Feed-down Contributions Research Articles

Forward J/ψ+J/ψ and J/ψ+ψ′ production with high-energy factorization

We calculate the cross sections of associated J/ψ+ψ′ and J/ψ+J/ψ production in pp collisions at s=13 TeV in the forward kinematic region. The high-energy factorization (kT-factorization) framework supplemented with the Catani-Ciafaloni-Fiorani-Marchesini evolution of gluon densities in a proton is applied. We demonstrate that the latest data on J/ψ+J/ψ production and first experimental data on J/ψ+ψ′ events taken very recently by the LHCb Collaboration can be described well by the color singlet terms and contributions from double parton scattering (DPS) with the standard choice for σeff parameter. The relative production rate σ(J/ψ+ψ′)/σ(J/ψ+J/ψ) is found to be sensitive to the DPS terms as well as to feeddown contributions. Published by the American Physical Society 2024

Studies of the relative suppression of excited quarkonium states with CMS

One of the findings of the LHC heavy ion program is the observation of stronger suppression of the excited quarkonium states compared to the ground states in lead-lead (PbPb) and proton-lead (pPb) collisions. Such differences among the states may imply dissociation effects occurring at late stages, after the evolution of heavy quark pairs into well-defined physical states. The variety of binding energies within the quarkonia families offers an experimental tool to characterize the phenomena at play. Measuring the excited states is crucial as they represent significant feed-down contributions to the production of the ground states and must be accounted for in the interpretation of the data. We present studies of the relative suppression of quarkonia in pPb and PbPb collisions performed by CMS. For the first time, the nuclear modification factor has been extended to the strongly suppressed Υ(3S) state. Moreover, nuclear modification factors as well as excited-to-ground state cross section ratios are measured as a function of particle transverse momentum and rapidity, and event activity. The results are compared with several model calculations incorporating initial- and final-state effects.

Bottomonium production and polarization in the NRQCD with k_T-factorization. III: Upsilon (1S) and chi _b(1P) mesons

The Upsilon (1S) meson production and polarization at high energies is studied in the framework of the k_T-factorization approach. Our consideration is based on the non-relativistic QCD formalism for a bound states formation and off-shell production amplitudes for hard partonic subprocesses. The direct production mechanism, feed-down contributions from radiative chi _b(mP) decays and contributions from Upsilon (3S) and Upsilon (2S) decays are taken into account. The transverse momentum dependent (TMD) gluon densities in a proton were derived from the Ciafaloni–Catani–Fiorani–Marchesini evolution equation and the Kimber-Martin–Ryskin prescription. Treating the non-perturbative color octet transitions in terms of multipole radiation theory, we extract the corresponding non-perturbative matrix elements for Upsilon (1S) and chi _b(1P) mesons from a combined fit to transverse momenta distributions measured at various LHC experiments. Then we apply the extracted values to investigate the polarization parameters lambda _theta , lambda _phi and lambda _{theta phi }, which determine the Upsilon (1S) spin density matrix. Our predictions have a reasonably good agreement with the currently available Tevatron and LHC data within the theoretical and experimental uncertainties.

Comprehensive studies of \u03d2 inclusive production in Z boson decay

In this paper, we present a comprehensive study of ϒ inclusive production in Z boson decay, including the first complete next-to-leading-order calculations of the color-octet (CO) contributions. With the inclusion of the newly-calculated remarkable QCD corrections, the CO processes exhibit crucially phenomenological influence on the existing predictions built on the color-singlet mechanism. We also include the exhaustive evaluations of the feed-down contributions, which remained ignored in the literature, and find them to be considerable. Summing up all the contributions, the ℬZ → ϒ(nS) + X still notably undershoot the data released by the L3 Collaboration.

Coupled Boltzmann transport equations of heavy quarks and quarkonia in quark-gluon plasma

We develop a framework of coupled transport equations for open heavy flavor and quarkonium states, in order to describe their transport inside the quark-gluon plasma. Our framework is capable of studying simultaneously both open and hidden heavy flavor observables in heavy-ion collision experiments and can account for both, uncorrelated and correlated recombination. Our recombination implementation depends on real-time open heavy quark and antiquark distributions. We carry out consistency tests to show how the interplay among open heavy flavor transport, quarkonium dissociation and recombination drives the system to equilibrium. We then apply our framework to study bottomonium production in heavy-ion collisions. We include ϒ(1S), ϒ(2S), ϒ(3S), χb(1P) and χb(2P) in the framework and take feed-down contributions during the hadronic gas stage into account. Cold nuclear matter effects are included by using nuclear parton distribution functions for the initial primordial heavy flavor production. A calibrated 2 + 1 dimensional viscous hydrodynamics is used to describe the bulk QCD medium. We calculate both the nuclear modification factor RAA of all bottomonia states and the azimuthal angular anisotropy coefficient v2 of the ϒ(1S) state and find that our results agree reasonably with experimental measurements. Our calculations indicate that correlated cross-talk recombination is an important production mechanism of bottomonium in current heavy-ion experiments. The importance of correlated recombination can be tested experimentally by measuring the ratio of RAA(χb(1P)) and RAA(ϒ(2S)).

