Twist Contributions Research Articles

Twist-3 contribution to deeply virtual electroproduction of pions

Twist-3 contribution to deeply virtual electroproduction of pions

Twist-3 contributions in semi-inclusive DIS in the target fragmentation region

Twist-3 contributions in semi-inclusive DIS in the target fragmentation region

Global QCD analysis of diffractive parton distribution function considering higher twist corrections within the xFitter framework

We present {\tt SKMHS22}, a new set of diffractive parton distribution functions (PDFs) and their uncertainties at next-to-leading-order accuracy in perturbative QCD within the {\tt xFitter} framework. We describe all available diffractive DIS data sets from HERA and the most recent high-precision H1/ZEUS combined measurements considering three different scenarios. First, we extract the diffractive PDFs considering the standard twist-2 contribution. Then, we include the twist-4 correction from the longitudinal virtual photons. Finally, the contribution of subleading Reggeon exchange to the structure-function $F_2^D$ is also examined. For the contribution of heavy flavors, we utilize the Thorne-Roberts general mass variable number scheme. We show that for those corrections, in particular, the twist-4 contribution allows to include the high-$\beta$ region and leads to a better description of the diffractive DIS data sets. We find that the inclusion of the subleading Reggeon exchange significantly improves the description of the diffractive DIS cross-section measurements. The resulting sets are in good agreement with all diffractive DIS data analyzed, which cover a wider kinematical range than in previous fits. The {\tt SKMHS22} diffractive PDFs sets presented in this work are available via the {\tt LHAPDF} interface. We also make suggestions for future research in this area.

Lattice results for the longitudinal spin structure and color forces on quarks in a nucleon

Using lattice QCD, we calculate the twist-2 contribution $a_2$ to the third Mellin moment of the spin structure functions $g_1$ and $g_2$ in the nucleon. In addition we evaluate the twist-3 contribution $d_2$. Our computations make use of $N_f=2+1$ gauge field ensembles generated by the Coordinated Lattice Simulations (CLS) effort. Neglecting quark-line disconnected contributions we obtain as our best estimates $a_2^{(p)}= 0.069(17)$, $d_2^{(p)}= 0.0105(68)$ and $a_2^{(n)}= 0.0068(88)$, $d_2^{(n)}= -0.0009(70)$ for the proton and the neutron, respectively, where we use the normalizations given in Eqs. (58) and (59). While the $a_2$ results have been converted to the $\overline{\mathrm{MS}}$ scheme using three-loop perturbation theory, the numbers for $d_2$ are given in the regularization independent momentum subtraction (RI$^\prime$-MOM) scheme, i.e., the conversion has been performed only in tree-level perturbation theory. The $d_2$ results can be interpreted as corresponding to a transverse color Lorentz force on a quark in a transversely polarized proton of size $F^{(u)} = 116(61)$ MeV/fm and $F^{(d)} = -38(66)$ MeV/fm for $u$ and $d$ quarks, respectively. The error estimates quoted include statistical and systematic uncertainties added in quadrature.

Pion-photon transition form factor in light cone sum rules and tests of asymptotics

We study the pion-photon transition form factor (TFF) ${F}^{\ensuremath{\gamma}*\ensuremath{\gamma}{\ensuremath{\pi}}^{0}}({Q}^{2})$ using a state-of-the art implementation of light cone sum rules (LCSRs) within fixed-order QCD perturbation theory. The spectral density in the dispersion relation includes all currently known radiative corrections up to the next-to-next-to-leading-order (NNLO) and all twist contributions up to order six. Predictions for the TFF are obtained for various pion distribution amplitudes (DAs) of twist two, including two-loop evolution which accounts for heavy-quark mass thresholds. The influence of the main theoretical uncertainties is quantified in order to enable a more realistic comparison with the data. The characteristics of various pion DAs are analyzed in terms of the conformal coefficients ${a}_{2}$ and ${a}_{4}$ in comparison with the $1\ensuremath{\sigma}$ and $2\ensuremath{\sigma}$ error regions of the data and the most recent lattice constraints on ${a}_{2}$ with NLO and NNLO accuracy. Our results provide more stringent bounds on the variation of the pion DA and illuminate the corresponding asymptotic behavior of the calculated TFF.

Twist-4 contributions to e+e− → ΩX process

The description of particles with spin in high energy reaction can be attained by using a spin density matrix. In this paper we introduce the spin density matrix for spin-3/2 particles. With this matrix, we present the complete twist-4 results for the e+e−→ΩX at the tree level of perturbative quantum chromodynamics. The calculations are carried out by applying the collinear expansion. In the collinear expansion formalism the multiple gluon scattering is taken into account and gauge links are obtained systematically and automatically. We present the complete results for structure functions and the polarizations of the produced hadron in terms of gauge invariant fragmentation functions up to twist-4. We obtain 28 structure functions, among them 8 are leading twist, 12 are twist-3, 4 are twist-4 and the others do not correspond to fragmentation functions. We also obtain 3 longitudinal and 6 transverse polarizations. For the complete twist-4 calculation, the four-quark correlator contributions are also considered in this paper.

