We evaluate the fermionic two-loop QCD corrections to the heavy-quark pair production process in the quark-antiquark channel. We obtain analytic results which are valid for any value of the Mandelstam invariants s and t, and of the heavy quark mass m. Our findings confirm previous results for the analytic evaluation in the small-mass limit and numerical results for the exact amplitude. We furthermore provide the expansion of the two-loop amplitude at the production threshold s ~ 4m^2.
We describe the analytic calculation of the fermionic two-loop QCD corrections to the heavy-quark pair production process in the quark-antiquark channel.
We present the NNLO corrections to top pair production in the quark-antiquark channel proportional to the number of light quark flavors $N_l$. While the double real corrections were derived previously, here we compute the real-virtual and virtual-virtual contributions in this partonic channel. Using the antenna subtraction formalism, we show that the subtraction terms correctly approximate the real-virtual contributions in all their infrared limits. Combined with the integrated forms of the double real and real-virtual subtraction terms, we show analytically that the explicit infrared poles ca…
In this review I cover recent developments concerning the construction of non-relativistic effective theories for perturbative heavy quark-antiquark systems and heavy quark mass definitions. I then discuss next-to-next-to-leading order results on quarkonium masses and decay, top quark pair production near threshold and QCD sum rules for $Υ$ mesons.
Recent developments for an effective theory for non-relativistic perturbative quark-antiquark systems are reviewed and some applications are discussed.
We model the spectral effect of open flavor meson-meson thresholds in heavy quarkonia. The proposed energy dependent quark-antiquark static potential tries to incorporate in a quark model scheme the results from unquenched lattice calculations. A good qualitative and a reasonable quantitative description of charmonium and bottomonium, including the "new charmonium-like" states, is obtained.
In the high-temperature quark-gluon plasma and its subsequent hadronic matter created in a high-energy nucleus-nucleus collision, the quark-antiquark potential depends on the temperature. The temperature-dependent potential is expected to be derived from the free energy obtained in lattice gauge theory calculations. This requires one to study the relation between the quark-antiquark potential and the quark-antiquark free energy. When the system's temperature is above the critical temperature, the potential of a heavy quark and a heavy antiquark almost equals the free energy, but the potential …
We explore the consequences of heavy flavour, heavy quark spin and heavy antiquark-diquark symmetries for hadronic molecules within an effective field theory framework.. Owing to heavy antiquark-diquark symmetry, the doubly heavy baryons have approximately the same light-quark structure as the heavy antimesons. As a consequence, the existence of a heavy meson-antimeson molecule implies the possibility of a partner composed of a heavy meson and a doubly-heavy baryon. In this regard, the D\bar D* molecular nature of the X(3872) will hint at the existence of several baryonic partners with isospin…
The heavy quark-antiquark potential in perturbative QCD is subject to ambiguities. We show how to derive a well-defined and stable short-distance potential that can be matched to results from lattice QCD simulations at intermediate distances. The static potential as well as the order 1/m potential are discussed.
Screening effects from sea pairs on the quark-antiquark static potential are analyzed phenomenologically from the light-quark to the heavy-quark meson spectra. From the high excited light-quark meson spectrum a universal form for the screened static potential is proposed. This potential is then succesfully applied to heavy quarkonia. Our results suggest the assignment of X(4260) to the 4s state of charmonium and the possible existence of a 5s bottomonium resonance around 10748 MeV.
An updated heavy quark-antiquark potential is constructed by matching the short-distance perturbative part to long-distance lattice QCD results at an intermediate r scale. The static potential and the order 1/m potential are both analyzed in this way. Effects if order 1/m in charmonium and bottomonium spectra are discussed in comparison. Charm and bottom quark masses are deduced from the spectra and related to the quark masses of other schemes.
The splittings between positive parity pentaquarks containing a single heavy (c,b) antiquark and four light (u,d) quarks are investigated in models having spin-dependent interactions generated by either effective Goldstone boson exchange or effective color magnetic exchange. Model-independent features of these splittings are emphasized. Overlaps to the ``fall-apart'' decay configurations ND, ND* or NB, NB*, relevant to decay couplings for the various 2-body pentaquark decays, are also computed.
