Production of $J/ψ$ quarkonia in color evaporation model based on $k_{T}$-factorization
Rafal Maciula, Antoni Szczurek
备注：
5 pages, 3 figures, talk given by R. Maciula at the XXVII International Workshop on Deep-Inelastic Scattering and Related Subjects - DIS2019, 8-12 April, 2019, Torino, Italy
We use a new approach to color evaporation model (CEM) for quarkonium production. The production of $c\bar c$ pairs is performed within $k_T$-factorization approach using different unintegrated gluon distribution functions (UGDF) from the literature. We include all recent improvements to color evaporation model. We get poor description of the large transverse momentum distributions of $J/ψ$ with the JH-2013 CCFM-based UGDF. Here explicit inclusion of $2 \to 3$ processes considerably improves the situation. Similar effects are discussed in the context of the KMR UGDF.
In this paper we analyze the exclusive photoproduction of heavy quarkonia pairs in the collinear factorization framework. We evaluate the amplitude of the process for $J/ψ\,-η_{c}$ quarkonia pair in the leading order of the strong coupling $α_{s},$ and express it in terms of generalized parton distributions (GPDs) of gluons in the proton. We made numerical estimates in the kinematics of the Electron Ion Collider, and found that in the photoproduction regime, when the virtuality of the photon is much smaller than the quarkonia mass, the cross-section of the process is sufficiently large for exp…
We present a new approach for the prompt production of quarkonia which is based on the $k_T$-factorization method. The production of even C-parity quarkonia proceeds via the fusion of two (off-shell) gluons. Especially in the kinematics of the LHCb experiment these processes are thus expected to be a sensitive probe of the small-$x$ gluon distribution. We calculate the relevant off-shell matrix elements in terms of the light-front wave functions of the quarkonium states. We present our results for scalar and pseudoscalar charmonia and discuss photon transition form factors as well as cross sec…
Quarkonia production in different high-energy processes has recently been proposed in order to probe gluon transverse-momentum-dependent parton distribution and fragmentation functions (TMDs in general). However, no proper factorization theorems have been derived for the discussed processes, but rather just ansatzs, whose main assumption is the factorization of the two soft mechanisms present in the process: soft-gluon radiation and the formation of the bound state. In this paper it is pointed out that, at low transverse momentum, these mechanisms are entangled and thus encoded in a new kind o…
We study inclusive processes involving two heavy quarkonia in nonrelativisitic QCD (NRQCD) and demonstrate that, in the presence of two P-wave Fock states, NRQCD factorization breaks down, leaving uncanceled infrared singularities. As phenomenologically important examples, we consider the decay $Υ\to χ_{cJ}+X$ via $b\bar{b}({}^3P_{J_b}^{[8]})\to c\bar{c}({}^3P_J^{[1]})+gg$ and the production process $e^+e^-\to J/ψ+χ_{cJ}+X$ via $e^{+}e^{-}\to c\bar{c}({}^3P_{J_1}^{[8]})+c\bar{c}({}^3P_J^{[1]})+g$. We infer that such singularities will appear for double quarkonium hadroproduction at next-to-lea…
A scheme is presented here to cancel out the topologically unfactorized infrared divergences in the inclusive production of heavy quarkonia, which affect the NRQCD factorization of these processes. The heavy quarkonia are defined as resonance states of QCD instead of color singlet heavy quark pair. Thus the final heavy quark pair is nor necessarily to be color singlet. In addition, the heavy quarkonia are reconstructed by their decay products. As the result, transition between states containing containing heavy quarks caused by exchanges of soft gluons are also taken into account here. Such ca…
In this work, we present a thorough analysis of scalar $P$-wave $χ_{Q0}$, $Q=c,b$ quarkonia electromagnetic form factors for the $γ^* γ^* \to χ_{Q0}$ couplings, as well as their hadroproduction observables in $k_\perp$-factorisation using the light-front potential approach for the quarkonium wave function. The electromagnetic form factors are presented as functions of photon virtualities. We discuss the role of the Melosh spin-rotation and relativistic corrections estimated by comparing our results with those in the standard nonrelativistic QCD (NRQCD) approach. Theoretical uncertainties of ou…
The detailed proof of cancellation of topologically unfactorized infrared divergences in the inclusive production of lepton pair close to the threshold of heavy quarkonia is presented. To make the effects of transition between states containing heavy quark pairs, which is important in such cancellation, the final detected states are constrained to be lepton pair near the threshold of the heavy quarkonia instead of heavy quarkonia themselves. Such cancellation is crucial for the NRQCD factorization of these processes.
