Hee Sok Chung, Jungil Lee, Chaehyun Yu
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.
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We review recent progress made in the theory of quarkonium production in hadronic collisions.
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.
We present a phenomenological study of the $x_F$ dependence of quarkonium production in high energy proton-nucleus collisions. The \xf~dependence of comover contributions is introduced to account for the observed quarkonium suppression at low $x_F$. Combining comover contributions, nuclear shadowing effect, energy loss mechanism and nuclear absorption together we reproduce the overall \xf~dependence of E772/E789 data.
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.
Broad meson phenomenology in vacuum is discussed in a single model containing scalar, pseudoscalar, vector and axial-vector states both in the non-strange and strange sectors. Emphasis is given to search for quark-antiquark (quarkonium) states in the scalar and axial-vector channels. In particular, the work examines the question whether the scalar quark-antiquark states are found in the energy region below or above 1 GeV in the physical spectrum. Contrarily to the naive expectation, the mentioned states are found in the region above 1 GeV. Additionally, the axial-vector isotriplet state $a_1(1…
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.
Some recent progress and a personal selection of open problems in heavy quarkonium physics (spectroscopy, decay and production) inspired by the activity of the Quarkonium Working Group are reviewed.
I briefly review how nonrelativistic effective field theories solve old puzzles and open problems in heavy quarkonium physics.
We report on a recent QCD based research on hybrid mesons containing $c\bar c$ or $b\bar b$ quarks. We present results for the spectrum, the decay widths to heavy quarkonium, and the role of mixing with the latter. We point out that mixing with heavy quarkonium provides a potentially large source of spin symmetry breaking. We identify candidates to hybrid mesons among the so called XYZ states in the charmonium and bottomonium spectrum.
The value of quarkonium wave function at the origin is an important quantity while studying many physical problems concerning a heavy quarkonium. This is because that it is widely used to evaluate the production and decay amplitudes of the heavy quarkonium within the effective filed theory framework, e.g., the non-relativistic QCD (NRQCD). In this paper, the value of the Schr${\rm \ddot{o}}$dinger radial wave function or its first nonvanishing derivative at zero quark-antiquark separation, i.e., $|(|c\bar{c})[n]\rangle$-, $|(|b\bar{c})[n]\rangle$-, and $|(b\bar{b})[n]\rangle$-quarkonium, have …
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.
We discuss the recent development of effective field theories for quarkonium at finite temperature.
A calculation of the melting temperatures of heavy quarkonium states with the holographic potential was introduced in a previous work. In this paper, we consider the holographic potential at sub-leading order, which permits finite coupling corrections to be taken into account. It is found that this correction lowers the dissociation temperatures of heavy quarkonium.
By employing the differential equations, we compute analytically the elliptic sectors of two-loop master integrals appearing in the NNLO QCD corrections to CP-even heavy quarkonium exclusive production and decays, which turns out to be the last and toughest part in the relevant calculation. The integrals are found can be expressed as Goncharov polylogarithms and iterative integrals over elliptic functions. The master integrals may be applied to some other NNLO QCD calculations about heavy quarkonium exclusive production, like $γ^*γ\rightarrow Q\bar{Q}$, $e^+e^-\rightarrow γ+ Q\bar{Q}$,~and~$H/…
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.
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.
I review some recent progress and open problems in the calculation of heavy-quarkonium inclusive decay widths into light particles in the framework of QCD non-relativistic effective field theories.
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.
FDCHQHP is a Fortran package to calculate the transverse momentum (p_t) distribution of yield and polarization for heavy quarkonium hadroproduction at next-to-leading-order (NLO) based on non-relativistic QCD(NRQCD) framework. It contains the complete color-singlet and color-octet intermediate states in present theoretical level, and is available to calculate different polarization parameters in different frames. As the LHC running now and in the future, it supplies a very useful tool to obtain theoretical prediction on the heavy quarkonium hadroproduction.
