Distance Matrix Elements Research Articles

Direct quarkonium production in DIS from a joint CGC and NRQCD framework

We compute the differential cross section for direct quarkonium production in high-energy electron-nucleus collisions at small x. Our computation is performed within the nonrelativistic QCD factorization formalism that separates the calculation into short distance coefficients and long distance matrix elements that depend on the color and spin of the state. We obtain the short distance coefficients of the production of the heavy quark pair within the framework of the color glass condensate effective field theory, which resums coherent multiple interactions of the heavy quark pair with the nucleus to all orders. Our results are expressed as the convolution of perturbatively calculable functions with multipoint lightlike Wilson line correlators. In the correlation limit, we establish the correspondence between our color glass condensate formulation with calculations employing the transverse momentum dependent (TMD) framework. We extend this correspondence by resumming kinematic power corrections within the improved TMD framework, which interpolates between the TMD formalism and k⊥-factorization formalism. We present a detailed numerical analysis, focusing on J/ψ production in the kinematics accessible at the future Electron-Ion Collider, highlighting the importance of genuine higher-order saturation contributions when the electron collides with a large nucleus. Our results are also valid in the photoproduction limit where we expect the largest contribution from genuine higher-order saturation contributions which could be accessed in ultraperipheral collisions of relativistic heavy ions. Published by the American Physical Society 2024

J/ψ polarization in large- PT semi-inclusive deep-inelastic scattering at the EIC

We present a detailed phenomenological study of $J/\psi$ polarization in semi-inclusive deep inelastic scattering processes, focusing on the kinematics accessible at the future Electron-Ion Collider. We show theoretical estimates for the standard polarization parameters for different frames usually adopted in the literature, in the large $P_T$ region, namely $P_T\gg \Lambda_\text{QCD}$, where collinear factorization is expected to hold. We adopt both the Color Singlet Model and the Nonrelativistic QCD approach, paying special attention to the role of different sets of Long Distance Matrix Elements. Finally we present a preliminary analysis of some frame independent polarization invariants.

SISTEM PENDUKUNG KEPUTUSAN PEMBERIAN PINJAMAN MENGGUNAKAN METODE MULTIATTRIBUTE APPROXIMATION BORDER AREA COMPARISON (MABAC)

The process of determining loan provision at Teacher Cooperative of SMAN 1 Jasinga is still using a manual system. Treasurer of Cooperative conduct the determining lending based on feasibility assessment of Cooperative members to receive loans without calculate the percentage of the borrower's eligibility value. This study aims to produce a Decision Support System (DSS) in assessing and ranking loan applications using the Multi-Attributive Border Approximation Area Comparison (MABAC) method in the Teacher Cooperative of SMAN 1 Jasinga. The MABAC method has 6 process steps, namely ordering the initial decision matrix, normalizing the initial matrix elements, calculating the weighted matrix elements, determining the area estimate matrix, calculating the alternative distance matrix elements from the border area and alternative ranking. The results of this study is a decision support system based on four predetermined criteria namely the purpose of loan, the amount of loan, the amount of saving and the amount of salary. This Decision Support System can accelerate the calculation process in determining loan provision by the Treasurer of Teacher Cooperative so that it becomes more efficient and right on target. Testing is done using 40 loan applications data. Based on the accuracy results of the comparison between the real data with DSS calculation data is obtained value 87.5%.

Cos(2ϕh) asymmetry in J/ψ production in unpolarized ep collision

We present a calculation of the $cos (2 \phi_h)$ asymmetry in $J/\psi$ production in electron-proton collision at the future electron-ion collider (EIC), a useful channel to probe the gluon TMDs. We calculate the asymmetry at next-to-leading order (NLO) in $\alpha_s$ in the framework of generalized factorization. The dominating sub-process is $\gamma^* +g \rightarrow J/\psi+g$. The production of $J/\psi$ is calculated in the non-relativistic QCD(NRQCD) framework with the inclusion of both color singlet and color octet contributions. Numerical estimates of the $cos(2\phi_h)$ asymmetry are given in the kinematical region to be accessed by the future EIC. The asymmetry depends on the parameterization of the gluon TMDs, as well as on the long distance matrix elements (LDMEs). We use both Gaussian-type parameterization and McLerran-Venugopalan model for the TMDs in the kinematical region of small-$x$, where the gluons play a dominant role. We obtain sizable asymmetry, which may be useful to probe the ratio of the linearly polarized and the unpolarized gluon distribution in the proton.

