Using some techniques of conformal field theories, we find a closed expression for the contribution of leading twist operators and their descendants, obtained by adding total derivatives, to the operator product expansion (OPE) of two electromagnetic currents in QCD. Our expression resums contributions of all twists and to all orders in perturbation theory up to corrections proportional to the QCD $β$-function. At tree level and to twist-four accuracy, our result agrees with the expression derived earlier by a different method. The results are directly applicable to deeply-virtual Compton scattering and, e.g., $γγ^\ast$ annihilation in two mesons. As a byproduct, we derive a simple representation for the OPE of two scalar currents that is convenient for applications.
We show that the well-known divergence of the perturbative expansion of resummed results for processes such as deep-inelastic scattering and Drell-Yan in the soft limit can be treated by Borel resummation. The divergence in the Borel inversion can be removed by the inclusion of suitable higher twist terms. This provides us with an alternative to the standard 'minimal prescription' for the asymptotic summation of the perturbative expansion, and it gives us some handle on the role of higher twist corrections in the soft resummation region.
We develop a formalism for the resummation of target mass corrections in off-forward two-photon amplitudes given by a chronological product of electromagnetic currents, arising in e.g. deeply virtual Compton scattering. The method is based on a relation of composite operators with a definite twist to harmonic tensors, which form an irreducible representation of the Lorentz group. We give an application of the framework for the matrix elements of twist-two operators.
We investigate higher twist contributions to the transverse momentum broadening of Drell Yan pairs in proton nucleus collisions. We revisit the contribution of matrix elements of twist-4 and generalize this to matrix elements of arbitrary twist. An estimate of the maximal nuclear broadening effect is derived. A model for nuclear enhanced matrix elements of arbitrary twist allows us to give the result of a resummation of all twists in closed form. Subleading corrections to the maximal broadening are discussed qualitatively.
We claim that factorization implies that the evolution kernel, defined by the logarithmic derivative of the N-th moment of the structure function d ln F_2^N / d ln Q^2, receives logarithmically enhanced contributions (Sudakov logs) from a single source, namely the constrained invariant mass of the jet. Available results from fixed-order calculations facilitate Sudakov resummation up to the next-to-next-to-leading logarithmic accuracy. We use additional all-order information on the physical kernel from the large-beta_0 limit to model the behaviour of further subleading logs and explore the unce…
Using the CCFR data for the Gross--Llewellyn Smith (GLS) sum rule, we extract the strong coupling constant via Borel resummation of the perturbative QCD calculation. The method incorporates the correct nature of the first infrared renormalon singularity, and employs a conformal mapping to improve the convergence of the QCD perturbation expansion. The important twist-four contribution is calculated from resummation of the perturbation theory, which is based on the ansatz that the higher--twist contribution has a cut singularity only along the positive real axis on the complex coupling plane. Th…
The improved next-to-next-to-leading order (NNLO) QCD analysis of the experimental data of the CCFR collaboration for the $xF_3$ structure function is made. Theoretical ambiguities of the NNLO fits are estimated by means of the Padé resummation technique, which was applied both in the expanded and non-expanded forms. The NNLO and the new N$^3$LO $α_s(Q^2)$ $\bar{MS}$-matching conditions are used. In the process of the fits we are taking into account the target mas corrections and the twist-4 $1/Q^2$-terms. Our NNLO results for $α_s(M_Z)$ values, extracted from the CCFR $xF_3$ data, are $α_s(M_…
A detailed next-to-next-to-leading order (NNLO) QCD analysis is performed for the experimental data of the CCFR collaboration for the $xF_3$ structure function. Theoretical ambiguities of the results of our NNLO fits are estimated by application of the Padé resummation technique and variation of the factorization and renormalization scales. The NNLO and N$^3$LO $α_s(Q^2)$ $\bar{MS}$-matching conditions are used. In the process of the fits we are taking into account of twist-4 $1/Q^2$-terms. We found that the amplitude of the $x$-shape of the twist-4 factor is decreasing in NLO and NNLO, though…
The impact of recently calculated next-to-next-to-leading order QCD corrections and soft gluon resummations on the extraction of higher twist contributions to the deep-inelastic structure function F_2 is studied using the BCDMS and SLAC data. It is demonstrated to which extent the need for higher twist terms is diminishing due to these higher order effects in the kinematical region, 0.35 \le x \le 0.85 and Q^2>1.2 GeV^2, investigated. In addition, theoretical uncertainties in the extraction of higher twist contributions are discussed, and comparisons to results obtained previously are made.
The results of the more detailed NNLO QCD analysis of the CCFR data for $xF_3$ SF are presented. The factorization scale uncertainties are analysed. The NNLO results for $alpha_s(M_Z)$ and twist-4 contributions are obtained. Despite the fact that the amplitude of the $x$-shape of the twist-4 factor is consequently decreasing at the NLO and NNLO, our new QCD analysis seems to reveal the remaining twist-4 structure at the NNLO level. The definite N$^3$LO uncertainties are fixed using the [0/2] Padé resummation technique.
