Higher Twist Contributions Research Articles

Bjorken sum rule and perturbative QCD frontier on the move

The reasonableness of the use of perturbative QCD notions in the region close to the scale of hadronization, i.e., below $\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{GeV}$ is under study. First, the interplay between higher orders of pQCD expansion and higher-twist contributions in the analysis of recent Jefferson Lab (JLab) data on the generalized Bjorken sum rule function ${\ensuremath{\Gamma}}_{1}^{p\ensuremath{-}n}({Q}^{2})$ at $0.1l{Q}^{2}l3\text{ }\text{ }{\mathrm{GeV}}^{2}$ is studied. It is shown that the inclusion of the higher-order pQCD corrections could be absorbed, with good numerical accuracy, by change of the normalization of the higher-twist terms. Second, to avoid the issue of unphysical singularity (Landau pole at $Q=\ensuremath{\Lambda}\ensuremath{\sim}400\text{ }\text{ }\mathrm{MeV}$), we deal with the ghost-free analytic perturbation theory (APT) that recently proved to be an intriguing candidate for a quantitative description of light quarkonia spectra within the Bethe-Salpeter approach. The values of the twist coefficients ${\ensuremath{\mu}}_{2k}$ extracted from the mentioned data by using the APT approach provide a better convergence of the higher-twist series than with the common pQCD. As the main result, a good quantitative description of the JLab data down to $Q\ensuremath{\simeq}350\text{ }\text{ }\mathrm{MeV}$ is achieved.

Next-to-next-to-leading order QCD contributions to the flavor nonsinglet sector ofF2(x,Q2)

We present the results of our QCD analysis for nonsinglet unpolarized quark distributions and structure function ${F}_{2}(x,{Q}^{2})$. New parameterizations are derived for the nonsinglet quark distributions for the kinematic wide range of $x$ and ${Q}^{2}$. The analysis is based on the Jacobi polynomials expansion of the structure function. The higher twist contributions of proton and deuteron structure function are obtained in the large $x$ region. Our calculations for nonsinglet unpolarized quark distribution functions based on the Jacobi polynomials method are in good agreement with the other theoretical models. The values of ${\ensuremath{\Lambda}}_{\mathrm{QCD}}$ and ${\ensuremath{\alpha}}_{s}({M}_{z}^{2})$ are determined.

Analytic QCD - a Short Review

Analytic versions of QCD are those whose coupling αs(Q2) does not have the unphysical Landau singularities on the space-like axis (-q2= Q2 > 0). The coupling is analytic in the entire complex plane except the time-like axis (Q2 < 0). Such couplings are thus suitable for application of perturbative methods down to energies of order GeV. We present a short review of the activity in the area which started with a seminal paper of Shirkov and Solovtsov ten years ago. Several models for analytic QCD coupling are presented. Strengths and weaknesses of some of these models are pointed out. Further, for such analytic couplings, constructions of the corresponding higher order analytic couplings (the analogs of the higher powers of the perturbative coupling) are outlined, and an approach based on the renormalization group considerations is singled out. Methods of evaluation of the leading-twist part of space-like observables in such analytic frameworks are described. Such methods are applicable also to the inclusive time-like observables. Two analytic models are outlined which respect the ITEP Operator Product Expansion philosophy, and thus allow for an evaluation of higher-twist contributions to observables.

The baryon anomaly: Evidence for color transparency and direct hadron production at RHIC

We show that the QCD color transparency of higher-twist contributions to inclusive hadroproduction cross sections, where baryons are produced directly in a short-distance subprocess, can explain several remarkable features of high-pT baryon production in heavy ion collisions which have recently been observed at RHIC: (a) the anomalous increase of the proton-to-pion ratio with centrality, (b) the increased power-law fall-off at fixed xT=2pT/s of the charged particle production cross section in high centrality nuclear collisions, and (c) the anomalous decrease of the number of same-side hadrons produced in association with a proton trigger as the centrality increases. We show that correlations between opposite-side hyperons and kaons can provide a clear signature of higher-twist contributions. These phenomena emphasize the importance of understanding hadronization at the amplitude level in QCD illustrate how heavy ion collisions can provide sensitive tools for interpreting and testing fundamental properties of QCD.

