Heavy Diquark Research Articles

HEAVY DIQUARK SYMMETRY CONSTRAINTS FOR STRONG DECAYS

The heavy diquark symmetry (HDS) of doubly heavy baryons (DHBs) provides new insights into the spectroscopy of these hadrons. We derive the consequences of this symmetry for the mass spectra and the decay widths of DHBs. We compare these symmetry constraints to results from a nonrelativistic quark model for the mass spectra and results from the 3P0 model for strong decays. The quark model we implement was not constructed with these symmetries and contains interactions which explicitly break HDS. Nevertheless these symmetries emerge. We argue that the 3P0 model and any other model for strong transitions which employs a spectator assumption explicitly respects HDS. We also explore the possibility of treating the strange quark as a heavy quark and apply these ideas to Ξ, Ξc and Ξb baryons.

SYMMETRIES AND SYSTEMATICS OF DOUBLY HEAVY HADRONS

We discuss the extension of the superflavor symmetry of doubly heavy baryons to states which contain an excited heavy diquark and we examine some of the consequences of this symmetry for the spectra of doubly heavy baryons and heavy mesons. We explore the ramifications of a proposed symmetry that relates heavy diquarks to doubly heavy mesons. We present a method for determining how the excitation energy of a system containing two heavy quarks will scale as one changes the strength of the interactions and the reduced mass of the system. We use this to derive consequences of the heavy diquark-doubly heavy meson symmetry. We compare these consequences to the results of a quark model as well as the experimental data for doubly and singly heavy mesons. We also discuss the possibility of treating the strange quark as a heavy quark and apply the ideas developed here to strange hadrons.

Study of Doubly Heavy Baryon Spectrum via QCD Sum Rules

In this work, we calculate the mass spectrum of doubly heavy baryons with the diquark model in terms of the QCD sum rules. The interpolating currents are composed of a heavy diquark field and a light quark field. Contributions of the operators up to dimension six are taken into account in the operator product expansion. Within a reasonable error tolerance, our numerical results are compatible with other theoretical predictions. This indicates that the diquark picture reflects the reality and is applicable to the study of doubly heavy baryons.

Spectroscopy and Regge trajectories of heavy baryons in the relativistic quark-diquark picture

Mass spectra of heavy baryons are calculated in the heavy-quark--light-diquark picture in the framework of the QCD-motivated relativistic quark model. The dynamics of light quarks in the diquark as well as the dynamics of the heavy quark and light diquark in the baryon are treated completely relativistically without application of nonrelativistic v/c and heavy quark 1/m_Q expansions. Such approach allows us to get predictions for the heavy baryon masses for rather high orbital and radial excitations. On this basis the Regge trajectories of heavy baryons for orbital and radial excitations are constructed, and their linearity, parallelism, and equidistance are verified. The relations between the slopes and intercepts of heavy baryons are considered and a comparison of the slopes of Regge trajectories for heavy baryons and heavy-light mesons is performed. All available experimental data on heavy baryons fit nicely to the constructed Regge trajectories. The possible assignment of the quantum numbers to the observed excited charmed baryons is discussed.

Bethe-Salpeter equation for doubly heavy baryons in the covariant instantaneous approximation

In the heavy quark limit, a doubly heavy baryon is regarded as composed of a heavy diquark and a light quark. We establish the Bethe-Salpeter (BS) equations for the heavy diquarks and the doubly heavy baryons, respectively, to leading order in a $1/m_{Q}$ expansion. The BS equations are solved numerically under the covariant instantaneous approximation with the kernels containing scalar confinement and one-gluon-exchange terms. The masses for the heavy diquarks and the doubly heavy baryons are obtained and the non-leptonic decay widths for the doubly heavy baryons emitting a pseudo-scalar meson are calculated within the model.

Analysis of the scalar and axial-vector heavy diquark states with QCD sum rules

In this article, we study the mass spectrum of the scalar and axial-vector heavy diquark states with the QCD sum rules in a systematic way. Once the reasonable values are obtained, we can take them as basic parameters and study the new charmonium-like states as the tetraquark states.

