Physical Sciences and Mathematics Commons^™

A Formalism For Extracting Track Functions From Jet Measurements, Kyle Lee, Ian Moult, Felix Ringer, Wouter J. Waalewijn

Physics Faculty Publications

The continued success of the jet substructure program will require widespread use of tracking information to enable increasingly precise measurements of a broader class of observables. The recent reformulation of jet substructure in terms of energy correlators has simplified the incorporation of universal non-perturbative matrix elements, so called “track functions”, in jet substructure calculations. These advances make it timely to understand how these universal non-perturbative functions can be extracted from hadron collider data, which is complicated by the use jet algorithms. In this paper we introduce a new class of jet functions, which we call (semi-inclusive) track jet functions, which …

Double Distributions And Pseudodistributions, A. V. Radyushkin

Physics Faculty Publications

We describe the approach to lattice extraction of generalized parton distributions (GPDs) that is based on the use of the double distribution (DD) formalism within the pseudodistribution framework. The advantage of using DDs is that GPDs obtained in this way have the mandatory polynomiality property, a nontrivial correlation between 𝓍 and ξ dependences of GPDs. Another advantage of using DDs is that the D-term appears as an independent entity in the DD formalism rather than a part of GPDs H and E. We relate the ξ dependence of GPDs to the width of the α profiles of the corresponding DDs …

Formulation Of Causality-Preserving Quantum Time Of Arrival Theory, Denny Lane B. Sombillo, Neris I. Sombillo

Physics Faculty Publications

We revisit the quantum correction to the classical time of arrival to address the unphysical instantaneous arrival in the limit of zero initial momentum. In this study, we show that the vanishing of arrival time is due to the contamination of the causality-violating component of the initial wave packet. Motivated by this observation, we propose to update the temporal collapse mechanism in Galapon (2009) [18] to incorporate the removal of causality-violating spectra of the arrival time operator. We found that the quantum correction to the classical arrival time is still observed. Thus, our analysis validates that the correction is an …

Non-Singlet Quark Helicity Pdfs Of The Nucleon From Pseudo-Distributions, Robert Edwards, Colin Egerer, Joseph Karpie, Nikhil Karthik, Christopher Monahan, Wayne Morris, Kostas Orginos, Anatoly Radyushkin, David Richards, Eloy Romero, Raza Sabbir Sufian, Savvas Zafeiropoulos, On Behalf Of The Hadstruc Collaboration

Physics Faculty Publications

The non-singlet helicity quark parton distribution functions (PDFs) of the nucleon are determined from lattice QCD, by jointly leveraging pseudo-distributions and the distillation spatial smearing paradigm. A Lorentz decomposition of appropriately isolated space-like matrix elements reveals pseudo-distributions that contain information on the leading-twist helicity PDFs, as well as an invariant amplitude that induces an additional z² contamination of the leading-twist signal. An analysis of the short-distance behavior of the space-like matrix elements using matching coefficients computed to next-to-leading order (NLO) exposes the desired PDF up to this additional z² contamination. Due to the non-conservation of the axial current, …

First Measurement Of Λ Electroproduction Off Nuclei In The Current And Target Fragmentation Regions, T. Chetry, L. El Fassi, W. K. Brooks, R. Dupré, A. El Alaoui, K. Hafidi, P. Achenbach, K. P. Adhikari, Z. Akbar, W.R. Armstrong, M. Arratia, H. Atac, H. Avakian, L. Baashen, N.A. Baltzell, M. Bashkanov, M. Battaglieri, I. Bedlinsky, B. Benkel, M. Zurek, Et Al., Clas Collaboration

Physics Faculty Publications

We report results of Λ hyperon production in semi-inclusive deep-inelastic scattering off deuterium, carbon, iron, and lead targets obtained with the CLAS detector and the Continuous Electron Beam Accelerator Facility 5.014 GeV electron beam. These results represent the first measurements of the Λ multiplicity ratio and transverse momentum broadening as a function of the energy fraction (z) in the current and target fragmentation regions. The multiplicity ratio exhibits a strong suppression at high zand an enhancement at low z. The measured transverse momentum broadening is an order of magnitude greater than that seen for light mesons. This …

Neutrino-Tagged Jets At The Electron Ion Collider, Miguel Arratia, Zhong-Bo Kang, Sebouh J. Paul, Alexei Prokudin, Felix Ringer, Fanyi Zhao

