More on the flavor dependence of $m_\varrho / f_π$

Kotov, Andrey Yu.; Nogradi, Daniel; Szabo, Kalman K.; Szikszai, Lorinc

doi:10.48550/arxiv.2107.05996

Cited by 1 publication

(3 citation statements)

References 16 publications

(31 reference statements)

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“…In order to compare with the lattice results we would need 𝑓 𝑉 , however only 𝑓 𝑃𝑆 was measured directly [22][23][24]. Here we use the KSRF relation 𝑓 𝑉 = √ 2 𝑓 𝑃𝑆 originating in vector meson universality to estimate 𝑓 𝑉 and assign a 12% uncertainty which holds in QCD.…”

Section: Pos(lattice2023)084mentioning

confidence: 99%

“…In this contribution a new approach is proposed [21]: by matching the fully controlled lattice results obtained for low fermion numbers [22][23][24] and fully controlled perturbative results obtained close to but below 𝑁 𝑓 = 16.5 where asymptotic freedom is still present. The latter calculation will be the focus of our contribution.…”

Section: Introductionmentioning

confidence: 97%

“…Figure1: Left: the 𝑓 𝑉 /𝑚 𝑉 ratio in increasing perturbative order. The non-perturbative result from combined lattice calculations[22][23][24] and the KSRF-relation is also shown. The smaller error band corresponds to the uncertainty of the lattice calculation, the wider one combines this with a conservative estimate of the uncertainty of the KSRF-relation itself.…”

mentioning

confidence: 96%

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Mesonic decay constant and mass ratios and the conformal window

Nogradi,

Chung

2023

Proceedings of the 40th International Symposium on Lattice Field Theory — PoS(LATTICE2023)

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Two particular ratios related to mesons are proposed for the study of the conformal window in 𝑆𝑈 (3) gauge theory and fundamental fermions. Lattice and other studies indicate that the lower end, 𝑁 * 𝑓 , is at around 7 -13 flavors which is a wide range without a clear consensus. Here we propose the decay constant to mass ratios of mesons, 𝑓 𝑃𝑆,𝑉 /𝑚 𝑉 , as a proxy since below the conformal window lattice studies have shown that they are largely 𝑁 𝑓 -independent while at the upper end of the conformal window they are vanishing. The drop from the non-zero constant value to zero at 𝑁 𝑓 = 16.5 might be indicative of 𝑁 * 𝑓 . We compute 𝑓 𝑉 /𝑚 𝑉 to N 3 LO and 𝑓 𝑃𝑆 /𝑚 𝑉 to NNLO order in (p)NRQCD. The results are unambiguously reliable just below 𝑁 𝑓 = 16.5, hence the results are expanded á la Banks-Zaks in 𝜀 = 16.5 − 𝑁 𝑓 . The convergence properties of the series and matching with the non-perturbative infinite volume, continuum and chiral extrapolated lattice results at 𝑁 𝑓 = 10 suggest that the perturbative results might be reliable down to 𝑁 𝑓 = 12. A sudden drop is observed at 𝑁 𝑓 = 12 and 𝑁 𝑓 = 13 in 𝑓 𝑉 /𝑚 𝑉 and 𝑓 𝑃𝑆 /𝑚 𝑉 , respectively.

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Section: Pos(lattice2023)084mentioning

confidence: 99%