In this work we push the matching between the QCD operator product expansion (OPE) and resonance chiral theory (RchiT) to order alpha_s. To this end we compute two- and three-point QCD Green functions (GFs) in both theories and compare the results. GFs which are order parameters of chiral symmetry breaking make this matching more transparent and thus we concentrate on those. On the OPE side one needs to calculate the hard-gluon virtual corrections to the quark condensate, and in particular for three-point GFs this computation was hitherto missing. We also discuss the need for including the infinite tower of hadronic states in the hadronic representation of the GF when non-analytic terms such as logarithms are present in the OPE Wilson coefficients.
We compute the O(1/N_f) correction to the predominantly gluonic flavour singlet twist-2 anomalous dimension used in polarized deep inelastic scattering. It is consistent with known two loop perturbation theory and we determine the three loop contribution at O(1/N_f). The treatment of the epsilon-tensor in the large N_f d-dimensional critical point formalism is also discussed.
We explore connections between high energy QCD spin physics and $CP$-odd scalar gluonic operators $\tilde{F}^{μν}F_{μν}$ and $\tilde{F}_{μν}F^{μα}F^ν_α$, the latter being called the Weinberg operator in the context of the nucleons' electric dipole moment. We first introduce the twist-four generalized parton distribution (GPD) associated with the topological operator $F_{μν}\tilde{F}^{μν}$. This has interesting applications in spin physics which go beyond the standard framework in terms of twist-two and twist-three distributions. In the second part, we show that the off-forward matrix element o…
Using large N_f methods we compute the anomalous dimension of the predominantly gluonic flavour singlet twist-2 composite operator which arises in the operator product expansion used in deep inelastic scattering. We obtain a d-dimensional expression for it which depends on the operator moment n. Its expansion in powers of epsilon = (4-d)/2 agrees with the explicit exact three loop MSbar results available for n less than or equal to 8 and allows us to determine some new information on the explicit n-dependence of the three and higher order coefficients. In particular the n-dependence of the thr…
The gauge-links connecting the parton field operators in the hadronic matrix elements appearing in the transverse momentum dependent distribution functions give rise to T-odd effects. Due to the process-dependence of the gauge-links the T-odd distribution functions appear with different pre-factors. A consequence is that in the description of single spin asymmetries the parton distribution and fragmentation functions are convoluted with gluonic pole cross sections rather than the basic partonic cross sections. In this paper we calculate the gluonic pole cross sections encountered in single spi…
We apply a fully automated extension of the $R^*$-operation capable of calculating higher-loop anomalous dimensions of n-point Green's functions of arbitrary, possibly non-renormalisable, local Quantum Field Theories. We focus on the case of the CP-violating Weinberg operator of the Standard Model Effective Field Theory whose anomalous dimension is so far known only at one loop. We calculate the two-loop anomalous dimension in full QCD and the three-loop anomalous dimensions in the limit of pure Yang-Mills theory. We find sizeable two-loop and large three-loop corrections, due to the appearanc…
The $B\to ππ$ hadronic matrix element of the chromomagnetic dipole operator $O_{8g}$ (gluonic penguin) is calculated using the QCD light-cone sum rule approach. The resulting sum rule for $<ππ|O_{8g}|B>$ contains, in addition to the $O(α_s)$ part induced by hard gluon exchanges, a contribution due to soft gluons. We find that in the limit $m_b\to \infty$ the soft-gluon contribution is suppressed as a second power of $1/m_b$ with respect to the leading-order factorizable $B\to ππ$ amplitude, whereas the hard-gluon contribution has only an $α_s$ suppression. Nevertheless, at finite $m_b$, soft a…
Recent results on the calculation of 3-loop massive operator matrix elements in case of one and two heavy quark masses are reported. They concern the $O(n_f T_F^2 C_{F,A})$ and $O(T_F^2 C_{F,A})$ gluonic corrections, two-mass quarkonic moments, and ladder- and Benz-topologies. We also discuss technical aspects of the calculations.
We consider diagrams with up to four t-channel gluons in order to specify gluonic twist-four contributions to deep inelastic structure functions. This enables us to extend the method developed by R.K.Ellis, W.Furmanski, and R.Petronzio (EFP) to the gluonic case. The method is based on low-order Feynman diagrams in combination with a dimensional analysis. It results in explicitly gauge invariant expressions for the factorization of twist-four gluon-operator matrix elements and the corresponding coefficient functions.
