arXiv subjects
Publications and source records attributed to Marek Karliner.
We discuss the seemingly contradictory constraints of simultaneously preserving the SU(3)-symmetric Cabibbo description of the weak vector baryon matrix elements, accounting for SU(3) flavor symmetry breaking and describing the observed violation of the Gottfried Sum Rule. We try to construct a simple model that will satisfy these constraints and use it to explain the generic difficulties and tradeoffs.
We discuss the puzzling experimental results on baryon-antibaryon production in e+e- annihilation close to the threshold, in particular the fact that sigma(e+e- --> nbar n) is somewhat greater than sigma(e+e- --> pbar p). We discuss an interpretation in terms of a two-step process, via an intermediate coherent isovector state serving as an intermediary between e+e- and the baryon-antibaryon system. We provide evidence that the isovector channel dominates both e+e- --> pions and from Nbar N annihilation at rest, and show that the observed ratio of sigma(e+e- --> nbar n)/sigma(e+e- --> pbar p) can be understood quantitatively in this picture.
We discuss the puzzling experimental results on baryon-antibaryon production in e+e- annihilation close to the threshold, in particular the fact that sigma(e+e- --> nbar n) >~ sigma(e+e- --> pbar p). We discuss an interpretation in terms of a two-step process, via an intermediate coherent isovector state serving as an intermediary between e+e- and the baryon-antibaryon system. We provide evidence that the isovector channel dominates both e+e- --> pions and from Nbar N annihilation at rest, and show that the observed ratio of sigma(e+e- --> nbar n)/sigma(e+e- --> pbarp p) can be understood quantitatively in this picture.
We sketch some recent ideas proposed as the mechanism behind the puzzling experimental results on baryon-antibaryon production in e+e- annihilation close to threshold. The essential new point in the proposed mechanism is that it is a two-stage process, with a coherent state of pions serving as an intermediary between e+e- and the baryon-antibaryon system. Skyrmion-antiskyrmion annihilation is proposed as a concrete computational framework for a quantitative description of the baryon-antibaryon annihilation. We also point out the possible connection to similarly puzzling data on baryon-antibaryon production in photon-photon collision.
We present a simple explanation of the underlying physics in the use of hyperon decay data to obtain information about proton spin structure. We also present an alternative input using nucleon magnetic moment data and show that the results from the two approaches are nearly identical. The role of symmetry breaking is clarified while pointing out that simple models explaining the violation of the Gottfried sum rule via pion emission tend to lose the good SU(3) predictions from Cabibbo theory for hyperon decays.
We investigate the possibility that alpha_s freezes as function of N_f within perturbation theory. We use two approaches -- direct search for a zero in the effective-charge (ECH) beta function, and the Banks-Zaks (BZ) expansion. We emphasize the fundamental difference between quantities with space-like vs. those with time-like momentum. We show that within the ECH approach several space-like quantities exhibit similar behavior. In general the 3-loop ECH beta functions can lead to freezing for N_f\gsim 5, but higher-order calculations are essential for a conclusive answer. The BZ expansion behaves differently for different observables. Assuming that the existence of a fixed point requires convergence of the BZ expansion for any observable, we can be pretty sure that there is no fixed point for N_f\lsim 12. The consequences of the Crewther relation concerning perturbative freezing are analyzed. We also emphasize that time-like quantities have a consistent infrared limit only when the corresponding space-like effective charge has one. We show that perturbative freezing can lead to an analyticity structure in the complex momentum-squared plane that is consistent with causality.
Solving the QCD renormalization group equation at the 2-loop and 3-loop orders we obtain explicit expressions for the coupling as a function of the scale in terms of the Lambert W function. We study the nature of the ``Landau singularities'' in the complex Q^2 plane and show that perturbative freezing can lead, in certain cases, to an analyticity structure that is consistent with causality. We analyze the Analytic Perturbation Theory (APT) approach which is intended to remove the ``Landau singularities'', and show that at 2-loops it is uniquely defined in terms of the Lambert W function, and that, depending on the value of the first two beta function coefficients beta_0 and beta_1, it is either consistent with perturbative freezing (for beta_1 < -beta_0^2) with an infrared limit of -beta_0/beta_1 or leads to a non-perturbative infrared coupling with a limit of 1/beta_0 (for beta_1 > -beta_0^2). The possibility of a causal perturbative coupling is in accordance with the idea that a purely perturbative Banks-Zaks phase with an infrared fixed-point exists in QCD if the number of flavours (N_f) is increased. The causality condition implies that the perturbative phase is realized for N_f \geq 10.
I review the recent work on obtaining precise estimates of higher-order corrections in QCD and field theory.
We use Asymptotic Pade Approximants (APAP's) to predict the four- and five-loop β-functions in QCD and N=1 supersymmetric QCD (SQCD), as well as the quark mass anomalous dimensions in Abelian and non-Abelian gauge theories. We show how the accuracy of our previous β-function predictions at the four-loop level may be further improved by using estimators weighted over negative numbers of flavours (WAPAP's). The accuracy of the improved four-loop results encourages confidence in the new five-loop β-function predictions that we present. However, the WAPAP approach does not provide improved results for the anomalous mass dimension, or for Abelian theories.
We show that the Pade Approximant (PA) approach for resummation of perturbative series in QCD provides a systematic method for approximating the flow of momentum in Feynman diagrams. In the large-$β_0$ limit, diagonal PA's generalize the Brodsky-Lepage-Mackenzie (BLM) scale-setting method to higher orders in a renormalization scale- and scheme-invariant manner, using multiple scales that represent Neubert's concept of the distribution of momentum flow through a virtual gluon. If the distribution is non-negative, the PA's have only real roots, and approximate the distribution function by a sum of delta-functions, whose locations and weights are identical to the optimal choice provided by the Gaussian quadrature method for numerical integration. We show how the first few coefficients in a perturbative series can set rigorous bounds on the all-order momentum distribution function, if it is positive. We illustrate the method with the vacuum polarization function and the Bjorken sum rule computed in the large-$β_0$ limit.
