Bloom-Gilman Duality Research Articles

Mystery of Bloom-Gilman duality: A light-front holographic QCD perspective

Light-front wave functions motivated by holographic constructions are used to study Bloom-Gilman duality, a feature of deep inelastic scattering. Separate expressions for structure functions in terms of quark and hadronic degrees of freedom (involving transition form factors) are presented, with an ultimate goal of obtaining a relationship between the two expressions. A specific two-parton model is defined and resonance transition form factors are computed using previously derived light-front wave functions. A new form of global duality (integral over all values of $x$ between 0 and 1) is derived from the valence quark-number sum rule. Using a complete set of hadronic states is necessary for this new global duality to be achieved, and the previous original work does not provide such a set. This feature is remedied by amending the model to include a longitudinal confining potential, and the resulting complete set is sufficient to carry out the study of Bloom-Gilman duality. Specific expressions for transition form factors are obtained and all are shown to fall as $1/{Q}^{2}$, at asymptotically large values. This is because the Feynman mechanism dominates the asymptotic behavior of the model. These transition form factors are used to assess the validity of the global and local duality sum rules, with the result that both are not satisfied within the given model. Evaluations of the hadronic expression for $q(x,{Q}^{2})$ provide more details about this lack. This result is not a failure of the current model because it shows that the observed validity of both global and local forms of duality for deep inelastic scattering must be related to a feature of QCD that is deeper than completeness. Our simple present model suggests a prediction that Bloom-Gilman duality would not be observed if deep inelastic scattering experiments were to be made on the pion. The underlying origin of the duality phenomenon in deep inelastic scattering is deeply buried within the confinement aspects of QCD, and its origin remains a mystery.

Quark-Hadron Duality of Spin Structure Functions in CLAS EG1b Data

The hypothesis of quark-hadron duality infers that physical observables of nucleons can be described by a complete set of basis states using either hadronic or quark degrees of freedom. In the EG1b experiment in Hall-B at Jefferson Lab, polarized electrons with energies of 1.6, 2.5, 4.2 and 5.7 GeV were scattered from proton and deuteron targets ( $$^{15}\hbox {NH}_3$$ and $$^{15}\hbox {ND}_3$$ dynamically polarized along the beam direction) and detected with CEBAF large acceptance spectrometer. Nucleon spin structure functions $$g_1$$ and $$g_2$$ were measured over a wide kinematic range ( $$0.05\,\hbox {GeV}^2< Q^2 <5\,\hbox {GeV}^2$$ and $$1.08\,\hbox {GeV}<{W}< 3\,\hbox {GeV}$$ ). These recently published data strongly constrain parametrization of world data in the resonance region, allowing comprehensive tests of Bloom–Gilman duality for polarized nucleons over a wide kinematic range.

Hawking radiation and the Bloom–Gilman duality

The decay widths of the quantum black hole precursors, determined from the poles of the resummed graviton propagator, are matched to the expected lifetime given by the Hawking decay. In this way, we impose a kind of duality between a perturbative description and an essentially non-perturbative description, bearing some similarity with the Bloom–Gilman duality for the strong interactions. General relations are then obtained for the widths and masses of the poles in terms of the number of particle species and the renormalisation scale of gravity. A lower bound on the lifetime of the quantum black holes is also obtained.

EXPLICIT MODEL REALIZING PARTON–HADRON DUALITY

We present a model that realizes both resonance-Regge (Veneziano) and parton–hadron (Bloom–Gilman) duality. We first review the features of the Veneziano model and we discuss how parton–hadron duality appears in the Bloom–Gilman model. Then we review limitations of the Veneziano model, namely that the zero-width resonances in the Veneziano model violate unitarity and Mandelstam analyticity. We discuss how such problems are alleviated in models that construct dual amplitudes with Mandelstam analyticity (so-called DAMA models). We then introduce a modified DAMA model, and we discuss its properties. We present a pedagogical model for dual amplitudes and we construct the nucleon structure function F2(x, Q2). We explicitly show that the resulting structure function realizes both Veneziano and Bloom–Gilman duality.

Semi-exclusive deeply virtual Compton scattering

We consider Semi-Exclusive Deeply Virtual Compton Scattering, {gamma}*p{yields}{gamma}Y (SECS), where Y is an inclusive state of intermediate mass, {lambda}{sub QCD}<<m{sub Y}<<Q. When the photon is produced with a large transverse momentum k{sub perpendicular}{approx}m{sub Y} the subprocess is hard and the struck quark fragments independently of the target spectators. Using completeness this allows us to express the SECS cross section in terms of ordinary parton distributions. Apart from direct comparisons with data (yet to come) new information on Bloom-Gilman duality may be obtained through comparisons of resonance production via DVCS ({gamma}*p{yields}{gamma}N*) with the SECS scaling distribution in m{sub Y}.

