Abstract
A novel method for the extraction of form factors of unstable particles on the lattice is proposed. The approach is based on the study of two-particle scattering in a static, spatially periodic external field by using a generalization of the Lüscher method in the presence of such a field. It is shown that the resonance form factor is given by the derivative of the resonance pole position in the complex plane with respect to the coupling constant to the external field. Unlike the standard approach, this proposal does not suffer from problems caused by the presence of the triangle diagram.
Article PDF
Similar content being viewed by others
References
D. Hoja, U.G. Meissner and A. Rusetsky, Resonances in an external field: The 1 + 1 dimensional case, JHEP 04 (2010) 050 [arXiv:1001.1641] [INSPIRE].
R.A. Briceño, M.T. Hansen and A.W. Jackura, Consistency checks for two-body finite-volume matrix elements: II. Perturbative systems, Phys. Rev. D 101 (2020) 094508 [arXiv:2002.00023] [INSPIRE].
L. Lellouch and M. Lüscher, Weak transition matrix elements from finite volume correlation functions, Commun. Math. Phys. 219 (2001) 31 [hep-lat/0003023] [INSPIRE].
M.T. Hansen and S.R. Sharpe, Multiple-channel generalization of Lellouch-Lüscher formula, Phys. Rev. D 86 (2012) 016007 [arXiv:1204.0826] [INSPIRE].
R.A. Briceño, M.T. Hansen and A. Walker-Loud, Multichannel 1 → 2 transition amplitudes in a finite volume, Phys. Rev. D 91 (2015) 034501 [arXiv:1406.5965] [INSPIRE].
R.A. Briceño and M.T. Hansen, Multichannel 0 → 2 and 1 → 2 transition amplitudes for arbitrary spin particles in a finite volume, Phys. Rev. D 92 (2015) 074509 [arXiv:1502.04314] [INSPIRE].
R.A. Briceño, J.J. Dudek and L. Leskovec, Constraining 1 + \( \mathcal{J} \) → 2 coupled-channel amplitudes in finite-volume, Phys. Rev. D 104 (2021) 054509 [arXiv:2105.02017] [INSPIRE].
R.A. Briceño, J.J. Dudek, R.G. Edwards, C.J. Shultz, C.E. Thomas and D.J. Wilson, The ππ → πγ* amplitude and the resonant ρ → πγ* transition from lattice QCD, Phys. Rev. D 93 (2016) 114508 [Erratum ibid. 105 (2022) 079902] [arXiv:1604.03530] [INSPIRE].
R.A. Briceno, J.J. Dudek, R.G. Edwards, C.J. Shultz, C.E. Thomas and D.J. Wilson, The resonant π+γ → π+π0 amplitude from Quantum Chromodynamics, Phys. Rev. Lett. 115 (2015) 242001 [arXiv:1507.06622] [INSPIRE].
A. Agadjanov, V. Bernard, U.-G. Meißner and A. Rusetsky, The B → K* form factors on the lattice, Nucl. Phys. B 910 (2016) 387 [arXiv:1605.03386] [INSPIRE].
A. Agadjanov, V. Bernard, U.G. Meißner and A. Rusetsky, A framework for the calculation of the ∆Nγ* transition form factors on the lattice, Nucl. Phys. B 886 (2014) 1199 [arXiv:1405.3476] [INSPIRE].
H.B. Meyer, Lattice QCD and the Timelike Pion Form Factor, Phys. Rev. Lett. 107 (2011) 072002 [arXiv:1105.1892] [INSPIRE].
K.H. Sherman, F.G. Ortega-Gama, R.A. Briceño and A.W. Jackura, Two-current transition amplitudes with two-body final states, Phys. Rev. D 105 (2022) 114510 [arXiv:2202.02284] [INSPIRE].
F. Müller and A. Rusetsky, On the three-particle analog of the Lellouch-Lüscher formula, JHEP 03 (2021) 152 [arXiv:2012.13957] [INSPIRE].