We calculate the production and polarization of direct $J/ψ$ in the improved color evaporation model at $\mathcal{O}(α_s^3)$ in the collinear factorization approach. We present the first calculation of polarization parameters $λ_\vartheta$, $λ_ϕ$, and $λ_{\vartheta ϕ}$ in the helicity and the Collins-Soper frames, as well as the frame-invariant polarization parameter $\tildeλ$ as a function of transverse momentum. We find agreement with both $J/ψ$ cross sections and the invariant polarization parameters at small and moderate $p_T$.
We calculate the polarization of prompt $J/ψ$ production in the improved color evaporation model at leading order employing the $k_T$-factorization approach. In this paper, we present the polarization parameter $λ_\vartheta$ of prompt $J/ψ$ as a function of transverse momentum in $p+p$ and $p$ + A collisions to compare with data in the helicity, Collins-Soper and Gottfried-Jackson frames. We also present calculations of the charmonium production cross sections as a function of rapidity and transverse momentum. This is the first $p_T$-dependent calculation of charmonium polarization in the impr…
We calculate the polarization of prompt $\varUpsilon$($n$S) production in the improved color evaporation model at leading order employing the $k_T$-factorization approach. We present the polarization parameter $λ_\vartheta$ of prompt $\varUpsilon$($n$S) as a function of transverse momentum in $p+p$ and $p+\bar{p}$ collisions to compare with data in the helicity, Collins-Soper and Gottfried-Jackson frames. We also present calculations of the bottomonium production cross sections as a function of transverse momentum and rapidity. This is the first $p_T$-dependent calculation of bottomonium produ…
This report is devoted to the analytical calculation of heavy quarkonia production processes in modern experiments such as LHC, B-factories and superB-factories in computer. Theoretical description of heavy quarkonia is based on the factorization theorem. This theorem leads to special structure of the production amplitudes which can be used to develop computer algorithm which calculates these amplitudes automatically. This report is devoted to the description of this algorithm. As an example of its application we present the results of the calculation of double charmonia production in bottomon…
We use a new approach to color evaporation model (CEM) for quarkonium production. The production of $c\bar c$ pairs is performed within $k_T$-factorization approach using different unintegrated gluon distribution functions (UGDF) from the literature. We include all recent improvements to color evaporation model. We cannot describe simultaneously mid and forward rapidity data measured at the LHC when using the KMR UGDF with the same normalization parameter. Furthermore we get somewhat too hard distribution in $J/ψ$ transverse momentum. Correcting the standard KMR distributions for saturation ef…
In collinear factorization, light-cone distribution amplitudes (LCDAs) are key ingredients to calculate the production rate of a hadron in high energy exclusive processes. For a doubly-heavy meson system (such as $B_c, J/ψ, Υ$ etc), the LCDAs contain perturbative scales that can be integrated out and then are re-factorized into products of perturbatively calculable distribution parts and non-relativistic QCD matrix elements. In this re-factorization scheme, the LCDAs are known at next-to-leading order in the strong coupling constant $α_s$ and at leading order in the velocity expansion. In this…
In this paper, we calculate twist-2 light-cone distribution amplitudes (LCDAs) of the S-wave and P-wave quarkonia (namely $^1S_0$ state $η_{Q}$, $^3S_1$ state $J/ψ(Υ)$, $^1P_1$ state $h_{Q}$ and $^3P_J$ states $χ_{QJ}$ with $J=0,1,2$ and $Q=c,b$) to the next-leading order of the strong coupling $α_s$ and leading order of the velocity expansion $v$ in the non-relativistic QCD (NRQCD). We apply these LCDAs to some single quarkonium exclusive productions at large center-of-mass energy, such as $γ^*\to η_Qγ, χ_{QJ}γ~(J=0,1,2)$, $Z\to η_Qγ, χ_{QJ}γ~(J=0,1,2), J/ψ(Υ)γ, h_Qγ$ and $h\to J/ψγ$, by adop…
