Hard QCD Processes Research Articles

Toward a NNLO calculation of theB¯→Xsγdecay rate with a cut on photon energy: II. Two-loop result for the jet function

The complete two-loop expression for the jet function J(p2,μ) of soft-collinear effective theory is presented, including non-logarithmic terms. Combined with our previous calculation of the soft function S(ω,μ), this result provides the basis for a calculation of the effect of a photon-energy cut in the measurement of the B¯→Xsγ decay rate at next-to-next-to-leading order in renormalization-group improved perturbation theory. The jet function is also relevant to the resummation of Sudakov logarithms in other hard QCD processes.

Behavior of single-scale hard small-xprocesses in QCD near the black disk limit

We argue that at sufficiently small Bjorken x where pQCD amplitudes rapidly increase with energy and violate probability conservation the shadowing effects in the single-scale small x hard QCD processes can be described by an effective quantum field theory of interacting quasiparticles--perturbative QCD ladders. We find, within the WKB approximation, that the smallness of the QCD coupling constant ensures the hierarchy among many-quasiparticle interactions evaluated within the physical vacuum and, in particular, the dominance in the Lagrangian of the triple quasiparticle interaction. It is explained that the effective field theory considered near the perturbative QCD vacuum contains a tachyon relevant for the divergency of the perturbative QCD series at sufficiently small x. We solve the equations of motion of the effective field theory within the WKB approximation and find the physical vacuum and the transitions between the false (perturbative) and physical vacua. Classical solutions which dominate transitions between the false and physical vacua are kinks that cannot be decomposed into perturbative series over the powers of {alpha}{sub s}. These kinks lead to color inflation and the Bose-Einstein condensation of quasiparticles. The account of the quantum fluctuations around the WKB solution reveals the appearance of the ''massless'' particles--phonons. It is explainedmore » that phonons are relevant for the black disk behavior of cross sections of small x processes. The Bose-Einstein condensation of the ladders produces a color network occupying a ''macroscopic'' longitudinal volume. We discuss briefly the possible detection of new QCD effects. We outline albeit briefly the relationship between the small x hard QCD processes and the coherent critical phenomena.« less

Soft rescattering in DIS: effects of helicity flip

Soft rescattering in hard QCD processes may involve non-perturbative, chiral symmetry breaking interactions. We find that rescattering which changes the helicity of the struck quark gives rise to a leading twist single spin asymmetry in semi-inclusive DIS, the angular dependence of which is the same as that usually ascribed to the Collins effect. We argue that helicity-changing rescattering can contribute also to $k_\perp$-integrated parton distributions.

Nonlinear k ⊥ factorization: A new paradigm for hard QCD processes in a nuclear environment

A large thickness of the heavy nuclei brings a new hard scale into the pQCD description of hard processes in a nuclear environment. This new scale breaks the conventional linear k⊥ factorization which must be replaced by a new concept of the nonlinear nuclear k⊥ factorization. Here, we review the recent progress in the theory of nonlinear k⊥ factorization. Our focus is on the role of diffractive interactions, the variation of the pattern of k⊥ factorization for single-jet processes from deep inelastic scattering to hadron-nucleus collisions and universality classes for dijet production off nuclei.

Soft and hard processes in QCD

QCD equations for the generating functions are applied to separate soft and hard jets in $e^+e^-$-processes of multiparticle production. The dependence of average multiplicities and higher moments of multiplicity distributions of particles created in a "newly born" soft subjets on the share of energy devoted to them is calculated in fixed coupling gluodynamics. This dependence is the same as for the total multiplicity up to a constant factor if soft jets are defined as those carrying out a fixed share of initial energy at all energies. The constant factor depends on this share in a non-trivial way. Other definitions are also proposed. The relation between these quantities for soft and hard processes is discussed.

Is the Belle result for the cross section [formula omitted] a real difficulty for QCD?

It is argued that difficulties in reconciling the values of the cross-section σ(e+e−→J/ψ+ηc) measured at Belle and calculated within non-relativistic QCD (NRQCD) are caused not by some misinterpretation of the data or other exotic explanations, but by poor applicability of NRQCD to such processes.We use general theory of hard exclusive processes in QCD together with more realistic models of charmonium wave functions, and show that the Belle result can be naturally explained.

