Peng Guo, Adam P. Szczepaniak, Giuseppe Galata, Andrea Vassallo, Elena Santopinto
Using the non-relativisitc reduction of Coulomb gauge QCD we compute spectrum of the low mass hybrid mesons containing a heavy quark-antiquark pair. The gluon degrees of freedom are treated in the mean field approximation calibrated to the gluelump spectrum. We discuss the role of the non-abelian nature of the QCD Coulomb interaction in the ordering of the spin-parity levels.
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We calculate O(alpha_S^4 m) and O(alpha_S^4 m log(alpha_S)) corrections to the quarkonium 1S energy level analytically, which have been overlooked in recent studies. These are the contributions from one Coulomb-gluon exchange with the 1-loop vacuum polarization insertion. A part of the corrections was computed numerically some time ago; we correct its error.
We compute the third-order correction to the S-wave quarkonium wave functions |ψ_n(0)|^2 at the origin from non-Coulomb potentials in the effective non-relativistic Lagrangian. Together with previous results on the Coulomb correction and the ultrasoft correction computed in a companion paper, this completes the third-order calculation up to a few unknown matching coefficients. Numerical estimates of the new correction for bottomonium and toponium are given.
We review the recent theoretical progress in heavy quarkonium spectroscopy within the boundstate theory based on perturbative QCD. New microscopic pictures of the heavy quarkonium systems are obtained.
In the framework of a specific scheme of the QCD sum rules for $S$-wave levels of the heavy quarkonium, one derives an expression, relating the energetic density of quarkonium states and universal characteristics in the heavy quarkonium physics, such as the difference between the masses of a heavy quark $Q$ and meson $(Q\bar q)$ and the number of heavy quarkonium levels below the threshold of $(Q\bar Q) \to (Q\bar q) + (\bar Q q)$ decay.
In the framework of a specific scheme of the QCD sum rules for $S$-wave levels of the heavy quarkonium, one derives expressions, relating the leptonic constants, the energetic density of quarkonium states and universal characteristics in the heavy quarkonium physics, such as the difference between the masses of heavy quark $Q$ and meson $(Q\bar q)$ and the number of heavy quarkonium levels below the threshold of $(Q\bar Q) \to (Q\bar q) + (\bar Q q)$ decay.
In this talk, I briefly review several models of the heavy quarkonium production at collider energies, and discuss the status of QCD factorization for these production models.
QCD nonrelativistic effective field theories (NREFT) are the modern and most suitable frame to describe heavy quarkonium properties. Here I summarize few relevant concepts and some of the interesting physical applications (spectrum, decays, production) of NREFT.
QCD nonrelativistic effective field theories (NREFT) are the modern and most suitable frame to describe heavy quarkonium properties. In this talk I summarize few relevant concepts and some interesting physical applications of NREFT.
Non-relativistic bound state theories for QED and QCD have become fairly mature and amenable to a textbook-level understanding and computation. In this talk we give an introductory review of the following subjects related to the recent computation of the heavy quarkonium spectrum using perturbative QCD: (1) Technological developments in higher-order computation, (2) Physics predictions, (3) Challenge towards analytic evaluation of the 3-loop static QCD potential.
We review the developments of QCD multipole expansion and its applications to hadronic transitions and some radiative decays of heavy quarkonia. Theoretical predictions are compsred with updated experimental results.
Using a specific scheme of the QCD sum rules, one derives an universal formula for the mass differences for the $nS$-levels of heavy qiarkonium. This relation does not depend on the flavours of the heavy quarks, composing the quarkonium, and it is in a good agreement with the experimental mass values for the $ψ$- and $Υ$-families.
We determine the hard-loop resummed propagator in an anisotropic QCD plasma in general covariant gauges and define a potential between heavy quarks from the Fourier transform of its static limit. We find that the potential exhibits angular dependence and that binding of very small quarkonium states is stronger than in an isotropic plasma.
The analytic continuation of the operator product expansion of the scattering amplitude allows to compute the heavy-quarkonium hadron total cross section. The energy dependence of the Upsilon and Upsilon' cross sections with a proton is discussed.