GENXICC2.0: An upgraded version of the generator for hadronic production of double heavy baryons [formula omitted], [formula omitted] and [formula omitted

An upgraded (second) version of the package GENXICC (A Generator for Hadronic Production of the Double Heavy Baryons Ξ c c , Ξ b c and Ξ b b by C.H. Chang, J.X. Wang and X.G. Wu [its first version in: Comput. Phys. Comm. 177 (2007) 467]) is presented. Users, with this version being implemented in PYTHIA and a GNU C compiler, may simulate full events of these processes in various experimental environments conveniently. In comparison with the previous version, in order to implement it in PYTHIA properly, a subprogram for the fragmentation of the produced double heavy diquark to the relevant baryon is supplied and the interface of the generator to PYTHIA is changed accordingly. In the subprogram, with explanation, certain necessary assumptions (approximations) are made in order to conserve the momenta and the QCD ‘color’ flow for the fragmentation. Program summary Program title: GENXICC2.0 Catalogue identifier: ADZJ_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADZJ_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 102 482 No. of bytes in distributed program, including test data, etc.: 1 469 519 Distribution format: tar.gz Programming language: Fortran 77/90 Computer: Any LINUX based on PC with FORTRAN 77 or FORTRAN 90 and GNU C compiler as well Operating system: Linux RAM: About 2.0 MByte Classification: 11.2 Catalogue identifier of previous version: ADZJ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 177 (2007) 467 Does the new version supersede the previous version?: No Nature of problem: Hadronic production of double heavy baryons Ξ c c , Ξ b c and Ξ b b Solution method: The code is based on NRQCD framework. With proper options, it can generate weighted and un-weighted events of hadronic double heavy baryon production. When the hadronizations of the produced jets and double heavy diquark are taken into account in the production, the upgraded version with proper interface to PYTHIA can generate full events. Reasons for new version: Responding to the feedback from users, we improve the generator mainly by carefully completing the ‘final non-perturbative process’, i.e. the formulation of the double heavy baryon from relevant intermediate diquark. In the present version, the information for fragmentation about momentum-flow and the color-flow, that is necessary for PYTHIA to generate full events, is retained although reasonable approximations are made. In comparison with the original version, the upgraded one can implement it in PYTHIA properly to do the full event simulation of the double heavy baryon production. Summary of revisions: 1. We try to explain the treatment of the momentum distribution of the process more clearly than the original version, and show how the final baryon is generated through the typical intermediate diquark precisely. 2. We present color flow of the involved processes precisely and the corresponding changes for the program are made. 3. The corresponding changes of the program are explained in the paper. Restrictions: The color flow, particularly, in the piece of code programming of the fragmentation from the produced colorful double heavy diquark into a relevant double heavy baryon, is treated carefully so as to implement it in PYTHIA properly. Running time: It depends on which option is chosen to configure PYTHIA when generating full events and also on which mechanism is chosen to generate the events. Typically, for the most complicated case with gluon–gluon fusion mechanism to generate the mixed events via the intermediate diquark in ( c c ) [ S 1 3 ] 3 and ( c c ) [ S 0 1 ] 6 states, under the option, IDWTUP = 1 , to generate 1000 events, takes about 20 hours on a 1.8 GHz Intel P4-processor machine, whereas under the option, IDWTUP = 3 , even to generate 106 events takes about 40 minutes on the same machine.

Doubly heavy baryons in a Salpeter model with AdS/QCD inspired potential

The spectrum of baryons with two heavy quarks is predicted, assuming a configuration of a light quark and a heavy diquark. The masses are computed within a semirelativistic quark model, using a potential obtained in a gauge-gravity (anti-de Sitter/QCD) framework. All the parameters defining the model are determined fitting the meson spectrum. The obtained mass of ${\ensuremath{\Xi}}_{cc}$ is in agreement with the measurements.

Erratum: Semileptonic decays of doubly heavy baryons in the relativistic quark model [Phys. Rev. D70, 014018 (2004)

Semileptonic decays of doubly heavy baryons are studied in the framework of the relativistic quark model. The doubly heavy baryons are treated in the quark-diquark approximation. The transition amplitudes of heavy diquarks bb and bc going respectively to bc and cc are explicitly expressed through the overlap integrals of the diquark wave functions in the whole accessible kinematic range. The relativistic baryon wave functions of the quark-diquark bound system are used for the calculation of the transition matrix elements, the Isgur-Wise function and decay rates in the heavy quark limit.