Twist-3 contributions to gamma gamma rightarrow pi ^+pi ^-,K^+K^- processes in perturbative QCD approach

As one of the simplest hadronic processes, gamma gamma rightarrow M^{+}M^{-} (M=pi ,K) could be a good testing ground for our understanding of the perturbative and nonperturbative structure of QCD, and will be studied with high precision at BELLE-II in the near future. In this paper, we revisit these processes with twist-3 corrections in the perturbative QCD approach based on the k_{T} factorization theorem, in which transverse degrees of freedom as well as resummation effects are taken into account. The influence of the distribution amplitudes on the cross sections are discussed in detail. Our work shows that not only the transverse momentum effects but also the twist-3 corrections play a significant role in the processes gamma gamma rightarrow M^{+}M^{-} in the intermediate energy region. Especially in the few GeV region, the twist-3 contributions become dominant in the cross sections. And it is noteworthy that both the twist-3 result of the pi ^{+}pi ^{-} cross section and that of the K^{+}K^{-} cross section agree well with the BELLE and ALEPH measurements. For the pion and kaon angular distributions, there still exist discrepancies between our results and the experimental measurements. Possible reasons for these discrepancies are discussed briefly.

Revealing minijet dynamics via centrality dependence of double parton interactions in proton\u2013nucleus collisions

One of the main challenges hampering an accurate measurement of the double parton scattering (DPS) cross sections is the difficulty in separating the DPS from the leading twist (LT) contributions. We argue that such a separation can be achieved, and cross section of DPS measured, in proton–nucleus scattering by exploiting the different centrality dependence of DPS and LT processes. We developed a Monte Carlo implementation of the DPS processes which includes realistic nucleon–nucleon (NN) correlations in nuclei, an accurate description of transverse geometry of both hard and soft NN collisions as well as fluctuations of the strength of interaction of nucleon with nucleus (color fluctuation effects). Our method allows the calculation of probability distributions of single and double dijet events as a function of centrality, also distinguishing double hard scatterings originating from a single target nucleon and from two different nucleons. We present numerical results for the rate of DPS as a function of centrality, following the model developed by the ATLAS collaboration which relates the distribution over the number of wounded nucleons to the distribution over the sum of transverse energies of hadrons produced at large negative (along the nucleus direction) rapidities, which is experimentally measurable. We suggest a new quantity which allows to test the geometry of DPS and we argue that it is a universal function of centrality for different DPS processes. This quantity can be tested by analyzing existing LHC data. The method developed in this work can be extended to the search for triple parton interactions.

The ratio mathcal {R}(D) and the D-meson distribution amplitude

In this paper, we calculate the Brightarrow D transition form factors (TFFs) within the light-cone sum rules (LCSRs) and predict the ratio mathcal {R}(D). More accurate D-meson distribution amplitudes (DAs) are essential to get a more accurate theoretical prediction. We construct a new model for the twist-3 DAs phi ^p_{3;D} and phi ^sigma _{3;D} based on the QCD sum rules under the background field theory for their moments as we have done for constructing the leading-twist DA phi _{2;D}. As an application, we observe that the twist-3 contributions are sizable in whole q^2-region. Taking the twist-2 and twist-3 DAs into consideration, we obtain f^{Brightarrow D}_{+,0}(0) = 0.659^{+0.029}_{-0.032}. As a combination of the Lattice QCD and the QCD LCSR predictions on the TFFs f^{Brightarrow D}_{+,0}(q^2), we predict mathcal {R}(D) = 0.320^{+0.018}_{-0.021}, which is about 1.5sigma deviation from the HFAG average of the Belle and BABAR data. At present the data still have large errors, and we need further accurate measurements of the experiment to confirm whether there is a signal of new physics from the ratio mathcal {R}(D).

Topological invariants for superconducting cosmic strings

Superconducting cosmic strings (SCSs) have received revived interests recently. In this paper we treat closed SCSs as oriented knotted line defects, and concentrate on their topology by studying the Hopf topological invariant. This invariant is an Abelian Chern–Simons action, from which the HOMFLYPT knot polynomial can be constructed. It is shown that the two independent parameters of the polynomial correspond to the writhe and twist contributions, separately. This new method is topologically stronger than the traditional (self-)linking number method, which fails to detect essential topology of knots sometimes, shedding new light upon the study of physical intercommunications of superconducting cosmic strings as a complex system.