An outstanding mystery of charmonium physics is why the J/ψdecays prominently to pseudoscalar plus vector meson channels, such as J/ψ-> ρπand J/ψ-> K^*K, whereas the ψ'(2S) does not. We show that such decays of J/ψand their suppression for ψ'(2S) follow naturally from the existence of intrinsic charm |qbar q cbar c> Fock components of the light vector mesons.
We predict that the four-loop contribution β_3 to the QCD βfunction in the MS-bar prescription is given by β_3\simeq 23,600(900) - 6,400(200) N_f + 350(70) N_f^2 + 1.5 N_f^3, where N_f is the number of flavours and the coefficient of N_f^3 is an exact result from large-N_f expansion. In the phenomenologically-interesting case N_f=3, we estimate β_3 = (7.6 \pm 0.1) x 10^3. We discuss our estimates of the errors in these QCD predictions, basing them on the demonstrated accuracy of our method in test applications to the O(N) Φ^4 theory, and on variations in the details of our estimation method, which goes beyond conventional Pade approximants by estimating and correcting for subasymptotic deviations from exact results.
We calculate in QCD$_2$ the ratios of baryonic matrix elements of $ΔI = 2$ and $ΔI = 0$ four-fermion operators, with a view to understanding better the mechanism of $ΔI = 1/2$ enhancement in QCD$_4$. We find relatively small suppressions of both the scalar-scalar and vector-vector $ΔI = 2$ four-fermion operators. We discuss the possible implications of these results, in view of a suggestion that gluon condensation may be an important contributing factor in the $ΔI = 1/2$ enhancement seen in QCD$_4$. At the technical level, our calculation of the vector-vector operator matrix element requires a treatment of the time dependence of the QCD$_2$ soliton which had not been developed in previous phenomenological calculations within this model.
We study the renormalization-scheme (RS) dependence of Pade Approximants (PA's), and compare them with the Principle of Minimal Sensitivity (PMS) and the Effective Charge (ECH) approaches. Although the formulae provided by the PA, PMS and ECH predictions for higher-order terms in a QCD perturbation expansion differ in general, their predictions can be very close numerically for a wide range of renormalization schemes. Using the Bjorken sum rule as a test case, we find that Pade Summation (PS) reduces drastically the RS dependence of the Bjorken effective charge. We use these results to estimate the theoretical error due to the choice of RS in the extraction of $α_s$ from the Bjorken sum rule, and use the available data at $Q^2=3 GeV^2$ to estimate $α_s(M_Z) = 0.117^{+0.004}_{-0.007} \pm 0.002$, where the first error is experimental, and the second is theoretical.
The recent series of experiments on polarized lepton-nucleon scattering have provided a strange new twist in the story of the nucleon, some of whose aspects are reviewed in these lectures. In the first lecture, we review some issues arising in the analysis of the data on polarized structure functions, focusing in particular on the importance and treatment of high-order QCD perturbation theory. In the second lecture some possible interpretations of the ``EMC spin effect" are reviewed, principally in the chiral soliton (Skyrmion) approach, but also interpretations related to the axial $U(1)$ anomaly. This lecture also discusses other indications from recent LEAR data for an $\bar{s} s$ component in the nucleon wave function, and discusses test of a model for this component. Finally, the third lecture reviews the implications of polarized structure functions measurements for experiments to search for cold dark matter particles, such as the lightest supersymmetric particle and the axion, after reviewing briefly the astrophysical and cosmological evidence for cold dark matter.
We review the theory of polarized deep inelastic scattering in light of the most recent experimental data. We discuss the nucleon spin decomposition and the Bjorken sum rule. The latter is used for extraction of $α_s(M_Z^2)=0.116^{{+}0.004}_{{-}0.006}$ and as a test case for a new method of analyzing divergent perturbation series in QCD.
We prove that Pade approximants yield increasingly accurate predictions of higher-order coefficients in QCD perturbation series whose high-order behaviour is governed by a renormalon. We also prove that this convergence is accelerated if the perturbative series is Borel transformed. We apply Pade approximants and Borel transforms to the known perturbative coefficients for the Bjorken sum rule. The Pade approximants reduce considerably the renormalization-scale dependence of the perturbative correction to the Bjorken sum rule. We argue that the known perturbative series is already dominated by an infra-red renormalon, whose residue we extract and compare with QCD sum-rule estimates of higher-twist effects. We use the experimental data on the Bjorken sum rule to extract $α_s(M_Z^2) = 0.116_{-0.006}^{+0.004}$, including theoretical errors due to the finite order of available perturbative QCD calculations, renormalization-scale dependence and higher-twist effects.
We critically re-examine our earlier derivation of the effective low energy action for QCD in 4 dimensions with chiral fields transforming non-trivially under both color and flavor, using the method of anomaly integration. We find several changes with respect to our previous results, leading to much more compact expressions, and making it easier to compare with results of other approaches to the same problem. With the amended effective action, we find that there are no stable soliton solutions. In the context of the quark soliton program, we interpret this as an indication that the full low-energy effective action must include additional terms, reflecting possible modifications at short distances and/or the non-trivial structure of the gauge fields in the vacuum, such as $ \neq 0$. Such terms are absent in the formalism based on anomaly integration.