Using a specific scheme of the QCD sum rules for heavy quarkonium in the leading approximation over the inverse heavy quark mass, one gets the estimate of the difference between the masses of the heavy meson and heavy quark $\bar Λ= 0.59\pm 0.02$ GeV.
Quarkonium production at low transverse momentum in hadron collisions can be used to extract Transverse-Momentum-Dependent(TMD) gluon distribution functions, if TMD factorization holds there. We show that TMD factorization for the case of P-wave quarkonium with $J^{PC}=0^{++}, 2^{++}$ holds at one-loop level, but is violated beyond one-loop level. TMD factorization for other P-wave quarkonium is also violated already at one-loop.
In this talk I review the calculation of the third order corrections to the heavy quarkonium spectrum in the nonrelativistic effective theory framework and its application to the phenomenology of top quark threshold production.
We calculate the heavy quarkonium production in double pomeron exchange processes in perturbative QCD by using two-gluon exchange model. For the $P$-wave $χ_J$ productions, we find $χ_1$ and $χ_2$ production amplitudes which vanish in the forward scattering limit. We also calculate direct $J/ψ(Υ)+γ$ production in the same approach, and these direct contributions are much smaller than the feeddown contributions from the $P$-wave states.
The hybrid quarkonium states are studied using the Born-Oppenheimer expansion. The first step in this expansion is the determination of the energy levels of the gluons in the presence of a static quark-antiquark pair as a function of the quark-antiquark separation. The spectrum of such gluonic excitations is determined from first principles using lattice QCD.
By using conformable fractional of the Nikiforov-Uvarov (CF-NU) method, the radial Schrodinger equation is analytically solved. The energy eigenvalues and corresponding functions are obtained, in which the dependent temperature potential is employed. The effect of fraction-order parameter is studied on heavy-quarkonium masses such as charmonium and bottomonium in a hot QCD medium in the 3D and the higher dimensional space. A comparison is studied with recent works. We conclude that the fractional-order plays an important role in a hot QCD medium in the 3D and higher-dimensional space.
We compute the total cross section of a heavy quarkonium on a hadron target in leading twist QCD, including target mass corrections. Our method relies on the analytical continuation of the operator product expansion of the scattering amplitude, obtained long ago by Bhanot and Peskin. The cross section has a simple partonic form, which allows us to investigate the phenomenology of J/psi and Upsilon dissociation by both pions and protons.
We study the masses and the leptonic decay widths of heavy quarkonium in the dual Ginzburg-Landau (DGL) theory of QCD, in which the abelian monopole condensation plays an essential role for color confinement. The effect of color screening due to the light quark pair creation is introduced by the infrared momentum cutoff in the gluon propagator. We find that the color screening effect is important to reproduce the properties of the heavy quarkonium, in particular the leptonic decay width. We also discuss the underlying systematics of the heavy quark spectroscopy in the DGL theory.
The process of exclusive electroproduction of vector quarkonium (EEQ), $e p\to epV$, is per se an interesting topic in studies of quarkonium production mechanism, QCD description of diffractive interaction and nucleon structure. We investigate this process in the framework of nonrelativistic QCD and QCD collinear factorization at the next-to-leading order QCD accuracy. The perturbative convergence behavior is discussed in a large range of photon virtuality $Q^2$. The $J/ψ$ large-$Q^2$ electroproduction data at HERA can be well explained, and the $Υ$ differential production rate is predicted. T…
In this talk, we present the QCD factorization formula for heavy quarkonium production at large $p_T$ with factorized leading-power and next-to-leading power contributions in the $1/p_T$ expansion. We show that the leading order analytical calculations in this QCD factorization approach can reproduce effectively the full next-to-leading order numerical results derived using non-relativistic QCD (NRQCD) factorization formalism. We demonstrate that the next-to-leading power contributions are crucial to the description of the channels that are the most relevant for the rate as well as polarizatio…
We use Ward identities of broken scale invariance to infer the amount of scalar glueball--$\bar{q}q$ meson mixing from the ratio of quark and gluon condensates in the QCD vacuum. Assuming dominance by a single scalar state, as suggested by a phase-shift analysis, we find a mixing angle $γ\sim 36^{\circ}$, corresponding to near-maximal mixing of the glueball and $\bar{s}s$ components.