Twist-3 contributions to wide-angle photoproduction of pions

We investigate wide-angle pi^0 photoproduction within the handbag approach to twist-3 accuracy. In contrast to earlier work both the 2-particle as well as the 3-particle twist-3 contributions are taken into account. It is shown that both are needed for consistent results that respect gauge invariance and crossing properties. The numerical studies reveal the dominance of the twist-3 contribution. With it fair agreement with the recent CLAS measurement of the pi^0 cross section is obtained. We briefly comment also on wide-angle photoproduction of other pseudoscalar mesons.

Twist-4 contributions to semi-inclusive e+e− annihilation process

We present the complete twist-4 results for the semi-inclusive annihilation process $e^+ +e^- \to h+ \bar q+X$ at the tree level of perturbative quantum chromodynamics. The calculations are carried out by using the formalism obtained by applying the collinear expansion to this process where the multiple gluon scattering is taken into account and gauge links are obtained systematically and automatically. We present the results for structure functions in terms of gauge invariant fragmentation functions up to twist-4 and the corresponding results for the azimuthal asymmetries and polarizations of hadrons produced. The results obtained show in particular that similar to that for semi-inclusive deeply inelastic scattering, for structure functions associated with sine or cosine of odd number of azimuthal angle(s), there are only twist-3 contributions, while for those of even number of azimuthal angle(s), there are leading twist and twist-4 contributions. For all those structure functions that have leading twist contributions, there are twist-4 addenda to them. Hence twist-4 contributions may even have large influences on extracting leading twist fragmentation functions from the data. We also suggest a method for a rough estimation of twist-4 contributions based on the leading twist fragmentation functions.

Reconsideration of the B→K* transition form factors within the QCD light-cone sum rules

In this paper, we study the $B\ensuremath{\rightarrow}{K}^{*}$ transition form factors (TFFs) within the QCD light-cone sum rules (LCSR) approach. Two correlators, i.e., the usual one and the right-handed one, are adopted in the LCSR calculation. The resultant LCSRs for the $B\ensuremath{\rightarrow}{K}^{*}$ TFFs are arranged according to the twist structure of the ${K}^{*}$-meson light-cone distribution amplitudes (LCDAs), whose twist-2, twist-3, and twist-4 terms behave quite differently by using different correlators. We observe that the twist-4 LCDAs, though generally small, shall have sizable contributions to the TFFs ${A}_{1/2}$, $V$, and ${T}_{1}$; thus, the twist-4 terms should be kept for a sound prediction. We also observe that, even though different choices of the correlator lead to different LCSRs with different twist contributions, the large correlation coefficients for most of the TFFs indicate that the LCSRs for different correlators are close to each order, not only for their values at the large recoil point ${q}^{2}=0$ but also for their ascending trends in the whole ${q}^{2}$ region. Such a high degree of correlation is confirmed by their application to the branching fraction of the semileptonic decay $B\ensuremath{\rightarrow}{K}^{*}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. Thus, a proper choice of correlator may inversely provide a chance for probing uncertain LCDAs; i.e., the contributions from those LCDAs can be amplified to a certain degree via a proper choice of correlator, thus amplifying the sensitivity of the TFFs and, hence, their related observables, to those LCDAs.

Twist-4 contributions to semi-inclusive deeply inelastic scatterings with polarized beam and target

We present for the first time the complete twist-4 result for the semi-inclusive deeply inelastic scattering $e^- N \to e^-qX$ with polarized electron and proton beams at the tree level of pQCD. The calculations have been carried out using the formulism obtained after collinear expansion where the multiple gluon scattering are taken into account and gauge links are obtained automatically in a systematical way. The results show in particular that there are twist-4 contributions to all the eight twist-2 structure functions for $e^- N \to e^-hX$ that correspond to the eight twist-2 transverse momentum dependent parton distribution functions. Such higher twist effects could be very significant and therefore have important impacts on extracting these three-dimensional parton distribution functions from the asymmetry data on $e^- N \to e^-hX$. We suggest also an approximate way for a rough estimation of such higher twist contributions.

Helicity within the vortex filament model.

Kinetic helicity is one of the invariants of the Euler equations that is associated with the topology of vortex lines within the fluid. In superfluids, the vorticity is concentrated along vortex filaments. In this setting, helicity would be expected to acquire its simplest form. However, the lack of a core structure for vortex filaments appears to result in a helicity that does not retain its key attribute as a quadratic invariant. By defining a spanwise vector to the vortex through the use of a Seifert framing, we are able to introduce twist and henceforth recover the key properties of helicity. We present several examples for calculating internal twist to illustrate why the centreline helicity alone will lead to ambiguous results if a twist contribution is not introduced. Our choice of the spanwise vector can be expressed in terms of the tangential component of velocity along the filament. Since the tangential velocity does not alter the configuration of the vortex at later times, we are able to recover a similar equation for the internal twist angle to that of classical vortex tubes. Our results allow us to explain how a quasi-classical limit of helicity emerges from helicity considerations for individual superfluid vortex filaments.