We discuss prompt production of $J/ψ$ mesons in proton-proton collisions at the LHC within NRQCD k$t$-factorization approach using Kimber-Martin-Ryskin (KMR) and Kutak-Stasto (KS) unintegrated gluon distribution (UGDF). We include both direct color-singlet production $gg \to J/ψg$ as well as a feed-down from $χ_{c} \to J/ψγ$ and $ψ' \to J/ψX$. The corresponding matrix elements for $gg \to J/ψ$, $gg \to ψ'$ and $gg \to χ_{c}$ include parameters of the nonrelativistic space wave functions of the quarkonia at $r=0$, which are taken from potential models from the literature. We calculate the ratio…
The universal fragmentation functions of gluon into the flavored quarkonia $B_c$ and (polarized) $B_c^*$ are computed within NRQCD factorization framework, at the lowest order in velocity expansion and strong coupling constant. It is mandatory to invoke the DGLAP renormalization program to render the NRQCD short-distance coefficients UV finite in a point-wise manner. The calculation is facilitated with the sector decomposition method, with the final results presented with high numerical accuracy. This knowledge is useful to enrich our understanding toward the large-$p_T$ behavior of $B_c^{(*)}…
We establish the factorization formula for scalar Glueball production through radiative decays of vector states of heavy quarkonia, e.g. $J/ψ$, $ψ(2S)$ and $Υ(nS)$, where the Glueball mass is much less than the parent heavy quarkonium mass. The factorization is demonstrated explicitly at one-loop level through the next-to-leading order (NLO) corrections to the hard kernel, the non-relativistic QCD (NRQCD) long-distance matrix element (LDMEs) of the heavy quarkonium, and the light-cone distribution amplitude (LCDA) of scalar Glueball. The factorization provides a comprehensive theoretical appro…
I review the current status of quarkonium production theory based on the non-relativistic QCD factorization formalism (NRQCD). While this theory describes much of the world's data on J/ψand Υproduction, there are still outstanding problems, most notably the polarization of quarkonia at large p_T in hadron colliders. In this talk we will present new tests of NRQCD involving the distribution of quarkonia within jets. The distribution of hadrons within jets is determined by nonperturbative functions called fragmenting jet functions (FJFs). FJFs are convolutions of fragmentation functions, evolved…
We apply our calculation of direct $J/ψ$ production in the improved color evaporation mode at ${\mathcal O}(α_s^3)$ in collinear factorization to Pb+Pb collisions. The cold nuclear matter effects of nuclear modifications of the parton densities and intrinsic transverse momentum broadening are included. We find that the polarization is independent of these effects. Our calculations are compared to the Pb+Pb polarization parameters extracted by the ALICE Collaboration at $\sqrt{s_{NN}} = 5.02$ TeV.
The production of the $f_{0}(980)$ meson at high energies is not well understood. We investigate two different potential mechanisms for inclusive scalar meson production in the $k_t$-factorization approach: color-singlet gluon-gluon fusion and color evaporation model. The $γ^* γ^* \to f_0(980)$ form factor(s) can be constraint from the $f_0(980)$ radiative decay width. The $g^* g^* \to f_0(980)$ form factors are obtained by a replacement of $α_{\rm{em}}$ electromagnetic coupling constant by $α_{\rm{s}}$ strong coupling constant and appropriate color factors. The form factors for the two coupli…
We show that the diffractive forward production of two quarkonia, especially the $χ_{cJ}$ and $η_c$ states, in proton-proton or proton-ion collisions can access the Weizsäcker-Williams gluon Wigner distribution of the proton. We use the hybrid factorization approach where the collinear, double gluon PDF is applied for one of the protons and the $k_T$-dependent (Wigner or GTMD) distribution for the other. The production of quarkonia is treated in the NRQCD framework. A particularly concise formula is obtained for double $χ_{J=1}$ production.
