Isospin breaking in the phases of the Ke4 form factors

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 K\pm -> 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.Comment: 48 pages, 7 figure

Chiral dynamics with strange quarks in the light of recent lattice simulations

Several lattice collaborations performing simulations with 2+1 light dynamical quarks have experienced difficulties in fitting their data with standard Nf=3 chiral expansions at next-to-leading order, yielding low values of the quark condensate and/or the decay constant in the Nf=3 chiral limit. A reordering of these expansions seems required to analyse these data in a consistent way. We discuss such a reordering, known as Resummed Chiral Perturbation Theory, in the case of pseudoscalar masses and decay constants, pion and kaon electromagnetic form factors and Kl3} form factors. We show that it provides a good fit of the recent results of two lattice collaborations (PACS-CS and RBC/UKQCD). We describe the emerging picture for the pattern of chiral symmetry breaking, marked by a strong dependence of the observables on the strange quark mass and thus a significant difference between chiral symmetry breaking in the Nf=2 and Nf=3 chiral limits. We discuss the consequences for the ratio of decay constants F_K/F_pi and the Kl3 form factor at vanishing momentum transfer.Comment: 31 pages. Published versio

Determining the chiral condensate from the distribution of the winding number beyond topological susceptibility

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 pattern 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.Comment: 31 pages, 7 figures. Accepted for publication in EPJ

Study of Bc->KK decay with perturbative QCD approach

In the framework of the perturbative QCD approach, we study the charmless pure weak annihilation Bc->KK decay and find that the branching ratio BR(Bc->KK) O(10^-7). This prediction is so tiny that the Bc->KK decay might be unmeasurable at the Large Hadron Collider.Comment: Revtex4, 12 pages, 1 figure

MRI/TRUS data fusion for brachytherapy

BACKGROUND: Prostate brachytherapy consists in placing radioactive seeds for tumour destruction under transrectal ultrasound imaging (TRUS) control. It requires prostate delineation from the images for dose planning. Because ultrasound imaging is patient- and operator-dependent, we have proposed to fuse MRI data to TRUS data to make image processing more reliable. The technical accuracy of this approach has already been evaluated. METHODS: We present work in progress concerning the evaluation of the approach from the dosimetry viewpoint. The objective is to determine what impact this system may have on the treatment of the patient. Dose planning is performed from initial TRUS prostate contours and evaluated on contours modified by data fusion. RESULTS: For the eight patients included, we demonstrate that TRUS prostate volume is most often underestimated and that dose is overestimated in a correlated way. However, dose constraints are still verified for those eight patients. CONCLUSIONS: This confirms our initial hypothesis

Chiral Extrapolation of the Strangeness Changing K pi Form Factor

We perform a chiral extrapolation of lattice data on the scalar K pi form factor and the ratio of the kaon and pion decay constants within Chiral Perturbation Theory to two loops. We determine the value of the scalar form factor at zero momentum transfer, at the Callan-Treiman point and at its soft kaon analog as well as its slope. Results are in good agreement with their determination from experiment using the standard couplings of quarks to the W boson. The slope is however rather large. A study of the convergence of the chiral expansion is also performed.Comment: few minor change

Predictions of selected flavour observables within the Standard Model

This letter gathers a selection of Standard Model predictions issued from the metrology of the CKM parameters performed by the CKMfitter group. The selection includes purely leptonic decays of neutral and charged B, D and K mesons. In the light of the expected measurements from the LHCb experiment, a special attention is given to the radiative decay modes of B mesons as well as to the B-meson mixing observables, in particular the semileptonic charge asymmetries a^d,s_SL which have been recently investigated by the D0 experiment at Tevatron. Constraints arising from rare kaon decays are addressed, in light of both current results and expected performances of future rare kaon experiments. All results have been obtained with the CKMfitter analysis package, featuring the frequentist statistical approach and using Rfit to handle theoretical uncertainties.Comment: 8 pages, 1 figure, 2 tables. Typos corrected and discussion of agreement between SM and data update

Two-loop representations of low-energy pion form factors and pi-pi scattering phases in the presence of isospin breaking

Dispersive representations of the pi-pi scattering amplitudes and pion form factors, valid at two-loop accuracy in the low-energy expansion, are constructed in the presence of isospin-breaking effects induced by the difference between the charged and neutral pion masses. Analytical expressions for the corresponding phases of the scalar and vector pion form factors are computed. It is shown that each of these phases consists of the sum of a "universal" part and a form-factor dependent contribution. The first one is entirely determined in terms of the pi-pi scattering amplitudes alone, and reduces to the phase satisfying Watson's theorem in the isospin limit. The second one can be sizeable, although it vanishes in the same limit. The dependence of these isospin corrections with respect to the parameters of the subthreshold expansion of the pi-pi amplitude is studied, and an equivalent representation in terms of the S-wave scattering lengths is also briefly presented and discussed. In addition, partially analytical expressions for the two-loop form factors and pi-pi scattering amplitudes in the presence of isospin breaking are provided.Comment: 57 pages, 12 figure

Convergence properties of η→3π\eta\to 3\pi decays in chiral perturbation theory

Theoretical efforts to describe and explain the $\eta\to 3\pi$ decays reach far back in time. Even today, the convergence of the decay widths and some of the Dalitz plot parameters seems problematic in low energy QCD. In the framework of resummed CHPT, we explore the question of compatibility of experimental data with a reasonable convergence of a carefully defined chiral series, where NNLO remainders are assumed to be small. By treating the uncertainties in the higher orders statistically, we numerically generate a large set of theoretical predictions, which are then confronted with experimental information. In the case of the decay widths, the experimental values can be reconstructed for a reasonable range of the free parameters and thus no tension is observed, in spite of what some of the traditional calculations suggest. The Dalitz plot parameters $a$ and $d$ can be described very well too. When the parameters $b$ and $\alpha$ are concerned, we find a mild tension for the whole range of the free parameters, at less than 2$\sigma$ C.L. This can be interpreted in two ways - either some of the higher order corrections are indeed unexpectedly large or there is a specific configuration of the remainders, which is, however, not completely improbable. Also, the distribution of the theoretical uncertainties is found to be significantly non-gaussian, so the consistency cannot be simply judged by the 1$\sigma$ error bars.Comment: 57 pages, 5 figure

Perturbative QCD Analysis of the Nucleon's Pauli Form Factor F_2(Q^2)

We perform a perturbative QCD analysis of the nucleon's Pauli form factor $F_2(Q^2)$ in the asymptotically large $Q^2$ limit. We find that the leading contribution to $F_2(Q^2)$ has a $1/Q^6$ power behavior, consistent with the well-known result in the literature. Its coefficient depends on the leading- and subleading-twist light-cone wave functions of the nucleon, the latter describing the quarks with one unit of orbital angular momentum. We also derive at the logarithmic accurary the asymptotic scaling $F_2(Q^2)/F_1(Q^2) \sim (\log^2 Q^2/\Lambda^2)/Q^2$ which describes recent Jefferson Lab data well.Comment: 4 papes, 3 figures include