Systematic phenomenological study of thecos2ϕasymmetry in unpolarized semi-inclusive DIS

We study the $\mathrm{cos}2\ensuremath{\phi}$ azimuthal asymmetry in unpolarized semi-inclusive DIS, taking into account both the perturbative contribution (gluon emission and splitting) and the nonperturbative effects arising from intrinsic transverse motion and transverse spin of quarks. In particular we explore the possibility to extract from $⟨\mathrm{cos}2\ensuremath{\phi}⟩$ some information about the Boer-Mulders function ${h}_{1}^{\ensuremath{\perp}}$, which represents a transverse-polarization asymmetry of quarks inside an unpolarized hadron. Predictions are presented for the HERMES, COMPASS and JLab kinematics, where $⟨\mathrm{cos}2\ensuremath{\phi}⟩$ is dominated by the kinematical higher-twist contribution, and turns to be of order of a few percent. We show that under reasonable assumptions a larger asymmetry in ${\ensuremath{\pi}}^{\ensuremath{-}}$ production, compared to ${\ensuremath{\pi}}^{+}$ production, would represent a signature of the Boer-Mulders effect.

Angular dependences in inclusive two-hadron production at BELLE

A collection of results is presented relevant for the analysis of azimuthal asymmetries in inclusive two-hadron production at BELLE. The aim of this overview is to provide theoretical ingredients necessary to extract the Collins effect fragmentation function. The latter arises within the Collins–Soper factorization formalism, which describes both the transverse momentum and Q 2 dependence of the cross section and its angular dependences at low and moderate transverse momentum. Since the Collins effect is not the only source of angular dependences, a discussion of various other effects is included. This concerns higher twist contributions, photon– Z-boson interference effects, radiative corrections, beam polarization and weak decays. Furthermore, different frames, transverse momentum weighting and ratios of asymmetries are discussed. These issues are all of relevance for the unambiguous measurement of the Collins effect.

HIGHER TWIST EFFECTS IN PHOTON–PHOTON COLLISIONS

In this article, we investigate the contribution of the high twist Feynman diagrams to the large-pT single pseudoscalar and vector mesons inclusive production cross section in two-photon collisions and we present the general formulae for the high and leading twist differential cross sections. The pion wave function where two non-trivial Gegenbauer coefficients a2 and a4 have been extracted from the CLEO data, Braun–Filyanov pion wave function, the asymptotic and the Chernyak–Zhitnitsky wave functions are all used in the calculations. For ρ-meson we used the Ball–Braun wave function. The results of the calculations reveal that the high twist cross sections, the ratio R, the dependence transverse momentum pT and the rapidity y of meson in the Φ CLEO (x, Q2) wave function case is very close to the Φ asy (x) asymptotic wave function case. It is shown that the high twist contribution to the cross section depends on the choice of the meson wave functions.

Higher twist contributions to the structure functions [formula omitted] and [formula omitted] at large x at higher orders

The higher twist contributions to the deeply inelastic structure functions F2p(x,Q2) and F2d(x,Q2) for larger values of the Bjorken variable x are extracted extrapolating the twist-2 contributions measured in the large W2 region to the region 4 GeV2⩽W2⩽12.5 GeV2 applying target mass corrections. We compare the results for the NLO, NNLO and N3LO analyzes and include also the large x at N4LO to the Wilson coefficients. A gradual lowering of the higher twist contributions going from NLO to N4LO is observed, which stresses the importance of higher order corrections.

Twist-3 effects and target mass corrections

We estimate the higher-twist contributions using Nachtmann moments, which provide a method for handling target mass corrections. The corrections to the Cornwall-Norton moments of nucleon spin structure functions are also addressed. Their sizable role in the twist-3 ${\stackrel{~}{d}}_{2}^{p,n,d}$ extracted from the Cornwall-Norton moments is discussed. Moreover, their role in the isoscalar and isovector structure functions is also shown.

Experimental moments of the nucleon structure function F2

Experimental data on the F 2 structure functions of the proton and deuteron, including recent results from CLAS at Jefferson Lab, have been used to construct their n ⩽ 12 moments. A comprehensive analysis of the moments in terms of the operator product expansion has been performed to separate the moments into leading and higher twist contributions. Particular attention was paid to the issue of nuclear corrections in the deuteron, when extracting the neutron moments from data. The difference between the proton and neutron moments was compared directly with lattice QCD simulations. Combining leading twist moments of the neutron and proton we found the d / u ratio at x → 1 approaching 0, although the precision of the data did not allow to exclude the 1/5 value. The higher twist components of the proton and neutron moments suggest that multi-parton correlations are isospin independent.