In the article, we study single and pair $J/ψ$ hadroproduction in the Improved Color Evaporation Model via the Parton Reggeization Approach. The last one is based on $k_T$-factorization of hard processes in multi-Regge kinematics, the Kimber-Martin-Ryskin-Watt model for unintegrated parton distribution functions, and the effective field theory of Reggezied gluons and quarks, suggested by L.N. Lipatov. We compare contributions from the single and double parton scattering mechanisms in the pair $J/ψ$ production. The numerical calculations are realized using the Monte-Carlo event generator KaTie.
Based on the potential nonrelativistic QCD formalism, we compute the nonrelativistic QCD long-distance matrix elements (LDMEs) for inclusive production of $S$-wave heavy quarkonia. This greatly reduces the number of nonperturbative unknowns and brings in a substantial enhancement in the predictive power of the nonrelativistic QCD factorization formalism. We obtain improved determinations of the LDMEs and find cross sections and polarizations of $J/ψ$, $ψ(2S)$, and excited $Υ$ states that agree well with LHC data. Our results may have important implications in pinning down the heavy quarkonium …
Within the nonrelativistic QCD (NRQCD) factorization framework, we compute the ${\mathcal O}(α_s v^2)$ corrections to the hadronic decay rate of vector quarkonia, exemplified by $J/ψ$ and $Υ$. Setting both the renormalization and NRQCD factorization scales to be $m_Q$, we obtain $Γ(J/ψ\to {\rm LH})= 0.0716\frac{α_s^3}{m_c^2} \langle \mathcal{O}_1({}^3S_1)\rangle_{J/ψ} [1-1.19α_s+(-5.32+3.03α_s)\langle v^2\rangle_{J/ψ}]$ and $Γ(Υ\to {\rm LH})= 0.0716\frac{α_s^3}{m_b^2}\langle\mathcal{O}_1({}^3S_1)\rangle_Υ[1-1.56α_s+(-5.32+4.61α_s)\langle v^2\rangle_Υ]$. We confirm the previous calculation of $…
We investigate the inclusive hadroproduction of a heavy quarkonium ($J/ψ$ or $Υ$), in association with a light-flavored jet, as a testing ground for the semi-hard regime of QCD. Our theoretical setup is the hybrid high-energy and collinear factorization, where the standard collinear approach is supplemented by the $t$-channel resummation of leading and next-to-leading energy logarithms à la BFKL. We present predictions for rapidity and azimuthal-angle differential distributions, hunting for stabilizing effects of the high-energy series under higher-order corrections. Our reaction represents an…
Recently we have proved NRQCD color octet factorization of S-wave and P-wave heavy quarkonia production at all orders in coupling constant in QCD in vacuum at high energy colliders in Eur. Phys. J. C76 (2016) 448 and in arXiv:1807.04722 [hep-ph] respectively. In this paper we extend this to prove NRQCD color octet factorization of P-wave heavy quarkonium production in non-equilibrium QCD at RHIC and LHC at all orders in coupling constant. This proof is necessary to study the quark-gluon plasma at RHIC and LHC.
