arXiv subjects
Publications and source records attributed to N. G. Stefanis.
We discuss different operator definitions of the transverse-momentum dependent (TMD) parton densities from the point of view of their renormalization-group (RG) properties and UV evolution. We also consider the structure of the gauge links (Wilson lines) in these operator definitions and examine the role of the soft factor in the factorization formula within the TMD approach to semi-inclusive processes.
We propose a consistent treatment of divergences emerging in the computation of transverse-momentum-dependent parton densities in leading $α_s$-order of QCD perturbation theory.
We discuss the end-point behavior of the pion distribution amplitude (DA) and calculate its slope using QCD sum rules with nonlocal condensates. This is done in terms of the standard derivative and also with the help of an "integral derivative", recently obtained by us. Our approach favors a value of the slope of the order (or less) of the asymptotic DA and is in clear disagreement with flat-type pion DAs.
Results on the resummation of non-power-series expansions of the Adler function of a scalar, $D_S$, and a vector, $D_V$, correlator are presented within fractional analytic perturbation theory (FAPT). The first observable can be used to determine the decay width $Γ_{H\to b\bar{b}}$ of a scalar Higgs boson to a bottom-antibottom pair, while the second one is relevant for the $e^+e^-$ annihilation cross section. The obtained estimates are compared with those from fixed-order (FOPT) and contour-improved perturbation theory (CIPT), working out the differences. We prove that although FAPT and CIPT are conceptually different, they yield identical results. The convergence properties of these expansions are discussed and predictions are extracted for the resummed series of $R_S$ and $D_V$ using one- and two-loop coupling running, and making use of appropriate generating functions for the coefficients of the perturbative series.
We summarize the renormalization-group properties of transverse-momentum dependent (TMD) parton distribution functions (PDF)s arguing that in the light-cone gauge the overlapping ultraviolet and rapidity divergences cannot be solely controlled by (dimensional) regularization, but necessitate their renormalization. In doing so, we show that at the one-loop order this additional divergence entails an anomalous dimension which can be attributed to a cusp in the gauge contour at light-cone infinity. Then, we present a recent analysis of TMD PDFs which incorporates in the gauge links the Pauli term $\sim F^{μν}[γ_μ,γ_ν]$. This generalized treatment of gauge invariance is shown to be justified, in the sense that it does not modify the behavior of the leading-twist contribution, though it contributes to the anomalous dimension of that of twist-three. An important consequence of the inclusion of the spin-dependent Pauli term is the appearance of a constant phase---the same for the leading twist-two and subleading distribution functions---that ensues from the interaction of the Pauli term in the transverse gauge link with the gauge field accompanying the fermion. Remarkably, this phase has opposite sign for the Drell-Yan process as compared to the semi-inclusive DIS.
We propose a new framework for transverse-momentum dependent parton distribution functions, based on a generalized conception of gauge invariance which includes into the Wilson lines the Pauli term $\sim F^{μν}[γ_μ, γ_ν]$. We discuss the relevance of this nonminimal term for unintegrated parton distribution functions, pertaining to spinning particles, and analyze its influence on their renormalization-group properties. It is shown that while the Pauli term preserves the probabilistic interpretation of twist-two distributions---unpolarized and polarized---it gives rise to additional pole contributions to those of twist-three. The anomalous dimension induced this way is a matrix, calling for a careful analysis of evolution effects. Moreover, it turns out that the crosstalk between the Pauli term and the longitudinal and the transverse parts of the gauge fields, accompanying the fermions, induces a constant, but process-dependent, phase which is the same for leading and subleading distribution functions. We include Feynman rules for the calculation with gauge links containing the Pauli term and comment on the phenomenological implications of our approach.
We discuss the state-of-the-art of the theory of transverse-momentum dependent parton densities (TMD)s, paying special attention to their renormalization properties, the structure of the gauge links in the operator definition, and the role of the soft factor in the factorization formula within the TMD approach to the semi-inclusive processes. We argue that the use of the lightcone axial gauge offers certain advantages for a consistent definition of TMDs as compared to the off-the-light-cone gauges, or covariant gauges with off-the-lightcone gauge links.
Starting from the QCD sum rules with nonlocal condensates for the pion distribution amplitude, we derive another sum rule for its derivative and its "integral" derivatives---defined in this work. We use this new sum rule to analyze the fine details of the pion distribution amplitude in the endpoint region $x\sim 0$. The results for endpoint-suppressed and flat-top (or flat-like) pion distribution amplitudes are compared with those we obtained with differential sum rules by employing two different models for the distribution of vacuum-quark virtualities. We determine the range of values of the derivatives of the pion distribution amplitude and show that endpoint-suppressed distribution amplitudes lie within this range, while those with endpoint enhancement---flat-type or CZ-like---yield values outside this range.