A new method for real radiation at next-to-next-to-leading order

We propose a new method of computing real emission contributions to hard QCD processes. Our approach uses sector decomposition of the exclusive final-state phase space to enable extraction of all singularities of the real emission matrix elements before integration over any kinematic variable. The exact kinematics of the real emission process are preserved in all regions of phase space. Traditional approaches to extracting singularities from real emission matrix elements, such as phase space slicing and dipole subtraction, require both the determination of counterterms for double real emission amplitudes in singular kinematic limits and the integration of these contributions analytically to cancel the resulting singularities against virtual corrections. Our method addresses both of these issues. The implementation of constraints on the final-state phase space, including various jet algorithms, is simple using our approach. We illustrate our method using ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}$ jets at $O({\ensuremath{\alpha}}_{S}^{2})$ as an example.

QCD saturation and soft processes

We show that an approximate solution to the amended non-linear Balitsky-Kovchegov evolution equation which was formulated for hard QCD processes, can be extended to provide a good description of photoproduction and soft hadronic (non perturbative) reactions.

Initial-state interactions in the unpolarized Drell-Yan process

We show that initial-state interactions contribute to the $\cos 2 \phi$ distribution in unpolarized Drell-Yan lepton pair production $p p$ and $ p \bar p \to \ell^+ \ell^- X$, without suppression. The asymmetry is expressed as a product of chiral-odd distributions $h_1^\perp(x_1,\bm{p}_\perp^2)\times \bar h_1^\perp(x_2,\bm{k}_\perp^2) $, where the quark-transversity function $h_1^\perp(x,\bm{p}_\perp^2)$ is the transverse momentum dependent, light-cone momentum distribution of transversely polarized quarks in an {\it unpolarized} proton. We compute this (naive) $T$-odd and chiral-odd distribution function and the resulting $\cos 2 \phi$ asymmetry explicitly in a quark-scalar diquark model for the proton with initial-state gluon interaction. In this model the function $h_1^\perp(x,\bm{p}_\perp^2)$ equals the $T$-odd (chiral-even) Sivers effect function $f^\perp_{1T}(x,\bm{p}_\perp^2)$. This suggests that the single-spin asymmetries in the SIDIS and the Drell-Yan process are closely related to the $\cos 2 \phi$ asymmetry of the unpolarized Drell-Yan process, since all can arise from the same underlying mechanism. This provides new insight regarding the role of quark and gluon orbital angular momentum as well as that of initial- and final-state gluon exchange interactions in hard QCD processes.

Renormalization group approach to soft gluon resummation

We present a simple proof of the all-order exponentiation of soft logarithmic corrections to hard processes in perturbative QCD. Our argument is based on proving that all large logs in the soft limit can be expressed in terms of a single dimensionful variable, and then using the renormalization group to resum them. Beyond the next-to-leading log level, our result is somewhat less predictive than previous all-order resummation formulae, but it does not rely on non-standard factorization, and it is thus possibly more general. We use our result to settle issues of convergence of the resummed series, we discuss scheme dependence at the resummed level, and we provide explicit resummed expressions in various factorization schemes.

Expanding running coupling effects in the hard Pomeron

We study QCD hard processes at scales of order k^2 > Lambda^2 in the limit in which the beta-function coefficient - b is taken to be small, but alphas(k) is kept fixed. The (nonperturbative) Pomeron is exponentially suppressed in this limit, making it possible to define purely perturbative high-energy Green's functions. The hard Pomeron exponent acquires diffusion and running coupling corrections which can be expanded in the b parameter and turn out to be dependent on the effective coupling b alphas^2 Y. We provide a general setup for this b-expansion and we calculate the first few terms both analytically and numerically.

Away-from-jet energy flow

We consider interjet observables in hard QCD processes given by the energy flow E_out in a region away from all hard jets. Here the QCD radiation is depleted (E_out << Q), and therefore these observables provide ideal means to study non-perturbative effects. We derive an evolution equation (in the large N_c limit) which resums, for large Q/E_out, all leading terms arising from large angle soft emission (double logarithms are absent). We discuss the analytical features of the result and identify universal and geometry-dependent contributions. Our analysis confirms features found using numerical methods by Dasgupta and Salam.