Feeddown contributions from unstable nuclei in relativistic heavy-ion collisions

We estimate the feeddown contributions from decays of unstable A=4 and A=5 nuclei to the final yields of protons, deuterons, tritons, 3He, and 4He produced in relativistic heavy-ion collisions at sNN>2.4 GeV, using the statistical model. The feeddown contribution effects do not exceed 5% at LHC and top RHIC energies due to the large penalty factors involved, but are substantial at intermediate collision energies. We observe large feeddown contributions for tritons, 3He, and 4He at sNN≲10 GeV, where they may account for as much as 70% of the final yield at the lower end of the collision energies considered. Sizable (>10%) effects for deuteron yields are observed at sNN≲4 GeV. The results suggest that the excited nuclei feeddown cannot be neglected in the ongoing and future analysis of light nuclei production at intermediate collision energies, including HADES and CBM experiments at FAIR, NICA at JINR, RHIC beam energy scan and fixed-target programmes, and NA61/SHINE at CERN. We further show that the freeze-out curve in the T-μB plane itself is affected significantly by the light nuclei at high baryochemical potential.

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

While the prompt mathrm{J}/psi cross section and polarization have been measured with good precision as a function of transverse momentum, p_mathrm{T}, those of the directly produced mathrm{J}/psi are practically unknown, given that the cross sections and polarizations of the chi _{{c}1} and chi _{{c}2} mesons, large indirect contributors to mathrm{J}/psi production, are only known with rather poor accuracy. The lack of precise measurements of the chi _{{c}J} polarizations induces large uncertainties in the level of their feed-down contributions to the prompt mathrm{J}/psi 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 , psi mathrm{(2S)} and chi _{c} cross sections and polarizations, faithfully respecting all the correlations and uncertainties. In particular, it is seen that the chi _{{c}J} polarizations and feed-down fractions to mathrm{J}/psi production have a negligible dependence on the mathrm{J}/psi p_mathrm{T}, with average values lambda _vartheta ^{chi _{{c}1}} = 0.55 pm 0.23, lambda _vartheta ^{chi _{{c}2}} = -0.39 pm 0.22, R^{chi _{{c}1}} = (18.8 pm 1.4)% and R^{chi _{{c}2}} = (6.5 pm 0.5)%. The analysis also shows that (67.2 pm 1.9)% of the prompt mathrm{J}/psi yield is due to directly-produced mesons, of polarization constrained to remarkably small values, lambda _vartheta ^{mathrm{J}/psi } = 0.04 pm 0.06.

Bottomonia production and polarization in the NRQCD with k_T-factorization. II: Upsilon (2S) and chi _b(2P) mesons

The Upsilon (2S) production and polarization at high energies is studied in the framework of k_T-factorization approach. Our consideration is based on the non-relativistic QCD formalism for bound states formation and off-shell production amplitudes for hard partonic subprocesses. The direct production mechanism, feed-down contributions from radiative chi _b(3P) and chi _b(2P) decays and contributions from Upsilon (3S) decays are taken into account. The transverse momentum dependent gluon densities in a proton were derived from the Ciafaloni–Catani–Fiorani–Marchesini evolution equation, Kimber-Martin-Ryskin prescription and Parton Branching method. Treating the non-perturbative color octet transitions in terms of the mulitpole radiation theory, we extract the corresponding non-perturbative matrix elements for Upsilon (2S) and chi _b(2P) mesons from a combined fit to Upsilon (2S) transverse momenta distributions measured by the CMS and ATLAS Collaborations at the LHC energies sqrt{s} = 7 and 13 TeV and from the relative production rate R^{chi _b(2P)}_{Upsilon (2S)} measured by the LHCb Collaboration at sqrt{s} = 7 and 8 TeV. Then we apply the extracted values to investigate the polarization parameters lambda _theta , lambda _phi and lambda _{theta phi }, which determine the Upsilon (2S) spin density matrix. Our predictions have a good agreement with the currently available data within the theoretical and experimental uncertainties.