Recent developments in heavy quarknoium physics are reviewed in brief, including (i) nonrelativistic QCD(NRQCD), (ii) the importance of color-octet $(Q\bar{Q})$ components in the decay and the production of a physical heavy quarkonium state, (iii) limitation of the NRQCD factorization and (iv) the double humps in the $ππ$ spectrum in the decay $Υ(3S) \to Υ(1S) ππ$.
We compute the complete leading-log terms of the next-to-next-to-next-to-leading-order corrections to potential NRQCD. As a by-product we obtain the leading logs at $O(mα_s^5)$ in the heavy quarkonium spectrum. These leading logs, when $Λ_{QCD} \ll mα_s^2$, give the complete $O(mα_s^5 \ln α_s)$ corrections to the heavy quarkonium spectrum.
We report on recent theory progress in understanding the production of heavy quarkonium in heavy-ion collisions based on the in-medium heavy-quark potential extracted from lattice QCD simulations. On the one hand, the proper in-medium potential allows us to study the spectral properties of heavy quarkonium in thermal equilibrium, from which we estimate the $ψ^\prime$ to $J/ψ$ ratio in heavy-ion collisions. On the other hand, the potential provides a central ingredient in the description of the real-time evolution of heavy-quarkonium formulated in the open-quantum-systems framework.
An introduction to the recent developments in perturbative heavy quarkonium physics is given. Covered are the effective theories NRQCD, pNRQCD and vNRQCD, the threshold expansion, the role of renormalons, and applications to bottom and top quark physics.
Heavy quarkonium production in the framework of the nonrelativistic quantum chromodynamics and leading order of the parton Reggeization approach at the Tevatron and LHC Colliders is discussed. The new results, which are reviewed in this report, include the comparison with recent data on chi_{c1,c2} production from ATLAS Collaboration and special discussion of heavy quarkonium polarization issues in the considered framework.
In this paper, we calculate the mass spectra of heavy quarkonium by using matrix Numerov's method to make the predictions of F and G states for further experiments. The method gives a very reasonable result which is in a good agreement with other methods and with recently published theoretical data. From the yielded wave functions we calculate the root mean square radius r_ms and \b{eta} coefficients of heavy quarkonium
Heavy quarkonium decays and transitions are discussed in the framework of non-relativistic effective field theories. Emphasis is put on the matching procedure in the non-perturbative regime. Some exact results valid for the magnetic dipole couplings are discussed.
Based on the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD), we calculate the production cross section for the charmonium and the bottomonium produced by the hard photoproduction processes and fragmentation processes in relativistic heavy ion collisions. It is shown that the existing experimental data on heavy quarkonium production at the Large Hadron Collider (LHC) can be described in the framework of the NRQCD formalism, and the phenomenological values of matrix elements for color-singlet and color-octet components give the main contribution. The numerical results …
Production cross sections of heavy quarkonia are considered as useful tools to study various aspects of QCD. We have entered a new era of quarkonium production phenomenology, with the help of new measurements from the LHC giving access to more varieties of observables, and recent theoretical developments that provided us a better understanding of the short-distance process in which quarkonia are produced. With a more concrete understanding of perturbative corrections and a prolific collection of data, a satisfactory description of the quarkonium production mechanism might now be within reach. …
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 compute the c \bar{b} spectrum from a first principle Salpeter equation obtained in a preceding paper. For comparison we report also the heavy-light quarkonium spectrum and the hyperfine separations previously presented only in a graphical form. Notice that all results are parameter free.
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.
We explore polarized heavy quarkonium production using the color evaporation model at leading order. We present the polarized to total yield ratio as a function of center of mass energy and rapidity in $p+p$ collisions. At energies far above the $Q \overline Q$ production threshold, we find charmonium and bottomonium production to be longitudinally polarized ($J_z=0$). The quarkonium states are also longitudinally polarized at central rapidity, becoming transversely polarized ($J_z=\pm1$) at the most forward rapidities.