Gluon fragmentation into 3 {P}_J^{left[1,8right]} quark pair and test of NRQCD factorization at two-loop level

The next-to-leading order (NLO) ( mathcal{O} ( {alpha}_s^3 )) corrections for gluon fragmentation functions to a heavy quark-antiquark pair in 3 {P}_J^{left[1,8right]} states are calculated within the NRQCD factorization. We use the integration-by-parts reduction and differential equations to semi-analytically calculate the fragmentation functions in full-QCD, and find that infrared divergences can be absorbed by the NRQCD long distance matrix elements. Thus, the NRQCD factorization conjecture is verified at two-loop level via a physical process, which is free of artificial ultraviolet divergences. Through the matching procedure, infrared-safe short distance coefficients and mathcal{O} ( {alpha}_s^2 ) perturbative NRQCD matrix elements ⟨ {mathcal{O}}^3{P}_J^{left[1,8right]} (3 {S}_1^{left[8right]} )⟩ are obtained simultaneously. The NLO short distance coefficients are found to have significant corrections comparing with the LO ones.

Bottomonia production in p + p collisions under NRQCD formalism

In this work, we present the calculation of the production cross sections of bottomonia states using Non-Relativistic Quantum Chromodynamics (NRQCD) formalism. The direct production cross-section of a resonance can be factorised in terms of short distance Quantum Chromodynamics (QCD) cross sections and long distance matrix elements (LDMEs) under NRQCD. We use a large set of measured ϒ(nS) production data at Tevatron and LHC energies in both central and forward rapidity regions to extract the LDMEs with better precision. The feed down contributions from the higher states including the χb(3P) state are taken into account for the LDME extraction. The formalism provides a good description of the bottomonia data in wide transverse momentum range at different collision energies.

Quarkonium TMD fragmentation functions in NRQCD

We study the transverse-momentum spectrum of quarkonium production from single light-parton fragmentation mechanism. In the case of semi-inclusive deep inelastic scattering, we observe that there are two possible initiating processes, namely photon-gluon fusion and light-quark fragmentation. For the second case we derive the factorization theorem, which involves a new hadronic quantity: the quarkonium transverse-momentum-dependent fragmentation functions in NRQCD. We calculate their matching onto the non-perturbative long distance matrix elements at the lowest order in the strong-coupling constant, mathcal{O}left({alpha}_s^2right) . Focusing on the case of the electron-ion collider, we make a comparative phenomenological study of the two production mechanisms and find the regions of the phase space where one is dominant over the other.

Relativistic corrections to the vector meson light front wave function

We compute a light front wave function for heavy vector mesons based on long distance matrix elements constrained by decay width analyses in the Non Relativistic QCD framework. Our approach provides a systematic expansion of the wave function in quark velocity. The first relativistic correction included in our calculation is found to be significant, and crucial for a good description of the HERA exclusive $\mathrm{J}/\psi$ production data. When looking at cross section ratios between nuclear and proton targets, the wave function dependence does not cancel out exactly. In particular the fully non-relativistic limit is found not to be a reliable approximation even in this ratio. The important role of the Melosh rotation to express the rest frame wave function on the light front is illustrated.

Prompt J/psi photoproduction within the non-relativistic QCD framework at the CEPC

The prompt J/psi photoproduction within the non-relativistic QCD (NRQCD) framework at the future Circular Electron Positron Collider (CEPC) is studied, including the contributions from both direct and resolved photons. Employing different sets of long distance matrix elements, the total cross section is dominated by the color-octet channel. We present different kinematic distributions of J/psi production and the results show there will be about 50 J/psi events when the transverse momentum of J/psi is up to 20 GeV. It renders that the J/psi photoprodution at the CEPC is a well laboratory to test the NRQCD and further clarify the universality problem in NRQCD between electron positron collider and hadron collider.

Study on the inclusive hadroproduction of ϒ+γ at next-to-leading order

In this paper we investigate the inclusive associated production of {\Upsilon} + {\gamma} at the hadron collider. We calculate the color-singlet sub-processes and all three color-octet sub-processes at the next-to-leading order. Seven sets of long distance matrix elements(LDMEs), which are extracted from the studies on the prompt production of {\Upsilon} at hadron colliders, are used to give the numerical results and we find that there are three sets of LDMEs give the unphysical results on the yield and the polarization for this process. The yield is enhanced by several or two orders times comparing to that of color-singlet process and the polarization changes from longitudinal to slightly transverse or even mainly transverse in the large pt region. The estimation results indicate that to study the process at the large hadron collider (LHC) is difficult and it may be well investigated at the future Super Proton-Proton Collider(SPPC).

