Narrow Results

A general, and very basic introduction to QCD sum rules is presented, with emphasis on recent issues to be described at length in other papers in this issue. Collectively, these papers constitute the proceedings of the International Workshop on Determination of the Fundamental Parameters of QCD, Singapore, March 2013.

The problems encountered in the determination of m_u and m_d are discussed. While their sum is known quite well, the difference m_d-m_u, which measures the breaking of isospin symmetry in the QCD Lagrangian, is still subject to significant uncertainties. I focus on recent work based on the dispersive analysis of the decay η→3π, which offers a good handle on isospin breaking, because in that transition, the contributions from the e.m. interaction are suppressed.

The measurment of the charge symmetry conserving reactions dd → ³He p π^- and dd → ³He n π⁰ is the first step of the charge symmetry breaking physics program with WASA-at-COSY. The analysis of these channels helps to understand the experimental conditions and provides additional parameters for theoretical studies. The data have been collected in November 2007.

The conventional quark mass is not continuous at thresholds. In this paper, we derive matching-invariant quark masses which are continuous everywhere. They are generally expanded as an obvious function of the logarithmic $\mathrm{\Lambda }$ scaled energy. The expansion coefficients are related to the gamma and beta functions, with concretization to four-loop level. Due to the maximal elimination of their direct dependence on the coupling with large uncertainties, the new expressions for quark masses converge much fast and accurate.

A Planck-scale model that includes quantum chromodynamics and goes beyond it, is tested against observations. The model is based on a single fundamental principle. Starting with Dirac’s proposal describing spin $1/2$ particles as tethered objects, quarks and elementary fermions are conjectured to be fluctuating rational tangles with unobservable tethers. Such tangles obey the free Dirac equation. Classifying rational tangles naturally yields the observed spectrum of elementary fermions, including the six quark types and their quantum numbers. Classifying tangle deformations naturally yields exactly three types of gauge interactions, three types of elementary gauge bosons, and the symmetry groups U(1), broken SU(2) and SU(3). The possible rational tangles for quarks, leptons, Higgs and gauge bosons allow only the observed Feynman diagrams. The complete Lagrangian of the standard model — without any modification and including the Lagrangian of quantum chromodynamics — arises in a natural manner.

Over 90 experimental consequences and tests about quark and gluon behavior are deduced from the single fundamental principle. No consequence is in contrast with observations. The consequences of the strand conjecture include the complete quark model for hadrons, the correct sign of hadron quadrupole moments, color flux tubes, confinement, Regge behavior, running quark masses, correctly predicted hadron mass sequences, the lack of CP violation for the strong interaction, asymptotic freedom, and the appearance of glueballs. Two consequences differ from quantum chromodynamics. First, the geometry of the strand process for the strong interaction leads to an ab-initio estimate for the running strong coupling constant. Second, the tangle shapes lead to ab-initio lower and upper limits for the mass values of the quarks.

The effects of intermediate charmed mesons on charmonium transitions with the emission of one pion or eta meson are studied systematically. Based on a non-relativistic effective field theory we show that charmed meson loops are enhanced compared to the corresponding tree-level contributions for transitions between two S-wave charmonia as well as for transitions between two P-wave charmonia. On the contrary, for the transitions between one S-wave and one P-wave charmonium state, the loops need to be analyzed case by case and often appear to be suppressed. Extending these considerations to the b-quark sector, we propose a new method to extract the light quark mass ratio m_u/m_d using the ϒ(4S) → h_bπ⁰(η) bottomonia transitions.

We perform a non-perturbative chiral study of the masses of the lightest pseudoscalar mesons. The pseudoscalar self-energies are calculated by the evaluation of the scalar self-energy loops with full S-wave meson-meson amplitudes taken from Unitary Chiral Perturbation Theory (UCHPT). These amplitudes, among other features, contain the lightest nonet of scalar resonances σ, f₀(980), a₀(980) and κ. The self-energy loops are regularized by a proper subtraction of the infinities within a dispersion relation formulation of the scattering amplitudes. Values for the bare masses of pions and kaons are obtained, as well as an estimate of the mass of the η₈. We then match to the self-energies from standard Chiral Perturbation Theory (CHPT) to and resum higher orders from our calculated scalar self-energies. The dependence of the self-energies on the quark masses allows a determination of the ratio of the strange quark mass over the mean of the lightest quark masses, , in terms of the CHPT low energy constant combinations and . In this way, we give a range for the values of these low energy counterterms and for , once the η meson mass is invoked. The low energy constants are further constraint by performing a fit to the recent MILC lattice data on the pseudoscalar masses. An excellent reproduction of the MILC data is obtained, at the level of 1% of relative error in the pseudoscalar masses, and results. This value is consistent with 24.4 ± 1.5 from CHPT and phenomenology and more marginally with the value 27.4 ± 0.5, obtained from Staggered CHPT and the lattice data. We report on the work¹ and more details can be found there.

Recent results on four-loop tadpoles amplitudes and their implications for precision calculations are presented.

In this contribution two recent analyses for the extraction of the charm quark mass are discussed. Although they rely on completely different experimental and theoretical input the two methods provide the same final results for the charm quark mass and have an uncertainty of about 1%.