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 …
Using a specific scheme of the QCD sum rules, one derives the relation for leptonic constants of $nS$-wave heavy qiarkonia, so $f^2_{n_1}/f^2_{n_2}= n_2/n_1$, that does not depend on the quarkonium content, and it is in a good agreement with the experimental values of constants for the $ψ$- and $Υ$-families.
Two-loop $O(ε)$ term of $1/(mr^2)$ heavy quarkonium potential
本文应用两圈重夸克偶素哈密顿量计算了 $1/(mr^2)$ 势的两圈 $O(ε)$ 项，发现与先前计算在最大非阿贝尔色因子系数上有微小差异，并进行了仔细核查。
I review heavy quarkonium physics in view of recent experimental results. In particular, I discuss new results on spin singlet states, photon and hadronic transitions, D-states and discovery of yet unexplained narrow X(3872) state.
We study some general aspects of the formalism of potential NRQCD (pNRQCD), an effective field theory that deals with ultrasoft degrees of freedom in Heavy Quarkonium systems. Specific attention is paid to its effective Lagrangian that it is displayed at the present level of accuracy.
In this brief review, I summarize the current theoretical knowledge of heavy quarkonium inclusive decays, with emphasis on recent progress made in the framework of QCD effective field theories. In appendix, I list the imaginary parts of the matching coefficients of the dimension 6 and dimension 8 NRQCD four-fermion operators as presently known.
The nuclear suppression of heavy quarkonium production at low transverse momentum in pA collisions in high energy scatterings is investigated in the small-x factorization formalism. A universal suppression is found in the large Nc limit between the two formalisms to describe the heavy quarkonium production: the non-relativistic QCD (NRQCD) and the color-evaporation model (CEM). This provides an important probe to the saturation momentum at small-x in big nucleus. We also comment on the phenomenological applications of our results.
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.
In this article, we study the radiative transitions among the vector and scalar heavy quarkonium states with the covariant light-front quark model. In calculations, we observe that the radiative decay widths are sensitive to the constituent quark masses and the shape parameters of the wave-functions, and reproduce the experimental data with suitable parameters.
By employing the method of differential equations, we compute the various types of two-loop master integrals involved in CP-even heavy quarkonium exclusive production and decays. All the integrals presented in this paper can be casted into canonical forms and expressed in terms of Goncharov polylogarithms and Harmonic polylogarithms. These master integrals are frequently used in the calculation of NNLO corrections of the heavy quarkonium production processes, as $γ^*γ\rightarrow Q\bar{Q}$, $e^+e^-\rightarrow γ+ Q\bar{Q}$, and $H/Z^0\rightarrow γ+ Q\bar{Q}$, and decay processes. They are also a…
We compute corrections of relative order v^4 to the rates for the decays of ^1S_0 heavy quarkonium into two photons and into light hadrons and for the decays of ^3S_1 heavy quarkonium into a lepton pair and into light hadrons. In particular, we compute the coefficients of the decay operators that have the same quantum numbers as the heavy quarkonium. We also confirm previous calculations of the order-v^2 corrections to these rates. We find that the v expansion converges well for the decays of ^1S_0 heavy quarkonium and for the decay of ^3S_1 heavy quarkonium into a lepton pair. Large higher-or…
Soft-gluon resummation within the framework of heavy quarkonium hadroproduction is considered. A few selected cases are studied in detail. A sizeable increase of the cross sections with respect to the next-to-leading order predictions with central factorization/renormalization scale choice can generally be observed. Improvements in the dependence of the cross sections on the two scales, especially when they are kept equal, are also found.
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.
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.
In this paper we solved Schrödinger equation with Song-Lin potential by using Asymptotic Iteration Method (AIM). We obtained spin-averaged energy levels of charmonium and bottomonium via AIM. Obtained results agree well with available experimental data and other theoretical studies.
