Sense and Nonsense on Parton Distribution functions of the Photon
The organization of finite order QCD approximations to $F_2^γ(x,Q^2)$ based on the separation of pure QED contribution from those of genuine QCD nature is discussed.
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arXiv subjects
Jiri Chyla
Publications and source records attributed to Jiri Chyla.
The implications of final L3 measurement of $σ_{tot}(γγ\to b\bar{b}
he excess of data on the total cross section of $\bar{b}b$ production in $γγ$ collisions over QCD predictions, observed by L3, OPAL and DELPHI Collaborations at LEP2, has so far defied explanation. The recent final analysis of L3 data has brought important new information concerning the dependence of the observed excess on the $γγ$ collisions energy $W_{γγ}$. The implications of this dependence are discussed.
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On higher order corrections to photon structure functions
The QCD corrections to photon structure functions are defined in a way consistent with the factorization scheme invariance. It is shown that the conventional DIS$_γ$ factorization scheme does not respect this invariance and is thus deeply flawed. The origins of the divergent behavior of photonic coefficient function at large $x$ are analyzed and recipe to remove it is suggested.
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Jet and inclusive particle production in photon induced collisions
Recent progress in application of higher order QCD calculations to jet and inclusive particle production in photon induced collisions is reviewed. Attention is paid to theoretical uncertainties of such calculations, particularly those coming from the choice of renormalization and factorization scales.
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Scale dependence of heavy quark production in pp and $\bar{\mathbf{p}}$p collisions - transverse momentum dependence
The dependence of the differential cross section ${\mathrm{d}σ}/{\mathrm{d}p_{\perp}}$ of inclusive heavy quark production in pp and $\bar{\mathrm{p}}$p collisions on the renormalization and factorization scales is investigated. The implications of our results for experiments at TEVATRON and LHC are discussed. In particular, it is shown that the NLO QCD predictions for $\bar{t}t$ production at the LHC based on the Principle of Minimal Sensitivity are by 30-50% higher than the standard ones.
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Dijet cross sections in ep collisions: who is afraid of symmetric cuts?
Three widely used scenaria for defining cuts on transverse energies of jets in ep collisions are discussed. All of them are shown to suffer from the same sort of unphysical behaviour when the cut regions are subject to additional constraints. This feature is inherent in the very way dijet cross sections are defined and cannot be avoided. In particular, the symmetric cut scenario is shown to be equally suitable for the comparison with NLO QCD calculations as the asymmetric or sum-like ones.
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Renormalization and factorization scale analysis of $\bar{b}b$ production in antiproton-proton collisions
There a sizable and systematic discrepancy between experimental data on the $\bar{b}b$ production in $\bar{\mathrm p}$p, $γ$p and $γγ$ collisions and existing theoretical calculations within perturbative QCD. Before interpreting this discrepancy as a signal of new physics, it is important to understand quantitatively the ambiguities of conventional calculations. In this paper the uncertainty coming from renormalization and factorization scale dependence of finite order perturbation calculations of the total cross section of $\bar{b}b$ production in $\bar{\mathrm{p}}$p collisions is discussed in detail. It is shown that the mentioned discrepancy is reduced significantly if these scales are fixed via the Principle of Minimal Sensitivity.
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Renormalization scheme dependence in the case of a QCD non-power perturbative expansion
A novel, non-power, expansion of QCD quantities replacing the standard perturbative expansion in powers of the renormalized couplant a has recently been introduced and examined by two of us. Being obtained by analytic continuation in the Borel plane, the new expansion functions W_n(a) share the basic analyticity properties with the expanded quantity. In this note we investigate the renormalization scale dependence of finite order sums of this new expansion for the phenomenologically interesting case of the tau-lepton decay rate.
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Heavy quark production in $γγ$ collisions
Current theoretical framework for the calculation of heavy quark production in $γγ$ collisions is reviewed. The importance of including direct photon contributions up to the order $α^2α_s^2$ and of the proper choice of renormalization and factorization scales in the evaluation of $σ(γγ\to Q\bar{Q})$ is emphasized.
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Hard collisions of photons: plea for a common language
An attempt is made to sort out ambiguities existing in the current usage of several basic concepts describing hard collisions of photons. It is argued that appropriate terminology is often a prerequisite for correct physics.