We have completed the ${\cal O}(α_s)$ QCD corrections to exclusive heavy quark-antiquark distributions in deep inelastic electroproduction and present here the differential distributions in the masses of charm-anticharm and bottom-antibottom pairs at the electron-proton collider HERA.
The single transverse spin asymmetries in heavy quark and anti-quark production from the quark-antiquark annihilation channel contribution is studied by taking into account the initial and final state interactions effects. Because of the different color charges, the final state interaction effects lead to about a factor of 3 difference in the spin asymmetry for heavy quark over that for the anti-quark in the valence region of low energy pp collisions. The experimental study of this model-independent prediction shall provide a crucial test for the underlying mechanism for the single spin asymme…
We compute the soft anomalous dimension (SAD) matrices for production of massive quarks $Q$ and $\bar{Q}$ in association with a gluon jet, from massless quarks $q$ and antiquarks $\bar{q}$: $q\bar{q}\rightarrow Q\bar{Q}g$, and in the gluon scattering $gg\rightarrow Q\bar{Q}g$. To analyze the behaviour of the eigenvalues of SAD matrices we perform numerical studies of their eigensystems at two special kinematical configurations.
A set of general relations between the spin-independent and spin-dependent potentials of heavy quark and anti-quark interactions are derived from reparameterization invariance in the Heavy Quark Effective Theory. It covers the Gromes relation and includes some new interesting relations which are useful in understanding the spin-independent and spin-dependent relativistic corrections to the leading order nonrelativistic potential.
A general approach to accounting for retardation effects in the long-range (confining) part of the quark-antiquark potential is presented. The charmonium and bottomonium mass spectra are calculated with the systematic account of relativistic and retardation effects and the one-loop radiative corrections. A good fit to available experimental data on the mass spectra is obtained.
We report some approximate analytic form of meson wave function constructed upon solving Schrodinger equation with linear plus Coulomb type Cornell potential. With this wave function, we study Isgur-Wise function and its derivatives for heavy-light mesons in the infinite heavy quark mass limit. We also explore the elastic form factors, charge radii and decay constants of pseudoscalar mesons in this QCD inspired quark model approach.
With the current state of similarity renormalisation group approach to light-front QCD, it is possible to address with a degree of generality the issue of light-cone zero modes. We find, contrary to earlier results in a less general framework, that infrared divergences associated with the zero modes do not cancel out in a color singlet heavy quark-antiquark states, except for the lowest order in the nonrelativistic expansion.
We evaluate the planar two-loop QCD diagrams contributing to the leading color coefficient of the heavy-quark pair production cross section, in the quark-antiquark annihilation channel. We obtain the leading color coefficient in an analytic form, in terms of one- and two-dimensional harmonic polylogarithms of maximal weight 4. The result is valid for arbitrary values of the Mandelstam invariants s and t, and of the heavy-quark mass m. Our findings agree with previous analytic results in the small-mass limit and numerical results for the exact amplitude.
We calculate the leading mass-suppressed two-loop contribution, proportional to alpha_s^3/(m_q r^2), to the potential of a heavy quark-antiquark system. This contribution originates in the nonabelian nature of quantum chromodynamics (QCD) and has no analogue in quantum electrodynamics (QED). For this purpose, we elaborate a technique based on the implementation of the threshold expansion within the effective theory of nonrelativistic QCD (NRQCD). We discuss phenomenological implications of our result for heavy-quarkonium physics. We also confirm a previous result for the two-loop O(alpha_s^2) …
A new formula for the heavy quark-antiquark spin dependent potential is given by using the techniques developed in the heavy quark effective theory. The leading logarithmic quark mass terms emerging from the loop contributions are explicitly extracted and summed up. There is no renormalization scale ambiguity in this new formula. The spin-dependent potential in the new formula is expressed in terms of three independent color-electric and color-magnetic field correlation functions, and it includes both the Eichten-Feinberg's formula and the one-loop QCD result as special cases.