We study radiative decays of heavy $Q{\bar Q}$ states, both for $Q=c$ and $Q=b$, using an effective Lagrangian approach which exploits spin symmetry for such states. We use existing data on radiative quarkonium transitions to predict some unmeasured decay rates. We also discuss how these modes can be useful to understand the structure of X(3872).
Resummation of threshold double logarithms in hadroproduction of heavy quarkonium
针对重夸克偶素遍举产生中固定阶微扰理论因大辐射修正导致大横动量截面可能为负的失效问题，通过重整化阈值双对数解决该问题，证实其对描述大横动量下$J/ψ$快产生速率的必要性。
Quarkonium suppression in heavy ion collisions is a potential signature of the formation of the quark-gluon plasma. After a very brief review of the J/psi result at CERN, we restrict our discussion to the effects of the high-energy multiple scattering of the quark pair in the colliding nuclei.
We briefly summarize some results obtained by potential NRQCD in the non perturbative regime: 1) a systematic procedure to obtain the heavy quarkonium potential in the 1/m expansion (with explicit expressions up to O(1/m^2) in terms of Wilson loops), and 2) a description of the heavy quarkonium inclusive decays to light particles, and of the NRQCD matrix elements (also the octet ones), in terms of the wave-function at the origen and some gluonic field-strength correlators.
We formulate a QCD-based effective theory approach to heavy quarkonia-like systems as $\bar{c} c$ and $\bar{b} b$ resonances and $B_c$ states. We apply the method to inclusive decays, working out a few examples in detail.
We present a recent calculation of $J/ψ$ and $Υ$ production in unpolarized $pp$ collision and show that this can be used to probe the unpolarized gluon as well as the linearly polarized gluon transverse momentum dependent parton distributions (TMDs). We use the color evaporation model for the heavy quarkonium production and use a generalized factorized form of the cross section. We compare the results with experimental data.
We propose a systematic, model-independent treatment of electric dipole transitions of heavy quarkonium. Within an effective field theory, concretely potential non-relativistic QCD, the relativistic corrections of relative order $v^2$ to the decay rate are derived. An existing formalism developed for M1 decays will be extended for our purpose. We scrutinize and complement former results from potential model calculations.
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.
In this paper, the quark distribution amplitudes of 1S and 2S heavy quarkonium states are studied in terms of Gaussian-type wave functions. The transverse momenta $p_\perp$ integrals of the formulae for the decay constant are performed analytically. Then the quark distribution amplitudes are obtained. In addition, the $ξ$-moments are also calculated. After fixing the relevant parameters appearing in the quark distribution amplitude, the curves of the quark distribution amplitude for 1S and 2S heavy quarkonium states are plotted. Finally, the numerical results of this approach are compared with…
The dominant production mechanism for heavy quark-antiquark bound states in very high energy processes is fragmentation, the splitting of a high energy parton into a quarkonium state and other partons. We show that the fragmentation functions $D(z,μ)$ describing these processes can be calculated using perturbative QCD. We calculate the fragmentation functions for a gluon to split into S-wave quarkonium states to leading order in the QCD coupling constant. The leading logarithms of $μ/m_Q$, where $μ$ is the factorization scale and $m_Q$ is the heavy quark mass, are summed up using Altarelli-Par…
We calculate the O(alpha_s^3 ln(alpha_s)) contributions to the heavy-quarkonium production and annihilation rates. Our result sheds new light on the structure of the high-order perturbative corrections and opens a new perspective for a high-precision theoretical analysis. We also determine the three-loop anomalous dimensions of the nonrelativistic vector and pseudoscalar currents.
In the framework of nonrelativistic QCD, we consider a new class of radiative corrections, which are generated at next-to-next-to-next-to-leading order through the chromoelectric dipole interaction of heavy quarkonium with ultrasoft virtual gluons. We provide analytical formulae from which the resulting shifts in the quarkonium energy levels and the wave functions at the origin may be calculated. We discuss the phenomenological implications for the top-antitop and Upsilon systems and point out some limitations of describing charmonium using a Coulomb potential.
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