There are many outstanding discrepancies comparing the predictions of perturbative QCD and measurements of the rate of production and decay of heavy quark systems. The problems include the $J/ψ\to ρπ$ puzzle, leading charmed particle effects, the anomalous behavior of the heavy quark sea components of structure functions, anomalous nuclear target effects, and the large rates observed for single and double quarkonium production at large $x_F$ and large $p_T$. I argue that these anomalies may be associated with nonperturbative effects in the higher Fock structure of hadron wavefunctions.
Encouraged by recent developments in AdS/QCD models for light quark system, we study heavy quarkonium in the framework of the AdS/QCD models. We calculate the masses of $c\bar c$ vector meson states using the AdS/QCD models at zero and at finite temperature. Among the models adopted in this work, we find that the soft wall model describes the low-lying heavy quark meson states at zero temperature relatively well. At finite temperature, we observe that once the bound state is above $T_c$, its mass will increase with temperature until it dissociates at a temperature of around $494 {\rm MeV}$. It…
QCD one-loop correction to Higgs boson decay into quarkonium-pair
本研究在NRQCD框架下分析希格斯玻色子衰变为夸克偶素对的稀有过程，考察主要机制与干涉，并首次纳入衰变宽度的QCD单圈修正。
The Abelian decomposition of QCD which decomposes the gluons to the color neutral binding gluons (the neurons) and the colored valence gluons (the chromons) gauge independently naturally generalizes the quark model to the quark and chromon model which could play the central role in hadron spectroscopy. We discuss the color reflection symmetry, the fundamental symmetry of the quark and chromon model, and explain how it describes the glueballs and the glueball-quarkonium mixing in QCD. We present the numerical analysis of glueball-quarkonium mixing in $0^{++}$, $2^{++}$, and $0^{-+}$ sectors bel…
On order $Λ_{\rm QCD}^2/m$ renormalons in quarkonium system
本文研究夸克偶素系统中 $\Lambda_{\rm QCD}^2/m$ 阶重整子的存在与抵消，通过分析微扰级数的稳定性和收敛性及与低阶重整子对比，给出其存在和抵消的迹象。
We use QCD Laplace sum-rules to explore mixing between conventional mesons and hybrids in the heavy quarkonium vector $J^{PC}\!=\!1^{--}$ channel. Our cross-correlator includes perturbation theory and contributions proportional to the four-dimensional and six-dimensional gluon condensates. We input experimentally determined charmonium and bottomonium hadron masses into both single and multi-resonance models in order to test them for conventional meson and hybrid components. In the charmonium sector we find evidence for meson-hybrid mixing in the $J/ψ$ and a $\approx4.3$ GeV resonance. In the b…
Applying asymptotic expansions at threshold, we compute the two-loop QCD correction to the short-distance coefficient that governs the leptonic decay $ψ\to l^+ l^-$ of a S-wave quarkonium state and discuss its impact on the relation between the quarkonium non-relativistic wave function at the origin and the quarkonium decay constant in full QCD.
The interaction of quarkonium with nuclei is studied in the $m_Q\rightarrow \infty$ limit of QCD, where the binding energy is found to be exactly computable. The dominant contribution to the interaction is from two-gluon operators. The forward matrix elements of these two-gluon operators can be determined from the QCD scale anomaly, and from deep inelastic scattering. We apply our results to the $Υ$ and $J/ψ$, treating the $\qqbar$ interaction as purely Coulombic. We find the $Υ$ binds in nuclear matter with a binding energy of a few $\mev$, while for the $J/ψ$ binding is of order 10 $\mev$. F…
The next to leading order (NLO) quarkonium-hadron cross section is calculated in perturbative QCD. The corresponding leading order (LO) result was performed by Peskin more than 20 years ago using the operator product expansion (OPE). In this work, the calculation is performed using the Bethe-Salpeter amplitude and the factorization formula. The soft divergence appearing in the intermediate stages of the calculations are shown to vanish after adding all possible crossed terms, while the collinear divergences are eliminated by mass factorization. Applying the result to the Upsilon system, one fi…
Hadronic annihilation rate of $1^{+-}$ heavy quarkonium is given to next-to-leading order in $α_s$ and leading order in $v^2$ using a recently developed factorization formalism which is based on NRQCD. The result includes both the annihilation of P-wave color-singlet $Q\bar{Q}$ component, and the annihilation of S-wave color-octet $Q\bar{Q}$ component of the quarkonium. The notorious infrared divergences due to soft gluons, i.e., the Logarithms associated with the binding energy, encountered in previous perturbative calculations of $1^{+-}$ quarkonium decays are found to be explicitly cancelle…
Thermodynamics of Heavy Quarkonium in a Bayesian Holographic QCD model
本文基于贝叶斯全息QCD模型研究重夸克偶素热力学，发现温度与化学势升高会减小夸克间距、增大熵和熵力并提高结合能与内能，从而促进其解离为自由夸克。
The perturbative QCD approach to quarkonium decay into a photon and hadrons is reconsidered. It is shown that a consistent treatment within perturbative QCD calls for the introduction of a fragmentation contribution which has been neglected so far. The ensuing phenomenological implications are discussed, and, in particular, the possibility of measuring the gluon fragmentation function of the photon is addressed. *To appear in the proceedings of the workshop QCD94, Montpellier, July '94.
