We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

We calculate the hadronic light-by-light contributions to the muon g−2.We use both 1/N c and chiral counting to organize the calculation. Then we calculate the leading and next-to-leading order in the 1/N c expansion low energy contributions using the Extended Nambu-Jona-Lasinio model as hadronic model. We do that to all orders in the external momenta and quark masses expansion. Although the hadronic light-by-light contributions to muon g − 2 are not saturated by these low energy contributions we estimate them conservatively. A detailed analysis of the different hadronic light-by-light contributions to muon g − 2 is done. The dominant contribution is the twice anomalous pseudoscalar exchange diagram. The final result we get is a light−by−light µ = (−9.2 ± 3.2) · 10 −10 . This is between two and three times the expected experimental uncertainty at the forthcoming BNL muon g − 2 experiment.

In the calculation of the contribution of the second diagram in Fig. 2(b), a global normalization factor was erroneously applied twice. Unfortunately, this changes the conclusions of our Letter rather significantly. Full details of this work and this Erratum will be given in a forthcoming publication. Below is Table I corrected.

We present results of lattice QCD simulations with mass-degenerate up and down and mass-split strange and charm (N f = 2 + 1 + 1) dynamical quarks using Wilson twisted mass fermions at maximal twist. The tuning of the strange and charm quark masses is performed at two values of the lattice spacing a ≈ 0.078 fm and a ≈ 0.086 fm with lattice sizes ranging from L ≈ 1.9 fm to L ≈ 2.8 fm. We measure with high statistical precision the light pseudoscalar mass m PS and decay constant f PS in a range 270 m PS 510 MeV and determine the low energy parameters f 0 andl 3,4 of SU(2) chiral perturbation theory. We use the two values of the lattice spacing, several lattice sizes as well as different values of the light, strange and charm quark masses to explore the systematic effects. A first study of discretisation effects in light-quark observables and a comparison to N f = 2 results are performed.

We quantify the important effect of strong final state interactions in the weak K ! 2p amplitudes, using the measured p-p phase shifts with J 0 and I 0, 2. The final rescattering of the two pions provides a strong enhancement of the DI 1͞2 amplitude, which so far has been neglected in the theoretical predictions of´0͞´. This correction increases the standard model prediction of´0͞´to values in good agreement with the experimental measurements.PACS numbers: 13.25. Es, 11.30.Er, 11.55.Fv, 13.75.Lb It is well known that, at center-of-mass energies around the kaon mass, the strong S-wave p-p scattering generates a large phase shift difference ͑d . In the usual description of K ! 2p decays, this effect is explicitly taken into account, through the following decomposition of the relevant isospin amplitudes with I 0, 2:It has also been suggested [2-4] that final state interactions (FSI) play an important role in the observed enhancement of the I 0 decay amplitude, A 0 ͞A 2 ഠ 22.2. However, their impact on the direct CP-violating parameter´0͞´has never been properly estimated. At lowest order in chiral perturbation theory (ChPT), O͑p 2 ͒, the decay amplitudes do not contain any strong phase:where C 0 g 8 1 1 9 g 27 and C 2 5 9 p 2 g 27 , with g 8 and g 27 unknown chiral couplings, corresponding to the two lowest-order DS 1 operators in the momentum expansion, transforming as ͑8 L , 1 R ͒ and ͑27 L , 1 R ͒, respectively, under the chiral group [5,6]. The phenomenological determination of these couplings from K ! 2p, taking the measured phase shifts into account through (1), gives jC 0 j ഠ 5.1 and jg 27 j ഠ 0.29.The above procedure is not quite consistent, because the strong phases d I 0 are put by hand. Those phases originate in the final rescattering of the two pions and, therefore, are generated by chiral loops which are of higher order in the momentum expansion. Since the strong phases are quite large, especially in the isospin zero case, one should expect large higher-order unitarity corrections. The existing oneloop analyses of K ! 2p [4,7,8] show, in fact, that pion loop diagrams provide an important enhancement of the A 0 amplitude, implying a sizable reduction (ϳ30%) of the fitted jg 8 j value. However, the phase shift d 0 0 predicted by the one-loop calculation is still lower than its measured value, which indicates that a further enhancement should be expected at higher orders.Many attempts have been made to compute the amplitudes A I from first principles [5,6,[9][10][11][12][13][14][15][16]. Although those calculations have provided encouraging results, we are still far from getting accurate predictions. In many approaches FSI are not included in the computational framework. This is the case of present lattice calculations [13], which are able to compute only the one pion ͗pjH DS1 jK͘ matrix elements, or estimates at leading order in the 1͞N C expansion [6,[10][11][12] (the phases d I J are zero at leading order). Other approaches [10,14,15] include some FSI effects, but in a rather incomplete way; however...

We study Quantum Chromodynamics with eight flavours by use of lattice simulations and present evidence that the theory still breaks chiral symmetry in the zero temperature, continuum limit. This confirms that the lower end of the conformal window of QCD lies above Nf = 8.Comment: 19 pages, 7 figures; added a number of relevant references and comments to introduction, enhanced captions for figures 6 and 7, corrected typos and minor lapses of styl

LU T P 01-37 D ecem ber 2001C om m ent on the P ion P ole P art of the Light-by-Light C ontribution to the M uon g 2

We present a detailed analysis of ε ′ /ε within the Standard Model, taking into account the strong enhancement through final-state interactions identified in refs. [1] and [2]. The relevant hadronic matrix elements are fixed at leading order in the 1/N C expansion, through a matching procedure between the effective short-distance Lagrangian and its corresponding low-energy description in Chiral Perturbation Theory. All large logarithms are summed up, both at short and long distances. Two different numerical analyses are performed, using either the experimental or the theoretical value for ε, with compatible results. We obtain Re (ε ′ /ε) = (1.7 ± 0.9) · 10 −3 . The error is dominated by the uncertainty in the value of the strange quark mass and the estimated corrections from unknown 1/N C -suppressed local contributions. A better estimate of the strange quark mass would reduce the uncertainty to about 30%. The Standard Model prediction agrees with the present experimental world average Re (ε ′ /ε) = (1.93 ± 0.24) · 10 −3 .