Physics Faculty Publications

We explore the potential of jet observables in charged-current deep inelastic scattering events at the future Electron-Ion Collider. Tagging jets with a recoiling neutrino, which can be identified by the event’s missing transverse momentum, will allow for flavor-sensitive measurements of transverse momentum dependent parton distribution functions. We present the first predictions for transverse-spin asymmetries in azimuthal neutrino-jet correlations and hadron-in-jet measurements. We study the kinematic reach and the precision of these measurements and explore their feasibility using parametrized detector simulations. We conclude that jet production in charged-current deep inelastic scattering, while challenging in terms of luminosity requirements, will complement the …

Full Treatment Of The Thrust Distribution In Single Inclusive E⁺E⁻ → H X Processes, M. Boglione, Andrea Simonelli

Physics Faculty Publications

Extending the transverse momentum dependent factorization to thrust dependent observables entails a series of difficulties, ultimately associated to the behavior of soft radiation. As a consequence, the definition of the transverse momentum dependent functions has to be revised, while preserving (and possibly extending) their universality properties. Moreover, the regularization of the rapidity divergences generates non trivial correlations between rapidity and thrust. In this paper, we show how to deal with these correlations in a consistent treatment of the thrust dependence of e⁺e⁻ → h X cross section, where the hadron transverse momentum is measured with respect to …

Observation Of Correlations Between Spin And Transverse Momenta In Back-To-Back Dihadron Production At Clas12, H. Avakian, T.B. Hayward, A. Kotzinian, W.R. Armstrong, H. Atac, C. Ayerbe Gayoso, L. Baashen, N.A. Balzell, L. Barion, M. Bashkanov, M. Battaglieri, I. Bedlinskiy, B. Benkel, F. Benmokhtar, A. Bianconi, L. Biondo, A. S. Biselli, M. Bondi, S. Boiarinov, M. Zurek, Et Al.

Physics Faculty Publications

We report the first measurements of deep inelastic scattering spin-dependent azimuthal asymmetries in back-to-back dihadron electroproduction in the deep inelastic scattering process. In this reaction, two hadrons are produced in opposite hemispheres along the z axis in the virtual photon-target nucleon center-of-mass frame, with the first hadron produced in the current-fragmentation region and the second in the target-fragmentation region. The data were taken with longitudinally polarized electron beams of 10.2 and 10.6 GeV incident on an unpolarized liquid-hydrogen target using the CLAS12 spectrometer at Jefferson Lab. Observed nonzero sinΔϕ modulations in ep→e'pπ⁺ X events, where Δϕ is the difference …

A Multidimensional Study Of The Structure Function Ratio Σlt'/ Σ₀ From Hard Exclusive ��⁺ Electro-Production Off Protons In The Gpd Regime, S. Diehl, A. Kim, K. Joo, P. Achenbach, Z. Akbar, M. J. Amaryan, H. Atac, H. Avagyan, C. Ayerbe Gayoso, L. Baashen, L. Barion, M. Bashkanov, M. Battaglieri, I. Bedlinsky, B. Benkel, F. Benmokhtar, A. Bianconi, A. S. Biselli, M. Bondi, W.A. Booth, M. Zurek, Et Al.

Physics Faculty Publications

A multidimensional extraction of the structure function ratio from the hard exclusive ^→ep → e'n��+ reaction above the resonance region has been performed. The study was done based on beam-spin asymmetry measurements using a 10.6 GeV incident electron beam on a liquid-hydrogen target and the CLAS12 spectrometer at Jefferson Lab. The measurements focus on the very forward regime (t/Q²≪ 1) with a wide kinematic range of in the valence regime (0.17 < ��_B < 0.55), and virtualities ranging from 1.5 GeV² up to 6 GeV². The results and their comparison to theoretical models based on Generalized Parton Distributions demonstrate the sensitivity to chiral-odd …

Scattered Spectra From Inverse Compton Sources Operating At High Laser Fields And High Electron Energies, Geoffrey A. Krafft, Balša Terzić, Erik Johnson, G. Wilson

Physics Faculty Publications

As Compton x-ray and gamma-ray sources become more prevalent, to understand their performance in a precise way, it becomes important to be able to compute the distribution of scattered photons precisely. For example, codes have been developed at Old Dominion University which were used to understand the performance of the Dresden Compton Source in detail. An ideal model would (i) include the full Compton effect frequency relations between incident and scattered photons, (ii) allow the field strength to be large enough that nonlinear effects are captured, and (iii) allow the effects of electron beam emittance to be introduced and studied. …