We study the transition widths of $Υ(10753)$ and $Υ(11020)$ into standard bottomonium under the hypothesis that they correspond to the two lowest laying $1^{--}$ hybrid bottomonium states. We employ weakly coupled potential NRQCD an effective filed theory incorporating the heavy quark and multipole expansions. We consider the transitions generated by the leading order and next-to-leading order singlet-octet operators. In the multipole expansion the heavy quark matrix elements factorize from the production of light-quark mesons by gluonic operators. For the leading order operator we compute the…
We calculate the two-mass QCD contributions to the massive operator matrix element $A_{gg,Q}$ at $\mathcal{O} (α_s^3)$ in analytic form in Mellin $N$- and $z$-space, maintaining the complete dependence on the heavy quark mass ratio. These terms are important ingredients for the matching relations of the variable flavor number scheme in the presence of two heavy quark flavors, such as charm and bottom. In Mellin $N$-space the result is given in the form of nested harmonic, generalized harmonic, cyclotomic and binomial sums, with arguments depending on the mass ratio. The Mellin inversion of the…
Gluonic pole matrix elements explain the appearance of single spin asymmetries (SSA) in high-energy scattering processes. They involve a combination of operators which are odd under time reversal (T-odd). Such matrix elements appear in principle both for parton distribution functions and parton fragmentation functions. We show that for parton fragmentation functions these gluonic pole matrix elements vanish as a consequence of the analytic structure of scattering amplitudes in Quantum Chromodynamics. This result is important in the study of the universality of transverse momentum dependent (TM…
By applying chiral-perturbation-theory methods to the QCD sector of the Lorentz-violating Standard-Model Extension, we investigate Lorentz violation in the strong interactions. In particular, we consider the CPT-even pure-gluon operator of the minimal Standard-Model Extension. We construct the lowest-order chiral effective Lagrangian for three as well as two light quark flavors. We develop the power-counting rules and construct the heavy-baryon chiral-perturbation-theory Lagrangian, which we use to calculate Lorentz-violating contributions to the nucleon self energy. Using the constructed effe…
Using a parametrization of the Wilson loop with the minimal-area law, we calculate the polarization operator of a valence gluon, which propagates in the confining background. This enables us to obtain the infrared freezing (i.e. finiteness) of the running strong coupling in the confinement phase, as well as in the deconfinement phase up to the temperature of dimensional reduction. The momentum scale defining the onset of freezing is found both analytically and numerically. The nonperturbative contribution to the thrust variable, originating from the freezing, makes the value of this variable c…
Fluctuation-Dissipation Relation for Hard Partons in a Gluonic Plasma
University of Regina（里贾纳大学）；Wayne State University（韦恩州立大学）；Bielefeld University（比勒费尔德大学）；Technische Universität Darmstadt（达姆施塔特工业大学）；Käthe-Kollwitz-Gymnasium（凯泽·科利维茨中学）
We look into the signatures of the effective Y-bosonic strings in the gluonic profile due to a system of three static quarks on the lattice. The gluonic distribution is calculated in pure Yang-Mills lattice gauge theory at finite temperature with Polyakov loops operators. The analysis of the action density unveils a filled-$Δ$ distribution. However, we found that these $Δ$-shaped action density profiles are structured from three Y-shaped Gaussian-like flux-tubes. The length of the revealed Y-flux system increases with the increasing of the color source separation and reaches maximum near the d…
We present a first study of gluonic twist-four corrections to the deep inelastic structure function F_2 at small x and small Q^2. The calculations are based upon the double logarithmic approximation of the coupled twist-four evolution equations of the gluonic twist-four operators that are expected to be dominant at small x. We first review the analytical results which are presently available and define the framework of our calculation. In the second part we discuss the connection with DIS diffractive dissociation which can be used to estimate the size of some of the twist-four corrections. In …
We investigate the relevant gluon-momentum region for confinement in lattice QCD on $16^4$ at $β$=5.7, 5.8 and 6.0, based on the Fourier expansion. We find that the string tension $σ$, i.e., the confining force, is almost unchanged even after removing the high-momentum gluon component above 1.5GeV in the Landau gauge. In fact, the confinement property originates from the low-momentum gluon component below 1.5GeV, which is the upper limit to contribute to $σ$. In the relevant region, smaller gluon momentum component is more important for confinement. Next, we develop a manifestly gauge-covarian…
The near threshold photo or electroproduction of heavy vector quarkonium off the proton is studied in quantum chromodynamics. Similar to the high-energy limit, the production amplitude can be factorized in terms of gluonic Generalized Parton Distributions and the quarkonium distribution amplitude. At the threshold, the threshold kinematics has a large skewness parameter $ξ$, leading to the dominance of the spin-2 contribution over higher-spin twist-2 operators. Thus threshold production data are useful to extract the gluonic gravitational form factors, allowing studying the gluonic contributio…
We report the calculation of next-to-next-to-leading order (NNLO) QCD corrections in the purely gluonic channel to dijet production and related observables at hadron colliders. Our result represents the first NNLO calculation of a massless jet observable at hadron colliders, and opens the path towards precision QCD phenomenology with the LHC.