Jet modification in three dimensional fluid dynamics at next-to-leading twist

The modification of the single inclusive spectrum of high transverse momentum (p{sub T}) pions emanating from an ultrarelativistic heavy-ion collision is investigated. The deconfined sector is modeled using a full three-dimensional (3-D) ideal fluid dynamics simulation. Energy loss of high p{sub T} partons and the ensuing modification of their fragmentation is calculated within perturbative QCD at next-to-leading twist, where the magnitude of the higher twist contribution is modulated by the entropy density extracted from the 3-D fluid dynamics simulation. The nuclear modification factor (R{sub AA}) for pions with a p{sub T}{>=}8 GeV as a function of centrality as well as with respect to the reaction plane is calculated. The magnitude of contributions to the differential R{sub AA} within small angular ranges, from various depths in the dense matter, is extracted from the calculation and demonstrates the correlation of the length integrated density and the R{sub AA} from a given depth. The significance of the mixed and hadronic phase to the overall magnitude of energy loss is explored.

QCD at small x and nucleus–nucleus collisions

At large collision energy and relatively low momentum transfer Q, one expects a new regime of quantum chromo-dynamics (QCD) known as ‘saturation’. This kinematical range is characterized by a very large occupation number for gluons inside hadrons and nuclei; this is the region where higher twist contributions are as large as the leading twist contributions incorporated in collinear factorization. In this talk, I discuss the onset of and dynamics in the saturation regime, some of its experimental signatures and its implications for the early stages of heavy ion collisions.

Non-singlet QCD analysis of deep inelastic world data at [formula omitted

A non-singlet QCD analysis of the structure function F 2 ( x , q 2 ) in LO, NLO, NNLO and N 3LO is performed based on the world data for charged lepton scattering. We determine the valence quark parton densities and present their parameterization and that of the correlated errors in a wide range of x and Q 2 . In the analysis we determined the QCD-scale Λ QCD , N f = 4 MS ¯ = 265 ± 27 MeV ( NLO ) , 226 ± 25 MeV ( NNLO ) , 234 ± 26 MeV ( N 3 LO ) , with a remainder uncertainty of ± 2 MeV for the yet unknown 4-loop anomalous dimension, corresponding to α s ( M Z 2 ) = 0.1148 ± 0.0019 NLO , 0.1134 −0.0021 +0.0019 NNLO , 0.1141 −0.0022 +0.0020 N 3 LO . A comparison is performed to other determinations of the QCD scale and α s ( M Z 2 ) in deeply inelastic scattering. The higher twist contributions of F 2 p ( x , Q 2 ) and F 2 d ( x , Q 2 ) are extracted in the large x region, subtracting the twist-2 contributions obtained in the NLO, NNLO and N 3LO analysis.

Leading and higher twists in proton, neutron and deuteron unpolarized structure functions F2

We summarize the results of a recent global analysis of proton and deuteron F2 structure function world data performed over a large range of kinematics, including recent measurements done at JLab with the CLAS detector. From these data the lowest moments (n≤10) of the unpolarized structure functions are determined with good statistics and systematics. The Q2 evolution of the extracted moments is analyzed in terms of an OPE-based twist expansion, taking into account soft-gluon effects at large x. A clean separation among the leading- and higher-twist terms is achieved. By combining proton and deuteron measurements the lowest moments of the neutron F2 structure function are determined and its leading-twist term is extracted. Particular attention is paid to nuclear effects in the deuteron, which become increasingly important for the higher moments. Our results for the non-singlet, isovector (p-n) combination of the leading-twist moments are used to test recent lattice simulations. We also determine the lowest few moments of the higher-twist contributions, and find these to be approximately isospin independent, suggesting the possible dominance of ud correlations over uu and dd in the nucleon.

Next-to-leading order versus quark off-shellness and intrinsickTin the Drell-Yan process

We calculate the effects of next-to-leading order perturbative QCD as well as of the quark transverse motion and off-shellness on the Drell-Yan process cross section. By studying the s{yields}{infinity} behavior of the cross section in these approaches, we find that the effects of quark off-shellness and intrinsic-k{sub T} parametrize those of higher twists. In particular, the off-shellness of partons generates part of the K-factor type corrections to the leading order cross section. Higher-twist contributions to the p{sub T}-spectrum of the Drell-Yan pairs are found to be large for presently accessible energies. The evolution of quark off-shellness distribution with the hard scale is also studied.