Relativistic properties of qqbar potentail, mass spectra of orbitally and radially excited B and D mesons as well as semileptonic decays of B mesons to orbitally excited D mesons are discussed in the framework of the relativistic quark model based on the quasipotential approach.
We investigate the symmetry property and the stability of the heptaquark containing two identical heavy antiquarks using color-spin interaction. We construct the wave function of the heptaquark from the Pauli exclusion principle in the SU(3) breaking case. The stability of the heptaquark against the strong decay into one baryon and two mesons is discussed in a simple chromomagnetic model. We find that $q^2 s^3 \bar{s}^2$ with $I=0,S=\frac{5}{2}$ is the most stable heptaquark configuration that could be probed by reconstructing the $Λ+ϕ+ϕ$ invariant mass.
It is demonstrated how perturbative O(alpha_s^2) relativistic corrections to the non-relativistic stable heavy quark-antiquark production cross section in e^+e^- annihilation based on a Coulombic QCD potential can be systematically calculated using the concept of effective field theories. The O(alpha_s^2) corrections from the relativistic energy-momentum relation, the relativistic phase space corrections and the O(alpha_s^2) corrections involving the group theoretical factors C_F^2 and C_F T are determined explicitly. For the case of $t\bar t$ production the sum of these corrections amounts to…
The charmonium and bottomonium mass spectra are calculated with the systematic account of all relativistic corrections of order v^2/c^2 and the one-loop radiative corrections. Special attention is paid to the contribution of the retardation effects to the spin-independent part of the quark-antiquark potential, and a general approach to accounting for retardation effects in the long-range (confining) part of the potential is presented. A good fit to available experimental data on the mass spectra is obtained.
The fragmentation function of vector particle into possible bound S-wave states with a heavy antiquark is calculated in the leading order of perturbative QCD for the high energy processes at large transverse momenta with the different behaviour of anomalous chromomagnetic moment. One-loop equations are derived for the evolution of fragmentation function moments, which is caused by the emission of hard gluons by the vector particle. The integrated probabilities of fragmentation are given. The distribution of bound state over the transverse momentum with respect to the axis of fragmentation is c…
We consider the ratio of the cross section of production of heavy bottom-antibottom pairs ($σ_{b\bar b}$) to the cross section of production of top-antitop pairs ($σ_{t\bar t}$) at LHC. We show that in this ratio a major fraction of virtual contributions (including QCD components) disappears, leaving a residual dominant electroweak Yukawa effect that might be strongly enhanced in the presence of supersymmetry. A quantitative numerical analysis of the size of the effect is also performed under the assumption of a relatively light supersymmetric scenario.
We calculate the next-to-next-to-leading order ${\cal O}(α_s^4)$ one-loop squared corrections to the production of heavy quark pairs in quark-antiquark annihilations. These are part of the next-to-next-to-leading order ${\cal O}(α_s^4)$ radiative QCD corrections to this process. Our results, with the full mass dependence retained, are presented in a closed and very compact form, in the dimensional regularization scheme. We have found very intriguing factorization properties for the finite part of the amplitudes.