Resolution To The Problem Of Consistent Large Transverse Momentum In Tmds, J. O. Gonzalez-Hernandez, Tommaso Rainaldi, Ted Rogers

Physics Faculty Publications

Parametrizing TMD parton densities and fragmentation functions in ways that consistently match their large transverse-momentum behavior in standard collinear factorization has remained notoriously difficult. We show how the problem is solved in a recently introduced set of steps for combining perturbative and nonperturbative transverse momentum in TMD factorization. Called a “bottom-up” approach in a previous article, here we call it a “hadron structure oriented” (HSO) approach to emphasize its focus on preserving a connection to the TMD parton model interpretation. We show that the associated consistency constraints improve considerably the agreement between parametrizations of TMD functions and their large-kT behavior, …

Searching For Prompt And Long-Lived Dark Photons In Electroproduced E⁺ E⁻ Pairs With The Heavy Photon Search Experiment At Jlab, P. H. Adrian, N. A. Baltzell, M. Battaglieri, M. Bondí, S. Boyarinov, S. Bueltmann, P. Butti, V. D. Burkert, D. Calvo, T. Cao, M. Carpinelli, A. Celentano, G. Charles, L. Colaneri, W. Cooper, D. Crowe, C. Cuevas, A. D'Angelo, N. Dashyan, B. Wojtsekhowski, Et Al.

Physics Faculty Publications

The heavy photon search experiment (HPS) at the Thomas Jefferson National Accelerator Facility searches for electroproduced dark photons. We report results from the 2016 engineering run consisting of 10 608  nb⁻¹ of data for both the prompt and displaced vertex searches. A search for a prompt resonance in the e⁺e⁻ invariant mass distribution between 39 and 179 MeV showed no evidence of dark photons above the large QED background, limiting the coupling of ε²≳10⁻⁵, in agreement with previous searches. The search for displaced vertices showed no evidence of excess signal over background …

Prospects For 𝛾*𝛾* → 𝜋𝜋 Via Lattice Qcd, Raúl Briceño, Andrew W. Jackura, Arkaitz Rodas, Juan V. Guerrero

Physics Faculty Publications

The 𝛾*𝛾* → 𝜋𝜋 scattering amplitude plays a key role in a wide range of phenomena, including understanding the inner structure of scalar resonances as well as constraining the hadronic contributions to the anomalous magnetic moment of the muon. In this work, we explain how the infinite-volume Minkowski amplitude can be constrained from finite-volume Euclidean correlation functions. The relationship between the finite-volume Euclidean correlation functions and the desired amplitude holds up to energies where 3𝜋 states can go on shell, and is exact up to exponentially small corrections that scale like 𝒪(e^−m𝜋L), where L is the spatial extent …

Machine Learning-Based Jet And Event Classification At The Electron-Ion Collider With Applications To Hadron Structure And Spin Physics, Kyle Lee, James Mulligan, Mateusz Płoskoń, Felix Ringer, Feng Yuan

Physics Faculty Publications

We explore machine learning-based jet and event identification at the future Electron-Ion Collider (EIC). We study the effectiveness of machine learning-based classifiers at relatively low EIC energies, focusing on (i) identifying the flavor of the jet and (ii) identifying the underlying hard process of the event. We propose applications of our machine learning-based jet identification in the key research areas at the future EIC and current Relativistic Heavy Ion Collider program, including enhancing constraints on (transverse momentum dependent) parton distribution functions, improving experimental access to transverse spin asymmetries, studying photon structure, and quantifying the modification of hadrons and jets in …

Basics Of Factorization In A Scalar Yukawa Field Theory, F. Aslan, L. Gamberg, J.O. Gonzalez-Hernandez, T. Rainaldi, T. C. Rogers

Physics Faculty Publications

The factorization theorems of QCD apply equally well to most simple quantum field theories that require renormalization but where direct calculations are much more straightforward. Working with these simpler theories is convenient for stress testing the limits of the factorization program and for examining general properties of the parton density functions or other correlation functions that might be necessary for a factorized description of a process. With this view in mind, we review the steps of factorization in a real scalar Yukawa field theory for both deep inelastic scattering and semi-inclusive deep inelastic scattering cross sections. In the case of …

