Heavy flavour production in the presence of a weak magnetic field
Abstract
We calculate analytic expression for the cross section up to order (eB)2 for the production of a heavy quark (Q) of mass mQ through the gluon (g) fusion process g+g→ Q+Q̅ in the presence of a constant weak external magnetic field (B) with strength eB ≪ mQ2. This is done using the weak-field expansion of the fermion propagator calculated within Schwinger's proper-time formalism. Owing to the hierarchy of scales (mQ2 ≫ eB), we neglect the effects of the magnetic field on the quark and antiquark spinors in the external lines. Since the magnetic field breaks rotational invariance, the cross section becomes anisotropic and depends on the relative orientation angle (θ) between the magnetic field and the incoming gluons in the center-of-mass frame. The lowest-order magnetic correction to the vacuum cross section scales as (eB)2 and is found to have cos 2θ and cos 4θ dependence, reflecting the breaking of rotational symmetry by the magnetic field. The cross section is maximized when the gluons propagate along the field direction (θ= 0, π) and minimized in the perpendicular configuration (θ= π/2). The resulting asymmetry peaks near the production threshold and falls with increasing center-of-mass energy, scaling as (eB)2/mQ4 with the quark mass. These results provide direct, calculable signatures of the initial-stage magnetic field in relativistic heavy-ion collisions which can, in principle, be imprinted on heavy-flavour observables measured in the final state of heavy-ion collisions.
Related
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BibTeX
@misc{saha2026heavy,
title = {{Heavy flavour production in the presence of a weak magnetic field}},
author = {Sudeep Saha and Sandeep Chatterjee and Ujjal Kumar Dey and Snigdh Ghosh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17787},
eprint = {2610.17787},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17787},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Heavy flavour production in the presence of a weak magnetic field
AU - Sudeep Saha
AU - Sandeep Chatterjee
AU - Ujjal Kumar Dey
AU - Snigdh Ghosh
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17787
UR - https://arxiv.org/abs/2610.17787
AB - We calculate analytic expression for the cross section up to order (eB)^2 for the production of a heavy quark (Q) of mass m_Q through the gluon (g) fusion process g+g→ Q+Q̅ in the presence of a constant weak external magnetic field (B) with strength eB ≪ m_Q^2. This is done using the weak-field expansion of the fermion propagator calculated within Schwinger's proper-time formalism. Owing to the hierarchy of scales (m_Q^2 ≫ eB), we neglect the effects of the magnetic field on the quark and antiquark spinors in the external lines. Since the magnetic field breaks rotational invariance, the cross section becomes anisotropic and depends on the relative orientation angle (θ) between the magnetic field and the incoming gluons in the center-of-mass frame. The lowest-order magnetic correction to the vacuum cross section scales as (eB)^2 and is found to have cos 2θ and cos 4θ dependence, reflecting the breaking of rotational symmetry by the magnetic field. The cross section is maximized when the gluons propagate along the field direction (θ= 0, π) and minimized in the perpendicular configuration (θ= π/2). The resulting asymmetry peaks near the production threshold and falls with increasing center-of-mass energy, scaling as (eB)^2/m_Q^4 with the quark mass. These results provide direct, calculable signatures of the initial-stage magnetic field in relativistic heavy-ion collisions which can, in principle, be imprinted on heavy-flavour observables measured in the final state of heavy-ion collisions.
ER -