Single transverse-spin asymmetries in forward pion production at high energy: Incorporating small-xeffects in the target

We consider single-inclusive forward pion production in high-energy proton-proton collisions at RHIC energies. A good baseline description of the transverse momentum distributions at high rapidity is obtained within Mueller's dipole formalism with an anomalous dimension incorporating an ``extended geometric scaling'' window between the saturation and DGLAP regimes. We then formulate pion production for transversely polarized projectiles within the same approach. We assume that an azimuthal, spin-dependent asymmetry arises from the so-called Sivers effect and investigate the single transverse-spin asymmetry ${A}_{N}$ at 200 GeV and 500 GeV center-of-mass energy. A simple parametrization of the Sivers functions from the literature compares reasonably well with the high-energy STAR data if the overall normalization is scaled up by at least a factor of 2. The STAR data might therefore indicate that the Sivers effect is significantly stronger than thought so far. We also analyze higher-twist contributions to ${A}_{N}$ and find that they largely cancel.

HIGHER TWIST EFFECTS IN PROTON-PROTON COLLISIONS

In this article, we investigate the contribution of the high twist Feynman diagrams to the large-pT pion production cross section in proton-proton collisions and we present the general formulae for the high and leading twist differential cross sections. The pion wave function where two non-trivial Gegenbauer coefficients a2 and a4 have been extracted from the CLEO data, two other pion model wave functions, P2, P3, the asymptotic and the Chernyak-Zhitnitsky wave functions are used in the calculations. The results of all the calculations reveal that the high twist cross sections, the ratios R, r, the dependence transverse momentum pT and the rapidity y of pion in the Φ CLEO (x,Q2) wave function case is very close to the Φ asy (x) asymptotic wave function case. It is shown that the high twist contribution to the cross section depends on the choice of the meson wave functions.

Non-singlet QCD analysis of [formula omitted] up to NNLO

The significance of NNLO (3-loop) QCD contributions to the flavor non-singlet sector of F 2 e p and F 2 e d has been studied as compared to uncertainties (different factorization schemes, higher twist and QED contributions) of standard NLO (and LO) QCD analyses. The latter effects turn out to be comparable in size to the NNLO contributions. Therefore the minute NNLO effects are unobservable with presently available (precision) data on non-singlet structure functions.

Investigating FL(x,Q2) at fixed energy in the color dipole formalism

At small-x, the structure function F_L(x,Q2) is driven by the gluon content of the nucleon target and consequently it can unravel the underlying QCD dynamics in that region. In this work, one studies its behavior on photon virtuality Q2 at fixed energy within the color dipole formalism for models considering parton saturation effects. The reason is that they resum a wide class of higher-twist contributions, which have important influence in F_L description towards low Q2. It is shown that the geometric scaling property holds for the longitudinal cross section. Moreover, the effective anomalous dimension in scaling dipole cross sections can be investigated by studing both the turn over and the large Q2 regions of the recent experimental measurements.

Higher twists in polarized DIS and the size of the constituent quark

The spontaneous breaking of chiral symmetry implies the presence of a short-distance scale in the QCD vacuum, which phenomenologically may be associated with the size of the constituent quark, $\ensuremath{\rho}\ensuremath{\approx}0.3\text{ }\text{ }\mathrm{fm}$. We discuss the role of this scale in the matrix elements of the twist-4 and 3 quark-gluon operators determining the leading power ($1/{Q}^{2}$)-corrections to the moments of the nucleon spin structure functions. We argue that the flavor-nonsinglet twist-4 matrix element, ${f}_{2}^{u\ensuremath{-}d}$, has a sizable negative value of the order ${\ensuremath{\rho}}^{\ensuremath{-}2}$, due to the presence of sea quarks with virtualities $\ensuremath{\sim}{\ensuremath{\rho}}^{\ensuremath{-}2}$ in the proton wave function. The twist-3 matrix element, ${d}_{2}$, is not related to the scale ${\ensuremath{\rho}}^{\ensuremath{-}2}$. Our arguments support the results of previous calculations of the matrix elements in the instanton vacuum model. We show that this qualitative picture is in agreement with the phenomenological higher-twist correction extracted from an NLO QCD fit to the world data on ${g}_{1}^{p}$ and ${g}_{1}^{n}$, which include recent data from the Jefferson Lab Hall A and COMPASS experiments. We comment on the implications of the short-distance scale $\ensuremath{\rho}$ for quark-hadron duality and the $x$-dependence of higher-twist contributions.