Nonlocal operators and distribution amplitudes of definite twist, WW—relations, EC—sum rules and power corrections for hard QCD processes

The decomposition of nonlocal operators (and of their matrix elements) into an (infinite) series w.r.t. geometric twist is used to introduce (new) parton distributions, generalized parton distributions and hadron wave functions of definite twist. Their comparision with the conventional distributions (of definite dynamical twist) leads to Wandzura-Wilczek like relations, Burkhardt-Cottingham like sum rules and allows for power corrections of the various distribution amplitudes. Some general aspects are reviewed.

Power corrections to exclusive processes in QCD

In practice applicability of twist expansion crucially depends on the magnitude to power corrections to the leading-twist amplitude. I illustrate this point by considering explicit examples of two hard exclusive processes in QCD. In the case of γ *γ → ππ amplitude power corrections are small enough such that it should be possible to describe current experimental data by the leading-twist QCD prediction. The photon helicity-flip amplitude in DVCS on a nucleon receives large kinematical power corrections which screen the leading-twist prediction up to large values of the hard photon virtuality.

Hard QCD processes and impact-parameter dependence of parton energy losses in ultrarelativistic nuclear collisions

Special features of particle and jet production in hard QCD processes induced by ultrarelativistic heavy-ion collisions are investigated. The energy loss of partons produced in hard collisions that is due to their multiple scattering in dense quark-gluon matter is analyzed as a function of the impact parameter of a nucleus-nucleus collision. The possibility of experimentally observing effects that are expected in this connection and which include different impact-parameter dependences of radiative and collision hard-jet energy losses, a modification to the shape of the impact-parameter distribution of dijets, and the suppression of the yield of muon pairs having large invariant masses is discussed.

Fracture functions

We describe here a new approach to semi-inclusive hard processes in QCD by means of Fracture Functions, hybrids between structure and fragmentation functions. We briefly motivate and describe our approach together with a list of possible applications.

Resummation in hard QCD processes

We show that the resummation of large radiative corrections in QCD processes can be performed both in covariant gauge and in axial gauge. We extend the resummation technique to inclusive processes, concentrating on deeply inelastic scattering, Drell-Yan production, and inclusive heavy meson decays in end-point regions. Leading and next-to-leading logarithms produced by radiative corrections are organized into Sudakov factors, whose expressions are the same as those derived from the conventional Wilson-loop approach. The gauge invariance of the resummation in the end-point region is demonstrated explicitly.

Hard Probes in High-Energy Heavy-Ion Collisions

Hard QCD processes in ultrarelativistic heavy-ion collisions become increasingly relevant and they can be used as probes of the dense matter formed during the violent scatterings. We will discuss how one can use these hard probes to study the properties of the dense matter and the associated phenomenologies. In particular, we study the effect of jet quenching due to medium-induced energy loss on inclusive particle $p_T$ distributions and investigate how one can improve the measurement of parton energy loss in direct photon events

Asymptotics of heavy-meson form factors

Using methods developed for hard exclusive QCD processes, we calculate the asymptotic behaviour of heavy-meson form factors at large recoil. It is determined by the leading- and subleading-twist meson wave functions. For $1\ll |v\cdot v'|\ll m_Q/\Lambda$, the form factors are dominated by the Isgur--Wise function, which is determined by the interference between the wave functions of leading and subleading twist. At $|v\cdot v'|\gg m_Q/\Lambda$, they are dominated by two functions arising at order $1/m_Q$ in the heavy-quark expansion, which are determined by the leading-twist wave function alone. The sum of these contributions describes the form factors in the whole region $|v\cdot v'|\gg 1$. As a consequence, there is an exact zero in the form factor for the scattering of longitudinally polarized $B^*$ mesons at some value $v\cdot v'\sim m_b/\Lambda$, and an approximate zero in the form factor of $B$ mesons in the timelike region ($v\cdot v'\sim -m_b/\Lambda$). We obtain the evolution equations and sum rules for the wave functions of leading and subleading twist as well as for their moments. We briefly discuss applications to heavy-meson pair production in $e^+ e^-$ collisions.

Power corrections in QCD hard processes and IR renormalons

I summarise results obtained in three papers covering the following areas: factorial growth of perturbative coefficients, dispersive approach to power corrections in hard processes, and the Wilson renormalization group approach to renormalons.