Bloom–Gilman Duality of Nucleon Spin Structure Function andElastic Peak Contribution

By employing the parametrization form of the nucleon spin structure functionin the resonance region, which includes the contributions of the resonancepeaks and of nonresonance background, we study Bloom–Gilman quark-hadronduality of g1 both in the inelastic resonance region and elastic one.

STUDY OF QUARK-HADRON DUALITY BASED ON A CONSTITUENT QUARK MODEL

The recent measurement of quark-hadron duality is shortly discussed by using a simple constituent quark model. Comparing with the moments of the structure functions in the resonance region and in the deep inelastic scattering region, we study the occurances of Bloom-Gilman quark-hadron duality for the nucleon structure function F2 and g1. Local duality is also analyzed.

Energy-weighted sum rules, y-scaling and duality

The phenomena of scaling and Bloom-Gilman duality are examined in the context of simple nonrelativistic and relativistic quantum-mechanical models. These models are shown to scale and to show the qualitative features of Bloom-Gilman duality. This suggests that these phenomena do not necessarily require the properties of QCD.

Quark-hadron duality in a relativistic, confining model

Quark-hadron duality is an interesting and potentially very useful phenomenon, as it relates the properly averaged hadronic data to a perturbative QCD result in some kinematic regions. While duality is well established experimentally, our current theoretical understanding is still incomplete. We employ a simple model to qualitatively reproduce all the features of Bloom-Gilman duality as seen in electron scattering. In particular, we address the role of relativity, give an explicit analytic proof of the equality of the hadronic and partonic scaling curves, and show how the transition from coherent to incoherent scattering takes place.

Quark–hadron duality: resonances and the onset of scaling

We examine the origin of Bloom-Gilman duality and the relationship between resonances and scaling in deep-inelastic scattering. A simple quantum mechanical model is used to illustrate the essential features of Bloom-Gilman duality at low momentum transfer. As an application of local duality, we discuss model-independent relations between structure functions at x ~ 1 and elastic electromagnetic form factors.

Duality in semi-exclusive processes

Semi-exclusive processes like \gamma p \to \pi^+ Y are closely analogous to DIS, ep \to eX, in the limit where the momentum transfer |t| to the pion and the mass of the inclusive system Y are large but still much smaller than the total CM energy. We apply Bloom-Gilman duality to this semi-exclusive process. The energy dependence of the \gamma p \to \pi^+ n cross section given by semi-local duality agrees with data for moderate values of |t|, but its normalization is underestimated by about two orders of magnitude. This indicates that rather high momentum transfers are required for the validity of PQCD in the hard subprocess \gamma u \to \pi^+ d. In the case of Compton scattering \gamma p \to \gamma p the analogous discrepancy is about one order of magnitude. In electroproduction the virtuality of the incoming photon can be used to directly measure the hardness of the subprocess.

Xandξscaling of the nuclear structure function at largex

Inclusive electron scattering data are presented for ^2H and Fe targets at an incident electron energy of 4.045 GeV for a range of momentum transfers from Q^2 = 1 to 7 (GeV/c)^2. Data were taken at Jefferson Laboratory for low values of energy loss, corresponding to values of Bjorken x greater than or near 1. The structure functions do not show scaling in x in this range, where inelastic scattering is not expected to dominate the cross section. The data do show scaling, however, in the Nachtmann variable \xi. This scaling may be the result of Bloom Gilman duality in the nucleon structure function combined with the Fermi motion of the nucleons in the nucleus. The resulting extension of scaling to larger values of \xi opens up the possibility of accessing nuclear structure functions in the high-x region at lower values of Q^2 than previously believed.

The origins of quark–hadron duality: how does the square of the sum become the sum of the squares?

Bloom–Gilman duality demonstrates empirically that the electroproduction of N∗'s at low momentum transfers averages smoothly around the scaling curve measured at large momentum transfers. The latter is proportional to the sum of the squares of the constituent charges whereas the former involves the coherent excitation of resonances and is driven by the square of summed constituent charges. We determine the minimal necessary conditions for this equality to be realised so that duality can occur and consider the implications for a range of processes that may be studied soon at CEBAF.

Target-mass corrections and the Bloom-Gilman duality of the nucleon structure function

The occurrence of the Bloom-Gilman local duality in the low-order moments of the nucleon structure function is investigated for values of the squared four-momentum transfer Q 2 between ∼0.5 and 10 ( GeV/c) 2 . At variance with previous analyses truncated Cornwall-Norton moments, limited to the nucleon-resonance production regions, are considered. The role played by target-mass corrections is illustrated, showing that target-mass effects are necessary (but not sufficient) for producing the observed Bloom-Gilman duality of the nucleon structure function. The possibility of a local duality between the unphysical region at large values of the Nachtmann variable and the nucleon elastic peak contribution is analyzed. It is found that the proton magnetic form factor extracted assuming local duality is significantly below the experimental data at low and intermediate values of Q 2.