Twist-3 contributions in semi-inclusive DIS with transversely polarized target

Abstract We study semi-inclusive DIS with a transversely polarized target in the approach of collinear factorization. The effects related to the transverse polarization are at twist-3. We derive the complete result of twist-3 contributions to the relevant hadronic tensor at leading order of α s , and construct correspondingly experimental observables. Measuring these observables will help to extract the twist-2 transversity distribution, twist-3 distributions and twist-3 fragmentation functions of the produced unpolarized hadron. A detailed comparison with the approach of transverse-momentum-dependent factorization is made.

Time-like pion electromagnetic form factors in [formula omitted] factorization with the next-to-leading-order twist-3 contribution

We calculate the time-like pion electromagnetic form factor in the kT factorization formalism with the inclusion of the next-to-leading-order (NLO) corrections of the leading-twist and sub-leading-twist contributions. It's found that the total NLO correction can enhance (reduce) the magnitude (strong phase) of the leading order form factor by 20%–30% (<15°) in the considered invariant mass squared q2>5 GeV2, and the NLO twist-3 correction plays the key role to narrow the gap between the pQCD predictions and the measured values for the time-like pion electromagnetic form factor.

On the derivation of the HOMFLYPT polynomial invariant for fluid knots

By using and extending earlier results (Liu &amp; Ricca,J. Phys. A, vol. 45, 2012, 205501), we derive the skein relations of the HOMFLYPT polynomial for ideal fluid knots from helicity, thus providing a rigorous proof that the HOMFLYPT polynomial is a new, powerful invariant of topological fluid mechanics. Since this invariant is a two-variable polynomial, the skein relations are derived from two independent equations expressed in terms of writhe and twist contributions. Writhe is given by addition/subtraction of imaginary local paths, and twist by Dehn’s surgery. HOMFLYPT then becomes a function of knot topology and field strength. For illustration we derive explicit expressions for some elementary cases and apply these results to homogeneous vortex tangles. By examining some particular examples we show how numerical implementation of the HOMFLYPT polynomial can provide new insight into fluid-mechanical behaviour of real fluid flows.

Conservation of writhe helicity under anti-parallel reconnection.

Reconnection is a fundamental event in many areas of science, from the interaction of vortices in classical and quantum fluids, and magnetic flux tubes in magnetohydrodynamics and plasma physics, to the recombination in polymer physics and DNA biology. By using fundamental results in topological fluid mechanics, the helicity of a flux tube can be calculated in terms of writhe and twist contributions. Here we show that the writhe is conserved under anti-parallel reconnection. Hence, for a pair of interacting flux tubes of equal flux, if the twist of the reconnected tube is the sum of the original twists of the interacting tubes, then helicity is conserved during reconnection. Thus, any deviation from helicity conservation is entirely due to the intrinsic twist inserted or deleted locally at the reconnection site. This result has important implications for helicity and energy considerations in various physical contexts.

B → ρ transition form factors and the ρ-meson transverse leading-twist distribution amplitude

The QCD light-cone sum rules (LCSR) provide an effective way for dealing with heavy-to-light transition form factors (TFFs), in which the non-perturbative dynamics are parameterized into the light-meson’s light-cone distribution amplitudes (LCDAs). By taking the chiral correlator as the starting point, we derive new LCSRs for TFFs up to twist-4 accuracy. In those LCSRs, the twist-2 transverse LCDA provides dominant contribution, while the twist-3 and twist-4 contributions are δ2-suppressed (). Thus, they provide good platforms for testing behavior. For the purpose, we suggest a WH-model for , in which a single parameter dominantly controls its longitudinal distribution. When setting , varies from the single-peak behavior to the double-humped behavior. We present a detailed comparison of the LCSR estimation for TFFs with those predicted by pQCD and lattice QCD calculations. The TFFs become smaller with the increment of and a larger is not allowed by lattice QCD predictions. By using the extrapolated TFFs, we further predict the Cabibbo–Kobayashi–Maskawa (CKM)-matrix element with the help of two semi-leptonic decays. The predicted increases with the increment of , i.e. we have for and for . If treating the BABAR prediction on as a criteria, we observe that should be within the region of [−0.20, +0.10], which indicates that the ρ-meson LCDA prefers a single-peak behavior rather than a double-humped behavior.