Color-octet nonrelativistic QCD matrix elements for heavy quarkonium decays in the refined Gribov-Zwanziger theory
该研究基于精制 Gribov-Zwanziger 理论计算 QCD 场强两点关联函数的矩，提取色八重态非相对论 QCD 矩阵元，并改进粲、底夸克偶素衰变率的有效场论描述。
We complete the leading-log renormalization group scaling of the NRQCD Lagrangian at $O(1/m^2)$. The next-to-next-to-leading-log renormalization group scaling of the potential NRQCD Lagrangian (as far as the singlet is concerned) is also obtained in the situation $mα_s \gg Λ_{QCD}$. As a by-product, we obtain the heavy quarkonium spectrum with the same accuracy in the situation $mα_s^2 \simg Λ_{QCD}$. When $Λ_{QCD} \ll mα_s^2$, this is equivalent to obtain the whole set of $O(mα_s^{(n+4)} \ln^n α_s)$ terms in the heavy quarkonium spectrum. The implications of our results in the non-perturbativ…
Recent advances in lattice and continuum QCD have given us new insights into quarkonium physics. These set of lectures are intend for the uninitiated. We first give a physical picture of quarkonium and describe the hybrids states established in lattice QCD. Then we give an unorthodox presentation of Non-Relativistic QCD (NRQCD) including a novel method for the application of spin-symmetries. Finally we describe the prototypical application of NRQCD: cancellation of infrared divergences in decays of P-wave quarkonia.
Hard diffractive photo- and electroproduction of heavy vector mesons ($J/ψ$ and $Υ$) is evaluated within the leading $α_s\ln{Q^2 \overΛ_{QCD}^2}$ approximation of QCD. In difference from our earlier work on that subject, also the production of transversely polarized vector mesons is calculated. Special emphasis is placed on the role of the vector meson's $q\bar q$ light-cone wave function. In that context, conventional non-relativistic quarkonium models and a light-front QCD bound state calculation are critically examined and confronted with QCD expectations. Our numerical analysis finds a sig…
Supersymmetric standard model has a parity violation in QCD through chiral quark-squark-gluino interactions with non-degenerate masses between left-handed and right-handed squarks. Since experiments have not show any parity violations in QCD yet, a bound for the mass degeneracy between left-handed and right-handed squarks should exist. In this paper we try to obtain this bound for each squark. At first, we investigate a non-degeneracy bound between $m_{\tilde{c}_L}$ and $m_{\tilde{c}_R}$ from experimental data of charmonium decay. Next, we estimate the non-degeneracy bounds for $\tilde{u}$ and…
We consider a different power counting in potential NRQCD by incorporating the static potential exactly in the leading order Hamiltonian. We compute the leading relativistic corrections to the inclusive electromagnetic decay ratios in this new scheme. The effect of this new power counting is found to be large (even for top). We produce an updated value for the $η_b$ decay to two photons. This scheme also brings consistency between the weak coupling computation and the experimental value of the charmonium decay ratio.
