Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · hep-ph/0310213

Light mesons and infrared behavior of the running coupling constant in QCD

M. Baldicchi·G. M. Prosperi
View original source ↗Read source document ↗Export metadata ↓

Abstract

A previous method for handling bound states in QCD is briefly revisited. Taking advantage of the Feynman-Schwinger representation for the iterated quark propagator in an external field, it is possible to give closed representations for certain appropriate (second order) two point and four point Green functions, H^(2)(x-y) and H^(4)(x_1,x_2,y_1,y_2), as path integrals on quark world lines. Then, starting from reasonable assumptions on the Wilson line correlators, a Bethe-Salpeter equation for H^(4) and a Dyson-Schwinger equation for H^(2) can be obtained, which are consistent with the Goldstone theorem in the chiral limit. Such equations are too complicate to be solved directly. However, a reduced Salpeter equation can be derived which is tractable and has been applied to a calculation of the meson spectrum. The results are in general good agreement with the data, but with the important exceptions of the light pseudo scalars (that are related to the breaking of the chiral symmetry). In this scenario two important improvements can be introduced: a) the fixed coupling constant can be replaced by a running coupling constant α_{s}(Q^2) appropriately modified in the infrared region; b) the fixed mass in the reduced equation can be replaced for light quarks by an effective mass depending on the momentum of the particle, as suggested by the form of the DS equation. Then even the light pseudo scalar mesons can be made to agree with to their experimental value.

Explore related subjects

hep-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

M. Baldicchi, G. M. Prosperi. 2003-10-17. Light mesons and infrared behavior of the running coupling constant in QCD. https://doi.org/10.1142/9789812702845_0014

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Extraction of the pion-nucleon coupling constant using the effective-range expansion with the left-hand cut

We apply the generalized effective-range expansion of Phys. Rev. Lett. 135, 011903(2025), which incorporates the left-hand cut from one-pion exchange, to low-energy neutron-proton scattering in the $^1S_0$ and $^3S_1$ channels. The amplitude zero for the center-of-mass momentum near 0.35 GeV in the $^1S_0$ channel is naturally accommodated within this framework. We extract the pole position, scattering length, effective range, and the pseudoscalar pion-nucleon coupling constant $g_{πN}^2/(4π)$ at different expansion orders. The low-energy parameters are stable and consistent with established values, while $g_{πN}^2/(4π)$ exhibits larger uncertainties. The extraction of $g_{πN}^2/(4π)$ is data-driven, relying on the analytic constraints from the left-hand cut and phase-shift data within the one-pion-exchange approximation. Despite larger uncertainties compared to high-precision extractions, the consistency with established values demonstrates that this framework can probe the left-hand-cut singularity.

hep-ph↗
arXiv2026

True Leptonium ($l^+ l^-$) Production in UPC Triphoton Interaction

True leptonium states ($l^+ l^-$) are compact pure QED systems, first theoretically predicted eight decades ago. Although considerable efforts have been devoted to their search, only positronium has been experimentally confirmed shortly after its theoretical prediction. By contrast, dimuonium ($μ^+ μ^-$) and tauonium ($τ^+ τ^-$) remain unobserved to date, partly due to their low production yields. In this work, we investigate ortho-leptonium production through triphoton interactions in ultraperipheral heavy-ion collisions (UPCs). Two photons originate from different ions in one beam, while the third is supplied by an ion in the opposing beam. Within the equivalent photon approximation, we compare continuum dimuon and $J/ψ$ production with UPC measurements and evaluate ortho-leptonium production at the LHC and FCC. The results illustrate the possible role of triphoton fusion in leptonium production and the sensitivity of the calculated rates to the low-energy photon input.

hep-ph↗
arXiv2026

Semi-analytical two-loop QCD corrections to $e^+e^-\to J/ψ+χ_{cJ}$ at B factories

In this work, we compute the next-to-next-to-leading-order (NNLO) QCD corrections to the process $e^+e^-\to J/ψ+χ_{cJ}$ at B factories within the NRQCD factorization framework. The helicity amplitudes are obtained via asymptotic expansions around $r=0$ and $r=1$, with $r=16m_c^2/s$. Our asymptotic expressions reproduce the exact numerical results with high accuracy across the kinematic range $0\le r \le 1$, achieving a relative error below $10^{-5}$, which is sufficient for phenomenological applications. Notably, the large logarithmic terms are obtained analytically, and the explicit expressions established in this work provide a useful basis for further theoretical investigations. We compute the unpolarized cross sections. The $\mathcal{O}(α_s)$ correction is found to be large, while the $\mathcal{O}(α_s^2)$ correction for $χ_{c0}$ production amounts to $33\%$ of the leading-order (LO) cross section, significantly reducing the scale uncertainties. For $χ_{c1}$, the $\mathcal{O}(α_s)$ and $\mathcal{O}(α_s^2)$ corrections correspond to $35\%$ and $-15\%$, respectively. For $χ_{c2}$, the corresponding corrections are $24\%$ and $-38\%$. The large cancellation between the corrections for $χ_{c2}$ brings the NNLO cross section close to the LO prediction. Our prediction for $χ_{c0}$ is consistent with both the {\tt Belle} and {\tt BaBar} data within uncertainties. We also predict the angular distribution parameters $α^J_θ$, which are independent of nonperturbative inputs. A sharp discrepancy between the theory and the {\tt Belle} measurement is observed for $α^0_θ$, calling for further experimental and theoretical investigations. Moreover, future measurements of the angular distribution parameters for $χ_{c1}$ and $χ_{c2}$ will provide important tests of the theoretical framework.

hep-ph↗