QCD sum rules study of [formula omitted] mesons

We use QCD sum rules to study the possible existence of Q Q − u ¯ d ¯ mesons, assumed to be a state with J P = 1 + . For definiteness, we work with a current with an axial heavy diquark and a scalar light anti-diquark, at leading order in α s . We consider the contributions of condensates up to dimension eight. For the b-quark, we predict M T b b = ( 10.2 ± 0.3 ) GeV , which is below the B ¯ B ¯ ∗ threshold. For the c-quark, we predict M T c c = ( 4.0 ± 0.2 ) GeV , in agreement with quark model predictions.

Production of [formula omitted] and [formula omitted] baryons in quark–diquark model

Using perturbative quantum chromodynamics and quark–diquark model of baryons, we have obtained an analytical fragmentation function which describes Ω b b c and Ω b c c baryons in b and c quarks fragmentation. The universal fragmentation probabilities, the average fragmentation parameters and the production cross sections resulting from this function are in a very good agreement with those obtained using a full perturbative regime. We conclude that the quark–diquark model of baryons works well when a scalar heavy diquark is considered in a heavy quark fragmentation into a triply heavy baryon.

Mesons and diquarks in a dense quark medium with color superconductivity

In the framework of the Nambu-Jona-Lasinio model with two quark flavors, we investigate the spectrum of meson and diquark excitations of dense quark matter in the phase with color superconductivity. The color SUc(3) symmetry is spontaneously broken to SUc(2) in this phase. But instead of the expected five Goldstone bosons in the mass spectrum, we observe only three, among which two bosons obey the quadratic dispersion law. We find the doublet of light diquark states with the mass ∼ 15 MeV and also the heavy diquark resonance (SUc(2) singlet) with the mass ∼ 1100 MeV. The π-and σ-mesons have the mass ∼ 330 Mev in the phase with color superconductivity. The π-mesons are then stable particles, while the σ-meson is stable only in the chiral limit in which the current quark mass m0 becomes zero. If m0 ≠ 0, then the σ-meson mixes with diquarks in the phase with color superconductivity and becomes a resonance with the width ∼ 30 MeV.

Diquark Bose–Einstein condensation and nuclear matter

We study a possible transition between symmetric nuclear matter and the diquark Bose–Einstein condensate (BEC) matter at zero temperature. We find that chiral restoration transition is first order and coincides with deconfinement. We investigate various possible coexistence patterns which may emerge from the first order deconfinement phase transition by assuming different values for the critical deconfinement chemical potential. If deconfinement takes place at higher chemical potential, there exists a mixed phase of nuclear and chirally restored diquark BEC matter. This coexistence region extends over a large density region for a bigger diquark BEC or a weaker diquark–diquark interaction. For model parameters with heavy diquark in vacuum, phase transition to diquark matter becomes of second-order. We also show that in the case of precocious deconfinement, droplets of nucleons and droplets of chirally restored Bose–Einstein condensed diquarks coexist surrounded by non-trivial vacuum. We show that a early deconfinement and a weak repulsive diquark–diquark interaction soften the equation of state. We propose a scenario in which nuclear matter saturates due to the formation of the diquark BEC and deconfinement phenomena. In this picture, instead of repulsive vector-meson exchange the compressibility of the equation of state is related to a repulsive diquark–diquark interaction. In general, we emphasize the importance of a diquark BEC phase at rather low density before quark BCS-pairing transition.

Scaling of Dirac fermions and the WKB approximation

We discuss a new method for obtaining the WKB approximation to the Dirac equation with a scalar potential and a time-like vector potential. We use the WKB solutions to investigate the scaling behavior of a confining model for quark-hadron duality. In this model, a light quark is bound to a heavy di-quark by a linear scalar potential. Absorption of virtual photons promotes the quark to bound states. The analog of the parton model for this case is for a virtual photon to eject the bound, ground-state quark directly into free continuum states. We compare the scaling limits of the response functions for these two transitions.