We examine angular distributions of leptons arising from the decay of J/psi in inclusive hadroproduction. Taking into account feed-down contributions from chi_{1,2}, a flat distribution emerges without fine tuning parameters. Changes in the ratio of direct to total J/psi cross sections would change this distribution significantly. Such angular distributions are, therefore, confirmatory tests of the J/psi suppression signal for the production of a quark-gluon plasma. Related effects are predicted for the Upsilon.
We calculate the fragmentation function for charm quark into J/psi at the QCD next-to-leading-order (NLO) and find that the produced J/psi is of larger momentum fraction than it is at the leading-order. Based on the fragmentation function and partonic processes calculated at the NLO, the transverse momentum distribution on J/psi hadroproduction associated with a charm c (or \bar{c}) jet are predicted. We find that the distribution is enhanced by a factor of 2.0--3.3 at the NLO as p_t increased from 10 GeV to 100 GeV and it is measurable at the LHC with charm tagger. The measurement at the LHC …
The bound--state problem for the pion as a quarkonium with the funnel (Coulomb--plus--linear) interaction is solved in a framework that combines the bilocal approach to mesons with the covariant generalization of the instantaneous--potential model. The potential interaction leads to dynamical breaking of chiral symmetry. However, the Coulomb potential leads to ultraviolet divergences that must be subtracted. A careful choice of the renormalization prescription is needed in order to get the correct chiral limit. The mass, the lepton decay constant of the pion, as well as the pion decay width in…
QCD Laplace sum rules are used to calculate heavy quarkonium (charmonium and bottomonium) hybrid masses in several distinct $J^{PC}$ channels. Previous studies of heavy quarkonium hybrids did not include the effects of dimension-six condensates, leading to unstable sum rules and unreliable mass predictions in some channels. We have updated these sum rules to include dimension-six condensates, providing new mass predictions for the spectra of heavy quarkonium hybrids. We confirm the finding of other approaches that the negative-parity $J^{PC}=(0,1,2)^{-+},\,1^{--}$ states form the lightest hybr…
We study the energy spectrum of bottomonium in perturbative QCD, taking alpha_s(Mz)=0.1181 +/- 0.0020 as input and fixing m_b^{MSbar}(m_b^{MSbar}) on the Upsilon(1S) mass. Contrary to wide beliefs, perturbative QCD reproduces reasonably well the gross structure of the spectrum as long as the coupling constant remains smaller than one. We perform a detailed analysis and discuss the size of non-perturbative effects. A new qualitative picture on the structure of the bottomonium spectrum is provided. The lowest-lying (c,cbar) and (b,cbar) states are also examined.
Study of the polarized heavy quarkonium production in recently proposed QCD factorization formalism requires knowledge of a large number of input fragmentation functions (FFs) from a single parton or a heavy quark-antiquark pair to a polarized heavy quarkonium. In this paper, we calculate these FFs at the input scale in terms of nonrelativistic QCD (NRQCD) factorization. We derive all relevant polarized NRQCD long-distance matrix elements based symmetries and propose a self-consistent scheme to define them in arbitrary $d$ dimensions. We then calculate polarized input FFs contributed from all …
We calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to $γ+γ\to η_c+c+\bar{c}$, $γ+γ\to η_b+b+\bar{b}$ and $γ+γ\to B_c+b+\bar{c}$ processes in the framework of non-relativistic QCD (NRQCD) factorization formalism. The cross sections at the SuperKEKB electron-positron collider, as well as the future collider like the Circular Electron Positron Collider (CEPC), are evaluated. Numerical results indicate that the NLO corrections are significant, and the uncertainties in theoretical predictions with NLO corrections are reduced as expected. Due to the high luminosity…
We review a number of results for the spectrum and inclusive decays of heavy quarkonium systems which can be derived from QCD under well controlled approximations. They essentially follow from the hierarchy of scales in these systems, which can be efficiently exploited using non-relativistic effective field theories. In particular, we discuss under which conditions non-relativistic potential models emerge as effective theories of QCD.
