Complex chromoelectric polarizability of a heavy-quarkonium resonance: pole response and channel-resolved effective-theory representation
Abstract
For a stable compact quarkonium state in the pNRQCD multipole regime, chromoelectric polarizability arises at leading order from two E1 transitions through virtual color-octet states. For an unstable state, we define the corresponding response through the quadratic displacement of its complex resonance pole in a weak chromoelectric background, so that its real and imaginary parts describe field-induced shifts of the pole mass and width. Starting from a renormalized background-field correlator, we show that the resonance polarizability is given by the complete two-field kernel normalized by the energy derivative of the full inverse propagator at the pole. In an effective theory with explicitly separated intermediate sectors, the kernel contains the standard E1-octet-E1 contribution, the complete source response of decay channels already coupled at zero field, and local contributions. This distinction becomes essential above open-flavor threshold and reduces to the standard pNRQCD polarizability in the stable, energy-independent limit. A simple DD̅ realization for the ψ(3770) gives the complex pole-residue factor 1/[1−σ'(zψ)]=0.800−0.336, illustrating that threshold dressing can substantially modify both the magnitude and phase of the response. The resulting pole-based relation identifies the quantity required for a source-dependent coupled-channel determination of the chromoelectric polarizability of a heavy-quarkonium resonance.
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BibTeX
@misc{syamtomov2026complex,
title = {{Complex chromoelectric polarizability of a heavy-quarkonium resonance: pole response and channel-resolved effective-theory representation}},
author = {Arkadiy I. Syamtomov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.00611},
eprint = {2608.00611},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.00611},
}
RIS
TY - UNPB
TI - Complex chromoelectric polarizability of a heavy-quarkonium resonance: pole response and channel-resolved effective-theory representation
AU - Arkadiy I. Syamtomov
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2608.00611
UR - https://arxiv.org/abs/2608.00611
AB - For a stable compact quarkonium state in the pNRQCD multipole regime, chromoelectric polarizability arises at leading order from two E1 transitions through virtual color-octet states. For an unstable state, we define the corresponding response through the quadratic displacement of its complex resonance pole in a weak chromoelectric background, so that its real and imaginary parts describe field-induced shifts of the pole mass and width. Starting from a renormalized background-field correlator, we show that the resonance polarizability is given by the complete two-field kernel normalized by the energy derivative of the full inverse propagator at the pole. In an effective theory with explicitly separated intermediate sectors, the kernel contains the standard E1-octet-E1 contribution, the complete source response of decay channels already coupled at zero field, and local contributions. This distinction becomes essential above open-flavor threshold and reduces to the standard pNRQCD polarizability in the stable, energy-independent limit. A simple DD̅ realization for the ψ(3770) gives the complex pole-residue factor 1/[1−σ'(z_ψ)]=0.800−0.336, illustrating that threshold dressing can substantially modify both the magnitude and phase of the response. The resulting pole-based relation identifies the quantity required for a source-dependent coupled-channel determination of the chromoelectric polarizability of a heavy-quarkonium resonance.
ER -