Factorization and infrared properties of non-perturbative contributions to DIS structure functions

In this paper we present a new derivation of QCD factorization. We deduce the k _T and collinear factorizations for the DIS structure functions by consecutive reductions of a more general theoretical construction. We begin by studying the amplitude of forward Compton scattering off a hadron target, representing this amplitude as a set of convolutions of two blobs connected by the simplest, two-parton intermediate states. Each blob in the convolutions can contain both the perturbative and non-perturbative contributions. We formulate conditions for separating the perturbative and non-perturbative contributions and attributing them to the different blobs. After that the convolutions correspond to QCD factorization. Then we reduce this totally unintegrated (basic) factorization first to k _T -factorization and finally to collinear factorization. In order to yield a finite expression for the Compton amplitude, the integration over the loop momentum in the basic factorization must be free of both ultraviolet and infrared singularities. This obvious mathematical requirement leads to theoretical restrictions on the non-perturbative contributions (parton distributions) to the Compton amplitude and the DIS structure functions related to the Compton amplitude through the Optical Theorem. In particular, our analysis excludes the use of the singular factors x ^−a (with a>0) in the fits for the quark and gluon distributions because such factors contradict the integrability of the basic convolutions for the Compton amplitude. This restriction is valid for all DIS structure functions in the framework of both k _T -factorization and collinear factorization if we attribute the perturbative contributions only to the upper blob. The restrictions on the non-perturbative contributions obtained in the present paper can easily be extended to other QCD processes where the factorization is exploited.     

Duality between different mechanisms of QCD factorization in <Emphasis Type="Italic">γ</Emphasis><Superscript>*</Superscript><Emphasis Type="Italic">γ</Emphasis> collisions

We study the phenomenon of duality in hard exclusive reactions to which QCD factorization applies. Considering “two-photon”-like processes in the scalar φ _E ³ model and also two-hadron (pion) production from the collisions of a real (transversely polarized) and a highly-virtual, longitudinally polarized photon in QCD, we identify two regimes of factorization, each of them associated with a distinct nonperturbative mechanism. One mechanism involves twist-3 Generalized Distribution Amplitudes, whereas the other one employs leading-twist Transition Distribution Amplitudes. In the case of the scalar φ _E ³ model, we find duality in that kinematical region where the two mechanisms overlap. In the QCD case, the appearance of duality is sensitive to the particular nonperturbative model applied and can, therefore, be used as an additional adjudicator.     

Photon-pion transition form factor at high photon virtualities within the nonlocal chiral quark model

Recently, the BABAR collaboration reported the measurements of the photon-pion transition form factor F _πγγ*(Q ²), which are in strong contradiction to the predictions of the standard factorization approach to perturbative QCD. In the present work, based on a nonperturbative approach to the QCD vacuum and on rather universal assumptions, we show that there exist two asymptotic regimes for the pion transition form factor. One regime with the asymptotic behavior F _πγ*γ(Q ²) ∼ 1/Q ² corresponds to the result of the standard QCD factorization approach, while other violates the standard factorization and leads to asymptotic behavior as F _πγ*γ(Q ²) ∼ ln(Q ²)/Q ². Furthermore, considering specific nonlocal chiral quark models, we find the region of parameters, where the existing CELLO, CLEO and BABAR data for the pion transition form factor are successfully described.     

One-Loop QCD Corrections to the Inclusive Production Cross-Section for Heavy Quarks in p Collisions at High Transverse Energies

We calculate one-loop QCD corrections to the production cross-section for heavy quarks in protonantiproton collisions. We are interested in the behaviour of the cross-section at high transverse energies. At high P_T the quark mass should become an irrelevant parameter. Therefore we work in the framework of massless QCD and absorb all mass singularities in a redefinition of the parton densities and fragmentation functions. Numerical results of the cross-section at √S = 0.63, 1.8 and 10 TeV are presented and the dependence of these results on the factorization scheme is examined.     

