From prompt to direct $$\mathrm{J}/\psi $$ production: new insights on the $$\chi _{{c}1} $$ and $$\chi _{{c}2} $$ polarizations and feed-down contributions from a global-fit analysis of mid-rapidity LHC data

Abstract

While the prompt $$\mathrm{J}/\psi $$J/ψ cross section and polarization have been measured with good precision as a function of transverse momentum, $$p_\mathrm{T}$$pT, those of the directly produced $$\mathrm{J}/\psi $$J/ψ are practically unknown, given that the cross sections and polarizations of the $$\chi _{{c}1} $$χc1 and $$\chi _{{c}2} $$χc2 mesons, large indirect contributors to $$\mathrm{J}/\psi $$J/ψ production, are only known with rather poor accuracy. The lack of precise measurements of the $$\chi _{{c}J} $$χcJ polarizations induces large uncertainties in the level of their feed-down contributions to the prompt $$\mathrm{J}/\psi $$J/ψ yield, because of the polarization-dependent acceptance corrections. The experimental panorama of charmonium production can be significantly improved through a consistent and model-independent global analysis of existing measurements of $$\mathrm{J}/\psi $$J/ψ, $$\psi \mathrm{(2S)}$$ψ(2S) and $$\chi _{c}$$χc cross sections and polarizations, faithfully respecting all the correlations and uncertainties. In particular, it is seen that the $$\chi _{{c}J} $$χcJ polarizations and feed-down fractions to $$\mathrm{J}/\psi $$J/ψ production have a negligible dependence on the $$\mathrm{J}/\psi $$J/ψ$$p_\mathrm{T}$$pT, with average values $$\lambda _\vartheta ^{\chi _{{c}1}} = 0.55 \pm 0.23$$λϑχc1=0.55±0.23, $$\lambda _\vartheta ^{\chi _{{c}2}} = -0.39 \pm 0.22$$λϑχc2=-0.39±0.22, $$R^{\chi _{{c}1}} = (18.8 \pm 1.4)\%$$Rχc1=(18.8±1.4)% and $$R^{\chi _{{c}2}} = (6.5 \pm 0.5)\%$$Rχc2=(6.5±0.5)%. The analysis also shows that $$(67.2 \pm 1.9)$$(67.2±1.9)% of the prompt $$\mathrm{J}/\psi $$J/ψ yield is due to directly-produced mesons, of polarization constrained to remarkably small values, $$\lambda _\vartheta ^{\mathrm{J}/\psi } = 0.04 \pm 0.06$$λϑJ/ψ=0.04±0.06.

Inclusive production of heavy quarkonia in pNRQCD

“…However, it is common practice in the phenomenological literature to assume that the polarized color-octet LDMEs do not depend on the direction of the gauge-completion Wilson lines, and, therefore, do not depend on the polarization λ (see for instance refs. [42,[49][50][51][52][53]). This amounts at assuming that the polarized color-octet LDMEs Ω|χ † σ i T a ψΦ †ab (0)P χ QJ (λ,P =0) Φ bc (0) ψ † σ i T c χ|Ω can be related for any polarization λ of the χ QJ state to the polarization-…”

“…These scale factors have mild effects on our phenomenological determinations of E, and slightly reduce the central values by less than the uncertainties in E. In ref. [53], a smaller scale factor of 0.85 has been obtained by using a data-driven analysis. In this case, the values of E determined from r 21 reduce by slightly more than the estimated uncertainties.…”

A technique to study the elastic and inelastic interaction of quarkonium with hadrons using femtoscopic correlations

“…The experimental evidence of charmonium production on the J/ψ, ψ(2s) and χ c cross section [51] indicates that χ cJ and ψ(2s) feed-down fraction to J/ψ production rates by considering all the correlation and uncertainties are (25.3 ± 1.8)% and (7.5±0.3)% respectively. The analysis [51] shows that (67.2 ± 1.9)% of the prompt J/ψ yield is due to the directly produced meson. According to the 2020 Review of Particle Physics [52], the χ cJ to J/ψ happens via radiative decay.…”

“…According to the 2020 Review of Particle Physics [52], the χ cJ to J/ψ happens via radiative decay. Although ψ(2s) decays to J/ψ + π + π − and J/ψ + π 0 π 0 has the fraction around 52%, for J/ψ+η around 3% and for J/ψ+π 0 around 0.0012%, in the studies on the feeddown fraction of ψ(2s) [51] for lower p T spectrum of the mother particle, it has been measured around 7.5%. In general, radiative decays complicate the interpretation of the measurements, but do not generate a background in the proposed study.…”

Inclusive Production of Heavy Quarkonia in pNRQCD

“…However, it is common practice in the phenomenological literature to assume that the polarized color-octet LDMEs do not depend on the direction of the gauge-completion Wilson lines, and, therefore, do not depend on the polarization λ (see for instance refs. [41,[44][45][46][47][48]). This amounts at assuming that the polarized color-octet LDMEs Ω|χ † σ i T a ψΦ †ab (0)P χ QJ (λ,P =0) Φ bc (0) ψ † σ i T c χ|Ω can be related for any polarization λ of the χ QJ state to the polarizationsummed color-octet LDME Ω|O χ QJ ( 3 S and similarly for h Q :…”