Pion, σ meson, and diquarks in the two-flavor color-superconducting phase of dense cold quark matter

The spectrum of meson and diquark excitations of dense cold quark matter is investigated within the framework of a Nambu--Jona-Lasinio-type model for light quarks of two flavors. It was found that a first-order phase transition occurs when the chemical potential \ensuremath{\mu} exceeds the critical value ${\ensuremath{\mu}}_{c}=350\phantom{\rule{0.3em}{0ex}}\text{MeV}$. Above ${\ensuremath{\mu}}_{c}$, the diquark condensate $\ensuremath{\langle}\mathit{qq}\ensuremath{\rangle}$ forms, breaking the color symmetry of strong interaction. The masses of \ensuremath{\pi} and \ensuremath{\sigma} mesons are shown to grow with the chemical potential \ensuremath{\mu} in the color-superconducting phase, but the mesons themselves become almost stable particles. Moreover, we have found in this phase an abnormal number of three, instead of five, Nambu-Goldstone bosons, together with a color doublet of light stable diquark modes and a color-singlet heavy diquark resonance with mass $~$1100 MeV. In the color-symmetric phase, i.e., for $\ensuremath{\mu}<{\ensuremath{\mu}}_{c}$, a mass splitting of diquarks and antidiquarks is shown to arise if $\ensuremath{\mu}\ensuremath{\ne}0$, contrary to the case of a vanishing chemical potential, in which the masses of antidiquarks and diquarks are degenerate at the value $~$700 MeV.

Properties of doubly heavy baryons in the relativistic quark model

Mass spectra and semileptonic decay rates of baryons consisting of two heavy (b or c) and one light quark are calculated in the framework of the relativistic quark model. The doubly heavy baryons are treated in the quark-diquark approximation. The ground and excited states of both the diquark and quark-diquark bound systems are considered. The quark-diquark potential is constructed. The light quark is treated completely relativistically, while the expansion in the inverse heavy-quark mass is used. The weak transition amplitudes of heavy diquarks bb and bc going, respectively, to bc and cc are explicitly expressed through the overlap integrals of the diquark wave functions in the whole accessible kinematic range. The relativistic baryon wave functions of the quark-diquark bound system are used for the calculation of the decay matrix elements, the Isgur-Wise function, and decay rates in the heavy-quark limit.

Semileptonic decays of doubly heavy baryons in the relativistic quark model

Semileptonic decays of doubly heavy baryons are studied in the framework of the relativistic quark model. The doubly heavy baryons are treated in the quark-diquark approximation. The transition amplitudes of heavy diquarks bb and bc going, respectively, to bc and cc are explicitly expressed through the overlap integrals of the diquark wave functions in the whole accessible kinematic range. The relativistic baryon wave functions of the quark-diquark bound system are used for the calculation of the transition matrix elements, the Isgur-Wise function, and decay rates in the heavy quark limit.

Mass spectra of doubly heavyΩQQ′baryons

We evaluate the masses of baryons composed of two heavy quarks and a strange quark, taking into account spin-dependent splittings in the framework of the potential model with the ${\mathrm{K}}^{2}\mathrm{O}$ potential [V. V. Kiselev, A. E. Kovalsky, and A. I. Onishchenko, Phys. Rev. D 64, 054009 (2001)] motivated by QCD with a three-loop $\ensuremath{\beta}$ function for the effective charge consistent with both the perturbative limit at short distances and a linear confinement term at long distances between the quarks. The factorization of dynamics is assumed and explored in the nonrelativistic Schr\"odinger equation for motion in a system of two heavy quarks constituting the doubly heavy diquark and the strange quark interaction with the diquark. The limits of the approach, its justification, and uncertainties are discussed. Excited quasistable states are classified by the quantum numbers of a heavy diquark composed of heavy quarks of the same flavor.

Pair production of doubly heavy diquarks

The differential and total cross sections for the pair production of doubly heavy diquarks are calculated analytically within the diquark model. The cases of electron-positron and quark-antiquark annihilation are considered. The ratios of the total cross sections to the corresponding cross sections for annihilation into two heavy quarks are estimated numerically.

Doubly heavy baryonsΩQQ′versusΞQQ′in sum rules of nonrelativistic QCD

In the framework of two-point sum rules of NRQCD, the masses and couplings of doubly heavy baryons to the corresponding quark currents are evaluated with account of coulomb-like corrections in the system of doubly heavy diquark as well as the contribution of nonperturbative terms determined by the quark, gluon, mixed condensates and the product of gluon and quark condensates. The introduction of nonzero light quark mass destroys the factorization of baryon and diquark correlators even at the perturbative level and provides the better convergency of sum rules. We estimate the difference M_Omega - M_Xi = 100+/- 10 MeV. The ratio of baryonic constants |Z_Omega|^2/|Z_Xi|^2 is equal to 1.3+/-0.2 indicating the violation of SU(3) flavor symmetry for the doubly heavy baryons.