We discuss and compare different approaches to include gluon transverse momenta for heavy quark-antiquark pair production. The correlations in azimuthal angle and in heavy quark, heavy antiquark transverse momenta are studied in detail. The results are illustrated with the help of different unintegrated gluon distribution functons (UGDF) from the literature. We compare results obtained with on-shell and off-shell matrix elements and kinematics and quantify where these effects are negligible and where they are essential. We concentrate on the region of asymmetric transverse momenta of charm qua…
The effective quark Lagrangian is written for a light quark in the field of a static antiquark, explicitly containing field correlators as coefficient functions of products of quark operators. At large N_c the closed system of equations for the gauge-invariant quark Green's function in the field of static source is examined analytically. The formation of the string connecting the light quark to the static source is observed numerically. The scalar Lorentz nature of the resulting confinement is shown to hold for the considered case, implying chiral symmetry breaking. The resulting spectrum with…
This paper focuses on tetraquarks containing one heavy quark and one heavy antiquark in the formal limit where the heavy quark masses go to infinity. It extends the theoretical framework developed for tetraquark containing two heavy quarks based on semi-classical analysis and the Born-Oppenheimer approximation. It is shown that for sufficiently small light quark masses, parametrically narrow $q\bar{q}'Q\bar{Q}$ tetraquarks must exist in the formal limit of arbitrarily large heavy quark masses. The analysis is model-independent; it requires no assumptions about the structure of the state or the…
We calculate the spectra of charmonium and bottomium in an approximation scheme which treats hard gluons perturbatively while soft gluons are expanded in a set of localized wave functions. Quark-antiquark and quark-antiquark-gluon sectors are included. Reasonable agreement with 2 parameters only is found but the spectra are too coulombic. Despite large coupling constant the admixture of the quark-antiquark-gluon sector is found to be remarkably small.
Starting from the QCD Lagrangian and taking into account both perturbative and nonperturbative effects, we use the method of vacuum correlators to derive the Dirac equation (rigorously for the Coulomb interaction and heuristically for the confining potential) for a system consisting of a light quark and heavy antiquark. As a result the confining potential is a Lorentz scalar, and the Coulomb part the fourth component of a 4-vector. The energy spectrum of the Dirac equation is considered for these potentials. Numerical calculations of energy eigenvalues $E=E_{nκ}$ are performed, and some exact …
It is pointed out that the recent data on charge fluctuations observed in heavy ion collisions are compatible with production of a system of weakly correlated constituent quarks and antiquarks.
We solve a Minkowski-space integral equation, derived in the Covariant Spectator Theory, for quark-antiquark bound states describing heavy and heavy-light mesons. The equation's kernel contains a one-gluon exchange interaction and a covariant generalization of a linear confining potential with a mixed scalar, pseudoscalar, and vector Lorentz structure, characterized by a continuous mixing parameter. We investigate to what extent the Lorentz structure of the confining kernel can be determined by fitting the mixing parameter to the meson spectrum.
Within the framework of nonrelativistic quark-antiquark Cornell potential model formalism, we study the annihilation of heavy quarkonia. We determine their annihilation widths resulting into digluon, dilepton, $3γ$, $3g$ and $γgg$ and compare our findings with the available theoretical results and experimental data. We also provide the charge radii and absolute square of radial Schrödinger wave function at zero quark-antiquark separation for heavy quarkonia and $B_c$ mesons.
We discuss results of the $k_t$ - factorization approach for heavy quark-heavy antiquark correlations in proton-proton and proton-antiproton collisions for RHIC, Tevatron and LHC. We consider correlations in the azimuthal angle as well as in the two-dimensional space of transverse momentum of heavy quark and heavy antiquark. We compare results obtained with the help of different unintegrated parton distributions (UPDF) from the literature.
Starting from a path integral representation of appropriate 4-point and 2-point gauge invariant Green functions and from the "Modified Area Law" model for the evaluation of the Wilson loop, a q \bar q Bethe-Salpeter like equation and a related Schwinger-Dyson equation can be obtained. From such equations an effective relativistic Hamiltonian can be derived by standard methods and then applied to the determination of the meson spectrum. The entire known heavy-heavy and heavy-light spectra and the lowest light-light Regge trajectories are rather well reproduced in terms of four parameters alone,…
Thermodynamics of a heavy quark-antiquark pair in SU(3)-QCD is studied below the deconfinement critical temperature, $T_c$. In the quenched case, a model of the string passing through heavy valence gluons yields a correct estimate of $T_c$ and a behavior of the string tension near $T_c$. For two light flavors, entropy and internal energy can be obtained from the partition function of heavy-light mesons and baryons. They are in a good qualitative agreement with the lattice results.