Existing data on the (unpolarised) transverse structure function of the proton are analyzed for large values of the Bjorken variable x. The leading-twist and a phenomenological higher-twist contributions are simultaneously determined from a power correction analysis of the Nachtmann moments for values of the squared four-momentum transfer between ~ 1 and 20 (GeV/c)**2. The results obtained adopting the next-to-leading order approximation and those including the effects of soft gluon resummation are compared. The sensitivity of the extraction of large-x higher twists to high-order radiative cor…
We propose the use of 1-jettiness, a global event shape, for exclusive single jet production in lepton-nucleus deep inelastic scattering (DIS). We derive a factorization formula, using the Soft-Collinear Effective Theory, differential in the transverse momentum and rapidity of the jet and the 1-jettiness event shape. It provides a quantitative measure of the shape of the final-state QCD radiation in the presence of the hard jet, providing a useful powerful probe of QCD and nuclear physics. For example, one expects differences in the observed pattern of QCD radiation between large and small nuc…
We discuss $\btorho$ form factors within the framework of perturbative QCD, including the higher twist contributions and study the validity of such an approach in calculating quantities such as form factors, which in principle and quite generally are thought to be completely non-perturbative objects and are expected to receive large contributions from the non-perturbative regime in the calculations. It is shown that including the Sudakov and threshold resummation effects, the general expectations of the pQCD approach are clearly met and the form factors do indeed receive most of the contributi…
As one of the simplest hadronic processes, $γγ\rightarrow M^{+}M^{-}$ ($M=π,K$) 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-\RNum{2} 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. O…
In this paper, we summarize the existing methods of solving the evolution equation of the leading-twist $B$-meson LCDA. Then, in the Mellin space, we derive a factorization formula with next-to-leading-logarithmic (NLL) resummation for the form factors $F_{A,V}$ in the $B \to γ\ellν$ decay at leading power in $Λ/m_b$. Furthermore, we investigate the power suppressed local contributions, factorizable non-local contributions (which are suppressed by $1/E_γ$ and $1/m_b$), and soft contributions to the form factors. In the numerical analysis, which employs the two-loop-level hard function and the …
Using the recent results on the contributions of descendants of the leading twist operators to the operator product expansion of two electromagnetic currents we derive explicit expressions for the kinematic finite-$t$ and target mass corrections to the DVCS helicity amplitudes to the $1/Q^4$ power accuracy. The cancellation of IR divergences for kinematic corrections is demonstrated to all powers in the leading order of perturbation theory. We also argue that target mass corrections in the coherent DVCS from nuclei are small and do not invalidate the factorization theorem.
Proton isovector helicity PDF at NNLO and the twist-3 moment $\tilde{d}_2$ from lattice QCD at physical quark masses
Brookhaven National Laboratory（布鲁克海文国家实验室）；Kent State University（肯特州立大学）；Central China Normal University（华中师范大学）；Massachusetts Institute of Technology（麻省理工学院）；Argonne National Laboratory（阿贡国家实验室）
We study the Drell-Yan production cross section and structure functions in proton (deuteron)-nucleus collisions using the Color Glass Condensate formalism. The nucleus is treated in the Color Glass Condensate framework which includes both higher twist effects due to the inclusion of multiple scatterings and leading twist pQCD shadowing due to the small x resummation, while the proton (or deuteron) is treated within the DGLAP improved parton model. In particular, the Drell-Yan structure functions are used in order to investigate the Lam-Tung relation at small x, which is known to be identically…
Power corrections to the Q**2 behavior of the Nachtmann moments of the proton polarized structure function g1p are investigated at large Bjorken-x by developing a phenomenological fit of both the resonance (including the photon point) and deep inelastic data up to Q**2 ~ 50 (GeV/c)**2. The leading twist is treated at NLO in the strong coupling constant and the effects of higher orders of the perturbative series are estimated using soft-gluon resummation techniques. In case of the first moment higher-twist effects are found to be quite small for Q**2 > 1 (GeV/c)**2, and the singlet axial charge…
We study the transverse spin structure of the squeezed limit of the three-point energy correlator, $\langle \mathcal{E}(\vec n_1) \mathcal{E}(\vec n_2) \mathcal{E}(\vec n_3) \rangle$. To describe its all orders perturbative behavior, we develop the light-ray operator product expansion (OPE) in QCD. At leading twist the iterated OPE of $\mathcal{E}(\vec n_i)$ operators closes onto light-ray operators $\mathbb{O}^{[J]}(\vec n)$ with spin $J$, and transverse spin $j=0,2$. We compute the $\mathcal{E}(\vec n_1) \mathcal{E}(\vec n_2)$, $\mathcal{E}(\vec n_1) \mathbb{O}^{[J]}(\vec n_2) $ and $\mathbb…
