Quark-hadron Duality Research Articles

Quark-hadron duality for heavy meson mixings in the \u2019t Hooft model

We study local quark-hadron duality and its violation for the {D}^0-{overline{D}}^0 , {B}_d^0-{overline{B}}_d^0 and {B}_s^0-{overline{B}}_s^0 mixings in the ’t Hooft model, offering a laboratory to test QCD in two-dimensional spacetime together with the large-Nc limit. With the ’t Hooft equation being numerically solved, the width difference is calculated as an exclusive sum over two-body decays. The obtained rate is compared to inclusive one that arises from four-quark operators to check the validity of the heavy quark expansion (HQE). In view of the observation in four-dimensions that the HQE prediction for the width difference in the {D}^0-{overline{D}}^0 mixing is four orders of magnitude smaller than the experimental data, in this work we investigate duality violation in the presence of the GIM mechanism. We show that the order of magnitude of the observable in the {D}^0-{overline{D}}^0 mixing is enhanced in the exclusive analysis relative to the inclusive counterpart, when the 4D-like phase space function is used for the inclusive analysis. By contrast, it is shown that for the {B}_d^0-{overline{B}}_d^0 and {B}_s^0-{overline{B}}_s^0 mixings, small yet non-negligible corrections to the inclusive result emerge, which are still consistent with what is currently indicated in four-dimensions.

Violation of quark–hadron duality

Violation of quark–hadron duality

Resonant contributions to inclusive nucleon structure functions from exclusive meson electroproduction data

Nucleon resonance contributions to the inclusive proton ${F}_{2}$ and ${F}_{L}$ structure functions are computed from resonance electroexcitation amplitudes in the mass range up to 1.75 GeV extracted from CLAS exclusive meson electroproduction data, taking into account interference between different excited nucleon states. The resonance contributions are compared with inclusive proton structure functions evaluated from $(e,{e}^{\ensuremath{'}}X)$ cross section data and the longitudinal to transverse cross section ratio. Contributions from isospin-1/2 and -3/2 resonances remain substantial over the entire range of photon virtualities ${Q}^{2}\ensuremath{\lesssim}4\phantom{\rule{4pt}{0ex}}{\mathrm{GeV}}^{2}$, where their electroexcitation amplitudes have been obtained, and their ${Q}^{2}$ evolution displays pronounced differences in the first, second, and third resonance regions. We compare the structure functions in the resonance region with those computed from parton distributions fitted to deep-inelastic scattering data, and extrapolated to the resonance region, providing new quantitative assessments of quark-hadron duality in inclusive electron-proton scattering.

Hadronic coupling constants of the lowest hidden-charm pentaquark state, using QCD sum rules with rigorous quark-hadron duality * *Supported by National Natural Science Foundation of China (11775079)

In this article, we illustrate how to calculate the hadronic coupling constants of the pentaquark states with QCD sum rules based on rigorous quark-hadron quality. We then study the hadronic coupling constants of the lowest diquark-diquark-antiquark type hidden-charm pentaquark state with spin-parity in detail, and calculate the partial decay widths. The total width is compatible with the experimental value from the LHCb collaboration, and favors assigning the to be the pentaquark state with . The hadronic coupling constants have the relation , and favor the hadronic dressing mechanism. The may have a diquark-diquark-antiquark type pentaquark core with the typical size of the -type baryon states. The strong couplings to the meson-baryon pairs lead to some pentaquark molecule components, and the may spend a rather large time as the molecular state.

The D\u2217D\u03c0 and B\u2217B\u03c0 couplings from light-cone sum rules

We revisit the calculation of the strong couplings D∗Dπ and B∗Bπ from the QCD light-cone sum rules using the pion light-cone distribution amplitudes. The accuracy of the correlation function, calculated from the operator product expansion near the light-cone, is upgraded by taking into account the gluon radiative corrections to the twist-3 terms. The double spectral density of the correlation function, including the twist-2, 3 terms at mathcal{O}left({alpha}_sright) and the twist-4 LO terms, is presented in an analytical form for the first time. This form allows us to use various versions of the quark-hadron duality regions in the double dispersion relation underlying the sum rules. We predict {g}_{D^{ast } Dpi}={14.1}_{-1.2}^{+1.3} and {g}_{B^{ast } Bpi}={30.0}_{-2.4}^{+2.6} when the decay constants of heavy mesons entering the light-cone sum rule are taken from lattice QCD results. We compare our results with the experimental value for the charmed meson coupling and with the lattice QCD calculations.