Contents: 1. Introduction 2. Operator Product Expansion for Quarkonium Interactions 3. Scale Anomaly, Chiral Symmetry and Low-Energy Theorems 4. Quarkonium Interactions in Matter 5. Conclusions and Outlook
Recently we have proved the NRQCD factorization in heavy quarkonium production at high energy colliders at all orders in coupling constant. In this paper we extend this to non-equilibrium QCD and prove the NRQCD factorization in heavy quarkonium production at all orders in coupling constant in non-equilibrium QCD. This proof is necessary to study heavy quarkonium production from quark gluon plasma at RHIC and LHC.
We report the current understanding of heavy quarkonium production at high transverse momentum ($p_T$) in hadronic collisions in terms of QCD factorization. In this presentation, we highlight the role of subleading power corrections to heavy quarkonium production, which are essential to describe the $p_T$ spectrum of quarkonium at a relatively lower $p_T$. We also introduce prescription to match QCD factorization to fixed-order NRQCD factorization calculations for quarkonium production at low $p_T$.
Heavy quarkonium production in the framework of the non-relativistic quantum chromodynamics and leading order of the parton Reggeization approach at the Tevatron and LHC is discussed. In this note, we compare our predictions for the bottomonium production at the LHC due to the color-singlet approximation of the non-relativistic quantum chromodynamics with CMS and LHCb data. It is found, that in the production of Upsilon(1S) states, the color-singlet mechanism is dominating, whereas to describe the data for the inclusive Upsilon(2S) and Upsilon(3S) production, the color- octet contributions sho…
Substantial anisotropies should occur in the hot expanding QCD plasma produced in relativistic heavy-ion collisions due to non-vanishing shear viscosity. We discuss the form of the real-time, hard thermal loop resummed propagator for static gluons in the presence of such anisotropies and the consequences for quarkonium binding. It has been predicted that the propagator develops an imaginary part due to Landau damping at high temperature. This generates a much larger width of quarkonium states than the Appelquist-Politzer vacuum estimate corresponding to decay into three gluons. We argue that t…
We use QCD Laplace sum-rules to study meson-hybrid mixing in vector ($1^{--}$) heavy quarkonium. We compute the QCD cross-correlator between a heavy meson current and a heavy hybrid current within the operator product expansion. In addition to leading-order perturbation theory, we include four- and six-dimensional gluon condensate contributions as well as a six-dimensional quark condensate contribution. We construct several single and multi-resonance models that take known hadron masses as inputs. We investigate which resonances couple to both currents and so exhibit meson-hybrid mixing. Compa…
We review recent developments in heavy-quarkonium phenomenology within the nonrelativistic QCD factorization approach. Main issues we consider in this work include the polarization of prompt J/psi at the Fermilab Tevatron and the large relativistic and QCD corrections to double-charmonium production at the B factories. We also consider inclusive charm production in bottomonia decays.
The research presented here uses QCD sum rules (QSR) to study exotic hadrons. There are several themes in this work. First is the use of QSR to predict the masses of exotic hadrons that may exist among the heavy quarkonium-like states. The second theme is the application of sophisticated loop integration methods in order to obtain more complete theoretical results. These in turn can be extended to higher orders in the perturbative expansion in order to predict the properties of exotic hadrons more accurately. The third theme involves developing a renormalization methodology for these higher or…
The heavy quark-antiquark potential is accessible in perturbative QCD and in lattice simulations. The perturbative short-distance part of the potential is contructed via a restricted Fourier transform, covering the momentum region where perturbative QCD is applicable. We show that for the leading order static term as well as for the mass dependent corrections, the perturbative part can be matched at intermediate distances with results from lattice QCD. From these matched potentials, quarkonium spectra with a single free parameter (the heavy quark mass) are derived and compared with empirical s…
Recent results on the QCD analysis of bound states of heavy $\bar{q}q$ quarks are reviewed, paying attention to what can be derived from the theory with a reasonable degree of rigour. We report a calculation of $\bar{b}c$ bound states; a very precise evaluation of $b, c$ quark masses from quarkonium spectrum; the NNLO evaluation of $Υ\to e^+e^-$; and a discussion of power corrections. For the $b$ quark {\sl pole} mass we get, including $O(m_c^2/m_b^2)$ and $O(α_s^5\log α_s)$ corrections, $m_b=5.020\pm0.058 GeV$; and for the $\bar{MS}$ mass the result, correct to $O(α_s^3)$, $O(m_c^2/m_b^2)$, $…
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