Bloom-Gilman duality of inelastic structure functions in nucleon and nuclei

The Bloom-Gilman local duality of the inelastic structure function of the proton, the deuteron, and light complex nuclei is investigated using available experimental data in the squared four-momentum transfer range from $0.3$ to $5 (\mathrm{GeV}{/c)}^{2}$. The results of our analysis suggest that the onset of the Bloom-Gilman local duality is anticipated in complex nuclei with respect to the case of the proton and the deuteron. A possible interpretation of this result in terms of a rescaling effect is discussed with particular emphasis on the possibility of reproducing the damping of the nucleon-resonance transitions observed in recent electroproduction data off nuclei.

Inclusive electron scattering from nuclei at x~=1.

The inclusive A(e,e′) cross section for x≃1 was measured on H2, C, Fe, and Au for momentum transfers Q2 from 1 to 6.8 (GeV/c)2. The scaling behavior of the data was examined in the region of transition from y scaling to x scaling. Throughout this transitional region, the data exhibit ξ scaling, reminiscent of the Bloom-Gilman duality seen in free nucleon scattering. © 1996 The American Physical Society.Received 6 March 1995DOI:https://doi.org/10.1103/PhysRevC.53.2248©1996 American Physical Society

How well determined is the N − Δ electromagnetic transition from factor at high Q 2?

We explore the sensitivity of the N - Δ(1232) electromagnetic transition form factor, extracted from the inclusive electroproduction data, to the choice of background. We find that the extraction of the transition form factor depends critically on it and the existing inclusive data are consistent with a transition form factor much larger than previous values, showing no serious discrepancy with the Bloom-Gilman duality.

Nucleon form factors in a VMD model with bothQ 2- andS-channel duality

VMD models fail in their descriptions of nucleon and nuclear form factors, not because they are wrong but because they are incomplete. The version of quark-hadron duality which they express, the so-calledQ2-duality, refers only to the spectrum of vector mesons which couple to the photon. This version is incomplete. Quark-hadron duality includes also thes-channel or Bloom-Gilman duality which allows to reproduce asymptotic quark model behavioure.g. in structure functions, by summing over the contributions of hadronic, not only vector meson, intermediate states. A VMD model which incorporates these two forms of duality is presented. It gives excellent fits to nucleon form factors in the spacelike region. When the corresponding formulae are continued to the timelike region they yield absolute predictions. Those for the proton agree remarkably well with the available data. The proton and neutron form factors in this region turn out to be approximately of the same order for all values of the momentum transfer. We therefore predict approximately equal values for the cross-sections\(\sigma \left( {e^ + e^ - \to p\bar p} \right)\) and\(\sigma \left( {e^ + e^ - \to n\bar n} \right)\) for all values of the e+e− centre-of-mass energy.

Quantum chromodynamics and Bloom-Gilman duality.

We study the quantum-chromodynamic explanation of the long-established empirical connection, called Bloom-Gilman duality, between scaling and resonance regimes of the inelastic structure function $\ensuremath{\nu}{W}_{2}({\ensuremath{\omega}}^{\ensuremath{'}})$, where $\ensuremath{\nu}$ and ${\ensuremath{\omega}}^{\ensuremath{'}}$ are the usual kinematic variables. We show how QCD expectations for the baryon transition form factors lead to the observed constancy with momentum transfer of the resonance/"background" ratio. We can also understand why the resonance contribution follows with changing ${Q}^{2}$, a curve whose shape is the same as the scaling-limit curve. We comment on the longitudinal response function and on possible contrasts in exciting resonances with different isospins. These await experimental scrutiny in newer-generation electron facilities.

An alternative to the dimensional counting rules

The asymptotic behaviour of hadron form factors and the threshold behaviours of structure functions are investigated in a model based on i) unitarity with\(q\bar q\) intermediate states in thet =q2 channel, and dispersion relations; ii) asymptotic behaviour of the quark-hadron amplitude governed by the spins of the exchanged (spectators) partons; iii) Bloom-Gilman duality. Our model emphasizes the infra-red region of the impulse diagram and is supposed to work in an intermediateq2 region in which scaling violation and gluon jets are not too important. We find, fort → ∞,\(\bar f_\lambda ^{hadron} (t) \sim \bar f_\lambda ^{quark} (t)\prod\limits_i {t^{S_i - 1} } \prod\limits_j {t^{\alpha _j (0)} } \), where\(\bar f_\lambda \) is the form factor for the current helicity ι, summed over the hadronic helicities,8i the spin of thei-th elementary spectator and α3 the Regge trajectory of thej-th composite spectator. The threshold behaviours of the structure functions are given by the Drell-Yan-West relation. For mesons we predict\(\bar f_0 \sim t^{ - 1} , \bar f_{ \pm 1} \sim t^{ - \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} } \) (in contradiction with helicity selection rules),νW2 (ω = 1) ≠ 0. For baryons, the dipole fit suggests the existence of a spin-zero neutral parton in addition to the quarks. The deuteron data are compatible with our predictions,\(F^d \sim F^\mathcal{N} t^{ - 1.3} \),vW2d∼(ω − 1)−5.6.