Trigonometric Rosen-Morse potential is suggested as the quark-antiquark interaction potential for studying the thermodynamic properties and the masses of heavy and heavy-light mesons. For this purpose, N-radial Schrodinger equation is analytically solved using an exact analytical iteration method (EAIM). The eigenvalues of energy and corresponding wave functions are obtained in the N-dimensional space. The present results are applied for calculating the mass of heavy mesons such as charmonium, bottomonium, bc, and cs mesons and thermodynamic properties such as the mean-internal energy, the spe…
The experiments at LHC have shown that the SUSY (exotic) bound states are likely to form bound states in an entirely similar fashion as ordinary quarks form bound states, i.e., quarkonium. Also, the interaction between two squarks is due to gluon exchange which is found to be very similar to that interaction between two ordinary quarks. This motivates us to solve the Schrödinger equation with a strictly phenomenological static quark-antiquark potential: $V(r)=-Ar^{-1}+κ\sqrt{r}+V_{0}$ using the shifted large $N$-expansion method to calculate the low-lying spectrum of a heavy quark with anti-sb…
We discuss the possible existence of exotic dibaryons with a heavy antiquark, being realized three-body systems, Dbar^(*)NN and B^(*)NN. These are genuinely exotic states with no quark-antiquark annihilation. We consider the heavy quark spin and chiral symmetries, and introduce the one pion exchange potential between a Dbar^(*) (B^(*)) meson and a nucleon N. As for the NN interaction, we employ the Argonne v^\prime_8 potential. By solving the coupled-channel equations for PNN and P^* NN (P^(*)=Dbar^(*) and B^(*)), we find bound states for (I,J^P)=(1/2,0^-) as well as resonant states for (I,J^P…
In the present work, we study meson systems consisting of quark-antiquark. We solve lippman-Schwinger equation numerically for heavy meson systems. We attempt to find a non-relativistic potential model through which we can solve the quark-antiquark bound state problem. The coefficients so obtained are in agreement with Martin potential coefficients. Via this method we also determine the strong coupling constant for the mesons tt, tc, and tb, which is a coefficient of Cornell potential.
Thermodynamics of a heavy quark-antiquark pair in SU(3)-QCD is studied both below and above the deconfinement critical temperature $T_c$. In the quenched case, a model of the string passing through heavy valence gluons yields a correct estimate of $T_c$ and the critical behavior of the string tension below $T_c$. For two light flavors, entropy and internal energy below $T_c$ can be obtained from the partition function of heavy-light mesons and baryons. To calculate the free energy of the system above $T_c$, we apply second-order perturbation theory in the interaction of the quark-gluon plasma …
The relativistic transformation properties of the heavy quark-antiquark interaction potential are considered in the framework of the relativistic quark model. A special attention is paid to the long-range (confining) contribution to the spin-independent part of qq bar interaction. The retardation effects are consistently taken into account.
When a heavy quark and the corresponding antiquark are separated by more than $1.4 - 1.5$ fm, it becomes energetically favorable for a light quark-antiquark pair to be produced, leading to fragmentation into a pair of flavored mesons. The relation of this critical quark separation to other dimensional constants of the strong interactions (such as the pion decay constant, the QCD scale, and the light-quark constituent mass) is discussed.
The binding system of a hadron and a nucleus is a topic of great interest for investigating the hadron properties. In the heavy-flavor region, the attraction between a $P(=\bar{D},B)$ meson and a nucleon $N$ can appear, where the $PN-P^\ast N$ mixing plays an important role in relation to the heavy-quark spin symmetry. The attraction can produce exotic heavy mesic nuclei that are stable against the strong decay. We study an exotic system where the $\bar{D}$ ($B$) meson and nucleus are bound. The meson-nucleus interaction is given by a folding potential with single-channel $PN$ interaction and …
The cross section for exclusive heavy quark and heavy antiquark pair ($Q \bar Q$) production in peripheral ultrarelativistic heavy ion collisions is calculated for the LHC energy $\sqrt{s_{NN}}$ = 5.5 TeV. Here we consider only processes with photon--photon interactions and omit diffractive contributions. We present results in the impact parameter equivalent photon approximation (EPA) and compare some of them with results obtained by exact calculations of the Feynman diagrams in the momentum space. We include both $Q \bar Q$, $Q \bar Q g$ and $Q \bar Q q \bar q$ final states as well as photon …
We discuss the fragmentation of a heavy quark to a baryon containing two heavy quarks of mass $m_Q\ggΛ_{\rm QCD}$. In this limit the heavy quarks first combine perturbatively into a compact diquark with a radius small compared to $1/Λ_{\rm QCD}$, which interacts with the light hadronic degrees of freedom exactly as does a heavy antiquark. The subsequent evolution of this $QQ$ diquark to a $QQq$ baryon is identical to the fragmentation of a heavy antiquark to a meson. We apply this analysis to the production of baryons of the form $ccq$, $bbq$, and $bcq$.