Two-Point Correlator Of Twist-2 Light-Ray Operators In N=Sym In Bfkl Approximation, Ian Balitsky, Vladimir Kazakov, Evgeny Sobko

Physics Faculty Publications

We generalize local operators of the leading twist-2 of 𝒩 = SYM theory to the case of complex Lorentz spin j using principal series representation of sl(2, R). We give the direct computation of correlation function of two such non-local operators in the BFKL regime when j → 1. The correlator appears to have the expected conformal coordinate dependence governed by the anomalous dimension of twist-2 operator in NLO BFKL approximation predicted by Kotikov and Lipatov.

Detailed Study Of Quark-Hadron Duality In Spin Structure Functions Of The Proton And Neutron, V. Lagerquist, S. E. Kuhn, N. Sato

Physics Faculty Publications

Background: The response of hadrons, the bound states of the strong force (QCD), to external probes can be described in two different, complementary frameworks: as direct interactions with their fundamental constituents, quarks and gluons, or alternatively as elastic or inelastic coherent scattering that leaves the hadrons in their ground state or in one of their excited (resonance) states. The former picture emerges most clearly in hard processes with high momentum transfer, where the hadron response can be described by the perturbative expansion of QCD, while at lower energy and momentum transfers, the resonant excitations of the hadrons dominate the cross …

Constraints On The Onset Of Color Transparency From Quasielastic ¹²C(E, E′P) Up To Q² = (14.2 Gev /C)², D. Bhetuwal, J. Matter, H. Szumila-Vance, C. Ayerbe Gayoso, M. L. Kabir, D. Dutta, R. Ent, D. Abrams, Z. Ahmed, B. Aljawrneh, S. Alsalmi, R. Ambrose, D. Androic, W. Armstrong, A. Asaturyan, K. Assumin-Gyimah, A. Bandari, S. Basnet, V. Berdnikov, J. Zhang, Et Al., Hall C. Collaboration

Physics Faculty Publications

Quasielastic scattering on ¹²C(e,e′p) was measured in Hall C at Jefferson Lab for spacelike four-momentum transfer squared Q² in the range of 8–14.2(GeV/c)² with proton momenta up to 8.3GeV/c. The experiment was carried out in the upgraded Hall C at Jefferson Lab. It used the existing high-momentum spectrometer and the new super-high-momentum spectrometer to detect the scattered electrons and protons in coincidence. The nuclear transparency was extracted as the ratio of the measured yield to the yield calculated in the plane wave impulse approximation. Additionally, the transparency of the 1s_1/2 and 1p_3/2 shell …

First Measurement Of The Emc Effect In ¹⁰B And ¹¹B, A. Karki, D. Biswas, F. A. Gonzalez, W. Henry, C. Morean, A. Nadeeshani, A. Sun, D. Abrams, Z. Ahmed, B. Aljawrneh, S. Alsalmi, R. Ambrose, D. Androic, W. Armstrong, J. Arrington, D. Asaturyan, K. Assumin-Gyimah, C. Ayerbe Gayoso, A. Bandari, J. Zhang, Et Al., Hall C. Collaboration

Physics Faculty Publications

The nuclear dependence of the inclusive inelastic electron scattering cross section (the EMC effect) has been measured for the first time in ¹⁰B and ¹¹B. Previous measurements of the EMC effect in A ≤ 12 nuclei showed an unexpected nuclear dependence; 10^B and 11^B were measured to explore the EMC effect in this region in more detail. Results are presented for ⁹Be, ¹⁰B, ¹¹B, and ¹²C at an incident beam energy of 10.6 GeV. The EMC effect in the boron isotopes was found to be similar to …

Gluon Transverse-Momentum-Dependent Distributions From Large-Momentum Effective Theory, Ruilin Zhu, Yao Ji, Jian-Hui Zhang, Shuai Zhao

Physics Faculty Publications

We demonstrate that gluon transverse-momentum-dependent parton distribution functions (TMDPDFs) can be extracted from lattice calculations of appropriate Euclidean correlations in large-momentum effective theory (LaMET). Based on perturbative calculations of gluon unpolarized and helicity TMDPDFs, we present a matching formula connecting them and their LaMET counterparts, where the latter are renormalized in a scheme facilitating lattice calculations and converted to the MS ¯ scheme. The hard matching kernel is given up to one-loop level. We also show that the perturbative result is independent of the prescription used for the pinch-pole singularity in the relevant correlations. Our results offer a guidance for …