M.T. Hansen, F. Romero-López and S.R. Sharpe, Decay amplitudes to three hadrons from finite-volume matrix elements, JHEP 04 (2021) 113 [arXiv:2101.10246] [INSPIRE].
V. Bernard, D. Hoja, U.G. Meissner and A. Rusetsky, Matrix elements of unstable states, JHEP 09 (2012) 023 [arXiv:1205.4642] [INSPIRE].
R.A. Briceño and M.T. Hansen, Relativistic, model-independent, multichannel 2 → 2 transition amplitudes in a finite volume, Phys. Rev. D 94 (2016) 013008 [arXiv:1509.08507] [INSPIRE].
A. Baroni, R.A. Briceño, M.T. Hansen and F.G. Ortega-Gama, Form factors of two-hadron states from a covariant finite-volume formalism, Phys. Rev. D 100 (2019) 034511 [arXiv:1812.10504] [INSPIRE].
R.A. Briceño, M.T. Hansen and A.W. Jackura, Consistency checks for two-body finite-volume matrix elements: I. Conserved currents and bound states, Phys. Rev. D 100 (2019) 114505 [arXiv:1909.10357] [INSPIRE].
R.A. Briceño, A.W. Jackura, F.G. Ortega-Gama and K.H. Sherman, On-shell representations of two-body transition amplitudes: Single external current, Phys. Rev. D 103 (2021) 114512 [arXiv:2012.13338] [INSPIRE].
H. Hellmann, Einführung in die Quantenchemie, Deuticke, Leipzig und Wien (1937).
R.P. Feynman, Forces in Molecules, Phys. Rev. 56 (1939) 340 [INSPIRE].
QCDSF, UKQCD and CSSM collaborations, Electromagnetic form factors at large momenta from lattice QCD, Phys. Rev. D 96 (2017) 114509 [arXiv:1702.01513] [INSPIRE].
A. Agadjanov, U.-G. Meißner and A. Rusetsky, Nucleon in a periodic magnetic field: Finite-volume aspects, Phys. Rev. D 99 (2019) 054501 [arXiv:1812.06013] [INSPIRE].
K.U. Can et al., Lattice QCD evaluation of the Compton amplitude employing the Feynman-Hellmann theorem, Phys. Rev. D 102 (2020) 114505 [arXiv:2007.01523] [INSPIRE].
CSSM/QCDSF/UKQCD collaboration, Generalized parton distributions from the off-forward Compton amplitude in lattice QCD, Phys. Rev. D 105 (2022) 014502 [arXiv:2110.11532] [INSPIRE].
A. Agadjanov, U.-G. Meißner and A. Rusetsky, Nucleon in a periodic magnetic field, Phys. Rev. D 95 (2017) 031502 [arXiv:1610.05545] [INSPIRE].
J. Ruiz de Elvira, U.G. Meißner, A. Rusetsky and G. Schierholz, Feynman-Hellmann theorem for resonances and the quest for QCD exotica, Eur. Phys. J. C 77 (2017) 659 [arXiv:1706.09015] [INSPIRE].
J. Gasser, V.E. Lyubovitskij and A. Rusetsky, Hadronic atoms in QCD + QED, Phys. Rept. 456 (2008) 167 [arXiv:0711.3522] [INSPIRE].
S. Mandelstam, Dynamical variables in the Bethe-Salpeter formalism, Proc. Roy. Soc. Lond. A 233 (1955) 248 [INSPIRE].
K. Huang and H.A. Weldon, Bound State Wave Functions and Bound State Scattering in Relativistic Field Theory, Phys. Rev. D 11 (1975) 257 [INSPIRE].
N.W. McLachlan, Theory and Application of Mathieu Functions, Dover Publications, Reprint edition (1964).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2205.11316
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Lozano, J., Meißner, UG., Romero-López, F. et al. Resonance form factors from finite-volume correlation functions with the external field method. J. High Energ. Phys. 2022, 106 (2022). https://doi.org/10.1007/JHEP10(2022)106
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2022)106