J/\u03c8 polarization in the CGC+NRQCD approach

We compute the J/ψ polarization observables λθ, λϕ, λθϕ in a Color Glass Condensate (CGC) + nonrelativistic QCQ (NRQCD) formalism that includes contributions from both color singlet and color octet intermediate states. Our results are compared to low pT data on J/ψ polarization from the LHCb and ALICE experiments on proton-proton collisions at center-of-mass energies of sqrt{s}=7 TeV and 8 TeV. Our CGC+NRQCD computation provides a better description of data for pT ≤ 15 GeV relative to extant next-to-leading (NLO) calculations within the collinear factorization framework. These results suggest that higher order computations in the CGC+NRQCD framework have the potential to greatly improve the accuracy of extracted values of the NRQCD universal long distance matrix elements.

Relativistic corrections to exclusive χcJ+γ production from e+e− annihilation

We calculate in the non-relativistic QCD (NRQCD) factorization framework all leading relativistic corrections to the exclusive production of $\chi_{cJ}+\gamma$ in $e^+ e^-$ annihilation. In particular, we compute for the first time contributions induced by octet operators with a chromoelectric field. The matching coefficients multiplying production long distance matrix elements (LDMEs) are determined through perturbative matching between QCD and NRQCD at the amplitude level. Technical challenges encountered in the non-relativistic expansion of the QCD amplitudes are discussed in detail. The main source of uncertainty comes from the not so well known LDMEs. Accounting for it, we provide the following estimates for the production cross sections at $\sqrt{s} = 10.6\textrm{ GeV}$: $\sigma (e^+ e^- \to \chi_{ c0} + \gamma) = (1.3 \pm 0.4) \textrm{ fb}$, $\sigma (e^+ e^- \to \chi_{ c1} + \gamma) = (15.4 \pm 6.7) \textrm{ fb}$, and $\sigma (e^+ e^- \to \chi_{ c2} + \gamma) = (4.7 \pm 2.6) \textrm{ fb}$.

Study of color-octet matrix elements through J/psi production in e^{+}e^{-} annihilation

In this paper, the color-octet long distance matrix elements are studied through the inclusive J/psi production in e^{+}e^{-} annihilation within the framework of non-relativistic QCD factorization. The calculations are up-to next-to-leading order with the radiative and relativistic corrections in the energy region of the B-factory and the near-threshold region of 4.6{-}5.6~mathrm{GeV}. A constraint of the long distance matrix elements (langle ^1S_0^{8}rangle , langle ^3P_0^{8}rangle ) is obtained. Through our estimation, the P-wave color-octet matrix element (langle 0|^3P^8_0|0rangle ) should be of the order of 0.008m_mathrm{c}^2~mathrm{GeV}^3 or less. The constrained region is not compatible with the values of the long distance matrix elements fitted at hadron colliders.

Quarkonium polarization and the long distance matrix elements hierarchies using jet substructure

We investigate the quarkonium production mechanisms in jets at the LHC, using the Fragmenting Jet Functions (FJF) approach. Specifically, we discuss the jet energy dependence of the $J/\psi$ production cross section at the LHC. By comparing the cross sections for the different NRQCD production channels ($^1S_0^{[8]}$,$^3S_1^{[8]}$,$^3P_J^{[8]}$, and $^3S_1^{[1]}$), we find that at fixed values of energy fraction $z$ carried by the $J/\psi$, if the normalized cross section is a decreasing function of the jet energy, in particular for $z > 0.5$, then the depolarizing $^1S_0^{[8]}$ must be the dominant channel. This makes the prediction made in [Baumgart et al., JHEP 1411, 003 (2014)] for the FJF's also true for the cross section. We also make comparisons between the long distance matrix elements extracted by various groups. This analysis could potentially shed light on the polarization properties of the $J/\psi$ production in high $p_T$ region.

