Abstract
We calculate, within massless QCD, two-point correlator of nonlocal (composite) vector quark currents with arbitrary-length chains of the simplest fermion loops being inserted into gluon lines. Within the large \({{n}_{f}}\) (or large \({{\beta }_{0}}\)) approximation, the correlator defines a perturbative contribution to the leading-twist distribution amplitudes for light mesons. Our results are consistent with a number of special cases in the literature. We consider functionals of the correlator, which are important for the phenomenology, and their properties as functional series.
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Notes
We work in QCD with \({{n}_{f}} = 3\) massless quark flavors; \({{N}_{c}} = 3\) is the number of colors; the Casimir invariants are \({{C}_{A}} = 3\) and \({{C}_{F}} = 4{\text{/}}3\); \({{\beta }_{0}} = \frac{{11}}{3}{{C}_{A}} - \frac{4}{3}{{T}_{F}}{{n}_{f}} = 9\) is the one-loop \(\beta \) function coefficient; \({{T}_{F}} = \frac{1}{2}\); \({{a}_{s}} = {{\alpha }_{s}}{\text{/}}(4\pi )\) is the coupling constant.
Note that, in this paper, arguments of the Mellin transform are underlined, i.e. \(f(\underline a ) = {{\hat {M}}}f(x) = \int_0^1 {\text{d}}x{\kern 1pt} f(x){{x}^{a}}\).
REFERENCES
S. V. Mikhailov and N. Volchanskiy, “Two-loop kite master integral for a correlator of two composite vertices,” J. High Energy Phys. 2019, 202 (2019). arXiv: 1812.02164.
E. Remiddi and J. A. M. Vermaseren, “Harmonic polylogarithms” Int. J. Mod. Phys. A 15, 725–754 (2000). arXiv:hep-ph/9905237.
P. A. Baikov, K. G. Chetyrkin, J. H. Kuhn, and J. Rittinger, “Vector correlator in massless QCD at order O(\(\alpha _{s}^{4}\)) and the QED beta-function at five loop,” J. High Energy Phys. 2012, 017 (2012). arXiv: 1206.1284 [hep-ph].
P. Ball, M. Beneke, and V. M. Braun, “Resummation of (β0αs)n corrections in QCD: Techniques and applications to the τ hadronic width and the heavy quark pole mass,” Nucl. Phys. B 452, 563–625 (1995). arXiv: hep-ph/9502300.
D. J. Broadhurst, “Large N expansion of QED: asymptotic photon propagator and contributions to the muon anomaly, for any number of loops,” Z. Phys. C 58, 339–345 (1993).
D. J. Broadhurst and A. L. Kataev, “Connections between deep inelastic and 65 annihilation processes at next to next-to-leading order and beyond,” Phys. Lett. B 315, 179—187 (1993). arXiv:hep-ph/9308274.
S. V. Mikhailov and A. V. Radyushkin, “Quark condensate nonlocality and pion wave function in QCD: general formalism,” Sov. J. Nucl. Phys. 49, 494–503 (1989), Preprint JINR-P2-70 88-103 (JINR, Dubna). http://inspirehep.net/record/262441/files/JINR-P2-88-103.pdf.
S. V. Mikhailov and N. Volchanskiy, “Correlators of vector, tensor, and scalar composite vertices of order O(\(\alpha _{s}^{2}{{\beta }_{0}}\)),” J. High Energy Phys. 2021, 197 (2021). arXiv: 2010.03557.
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Mikhailov, S.V., Volchanskiy, N.I. Renormalon-Chain Contributions to Two-Point Correlators of Nonlocal Quark Currents. Phys. Part. Nuclei Lett. 20, 296–299 (2023). https://doi.org/10.1134/S1547477123030470
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DOI: https://doi.org/10.1134/S1547477123030470