This letter summarises the status of the global fit of the CKM parameters within the Standard Model performed by the CKMfitter group. Special attention is paid to the inputs for the CKM angles $alpha$ and $gamma$ and the status of $B_stomumu$ and $B_
dto mumu$ decays. We illustrate the current situation for other unitarity triangles. We also discuss the constraints on generic $Delta F=2$ New Physics. All results have been obtained with the CKMfitter analysis package, featuring the frequentist statistical approach and using Rfit to handle theoretical uncertainties.
We consider the evaluation of the $etapi$ isospin-violating vector and scalar form factors relying on a systematic application of analyticity and unitarity, combined with chiral expansion results. It is argued that the usual analyticity properties do
hold (i.e. no anomalous thresholds are present) in spite of the instability of the $eta$ meson in QCD. Unitarity relates the vector form factor to the $etapi to pipi$ amplitude: we exploit progress in formulating and solving the Khuri-Treiman equations for $etato 3pi$ and in experimental measurements of the Dalitz plot parameters to evaluate the shape of the $rho$-meson peak. Observing this peak in the energy distribution of the $tauto eta pi u$ decay would be a background-free signature of a second-class amplitude. The scalar form factor is also estimated from a phase dispersive representation using a plausible model for the $etapi$ elastic scattering $S$-wave phase shift and a sum rule constraint in the inelastic region. We indicate how a possibly exotic nature of the $a_0(980)$ scalar meson manifests itself in a dispersive approach. A remark is finally made on a second-class amplitude in the $tautopipi u$ decay.
Isospin breaking in the Kl4 form factors induced by the difference between charged and neutral pion masses is studied. Starting from suitably subtracted dispersion representations, the form factors are constructed in an iterative way up to two loops
in the low-energy expansion by implementing analyticity, crossing, and unitarity due to two-meson intermediate states. Analytical expressions for the phases of the two-loop form factors of the Kpm -> pi^+ pi^- e^pm nu_e channel are given, allowing one to connect the difference of form-factor phase shifts measured experimentally (out of the isospin limit) and the difference of S- and P-wave pi-pi phase shifts studied theoretically (in the isospin limit). The isospin-breaking correction consists of the sum of a universal part, involving only pi-pi rescattering, and a process-dependent contribution, involving the form factors in the coupled channels. The dependence on the two S-wave scattering lengths a_0^0 and a_0^2 in the isospin limit is worked out in a general way, in contrast to previous analyses based on one-loop chiral perturbation theory. The latter is used only to assess the subtraction constants involved in the dispersive approach. The two-loop universal and process-dependent contributions are estimated and cancel partially to yield an isospin-breaking correction close to the one-loop case. The recent results on the phases of K^pm -> pi^+ pi^- e^pm nu_e form factors obtained by the NA48/2 collaboration at the CERN SPS are reanalysed including this isospin-breaking correction to extract values for the scattering lengths a_0^0 and a_0^2, as well as for low-energy constants and order parameters of two-flavour ChPT.
The first two non-trivial moments of the distribution of the topological charge (or gluonic winding number), i.e., the topological susceptibility and the fourth cumulant, can be computed in lattice QCD simulations and exploited to constrain the patte
rn of chiral symmetry breaking. We compute these two topological observables at next-to-leading order in three-flavour Chiral Perturbation Theory, and we discuss the role played by the eta propagation in these expressions. For hierarchies of light-quark masses close to the physical situation, we show that the fourth cumulant has a much better sensitivity than the topological susceptibility to the three-flavour quark condensate, and thus constitutes a relevant tool to determine the pattern of chiral symmetry breaking in the limit of three massless flavours. We provide the complete formulae for the two topological observables in the isospin limit, and predict their values in the particular setting of the recent analysis of the RBC/UKQCD collaboration. We show that a combination of the topological susceptibility and the fourth cumulant is able to pin down the three-flavour condensate in a particularly clean way in the case of three degenerate quarks.
The charm quark offers interesting opportunities to cross-check the mechanism of CP violation precisely tested in the strange and beauty sectors. In this paper, we exploit the angular and quantum correlations in the Dbar{D} pairs produced through the
decay of the psi(3770) resonance in a charm factory to investigate CP-violation in two different ways. We build CP-violating observables in psi(3770) -> Dbar{D} -> (V_1V_2)(V_3 V_4) to isolate specific New Physics effects in the charm sector. We also consider the case of psi(3770) -> Dbar{D} -> (V_1V_2)(Kpi) decays, which provide a new way to measure the strong phase difference delta between Cabibbo-favored and doubly-Cabibbo suppressed D decays required in the determination of the CKM angle gamma. Neglecting the systematics, we give a first rough estimate of the sensitivities of these measurements at BES-III with an integrated luminosity of 20 fb^-1 at psi(3770) peak and at a future Super tau-charm factory with a luminosity of 10^35 cm^-2.s^-1.