Rapidity-Only Tmd Factorization At One Loop, Ian Balitsky

Physics Faculty Publications

Typically, a production of a particle with a small transverse momentum in hadron-hadron collisions is described by CSS-based TMD factorization at moderate Bjorken x_B ~ 1 and by k_T-factorization at small x_B. A uniform description valid for all x_B is provided by rapidity-only TMD factorization developed in a series of recent papers at the tree level. In this paper the rapidity-only TMD factorization for particle production by gluon fusion is extended to the one-loop level.

First Clas12 Measurement Of Deeply Virtual Compton Scattering Beam-Spin Asymmetries In The Extended Valence Region, G. Christiaens, M. Defurne, D. Sokhan, P. Achenbach, Z. Akbar, M. J. Amaryan, H. Atac, H. Avakian, C. Ayerbe Gayoso, L. Baashen, N. A. Baltzell, L. Barion, M. Bashkanov, M. Battaglieri, I. Bedlinskiy, B. Benkel, F. Benmokhtar, A. Bianconi, A. S. Biselli, M. Zurek, Et Al., Clas Collaboration

Physics Faculty Publications

Deeply virtual Compton scattering (DVCS) allows one to probe generalized parton distributions describing the 3D structure of the nucleon. We report the first measurement of the DVCS beam-spin asymmetry using the CLAS12 spectrometer with a 10.2 and 10.6 GeV electron beam scattering from unpolarized protons. The results greatly extend the Q² and Bjorken-x phase space beyond the existing data in the valence region and provide 1600 new data points measured with unprecedented statistical uncertainty, setting new, tight constraints for future phenomenological studies.

First Measurement Of Hard Exclusive 𝛑⁻Δ⁺⁺ Electroproduction Beam-Spin Asymmetries Off The Proton, S. Diehl, N. Trotta, K. Joo, P. Achenbach, Z. Akbar, W. R. Armstrong, H. Atac, H. Avakian, L. Baashen, N. A. Baltzell, L. Barion, M. Bashkanov, M. Battaglieri, I. Bedlinskiy, F. Benmokhtar, A. Bianconi, A. S. Biselli, F. Bossù, K.-T. Brinkman, M. Zurek, Et Al., Clas Collaboration

Physics Faculty Publications

The polarized cross-section ratio σLT′/σ₀ from hard exclusive π⁻Δ⁺⁺ electroproduction off an unpolarized hydrogen target has been extracted based on beam-spin asymmetry measurements using a 10.2  GeV/10.6  GeV incident electron beam and the CLAS12 spectrometer at Jefferson Lab. The study, which provides the first observation of this channel in the deep-inelastic regime, focuses on very forward-pion kinematics in the valence regime, and photon virtualities ranging from 1.5  GeV² up to 7  GeV². The reaction provides a novel access to the d-quark content of the nucleon and to p→Δ⁺⁺ transition generalized parton …

Liouvillian Dynamics Of The Open Schwinger Model: String Breaking And Kinetic Dissipation In A Thermal Medium, Kyle Lee, James Mulligan, Felix Ringer, Xiaojun Yao

Physics Faculty Publications

Understanding the dynamics of bound state formation is one of the fundamental questions in confining quantum field theories such as Quantum Chromodynamics (QCD). One hadronization mechanism that has garnered significant attention is the breaking of a string initially connecting a fermion and an antifermion. Deepening our understanding of real-time string-breaking dynamics with simpler, lower dimensional models like the Schwinger model can improve our understanding of the hadronization process in QCD and other confining systems found in condensed matter and statistical systems. In this paper, we consider the string-breaking dynamics within the Schwinger model and investigate its modification inside a thermal …

Two-Current Transition Amplitudes With Two-Body Final States, Keegan H. Sherman, Feliipe G. Ortega-Gama, Raúl A. Briceño, Andrew W. Jackura

Physics Faculty Publications

We derive the on-shell form of amplitudes containing two external currents with a single hadron in the initial state and two hadrons in the final state, denoted as 1 + J → 2 + J . This class of amplitude is relevant in precision tests of the Standard Model as well as for exploring the structure of excited states in the QCD spectrum. We present a model-independent description of the amplitudes where we sum to all orders in the strong interaction. From this analytic form we are able to extract transition and elastic resonance form factors consistent with previous work …