We present a local subtraction scheme for computing next-to-next-to-leading order QCD corrections to the production of a massive quark-antiquark pair from a colourless initial state. The subtraction terms are built following the CoLoRFulNNLO method and refined in such a way that their integration gives rise to compact, fully analytic expressions. All ingredients necessary for a numerical implementation of our subtraction scheme are provided in detail. As an example, we calculate the fully differential decay rate of the Standard Model Higgs boson to massive bottom quarks at next-to-next-to-lead…
Classical color fields produced by the small-x wave functions of colliding ultrarelativistic nuclei have been numerically computed. We set up the framework for computing the production of small-mass quark-antiquark pairs in these color fields by numerically integrating the Dirac equation. This computation is essential for understanding the conversion of the initial gluonic state to chemically equilibrated quark-gluon plasma. To illustrate and overcome technical difficulties associated with the longitudinal dimension, we first consider numerically the case of one time + one longitudinal space d…
We use the covariant spectator theory with an effective quark-antiquark interaction, containing Lorentz scalar, pseudoscalar, and vector contributions, to calculate the masses and vertex functions of, simultaneously, heavy and heavy-light mesons. We perform least-square fits of the model parameters, including the quark masses, to the meson spectrum and systematically study the sensitivity of the parameters with respect to different sets of fitted data. We investigate the influence of the vector confining interaction by using a continuous parameter controlling its weight. We find that vector co…
In the heavy quark limit, properties of heavy mesons and doubly heavy baryons are related by heavy quark-diquark symmetry. This problem is reanalyzed in the framework of Non-Relativistic QCD (NRQCD). We introduce a novel method for deriving Potential NRQCD (pNRQCD) Lagrangians for composite fields from vNRQCD, which contains quarks and antiquarks as explicit degrees of freedom and maintains manifest power counting in the velocity via a label formalism. A Hubbard-Stratonovich transformation is used to eliminate four quark interactions in vNRQCD and then quarks and antiquarks are integrated out …
Within an effective field theory framework we study heavy-quark--antiquark systems with a typical distance between the heavy quark and the antiquark smaller than $1/Λ_{\rm QCD}$. A suitable definition of the potential is given within this framework, while non-potential (retardation) effects are taken into account in a systematic way. We explore different physical systems. Model-independent results on the short distance behavior of the energies of the gluonic excitations between static quarks are obtained. Finally, we show how infrared renormalons affecting the static potential get cancelled in…
Starting from the NRQCD Lagrangian the heavy quark-antiquark potential is written in terms of field strength insertions on a static Wilson loop. The relevant matching coefficients are given at the present status of knowledge. The short-range, perturbatively dominated, behaviour of the spin-dependent terms is discussed.
Quantum chromodynamics (QCD) predicts the existence of both nonperturbative intrinsic and perturbative extrinsic heavy quark contributions to the fundamental structure of hadrons. The existence of intrinsic charm at the 3-standard-deviation level in the proton has recently been established from structure function measurements by the NNPDF Collaboration. Here we revisit the physics of intrinsic heavy quarks using light-front holographic QCD (LFHQCD) - a novel comprehensive approach to hadron structure which provides detailed predictions for dynamical properties of the hadrons, such as form fact…