The studies on Z rightarrow Upsilon (1S)+g+g at the next-to-leading-order QCD accuracy

In this paper, we carry out the next-to-leading-order (NLO) studies on Z rightarrow Upsilon (1S)+g+g via the color-singlet (CS) b{bar{b}} state. We find the newly calculated NLO QCD corrections to this process can significantly influence its leading-order (LO) results and greatly improve the dependence on the renormalization scale. By including the considerable feeddown contributions, the branching ratio {mathcal {B}}_{Z rightarrow Upsilon (1S)+g+g} is predicted to be (0.56–0.95) times 10^{-6}, which can reach up to 19–31% of the LO predictions given by the CS dominant process Z rightarrow Upsilon (1S)+b+{bar{b}}. Moreover, Z rightarrow Upsilon (1S)+g+g also seriously affects the CS predictions on the Upsilon (1S) energy distributions, especially when z is relatively small. In summary, for the inclusive Upsilon (1S) productions in Z decay, besides Z rightarrow Upsilon (1S)+b+{bar{b}}, the gluon radiation process Z rightarrow Upsilon (1S)+g+g can provide indispensable contributions as well.

Bottomonia production and polarization in the NRQCD with k_T-factorization. I: Upsilon (3S) and chi _b(3P) mesons

The Upsilon (3S) production and polarization at high energies is studied in the framework of k_T-factorization approach. Our consideration is based on the non-relativistic QCD formalism for bound states formation and off-shell production amplitudes for hard partonic subprocesses. The transverse momentum dependent (TMD, or unintegrated) gluon densities in a proton were derived from the Ciafaloni-Catani-Fiorani-Marchesini (CCFM) evolution equation as well as from the Kimber–Martin–Ryskin (KMR) prescription. Treating the non-perturbative color octet transitions in terms of the multipole radiation theory and taking into account feed-down contributions from radiative chi _b(3P) decays, we extract the corresponding non-perturbative matrix elements for Upsilon (3S) and chi _b(3P) mesons from a combined fit to Upsilon (3S) transverse momenta distributions measured by the CMS and ATLAS Collaborations at the LHC energies sqrt{s} = 7 and 13 TeV and central rapidities. Then we apply the extracted values to describe the CDF and LHCb data on Upsilon (3S) production and to investigate the polarization parameters lambda _theta , lambda _phi and lambda _{theta phi }, which determine the Upsilon (3S) spin density matrix. Our predictions have a good agreement with the currently available data within the theoretical and experimental uncertainties.

Next-to-leading-order QCD corrections to the decay of Z boson into χc(χb)

Based on the framework of nonrelativistic Quantum Chromodynamics (NRQCD), we carry out next-to-leading order (NLO) QCD corrections to the decay of $Z$ boson into $\chi_c$ and $\chi_b$, respectively. The branching ratio of $Z \to \chi_{c}(\chi_b)+X$ is about $10^{-5}(10^{-6})$. It is found that, for $Z \to \chi_c(\chi_b)+X$, the single gluon fragmentation diagrams of $^3S_1^{[8]}$, which first appear at the NLO level, can provide significant contributions, leading to a great enhancement on the leading-order results. Consequently the contributions from the color octet (CO) channels will account for a large proportion of the total decay widths. Moreover, the introduction of the CO processes will thoroughly change the color singlet (CS) predictions on the ratios of $\Gamma_{\chi_{c1}}/\Gamma_{\chi_{c0}}$, $\Gamma_{\chi_{c2}}/\Gamma_{\chi_{c0}}$, $\Gamma_{\chi_{b1}}/\Gamma_{\chi_{b0}}$ and $\Gamma_{\chi_{b2}}/\Gamma_{\chi_{b0}}$, which can be regarded as an outstanding probe to distinguish the CO and CS mechanism. With regard to the CS ($^3P_J^{[1]}$) channels, the heavy quark pair associated processes serve as the leading role, however, in the case of $\chi_b$, $Z \to b\bar{b}[^3P_J^{[1]}]+g+g$ can also contribute significantly. Summing over all the feeddown contributions from $\chi_{cJ}$ and $\chi_{bJ}$, respectively, we find $\Gamma(Z \to J/\psi+X)|_{\chi_c-\textrm{feeddown}}=(0.28 - 2.4) \times 10^{-5}$ and $\Gamma(Z \to \Upsilon(1S)+X)|_{\chi_b-\textrm{feeddown}}=(0.15 - 0.49) \times 10^{-6}$.