Dynamics of high energy scattering in Quantum Chromodynamics (QCD) are primarily probed through detector energy flow correlations. One important example is the Energy-Energy Correlator (EEC), whose back-to-back limit probes correlations of QCD on the lightcone and can be described by a transverse-momentum dependent factorization formula in the leading power approximation. In this work, we develop a systematic method to go beyond this approximation. We identify the origin of logarithmically enhanced contributions in the back-to-back limit as the exchange of operators with low twists and large s…
A phenomenological parameterization of the proton polarized structure function has been developed for x > 0.02 using deep inelastic data up to ~ 50 (GeV/c)**2 as well as available experimental results on both photo- and electro-production of proton resonances. According to the new parameterization the generalized Drell-Hearn-Gerasimov sum rule is predicted to have a zero-crossing point at Q**2 = 0.16 +/- 0.04 (GeV/c)**2. Then, low-order polarized Nachtmann moments have been estimated and their Q**2-behavior has been investigated in terms of leading and higher twists for Q**2 > 1 (GeV/c)**2. Th…
In this work, we study the radiative decay of $Z$ boson to a $P$-wave quarkonium $H$ in association with a photon, where $H$ can be $χ_{QJ}$, $h_Q$ with $Q=c,b$ and $J=0,1,2$. The helicity amplitudes and the unpolarized decay widths are evaluated up to QCD next-to-next-to-leading order (NNLO) within the framework of nonrelativistic QCD (NRQCD). For the first time, we check the NRQCD factorization for $h_Q$ exclusive production at two-loop order. The leading logarithms (LL) of $m_Z^2/m_Q^2$ in the leading-twist short-distance coefficients, which may potentially ruin the perturbative convergence…
Inspired by recent measurements with the CLAS detector at Jefferson Lab, we perform a self-consistent analysis of world data on the proton structure function g1 in the range 0.17 < Q2 < 30 (GeV/c)**2. We compute for the first time low-order moments of g1 and study their evolution from small to large values of Q2. The analysis includes the latest data on both the unpolarized inclusive cross sections and the ratio R = sigmaL / sigmaT from Jefferson Lab, as well as a new model for the transverse asymmetry A2 in the resonance region. The contributions of both leading and higher twists are extracte…
In this paper we calculate the power corrections to the pion transition form factor within the framework of perturbative QCD approach on the basis of $k_T$ factorization. The power suppressed contributions from higher twist pion wave functions and the hadronic structure of photon are investigated. We find that there exists strong cancellation between the two kinds contributions, thus the total power corrections considered currently are very small, and the prediction of the leading power contribution with joint resummation improved perturbative QCD approach is almost unchanged. This result conf…
The energy loss of hard jets produced in the Deep-Inelastic scattering (DIS) off a large nucleus is considered in the collinear limit. In particular, the single gluon emission cross section due to multiple scattering in the medium is calculated. Calculations are carried out in the higher-twist scheme, which is extended to include contributions from multiple transverse scatterings on both the produced quark and the radiated gluon. The leading length enhanced parts of these power suppressed contributions are resummed. Various interferences between such diagrams lead to the Landau-Pomeranchuk-Mig…
Employing the QCD factorization formalism we compute $B_{u}^{-} \to γ^{\ast} \, \ell \, \bar ν_{\ell}$ form factors with an off-shell photon state possessing the virtuality of order $m_b \, Λ_{\rm QCD}$ and $m_b^2$, respectively, at next-to-leading order in QCD. Perturbative resummation for the enhanced logarithms of $m_b / Λ_{\rm QCD}$ in the resulting factorization formulae is subsequently accomplished at next-to-leading logarithmic accuracy with the renormalization-group technique in momentum space. In particular, we derive the soft-collinear factorization formulae for a variety of the subl…
We present an updated version of a QCD coupling which fulfills various physically motivated conditions: at high momenta it practically coincides with the perturbative QCD (pQCD) coupling; at intermediate momenta it reproduces correctly the physics of the semihadronic tau decay; and at very low momenta it is suppressed as suggested by large-volume lattice calculations. An earlier presented analysis is updated here in the sense that the Adler function, in the regime $|Q^2| \lesssim 1 \ {\rm GeV}^2$, is evaluated by a renormalon-motivated resummation method. This Adler function is then used here …
We provide the proper definition of all the leading-twist (un)polarized gluon transverse momentum dependent parton distribution functions (TMDPDFs), by considering the Higgs boson transverse momentum distribution in hadron-hadron collisions and deriving the factorization theorem in terms of them. We show that the evolution of all the (un)polarized gluon TMDPDFs is driven by a universal evolution kernel, which can be resummed up to next-to-next-to-leading-logarithmic accuracy. Considering the proper definition of gluon TMDPDFs, we perform an explicit next-to-leading-order calculation of the unp…
