On-shell representations of two-body transition amplitudes: Single external current

Briceño, Raúl A.; Jackura, A.; Ortega-Gama, Felipe G.; Sherman, Keegan H.

doi:10.1103/physrevd.103.114512

Cited by 22 publications

(45 citation statements)

References 64 publications

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“…To arrive at the on-shell forms for these amplitudes, we use all-orders perturbation theory in which we assume some generic effective field theory where our hadronic states are stable against strong decay as was done in Ref. [34]. We also make two simplifying assumptions here, the first being that our incoming and outgoing hadronic states are spinless, i.e.…”

Section: Resultsmentioning

confidence: 99%

Two-current transition amplitudes with two-body final states

Sherman,

Ortega-Gama,

Briceño

et al. 2022

Preprint

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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 as well as a novel Compton-like amplitude coupling a single particle state to a resonance. The results also hold for reactions where the one-particle state is replaced with the vacuum, namely J → 2 + J amplitudes. We also investigate constraints placed upon the formalism for the case of a conserved vector current in the form of the Ward-Takahashi identity. The formalism presented here is valid for currents of arbitrary Lorentz structure and quantum numbers with spinless hadrons where any number of two-particle intermediate channels may be open. When combined with the appropriate finite-volume framework, this work facilitates the extraction of physical observables from this class of amplitudes via lattice QCD calculations.

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Section: Resultsmentioning

confidence: 99%

Two-current transition amplitudes with two-body final states

Sherman,

Ortega-Gama,

Briceño

et al. 2022

Preprint

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“…For details, we refer to Refs. [19,20,22] where 𝑄 2 = −(𝑃 − 𝑃) 2 is the invariant momentum transfer to the system via the external current, and W df removes the contributions where the external current couples to one of the external legs infinite volume 2 + J → 2 amplitude W, as discussed in Refs. [19,20,22] and shown in Fig.…”

Section: Bound and Resonant States Of Two-hadron Systemsmentioning

confidence: 99%

“…[19,20,22] where 𝑄 2 = −(𝑃 − 𝑃) 2 is the invariant momentum transfer to the system via the external current, and W df removes the contributions where the external current couples to one of the external legs infinite volume 2 + J → 2 amplitude W, as discussed in Refs. [19,20,22] and shown in Fig. 3, Note that the terms which contain the current insertion on one of the external legs do not contribute as one of the two spectral poles will cancel against this term, meaning the spectral poles can be determined from W df alone.…”

Section: Bound and Resonant States Of Two-hadron Systemsmentioning

confidence: 99%

“…The path to bound or resonant state form factors is as follows: First, one computes the twoparticle finite volume spectrum for some channel and determines the 𝐾 matrix and resulting 2 → 2 amplitude for a given channel using Eq. ( 9) and (22). The single particle form factors 𝑓 𝑗 of the hadrons in the channel must also be determined for the desired current.…”

Section: Resonant Form-factors From On-shell Amplitudesmentioning

confidence: 99%

“…where for resonances the expression is defined with G on the second Riemann sheet as detailed in Ref. [22]. At zero-momentum transfer, the charge of the resonance must be the sum of the constituent hadrons.…”

Section: Resonant Form-factors From On-shell Amplitudesmentioning

confidence: 99%

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Connecting Matrix Elements to Multi-Hadron Form-Factors

Jackura¹

2021

Preprint

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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.

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Electroweak three-body decays in the presence of two- and three-body bound states

Briceño,

Jackura,

Pefkou

et al. 2024

J. High Energ. Phys.

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Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.

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On-shell representations of two-body transition amplitudes: Single external current

Cited by 22 publications

References 64 publications

Two-current transition amplitudes with two-body final states

Two-current transition amplitudes with two-body final states

Connecting Matrix Elements to Multi-Hadron Form-Factors

Electroweak three-body decays in the presence of two- and three-body bound states

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