The curvature of F<Subscript>2</Subscript><Superscript>p</Superscript>(x,Q<Superscript>2</Superscript>) as a probe of the range of validity of perturbative QCD evolutions in the small-x region

Perturbative NLO and NNLO QCD evolutions of parton distributions are studied, in particular in the (very) small-x region, where they are in very good agreement with all recent precision measurements of F₂ ^p(x,Q²). These predictions turn out to be also rather insensitive to the specific choice of the factorization scheme (MS̄ or DIS). A characteristic feature of perturbative QCD evolutions is a positive curvature of F₂ ^p which increases as x decreases. This perturbatively stable prediction provides a sensitive test of the range of validity of perturbative QCD.     

Sum rule estimate of the subleading non-perturbative contributions to Bs–$\bar{ B}_{s}$ mixing

We use QCD sum rules to compute the matrix elements of the ΔB=2 operators appearing in the heavy-quark expansion of the width difference of the B _s mass eigenstates. The main focus of our analysis is on the subleading operators R ₂ and R ₃, which appear at next-to-leading order in the 1/m _b expansion. The matrix elements of these operators are already essential for precise phenomenology, but their calculation in lattice QCD is lacking and the values given here provide a first estimate of their values. We conclude that the violation of the factorization approximation for these matrix elements due to non-perturbative vacuum condensates is as low as 1–2%.     

QCD factorization for the DIS structure functions at small x

We suggest a new form of QCD factorization for inclusive processes at high energies and then reduce it to K _T -factorization. In turn, K _T -factorization can be reduced to collinear factorization when the unintegrated parton distributions have at least one maximum in k _⊥. This property of the parton distributions can be checked with studying data of experiment. The sharper the maximum is, the more accurate the transition to collinear factorization can be done. We apply our results to deduce theoretical restrictions requirements on fits for parton distributions in both K _T - and collinear factorizations contrary to the present situation where the fits are introduced from purely phenomenological consideration so that any formula for them is acceptable if it matches experimental data.     

Nonfactorization in D+→K0K+ Decays

We analyze D⁺→K⁰K⁺decay at the leading order, α s corrections with the QCD factorization approach and the soft-gluon effects with the light cone QCD sum rules. We find the prediction of naive factorization is far from the experimental data, and the QCD factorization result approaches to the experimental data. However, in QCD factorization method, if we consider the soft-gluon effects, then the result is in accordance with the experimental data well. Our calculation shows that the soft-gluon contributions which are firstly calculated in D meson nonleptonic decay are noticeable. So, it can't be neglected in the decay channel.     

Factorization and polarization in two charmed-meson B decays

We provide a comprehensive test of factorization in the heavy–heavy B decays motivated by the recent experimental data from the BELLE and BABAR collaborations. The penguin effects are not negligible in the B decays with two pseudoscalar mesons. The direct CP asymmetries are found to be a few percent. We give estimates on the weak annihilation contributions by analogy to the observed annihilation-dominated processes. The N_c insensitivity of branching ratios indicates that the soft final state interactions are not dominant. We also study the polarizations in B→D^*D_(s)^* decays. The power law shows that the transverse perpendicular polarization fraction is small. The effects of the heavy quark symmetry breaking caused by the perturbative QCD and power corrections on the transverse polarization are also investigated.     

Photoproduction of W bosons at HERA: QCD corrections

W bosons can be produced in the channels at HERA thus allowing to probe for anomalous trilinear couplings among the gauge bosons. We discuss the next-to-leading order (NLO) QCD corrections to the photoproduction of W bosons with finite transverse momentum at HERA. The higher-order QCD corrections reduce the factorization scale dependence significantly and modify the leading-order (LO) cross sections by . Received: 18 April 2002 / Published online: 30 August 2002 RID="*" ID="*" Present address: Deutsches Elektronen-Synchrotron DESY, 22603 Hamburg, Germany     

Transversity in hard exclusive electroproduction of pseudoscalar mesons

Estimates for electroproduction of pseudoscalar mesons at small values of skewness are presented. Cross-sections and asymmetries for these processes are calculated within the handbag approach which is based on factorization in hard parton subprocesses and soft generalized parton distributions (GPDs). The latter are constructed from double distributions. Transversity GPDs are taken into account; they are accompanied by twist-3 meson wave functions. For most pseudoscalar-meson channels a combination of ˜_T and [`(E)]_T \bar{{E}}_{T}^{} plays a particularly prominent role. This combination of GPDs, which we constrain by moments obtained from lattice QCD, leads, with the exception of the p⁺ \pi^{+}_{} and h^￠ \eta^{\prime}_{} channels, to large transverse cross-sections.     