OPE and quark-hadron duality for two-point functions of tetraquark currents in the 1/Nc expansion

We discuss the Operator Product Expansion (OPE) and quark-hadron duality for two-point Green functions of tetraquark currents. We emphasize that the factorizable part of the OPE series for such Green functions, including nonperturbative contributions described by QCD condensates, is saturated by the full system of ordinary hadrons and therefore cannot have any relationship to the possible tetraquark bound states. Possible tetraquark bound states may be contained in nonfactorizable parts of these Green functions. In the framework of the $1/N_c$ expansion in QCD$(N_c)$, nonfactorizable parts of the two-point Green functions of tetraquark currents provide $N_c$-suppressed contributions compared to the $N_c$-leading factorizable parts. A possible exotic tetraquark state may appear only in $N_c$-subleading contributions to the QCD Green functions, in full accord with the well-known rigorous properties of large-$N_c$ QCD.

QCD sum rules with spectral densities solved in inverse problems

We construct QCD sum rules for nonperturbative studies without assuming the quark-hadron duality for the spectral density at low energy on the hadron side. Instead, both resonance and continuum contributions to the spectral density are solved with the operator-product-expansion input on the quark side by treating sum rules as an inverse problem. This new formalism does not involve the continuum threshold, does not require the Borel transformation and stability analysis, and can be extended to extract properties of excited states. Taking the two-current correlator as an example, we demonstrate that the series of $\rho$ resonances can emerge in our formalism, and the decay constants $f_{\rho(770)} (f_{\rho(1450)},f_{\rho(1700)},f_{\rho(1900)})\approx$ 0.22 (0.19, 0.14, 0.14) GeV for the masses $m_{\rho(770)} (m_{\rho(1450)},m_{\rho(1700)},m_{\rho(1900)})\approx$ 0.78 (1.46, 1.70, 1.90) GeV are determined. We also show that the decay width $\Gamma_{\rho(770)}\approx 0.17$ GeV can be obtained by substituting a Breit-Wigner parametrization for the $\rho(770)$ pole on the hadron side. It is observed that quark condensates of dimension-six on the quark side are crucial for establishing those $\rho$ resonances. Handling the conventional sum rules with the duality assumption as an inverse problem, we find that the multiple pole sum rules widely adopted in the literature do not describe the $\rho$ excitations reasonably. The precision of our theoretical outcomes can be improved systematically by including higher-order and higher-power corrections on the quark side. Broad applications of this formalism to abundant low energy QCD observables are expected.

Scaled variables and the quark-hadron duality

The thermodynamic quantities of the ideal gas of hadrons and the $(2+1)$--flavor lattice QCD scaled by the effective degeneracy factors of the corresponding models are compared. We have found that in terms of the scaled variables the quark-hadron duality of the lattice QCD and the hadron resonance gas (HRG) model disappears. However, we have unexpectedly revealed that the scaled variables lead to the quark-hadron duality of the lattice QCD and the quantum ideal gas of kaons and antikaons, namely, the ideal gas of those hadrons that contain all the three quarks $u,d,s$ and their antiquarks. Satisfactory agreement between the scaled results of the kaon ideal gas and the lattice QCD data is achieved at large values of the volume in the entire temperature range. In the ideal gas of kaons there is no any phase transition. Nevertheless, in our calculations the scaled thermodynamic quantities of the ideal gas and the lattice QCD follow the same qualitative behavior and are consistent with each other especially at high temperatures in the perturbative region.

Complete NLO QCD study of single- and double-quarkonium hadroproduction in the colour-evaporation model at the Tevatron and the LHC

We study the Single-Parton-Scattering (SPS) production of double quarkonia (J/ψ+J/ψ, J/ψ+ϒ, and ϒ+ϒ) in pp and pp¯ collisions at the LHC and the Tevatron as measured by the CMS, ATLAS, LHCb, and D0 experiments in the Colour-Evaporation Model (CEM), based on the quark-hadron duality, including Next-to-Leading Order (NLO) QCD corrections up to αs5. To do so, we also perform the first true NLO –up to αs4– study of the pT-differential cross section for single-quarkonium production. This allows us to fix the non-perturbative CEM parameters at NLO accuracy in the region where quarkonium-pair data are measured. Our results show that the CEM at NLO in general significantly undershoots these experimental data and, in view of the other existing SPS studies, confirm the need for Double Parton Scattering (DPS) to account for the data. Our NLO study of single-quarkonium production at mid and large pT also confirms the difficulty of the approach to account for the measured pT spectra; this is reminiscent of the impossibility to fit single-quarkonium data with the sole S1[8]3 NRQCD contribution from gluon fragmentation. We stress that the discrepancy occurs in a kinematical region where the new features of the improved CEM are not relevant.