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Heavy quark production in $γγ$ collisions: a theoretical reappraisal
Heavy quark production in $γγ$ collisions is reanalyzed. It is argued that evaluating the cross section $σ(γγ\to Q\overline{Q})$ in a well-defined renormalization scheme requires the inclusion of direct photon contributions up to the order $α^2α_s^2$. The order $α^2α_s^2$ direct photon contributions are furthermore needed for factorization scale invariance of the sum of direct and resolved photon contributions. The importance of quantitative analysis of renormalization and factorization scale dependence of the approximation currently used for the evaluation of $σ(γγ\to Q\overline{Q})$ is emphasized as the only way of estimating the theoretical uncertainty related to the ambiguity in choosing these scales.
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QCD analysis of $F_2^γ(x,Q^2)$: an unconventional view
Elements of the alternative approach to hard collisions of photons, proposed recently by the author, are reviewed, with particular attention to QCD analysis of $F^γ_2$. This approach is based on clear separation of genuine QCD effects from those of pure QED origin and does not rely on the assumption that parton distribution functions of the photon behave as $α/α_s$. It differs significantly from the conventional one, as illustrated on the example of charm contribution to $F_{2}^γ$, recently measured at LEP.
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Resolved ${\mathbf {γ^*_L}}$ in hard collisions of virtual photons: QCD effects
The manifestations of QCD effects on quark and gluon distribution functions of longitudinally polarized virtual photons involved in hard collisions are investigated. It is shown that for moderate photon virtualities and in the kinematical region accessible at HERA and LEP these effects are sizable and significantly enhance theoretical predictions based on contributions of transversally polarized virtual photon only.
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Partonic structure of $γ_L^*$ in hard collisions
Manifestation of QCD improved partonic structure of longitudinally polarized virtual photons in hard collisions is discussed. As an example, dijet production in ep collisions at HERA is investigated in detail.
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QCD improved parton distribution functions of ${\mathbf{γ^*_L}}$
QCD corrections to the QED formula for parton distribution functions of the longitudinal virtual photon are derived in the leading--logarithmic approximation. It is shown that the resulting PDF satisfy the same homogeneous evolution equations as those of hadrons, but contrary to the latter are perturbatively calculable. Properties of these distribution functions are discussed and their phenomenological consequences outlined.
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The relevance of $γ_L^*$ in hard collisions of virtual photons
We explore the relevance of extending the concept of the structure to the longitudinally polarized virtual photon involved in hard collisions. We show that for moderate photon virtualities and in the kinematical region accessible in current experiments at HERA and LEP, the contributions of its longitudinal polarization to hard collisions are sizable and should be taken into account as part of the resolved photon component.
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Interpreting virtual photon interactions in terms of parton distribution functions
Interactions of virtual photons are analyzed in terms of photon structure. It is argued that the concept of parton distribution functions is phenomenologically very useful even for highly virtual photons involved in hard collisions. This claim is illustrated on leading order expressions for $F_2^γ(x,P^2,Q^2)$ and effective parton distribution function $D_{\mathrm eff}(x,P^2,Q^2)$ relevant for jet production, as well as within the next-to-leading order QCD calculations of jet cross-sections in electron-proton collisions.
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When semantics turns to substance: reformulating QCD analysis of F_2^γ(x,Q^2)}
QCD analysis of F_2^γ(x,Q^2) is revisited. It is emphasized that the presence of the inhomogeneous term in the evolution equations for quark distribution functions of the photon implies important difference in the way factorization mechanism works in photon-hadron and photon-photon collisions as compared to the hadronic ones. Moreover, a careful definitions of the very concepts of the ``leading order'' and ``next-to-leading order'' QCD analysis of F_2^γ are needed in order to separate genuine QCD effects from those of pure QED origin. After presenting such definitions, I show that all existing allegedly LO, as well as NLO analyses of F_2^γ(x,Q^2) are incomplete. The source of this incompleteness of the conventional approach is traced back to the lack of clear identification of QCD effects and to the misinterpretation of the behaviour of q^γ(x,M) as a function of α_s(M). Complete LO and NLO QCD analyses of F_2^γ(x,Q^2) are shown to differ substantially from the conventional ones. Whereas complete NLO analysis requires the knowledge of two so far uncalculated quantities, a complete LO one is currently possible, but compared to the conventional formulation requires the inclusion of four known, but in the existing LO analyses unused quantities. The arguments recently advanced in favour of the conventional approach are analyzed and shown to contain a serious flaw. If corrected, they actually lends support to my claim.
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