QCD Aspects of Exclusive B Decays

We review QCD approaches to exclusive B meson decays, concentrating on QCD-improved factorization and perturbative QCD. The ideas of soft-collinear effective theory and light-cone sum rules are briefly explained. We discuss the recently measured time-dependent CP asymmetry of the B⁰ _d^{+ –} modes, from which the unitarity angle can be extracted.     

B c-meson decays and lifetime within QCD sum rules

On the basis of three-point sum rules, the form factors for the semileptonic decays B _c ⁺ → B _s(B _s ^* )l ⁺ ν _l are calculated with allowance for α _s/v Coulomb corrections for the heavy quarkonium. Generalized relations associated with spin symmetry within the approach combining heavy-quark effective theory and nonrelativistic QCD are derived for form factors in the region of recoil momenta close to zero. The nonleptonic decays of the B _c meson are studied on the basis of the factorization hypothesis. By summing the main exclusive modes of c-quark decays and by using the results of a previous analysis of b-quark decays, the B _c-meson lifetime is estimated within QCD sumrules and within nonrelativistic QCD.     

Gluon bremsstrahlung in supersymmetric QCD

In the lowest α_s³ order perturbation theory of SUSY QCD gluon bremsstrahlung in scalar quark-pair production is calculated. The factorization of the corresponding Born cross sections and generalized “infrared” factors is shown.     

Order αs QCD corrections to the Burkhardt-Cottingham sum rule

We have computed theO(_s) QCD corrections to the transverse spin dependent structure functiong ₂(x, Q ²). The calculation reveals that the Burkhardt-Cottingham sum rule is violated in first order of _s. This result contradicts earlier findings in the literature. Its implication in the context of the operator product expansion and the mass factorization will be discussed.     

Determination of heavy-meson wave functions from B decays

We extract the B, D, and meson wave functions from the CLEO data of the decays and in the perturbative QCD framework. In this formalism, various logarithmic corrections are organized to give the Wilson evolution from the W boson mass down to the characteristic scale of a decay process, which is of order of the b quark mass, and the Sudakov evolution from the characteristic scale to a lower factorization scale of order . With large logarithms organized, the b quark decay amplitudes are evaluated reliably in perturbation theory. Below the factorization scale, QCD dynamics is regarded as being nonperturbative, and absorbed into meson wave functions. Because of their universality, the heavy-meson wave functions determined in this work, can be employed to make predictions of other decay modes. We also observe that the dependence of heavy meson wave functions on intrinsic parton transverse momenta plays an important role in the explanation of data. Received: 18 February 1999 / Revised version: 24 June 1999 / Published online: 3 November 1999     

Exclusive decay to double at next-to-leading order in

Within the non-relativistic QCD (NRQCD) factorization framework, we calculate the exclusive decay process η_b→J/ψJ/ψ to next-to-leading order in the strong coupling constant, and, at leading order, in the charm quark relative velocity. It is found that this new contribution to the amplitude is comparable in magnitude to the previously calculated relativistic correction piece, but differs by a phase of about 90°. Including this new contribution will increase the previous prediction of substantially, thus brightening the discovery potential of this clean hadronic decay channel of η_b in the forthcoming LHC experiment.     

Branching ratio and CP violation of <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript>→<Emphasis Type="Italic">DK</Emphasis> decays in the perturbative QCD approach

In this paper, we calculate the branching ratio and direct CP asymmetry parameter of B _c ^±→D ⁰ K ^± in the framework of a perturbative QCD approach based on k _T factorization. Besides the usual factorizable diagrams, both nonfactorizable and annihilation type contributions are taken into account. We find that (a) the branching ratio is at the order of 10⁻⁵; (b) the tree annihilation diagrams and the penguin diagrams dominate the total contribution; and (c) the direct CP asymmetry is about 7%, which can be tested in the Large Hadron Collider beauty experiments (LHC-b) at CERN.     

Jet production in hadronic collisions to0(α s 3 )

We present the full0(α _s ³ ) QCD corrections to jet production within a small opening angle δ at large transverse momenta for all partonic subprocesses. Results for CERN and Tevatron colliders are given with particular emphasis on the sensitivity to renormalization and factorization mass scales.