Charmonia production in p + p collisions under NRQCD formalism

This work presents the differential charmonia production cross sections in high energy p + p collisions calculated using non-relativistic quantum chromodynamics (NRQCD) formalism. The NRQCD formalism, factorizes the quarkonia production cross sections in terms of short distance quantum chromodynamics (QCD) cross sections and long distance matrix elements (LDMEs). The short distance cross sections are calculated in terms of perturbative QCD, and LDMEs are obtained by fitting the experimental data. Measured transverse momentum distributions of , ψ(2S) and J/ψ in p + collisions at TeV and in p + p collisions at and 13 TeV are used to constrain LDMEs. The feed-down contribution to each state from the higher states are taken into account. The formalism provides a very good description of the data in a wide energy range. The values of LDMEs are used to predict the charmonia cross sections in p + p collisions at 13 and 5 TeV in kinematic bins relevant for the LHC detectors.

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.

Relativistic correction to color-octetJ/ψproduction at hadron colliders

The relativistic corrections to the color-octet $J/\psi$ hadroproduction at the Tevatron and LHC are calculated up to $\mathcal{O}(v^2)$ in nonrelativistic QCD factorization frame. The short distance coefficients are obtained by matching full QCD with NRQCD results for the partonic subprocess $g+g\to J/\psi ({}^1S_0^{[8]},{}^3S_1^{[8]}, {}^3P_J^{[8]})+g$, $q+\bar{q}\to J/\psi ({}^1S_0^{[8]},{}^3S_1^{[8]}, {}^3P_J^{[8]})+g$ and $g+q({\bar{q}})\to J/\psi ({}^1S_0^{[8]},{}^3S_1^{[8]}, {}^3P_J^{[8]})+q({\bar{q}})$. The short distance coefficient ratios of relativistic correction to leading order for color-octet states ${^1}S_{0}^{[8]}$, ${^3}S_{1}^{[8]}$, and ${^3}P_{J}^{[8]}$ at large $p_T$ are approximately -5/6, -11/6, and -31/30, respectively, for each subprocess, and it is 1/6 for color-singlet state ${^3}S_{1}^{[1]}$. If the higher order long distance matrix elements are estimated through velocity scaling rule with adopting $v^2=0.23$ and the lower order long distance matrix elements are fixed, the leading order cross sections of color-octet states are reduced by about a factor of $20\sim40%$ at large $p_T$ at both the Tevatron and the LHC. Comparing with QCD radiative corrections to color-octet states, relativistic correction is ignored along with $p_T$ increasing. Using long distance matrix elements extracted from the fit to $J/\psi$ production at the Tevatron, we can find the unpolarization cross sections of $J/\psi$ production at the LHC taking into account both QCD and relativistic corrections are changed by about $20\sim50%$ of that considering only QCD corrections. These results indicate that relativistic corrections may play an important role in $J/\psi$ production at the Tevatron and the LHC.

Color-octet quarkonia production. II.

We calculate the lowest order hadronic cross sections for producing colored heavy quark-antiquark pairs in $L=S=0$ and $L=S=1$ configurations. Such $Q\Qbar[{}^1S_0^{(8)}]$ and $Q\Qbar[{}^3P_J^{(8)}]$ states hadronize into $\psi_\Q$ quarkonia at the same order in the NRQCD velocity expansion as previously considered $Q\Qbar[{}^3S_1^{(8)}]$ pairs. Their contributions to prompt Psi and Upsilon production at the Tevatron bring the shapes of theoretical transverse momentum distributions into line with recent CDF measurements. We find that the best fit values for the linear combinations of $Q\Qbar[{}^1S_0^{(8)}]$ and $Q\Qbar[{}^3P_J^{(8)}]$ long distance matrix elements which can be extracted from the data are generally consistent with NRQCD scaling rules.

Decays rates for S- and P-wave bottomonium

The authors use the Bodwin-Braaten-Lepage factorization scheme to separate the long- and short-distance factors that contribute to the decay rates of {Upsilon}, {eta}{sub b} (S-wave) and {chi}{sub b},h{sub b} (P-wave). The long distance matrix elements are calculated on the lattice in the quenched approximation using a non-relativistic formulation of the b quark dynamics.

Topologische Indices alternierender polycyclischer aromatischer Kohlenwasserstoffe und ihre Korrelationen mit elektronischen Eigenschaften / Topological Indices of Alternant Polycyclic Aromatic Hydrocarbons and their Correlations with Electronic Properties

The half-sum of the distance matrix elements derived from the characteristic graphs, i.e. the Wiener number of these graphs is proposed as a new topological index for alternant polycyclic aromatic hydrocarbons. It is shown by regression analysis that correlations between topological indices and electronic properties of alternant aromatic systems do only exist for those indices and properties which depend to the same degree from the size of the systems and for which the corresponding relation applies to the topology.