The recently-proposed quasi distributions point out a promising direction for lattice QCD to investigate the light-cone correlators, such as parton distribution functions (PDF) and distribution amplitudes (DA), directly in the $x$-space. Owing to its excessive simplicity, the heavy quarkonium can serve as an ideal theoretical laboratory to ascertain certain features of quasi-DA. In the framework of non-relativistic QCD (NRQCD) factorization, we compute the order-$α_s$ correction to both light-cone distribution amplitudes (LCDA) and quasi-DA associated with the lowest-lying quarkonia, with the …
In this work, we present a thorough analysis of $η_c(1S,2S)$ quarkonia hadroproduction in $k_\perp$-factorisation in the framework of the light-front potential approach for the quarkonium wave function. The off-shell matrix elements for the $g^* g^* η_c(1S,2S)$ vertices are derived. We discuss the importance of taking into account the gluon virtualities. %We discuss the role of relativistic corrections, the Melosh spin-rotation and theoretical uncertainties by comparing our results with the standard NRQCD approach. We present the transverse momentum distributions of $η_c$ for several models of…
We calculate the ${\cal O}(α_s^3)$ short-distance, QCD collinear-factorized coefficient functions for all partonic channels that include the production of a heavy quark pair at short distances. This provides the first power correction to the collinear-factorized inclusive hadronic production of heavy quarkonia at large transverse momentum, $p_T$, including the full leading-order perturbative contributions to the production of heavy quark pairs in all color and spin states employed in NRQCD treatments of this process. We discuss the role of the first power correction in the production rates and…
We compare two existing approaches to calculating the decay of molecular quarkonium states to conventional quarkonia in effective field theory, using $X(3872) \to χ_{cJ} π^0$ as an example. In one approach the decay of the molecular quarkonium proceeds through a triangle diagram with charmed mesons in the loop. We argue this approach predicts excessively large rates for $Γ[X(3872) \to χ_{cJ}π^0]$ unless both charged and neutral mesons are included and a cancellation between these contributions is arranged to suppress the decay rates. This cancellation occurs naturally if the $X(3872)$ is prima…
We study exclusive production of scalar $χ_{c0}\equiv χ_c(0^{++})$ and pseudoscalar $η_c$ charmonia states in proton-proton collisions at the LHC energies. The amplitudes for $gg \to χ_{c0}$ as well as for $gg \to η_c$ mechanisms are derived in the $k_{T}$-factorization approach. The $p p \to p p η_c$ reaction is discussed for the first time. We have calculated rapidity, transverse momentum distributions as well as such correlation observables as the distribution in relative azimuthal angle and $(t_1,t_2)$ distributions. The latter two observables are very different for $χ_{c0}$ and $η_c$ case…
Heavy-flavored emissions have been always considered as an excellent channel to test properties of Quantum chromodynamics (QCD) at present and future colliders. Among different regimes, in which heavy-flavor production can be investigated, we focus our attention on the semi-hard one, where $s \gg \{ Q^2 \} \gg Λ_{QCD}$ ($s$ is the squared center-of-mass energy, $\{ Q^2 \}$ a (set of) hard scale(s) characteristic of the process and $Λ_{QCD}$ the QCD mass scale). Here, we build predictions in a hybrid collinear/high-energy factorization, in which the standard collinear description is supplemente…
We present a factorization formalism for inclusive production of heavy quarkonia of large transverse momentum, $p_T$ at collider energies, including both leading power (LP) and next-to-leading power (NLP) behavior in $p_T$. We demonstrate that both LP and NLP contributions can be factorized in terms of perturbatively calculable short-distance partonic coefficient functions and universal non-perturbative fragmentation functions, and derive the evolution equations that are implied by the factorization. We identify projection operators for all channels of the factorized LP and NLP infrared safe s…
We present a novel study on the inclusive production of a heavy quarkonium ($J/ψ$ or $Υ$), in association with a light-flavored jet, as a test field of the high-energy QCD dynamics. The large transverse momenta at which the two final-state objects are detected permits us to perform an analysis in the spirit of the variable-flavor number scheme (VFNS), in which the cross section for the hadroproduction of a light parton is convoluted with a perturbative fragmentation function that describes the transition from a light quark to a heavy hadron. The quarkonium collinear fragmentation function is b…