Remaining parts of the long-standing J/ψ polarization puzzle

Based on the non-relativistic quantum chromodynamics factorization formalism, the polarization parameters $\lambda_{\theta\phi}$ and $\lambda_{\phi}$ of $J/\psi$ hadroproduction are analyzed in helicity frame and calculated at QCD next-to-leading order for the first time. For prompt $J/\psi$ production, we take into account the feeddown contributions from $\chi_{cJ}$ and $\psi(2S)$ decays. The theoretical predictions for the polarization parameters $\lambda_{\theta\phi}$ and $\lambda_{\phi}$ of $J/\psi$ are presented. With the theoretical results we have done the fit to the experimental measurements on yield and polarization for $J/\psi$ hadroproduction simultaneously, and found that the results are coincide with the experimental measurements at the LHC quite well.

Observation of Transverse Λ/Λ[over ¯] Hyperon Polarization in e^{+}e^{-} Annihilation at Belle.

We report the first observation of the spontaneous polarization of Λ and Λ[over ¯] hyperons transverse to the production plane in e^{+}e^{-} annihilation, which is attributed to the effect arising from a polarizing fragmentation function. For inclusive Λ/Λ[over ¯] production, we also report results with subtracted feed-down contributions from Σ^{0} and charm. This measurement uses a dataset of 800.4 fb^{-1} collected by the Belle experiment at or near a center-of-mass energy of 10.58GeV. We observe a significant polarization that rises with the fractional energy carried by the Λ/Λ[over ¯] hyperon.

ϒ(3S) and χb(3P) production and polarization in the NRQCD with kT–factorization

The ϒ(3S) production and polarization at high energies is studied in the framework of kT–factorization approach. Our consideration is based on the non-relativistic QCD formalism for bound states formation and off-shell production amplitudes for hard partonic subprocesses. The transverse momentum dependent (TMD, or unintegrated) gluon densities in a proton were derived from the CiafaloniCatani-Fiorani-Marchesini (CCFM) evolution equation as well as from the Kimber–Martin–Ryskin (KMR) prescription. Treating the nonperturbative color octet transitions in terms of the mulitpole radiation theory and taking into account feed-down contributions from radiative χb(3P) decays, we extract the corresponding non-perturbative matrix elements for ϒ(3S) and χb(3P) mesons from a combined fit to ϒ(3S) transverse momenta distributions measured by the CMS and ATLAS Collaborations at the LHC energies √s = 7 and 13 TeV and central rapidities. Then we apply the extracted values to investigate the polarization parameters λθ, λφ and λθφ, which determine the ϒ(3S) spindensity matrix. Our predictions have a good agreement with the currently available data within the theoretical and experimental uncertainties.

Production cross sections of hyperons and charmed baryons from e+e− annihilation near s=10.52 GeV

We measure the inclusive production cross sections of hyperons and charmed baryons from $e^+e^-$ annihilation using a 800 fb$^{-1}$ data sample taken near the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. The feed-down contributions from heavy particles are subtracted using our data, and the direct production cross sections are presented for the first time. The production cross sections divided by the number of spin states for $S=-1$ hyperons follow an exponential function with a single slope parameter except for the $\Sigma(1385)^+$ resonance. Suppression for $\Sigma(1385)^+$ and $\Xi(1530)^0$ hyperons is observed. Among the production cross sections of charmed baryons, a factor of three difference for $\Lambda_c^+$ states over $\Sigma_c$ states is observed. This observation suggests a diquark structure for these baryons.

Applicability of transverse mass scaling in hadronic collisions at energies available at the CERN Large Hadron Collider

We present a study on the applicability of transverse mass scaling for identified particle spectra in proton-proton collisions at $\sqrt{s}=7$ TeV based on data taken by the ALICE experiment at the LHC. The measured yields are parametrized and compared to estimates obtained from a generalized transverse mass scaling approach applied to different reference particle spectra. It is found that generalized transverse mass scaling is not able to describe the measured spectra over the full range in transverse momentum. At low $p_{\rm T}$, deviations of $20$% or more are obtained, in particular if pions are used as reference particles. A better scaling performance is obtained, when kaons are used as reference particles. At high $p_{\rm T}$ all tested spectra with the possible exception of the charged kaons exhibit a scaling behavior. Investigating the feed-down contributions from resonance decays to the charged pion yields reveals, that using them as reference a general scaling may not be achievable. Our findings imply that for precision measurements of direct photon and di-electron spectra at low transverse momentum one should measure the relevant hadronic background, instead of relying on $m_{\rm T}$ scaling for its estimate.