Reconstruction of smeared spectral functions from Euclidean correlation functions

Abstract We propose a method to reconstruct smeared spectral functions from two-point correlation functions measured on the Euclidean lattice. An arbitrary smearing function can be considered as long as it is smooth enough to allow an approximation using Chebyshev polynomials. We test the method with numerical lattice data of charmonium correlators. The method provides a framework to compare lattice calculation with experimental data including excited-state contributions without assuming quark–hadron duality.

Towards a combined analysis of inclusive/exclusive electroproduction

In view of the major advances achieved by the CLAS experiments in studying theN* electroex citation amplitudes, as well as further extension of these studies in the experiments with CLAS12, we present an approach for the evaluation of the resonant contributions to inclusive electron scattering off protons. For the first time, the resonant contributions are determined from the experimental results onN* electrocouplings available from the data analyses of exclusive meson electroproduction off protons. This is a useful benchmark for future endeavours on understanding the transition region between low and high-energy regions, strongly related to tests on quark-hadron duality.

Transition Form Factors of Pseudoscalar Mesons and the Contribution of the Gluon Anomaly

The expressions for the transition form factors (TFFs) of pseudoscalar mesons are derived in the context of the anomaly sum rule approach based on the dispersion representation of the axial anomaly and hypothesis of the global quark-hadron duality. The obtained solutions take into account the π$^{0}$-η-η′ mixing and the contribution of the gluon anomaly. It is shown that this method allows one to describe the TFFs for spacelike and timelike photon virtualities. The contribution of the gluon anomaly is estimated.

Tetraquark-adequate QCD sum rules for quark-exchange processes

We consider quark-hadron duality relations and QCD sum rules for correlators involving exotic tetraquark currents, here specializing to the case of quark-exchange processes. We point out the differences they exhibit with respect to the cases involving ordinary bilinear quark currents. Based on the observation that only diagrams possessing at least four-quark singularities can contribute to the formation of tetraquark states, we show that the quark-hadron duality relations and the corresponding sum rules split into two non-overlapping relations. The ultimate tetraquark-adequate QCD sum rule is concerned only with one of these relations, in which the operator product expansion starts with diagrams of order $O(\alpha_s^2)$.

Baryon as a Quantum Hall Droplet and the Quark-Hadron Duality.

We show that the recent proposal to describe the N_{f}=1 baryon in the large number of the color limit as a quantum Hall droplet can be understood as a chiral bag in a (1+2)-dimensional strip using the Cheshire Cat principle. For a small bag radius, the bag reduces to a vortex line which is the smile of the cat with flowing gapless quarks all spinning in the same direction. The disk enclosed by the smile is described by a topological field theory due to the Callan-Harvey anomaly outflow. The chiral bag naturally carries the unit baryon number and spin 1/2N_{c}. The generalization to arbitrary N_{f} is discussed.

Nucleon resonance contributions to unpolarized inclusive electron scattering

The first CLAS12 experiments will provide high-precision data on inclusive electron scattering observables at a photon virtuality $Q^2$ ranging from 0.05 GeV$^2$ to 12 GeV$^2$ and center-of-mass energies $W$ up to 4 GeV. In view of this endeavour, we present the modeling of the resonant contributions to the inclusive electron scattering observables. As input, we use the existing CLAS electrocoupling results obtained from exclusive meson electroproduction data off protons, and evaluate for the first time the resonant contributions based on the experimental results on the nucleon resonance electroexcitation. The uncertainties are given by the data and duly propagated through a Monte Carlo approach. In this way, we obtain estimates for the resonant contributions, important for insight into the nucleon parton distributions in the resonance region and for the studies of quark-hadron duality.

Analysis of strong decays of the Zc(4600) with the QCD sum rules

In this paper, we tentatively assign the [Formula: see text] to be the [Formula: see text] type vector tetraquark state and study its two-body strong decays with the QCD sum rules based on solid quark–hadron duality, the predictions for the partial decay widths [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] can be compared to the experimental data in the future to diagnose the nature of the [Formula: see text].