Partial Muon Capture Rates In A = 3 And A = 6 Nuclei With Chiral Effective Field Theory, G. B. King, S. Pastore, M. Piarulli, Rocco Schiavilla

Physics Faculty Publications

Searches for neutrinoless double-β decay rates are crucial in addressing questions within fundamental symmetries and neutrino physics. The rates of these decays depend not only on unknown parameters associated with neutrinos, but also on nuclear properties. In order to reliably extract information about the neutrino, one needs an accurate treatment of the complex many-body dynamics of the nucleus. Neutrinoless double-β decays take place at momentum transfers on the order of 100MeV /c and require both nuclear electroweak vector and axial current matrix elements. Muon capture, a process in the same momentum transfer regime, has readily available experimental data to validate …

Measurement Of Charged-Pion Production In Deep-Inelastic Scattering Off Nuclei With The Clas Detector, Clas Collaboration, S. Morán, R. Dupre, H. Hakobyan, Moskov J. Amaryan, Dilini Bulumulla, Mohammad Hattawy, Florian Hauenstein, Sebastian Kuhn, Pushpa Pandey, Jiwan Poudel, Yelena Prok, Lawrence B. Weinstein, N. Zachariou, J. Zhang, Z. W. Zhao, Et Al.

Physics Faculty Publications

Background: Energetic quarks in nuclear deep-inelastic scattering propagate through the nuclear medium. Processes that are believed to occur inside nuclei include quark energy loss through medium-stimulated gluon bremsstrahlung and intranuclear interactions of forming hadrons. More data are required to gain a more complete understanding of these effects.

Purpose: To test the theoretical models of parton transport and hadron formation, we compared their predictions for the nuclear and kinematic dependence of pion production in nuclei.

Methods: We have measured charged-pion production in semi-inclusive deep-inelastic scattering off D, C, Fe, and Pb using the CLAS detector and the CEBAF 5.014-GeV electron beam. …

Measuring Recoiling Nucleons From The Nucleus With The Future Electron Ion Collider, Florian Hauenstein, A. Jentsch, J. R. Pybus, A. Kiral, M. D. Baker, Y. Furletova, O. Hen, D. W. Higinbotham, Charles Hyde, V. Morozov, D. Romanov, Lawrence B. Weinstein

Physics Faculty Publications

Short range correlated nucleon-nucleon (NN) pairs are an important part of the nuclear ground state. They are typically studied by scattering an electron from one nucleon in the pair and detecting its spectator correlated partner (“spectator-nucleon tagging”). The Electron Ion Collider (EIC) should be able to detect these nucleons, since they are boosted to high momentum in the laboratory frame by the momentum of the ion beam. To determine the feasibility of these studies with the planned EIC detector configuration, we have simulated quasielastic scattering for two electron and ion beam energy configurations: 5 GeV e− and 41 …

Unpolarized And Polarized Gluon Pseudo-Distributions At Short Distances: Forward Case, Ian Balitsky, Wayne Morris, Anatoly Radyushkin

Physics Faculty Publications

We present the results that are necessary in the ongoing lattice calculations of the unpolarized and polarized gluon parton distribution functions (PDFs) within the pseudo-PDF approach. We give a classification of possible two-gluon correlator functions and identify those that contain the invariant amplitude determining the gluon PDF in the light-cone z² → 0 limit. One-loop calculations have been performed in the coordinate representation and in an explicitly gauge-invariant form. We made an effort to separate ultraviolet (UV) and infrared (IR) sources of the ln(−z²)-dependence at short distances z². The UV terms cancel in the reduced …

Connecting Matrix Elements To Multi-Hadron Form-Factors, Andrew W. Jackura

Physics Faculty Publications

We discuss developments in calculating multi-hadron form-factors and transition processes via lattice QCD. Our primary tools are finite-volume scaling relations, which map spectra and matrix elements to the corresponding multi-hadron infinite-volume amplitudes. We focus on two hadron processes probed by an external current, and provide various checks on the finite-volume formalism in the limiting cases of perturbative interactions and systems forming a bound state. By studying model-independent properties of the infinite-volume amplitudes, we are able to rigorously define form-factors of resonances.