Prompt charmonia production and polarization at the LHC in the NRQCD with kT -factorization. III. J/ψ meson

In the framework of $k_T$-factorization approach, the production and polarization of prompt $J/\psi$ mesons at the LHC energies is studied. Our consideration is based on the non-relativistic QCD formalism for bound states and off-shell amplitudes for hard partonic subprocesses. Both the direct production mechanism and feed-down contributions from $\chi_c$ and $\psi(2S)$ decays are taken into account. The transverse momentum dependent (or unintegrated) gluon densities in a proton were derived from Ciafaloni-Catani-Fiorani-Marchesini evolution equation or, alternatively, were chosen in accordance with Kimber-Martin-Ryskin prescription. The non-perturbative color-octet matrix elements were first deduced from the fits to the latest CMS data on $J/\psi$ transverse momentum distributions and then applied to describe the ATLAS and LHCb data on $J/\psi$ production and polarization at $\sqrt s = 7$, $8$ and $13$ TeV. We perform an estimation of polarization parameters $\lambda_\theta$, $\lambda_\phi$ and $\lambda_{\theta \phi}$ which determine $J/\psi$ spin density matrix and demonstrate that treating the soft gluon emission as a series of explicit color-electric dipole transitions within NRQCD leads to unpolarized $J/\psi$ production at high transverse momenta, that is in qualitative agreement with the LHC data.

ϒ(nS)andχb(nP)production at hadron colliders in nonrelativistic QCD

$\Upsilon(nS)$ and $\chi_b(nP)$ (n=1,2,3) production at the LHC is studied at next-to-leading order in $\alpha_s$ in nonrelativistic QCD. Feeddown contributions from higher $\chi_b$ and $\Upsilon$ states are all considered for lower $\Upsilon$ cross sections and polarizations. The long distance matrix elements (LDMEs) are extracted from the yield data, and then used to make predictions for the $\Upsilon(nS)$ polarizations, which are found to be consistent with the measured polarization data within errors. In particular, the $\Upsilon(3S)$ polarization puzzle can be understood by a large feeddown contribution from $\chi_b(3P)$ states. Our results may provide a good description for both cross sections and polarizations of prompt $\Upsilon(nS)$ and $\chi_b(nP)$ production at the LHC.

Statistical hadronization model analysis of hadron yields in p + Nb and Ar + KCl at SIS18 energies

The HADES data from p + Nb collisions at a center-of-mass energy of $ \sqrt{s_{NN}} = 3.2$ GeV are analyzed employing a statistical hadronization model. The model can successfully describe the production yields of the identified hadrons $ \pi^{0}$ , $ \eta$ , $ \Lambda$ , K 0 s, $ \omega$ with parameters $ T_{chem} = (99\pm 11)$ MeV and $ \mu_{b} = (619\pm 34)$ MeV, which fit well into the chemical freeze-out systematics found in heavy-ion collisions. In addition, we reanalyze our previous HADES data from Ar + KCl collisions at $ \sqrt{s_{NN}} = 2.6$ GeV with an updated version of the model. We address equilibration in heavy-ion collisions by testing two aspects: the description of yields and the regularity of freeze-out parameters from a statistical model fit as a function of colliding energy and system size. Despite its success, the model fails to describe the observed $ \Xi^{-}$ yields in both, p + Nb and Ar + KCl . Special emphasis is put on feed-down contributions from higher-lying resonance states as a possible explanation for the observed excess.

An updated study of ϒ production and polarization at the Tevatron and LHC**Supported by National Nature Science Foundation of China (11475183) and Youth Innovation Promotion Association of CAS (2014010)

Following the nonrelativistic QCD factorization scheme, by taking the latest available measurements of χbJ(3P) into consideration, we present an updated study on the yield and polarization of ϒ(1S, 2S, 3S) hadroproduction, and the fractions of χbJ(mP) feed-down in ϒ(nS) production at QCD next-to-leading order. In the fitting, three schemes are applied with different choices of χbJ(mP) feed-down ratios and NRQCD factorization scale. The results can explain the measurements of yield very well. The polarization puzzle to ϒ(3S) is now solved by considering the χbJ(3P) feed-down contributions. The ratio of σ[χb2(1P)]/σ[χb1(1P)] measured by the CMS experiment can also be reproduced in our prediction. Among the different schemes, the results show little difference, but there are sizeable differences for the fitted long-distance color-octet matrix elements. This may bring large uncertainties when the values are applied in theoretical predictions for other experiments such as those at ee, ep colliders.