Baryonic susceptibilities, quark-diquark models, and quark-hadron duality at finite temperature

Fluctuations of conserved charges such as baryon number, electric charge and strangeness may provide a test for completeness of states in lattice QCD for three light flavors. We elaborate on the idea that the corresponding susceptibilities can be saturated with excited baryonic states with an underlying quark-diquark structure with a linearly confining interaction. Using Polyakov-loop correlators we show that in the static limit, the quark-diquark potential coincides with the quark-antiquark potential in marked agreement with recent lattice studies. We thus study in a quark-diquark model the baryonic fluctuations of electric charge, baryon number and strangeness: $\chi_{BQ}$, $\chi_{BB}$ and $\chi_{BS}$; by considering a realization of the hadron resonance gas model in the light flavor sector of QCD. These results have been obtained by using the baryon spectrum computed within a relativistic quark-diquark model, leading to an overall good agreement with the spectrum obtained with other quark models and with lattice data for the fluctuations.

Strong decays of the Y(4660) as a vector tetraquark state in solid quark-hadron duality

In this article, we choose the [sc]_P[bar{s}bar{c}]_A-[sc]_A[bar{s}bar{c}]_P type tetraquark current to study the hadronic coupling constants in the strong decays Y(4660)rightarrow J/psi f_0(980), eta _c phi (1020), chi _{c0}phi (1020), D_s bar{D}_s, D_s^* bar{D}^*_s, D_s bar{D}^*_s, D_s^* bar{D}_s, psi ^prime pi ^+pi ^-, J/psi phi (1020) with the QCD sum rules based on solid quark-hadron quality. The predicted width Gamma (Y(4660) )= 74.2^{+29.2}_{-19.2},mathrm{{MeV}} is in excellent agreement with the experimental data 68pm 11pm 1 { text{ MeV }} from the Belle collaboration, which supports assigning the Y(4660) to be the [sc]_P[bar{s}bar{c}]_A-[sc]_A[bar{s}bar{c}]_P type tetraquark state with J^{PC}=1^{--}. In calculations, we observe that the hadronic coupling constants |G_{Ypsi ^prime f_0}|gg |G_{Y J/psi f_0}|, which is consistent with the observation of the Y(4660) in the psi ^prime pi ^+pi ^- mass spectrum, and favors the psi ^{prime }f_0(980) molecule assignment. It is important to search for the process Y(4660)rightarrow J/psi phi (1020) to diagnose the nature of the Y(4660), as the decay is greatly suppressed.

Bounds on lepton flavor violating physics and decays of neutral mesons from τ(μ)→3ℓ , ℓγγ -decays

We study two- and three-body lepton flavor violating (LFV) decays involving leptons and neutral vector bosons $V=\rho^0, \omega, \phi, J/\psi, \Upsilon, Z^0$, as well as pseudo-scalar $P=\pi^0, \eta, \eta', \eta_c$ and scalar $S=f_0(500), f_0(980), a_0(980), \chi_{c0}(1P)$ mesons, without referring to a specific mechanism of LFV realization. In particular, we relate the rates of the three-body LFV decays $\tau(\mu) \to 3 \ell$, where $\ell = \mu$ or $e$, to the two-body LFV decays $(V,P) \to \tau\mu(\tau e, \mu e)$, where $V$ and $P$ play the role of intermediate resonances in the decay process $\tau(\mu) \to 3 \ell$. From the experimental upper bounds for the branching ratios of $\tau(\mu) \to 3 \ell$ decays, we derive upper limits for the branching ratios of $(V,P) \to \tau\mu(\tau e, \mu e)$. We compare our results to the available experimental data and known theoretical upper limits from previous studies of LFV processes, and find that some of our limits are several orders of magnitude more stringent. Using the idea of quark-hadron duality, we extract limits on various quark-lepton dimension-six LFV operators from data on lepton decays. Some of these limits are either new or stronger than those existing in the literature.

Analysis of the mass and width of the X(4140) as axialvector tetraquark state

In this article, we construct both the [sc]_T[{bar{s}}{bar{c}}]_A+[sc]_A[{bar{s}}{bar{c}}]_T type and [sc]_T[{bar{s}}{bar{c}}]_V-[sc]_V[{bar{s}}{bar{c}}]_T type axialvector currents with J^{PC}=1^{++} to study the mass of the X(4140) with the QCD sum rules. The predicted masses support assigning the X(4140) to be the [sc]_T[{bar{s}}{bar{c}}]_V-[sc]_V[{bar{s}}{bar{c}}]_T type axialvector tetraquark state. Then we study the hadronic coupling constant g_{XJ/psi phi } with the QCD sum rules based on solid quark-hadron duality, and obtain the decay width Gamma (X(4140)rightarrow J/psi phi )=86.9pm 22.6,{mathrm{MeV}}, which is in excellent agreement with the experimental data 83pm 21^{+21}_{-14} { text{ MeV }} from the LHCb collaboration.