We present the first comprehensive study of hybrid baryons using lattice QCD methods. Using a large basis of composite QCD interpolating fields we extract an extensive spectrum of baryon states and isolate those of hybrid character using their relatively large overlap onto operators which sample gluonic excitations. We consider the spectrum of Nucleon and Delta states at several quark masses finding a set of positive parity hybrid baryons with quantum numbers N_1/2+, N_1/2+, N_3/2+, N_3/2+, N_5/2+ and Delta_1/2+, Delta_3/2+ at an energy scale above the first band of `conventional' excited posi…
We exhibit the method for obtaining non perturbative quark and gluonic vacuum condensates from a model truncation of QCD. The truncation allows for a phenomenological description of the quark-quark interaction in a framework which maintains all global symmetries of QCD and allows an 1/N_c expansion. Within this approach the functional integration over the gluon fields can be performed and therefore any gluonic vacuum observable can be expressed in terms of a quark operator and the gluon propagator. As a special case we calculate the mixed quark gluon condensate. We investigate how the value de…
The paper presents the short review of our to-day knowledge of vacuum condensates in QCD. The condensates are defined as vacuum averages of the operators which arise due to nonperturbative effects. The important role of condensates in determination of physical properties of hadrons and of their low-energy interactions in QCD is underlined. The special value of quark condensate, connected with the existence of baryon masses is mentioned. Vacuum condensates induced by external fields are discussed. QCD at low energy is checked on the basis of the data on hadronic tau-decay. In the theoretical an…
Deep Inelastic scattering experiments using transversely polarised targets yield information on the structure function $g_2$. By means of a free-field analysis, we study the operator structure of $g_2$ and demonstrate the need for retaining the twist three mass terms in order to maintain current-conservation. We show that the structure function $g_T=g_1+g_2$ has a much simpler operator structure as compared to $g_2$, in spite of the fact that, like $g_2$, $g_T$ has a twist-three component. We demonstrate factorisation of the hadronic tensor into hard and soft parts for the case of $g_T$. We sh…
We discuss the polarised fragmentation functions of quarks and gluons in Perturbative Quantum Chromodynamics. The Altarelli-Parisi evolution equations governing these fragmentation functions are presented. We find that the first moment of the polarised gluon fragmentation function to order $α_s$ is as important as that of the quark and anti-quark fragmentation functions. The $Λ$ production in polarised $e^+ e^-$ annihilation where this can be realised is discussed. We propose the factorisation method to compute the gluonic contribution to $Λ$ production to order $α_s$. With appropriate operato…
The correlator of two gluonic operators plays an important role for example in transport properties of a Quark Gluon Plasma (QGP) or in sum rules for glueballs. In [1] an operator product expansion (OPE) at zero temperature was performed for the correlators of two scalar operators $O_1=-\frac{1}{4} G^{μν}G_{μν}$ and two QCD energy-momentum tensors $T^{μν}$. There we presented analytical two-loop results for the Wilson coefficient $C_1$ in front of the gluon condensate operator $O_1$. In this paper these results are extended to three-loop order. The three-loop Wilson coefficient $C_0$ in front …
In the framework of Euclidean QCD on a torus, we study the spectrum of the Dirac operator through inverse moments of its eigenvalues, averaged over topological sets of gluonic configurations. The large-volume dependence of these sums is related to chiral order parameters. We sketch how these results may be applied to lattice simulations in order to investigate the chiral phase transitions occurring when N_f increases. In particular, we demonstrate how Dirac inverse moments at different volumes could be compared to detect in a clean way the phase transition triggered by the suppression of the q…
In this paper we address various issues connected with transverse spin in light front QCD. The transverse spin operators, in $A^+ = 0$ gauge, expressed in terms of the dynamical variables are explicitly interaction dependent unlike the helicity operator which is interaction independent in the topologically trivial sector of light-front QCD. Although it cannot be separated into an orbital and a spin part, we have shown that there exists an interesting decomposition of the transverse spin operator. We discuss the physical relevance of such a decomposition. We perform a one loop renormalization o…
We analyze the universal critical behavior at the chiral critical point in QCD with three degenerate quark masses. We confirm that this critical point lies in the universality class of the three dimensional Ising model. The symmetry of the Ising model, which is Z(2), is not directly realized in the QCD Hamiltonian. After making an ansatz for the magnetization- and energy-like operators as linear admixtures of the chiral condensate and the gluonic action, we determine several non-universal mixing and normalization constants. These parameters determine an unambiguous mapping of the critical beha…
