hybrid meson candidates within the spectrum.

Finite volume corrections for form factors of two-nucleon systems

• Felipe Ortega-Gama (William & Mary)

A complete understanding of the QCD spectrum calls for a dynamical description of the nature of resonances, which can be nourished by the determination of the strength and features of the coupling between hadronic states and electroweak currents. In order to utilize lattice QCD to calculate these, a formulation of analytic mappings that relate finite volume results to infinite volume amplitudes is required. Currently, the ingredients to analyze finite volume matrix elements of two *scalar* hadrons and an external current insertion are on place. In this talk I will describe the current progress towards the *extension* of this formalism to hadrons with non-trivial spin degrees of freedom. I will present the main ingredients of our derivation, which are mainly related to the study of the finite volume version of the triangle loop, and an outlook for future calculations. A case study of the significance of the finite-volume corrections will be presented for a deuteron-like state.

Theoretical Model of Two-Pion Photoproduction: Part 1

• Nadine Hammoud (Institute of Nuclear Physics, IFJ- PAS)

Photoproduction is an important reaction in studies of hadron spectroscopy. In particular, a study of two-pion photoproduction allows for an investigation of meson resonances in the pi-pi system and also allows one to study the process $\gamma p\to \pi \Delta$. Under the assumption of single pion exchange, this two-to-three process may be factorized into two sub-processes; a photon dissociation to two (off-shell) pions, and a further two-body $\pi N$ scattering event which brings the system on-shell. This interpretation allows for a description of two-pion photoproduction in terms of the well-known elastic $\pi N$ scattering amplitudes. Augmenting this so-called 'Deck Mechanism' with the $\rho$ resonance leads to a reasonable description of the differential cross section in the vicinity of the $\rho$ resonance. Encouraged by this success, we predict the angular moments of the two-pion system and compare with CLAS data. We also make predictions for the process $\gamma p\to \pi \Delta$.

Theoretical Model of Two-Pion Photoproduction: Part 2

• Robert Perry (Univerisity of Barcelona)

Photoproduction is an important reaction in studies of hadron spectroscopy. In particular, a study of two-pion photoproduction allows for an investigation of meson resonances in the pi-pi system and also allows one to study the process $\gamma p\to \pi \Delta$. Under the assumption of single pion exchange, this two-to-three process may be factorized into two sub-processes; a photon dissociation to two (off-shell) pions, and a further two-body $\pi N$ scattering event which brings the system on-shell. This interpretation allows for a description of two-pion photoproduction in terms of the well-known elastic $\pi N$ scattering amplitudes. Augmenting this so-called 'Deck Mechanism' with the $\rho$ resonance leads to a reasonable description of the differential cross section in the vicinity of the $\rho$ resonance. Encouraged by this success, we predict the angular moments of the two-pion system and compare with CLAS data. We also make predictions for the process $\gamma p\to \pi \Delta$.

Regge phenomenoly of the $N^*$ and $\Delta^*$ poles

• Jorge Antonio Silva-Castro (Nuclear Science Institute, National Autonomous University of Mexico)

We use Regge phenomenology to study the structure of the poles of the N∗ and Δ∗ spectrum. We employ the available pole extractions from partial wave analysis of meson scattering and photoproduction data. We assess the importance of the imaginary part of the poles (widths) to obtain a consistent determination of the parameters of the Regge trajectory. We compare the several pole extractions and show how Regge phenomenology can be used to gain insight in the internal structure of baryons. We find that the majority of the states in the parent Regge trajectories are compatible with a mostly compact three-quark state picture.