We discuss the status of the pion distribution amplitude (DA) in connection with QCD sum rules and experimental data on the $γ^*γ^\to π^0$ transition form factor. Contents: (a) Pion DA in generalized QCD Sum Rules (SRs); (b) Light Cone Sum Rules (LCSR) analysis of the CLEO data for the $γ^*γ\toπ^{0}$ transition form factor; (c) Recent lattice QCD data for the pion DA; (d) BaBar data---a challenge for QCD?
We present predictions for the pion-photon transition form factor, derived with the help of light-cone sum rules and including the main part of the NNLO radiative corrections. We show that, when the Bakulev-Mikhailov-Stefanis (BMS) pion distribution amplitude is used, the obtained predictions agree well with the CELLO and the CLEO data. We found that no model distribution amplitude can reproduce the observed $Q^2$ growth of the new BaBar data, though the BMS model complies with several BaBar data points.
We use light-cone QCD sum rules to calculate the pion-photon transition form factor, taking into account radiative corrections up to the next-to-next-to-leading order of perturbation theory. We compare the obtained predictions with all available experimental data from the CELLO, CLEO, and the BaBar Collaborations. We point out that the BaBar data are incompatible with the convolution scheme of QCD, on which our predictions are based, and can possibly be explained only with a violation of the factorization theorem. We pull together recent theoretical results and comment on their significance.
Different approaches to define transverse-momentum dependent parton distribution functions are considered from the point of view of their renormalization-group properties. The associated one-loop anomalous dimensions of these quantities are presented and compared to each other. We give arguments in favor of the "pure light-like" definition, and the use of the light-cone gauge.
We present results of a calculation of the electromagnetic pion form factor within the framework of QCD Sum Rules with nonlocal condensates, using a perturbative spectral density which includes $O(α_s)$ contributions.
We discuss the QCD sum-rule approach for the spacelike electromagnetic pion form factor in the $O(α_s)$ approximation. We show that the nonlocality of the condensates is a key point to include nonperturbative contributions to the pion form factor. We compare our results with the Local-Duality predictions and show that the continuum threshold $s_0(Q^2)$ parameter is highly underestimated in the Local-Duality approach at $Q^2\gtrsim 2$ GeV$^2$. Using our fit for this parameter, $s_0^\text{LD}(Q^2)$, and applying the fractional analytic perturbation theory, we estimate with an accuracy of the order of 1% the $O(α_s^2)$ contribution to the pion's form factor.
The ultraviolet and rapidity divergences of transverse-momentum dependent parton distribution functions with lightlike and transverse gauge links is studied, also incorporating a soft eikonal factor. We find that in the light-cone gauge with $q^-$-independent pole prescriptions extra divergences appear which amount, at one-loop, to a cusp-like anomalous dimension. We show that such contributions are absent when the Mandelstam-Leibbrandt prescription is used. In the first case, the soft factor cancels the anomalous-dimension defect, while in the second case its ultraviolet-divergent part reduces to unity.
We review a nonlocal-condensate approach and its application in QCD sum rules for the spacelike electromagnetic pion form factor. It is shown that the nonlocality of the condensates is a key point to include nonperturbative contributions to the pion form factor.
The renormalization-group properties of transverse-momentum dependent parton distribution functions in the light-cone gauge with the Mandelstam-Leibbrandt prescription for the gluon propagator are addressed. An expression for the transverse component of the gauge field at light-cone infinity, which plays a crucial role in the description of the final-/initial-state interactions in the light-cone axial gauge, is obtained. The leading-order anomalous dimension is calculated in this gauge and the relation to the results obtained in other gauges is worked out. It is shown that, using the Mandelstam-Leibbrandt prescription, the ensuing anomalous dimension does not receive contributions from extra rapidity divergences related to a cusped junction point of the Wilson lines.
We discuss duality in ``two-photon''-like processes in the scalar $φ^3_E$ model and also in the process $γ^*γ\toππ$ in QCD. Duality implies the equivalence between two distinct nonperturbative mechanisms. These two mechanisms, one involving a twist-3 Generalized Distribution Amplitude, the other employing a leading-twist Transition Distribution Amplitude, are associated with different regimes of factorization. In the kinematical region, where the two mechanisms overlap, duality is observed for the scalar $φ^3_E$ model, while in the QCD case the appearance of duality turns out to be sensitive to the particular nonperturbative model applied and can, therefore, be used as a tool for selecting the most appropriate one.