πK\pi K Scattering in Three Flavour ChPT

We present the scattering lengths for the $\pi K$ processes in the three flavour Chiral Perturbation Theory (ChPT) framework at next-to-next-to-leading order (NNLO). The calculation has been performed analytically but we only include analytical results for the dependence on the low-energy constants (LECs) at NNLO due to the size of the expressions. These results, together with resonance estimates of the NNLO LECs are used to obtain constraints on the Zweig rule suppressed LECs at NLO, $L_4^r$ and $L_6^r$. Contrary to expectations from NLO order calculations we find them to be compatible with zero. We do a preliminary study of combining the results from $\pi\pi$ scattering, $\pi K$ scattering and the scalar form-factors and find only a marginal compatibility with all experimental/dispersive input data.Comment: 23 page

The Inverse Amplitude Method in ππ\pi\pi Scattering in Chiral Perturbation Theory to Two Loops

The inverse amplitude method is used to unitarize the two loop $\pi\pi$ scattering amplitudes of SU(2) Chiral Perturbation Theory in the $I=0,J=0$, $I=1,J=1$ and $I=2,J=0$ channels. An error analysis in terms of the low energy one-loop parameters $\bar l_{1,2,3,4,}$ and existing experimental data is undertaken. A comparison to standard resonance saturation values for the two loop coefficients $\bar b_{1,2,3,4,5,6}$ is also carried out. Crossing violations are quantified and the convergence of the expansion is discussed.Comment: (Latex, epsfig) 30 pages, 13 figures, 8 table

The X-/Gamma-ray camera ECLAIRs for the Gammay-ray burst mission SVOM

We present ECLAIRs, the Gamma-ray burst (GRB) trigger camera to fly on-board the Chinese-French mission SVOM. ECLAIRs is a wide-field ($\sim 2$\,sr) coded mask camera with a mask transparency of 40\% and a 1024 $\mathrm{cm}^2$ detection plane coupled to a data processing unit, so-called UGTS, which is in charge of locating GRBs in near real time thanks to image and rate triggers. We present the instrument science requirements and how the design of ECLAIRs has been optimized to increase its sensitivity to high-redshift GRBs and low-luminosity GRBs in the local Universe, by having a low-energy threshold of 4 keV. The total spectral coverage ranges from 4 to 150 keV. ECLAIRs is expected to detect $\sim 200$ GRBs of all types during the nominal 3 year mission lifetime. To reach a 4 keV low-energy threshold, the ECLAIRs detection plane is paved with 6400 $4\times 4~\mathrm{mm}^2$ and 1 mm-thick Schottky CdTe detectors. The detectors are grouped by 32, in 8x4 matrices read by a low-noise ASIC, forming elementary modules called XRDPIX. In this paper, we also present our current efforts to investigate the performance of these modules with their front-end electronics when illuminated by charged particles and/or photons using radioactive sources. All measurements are made in different instrument configurations in vacuum and with a nominal in-flight detector temperature of $-20^\circ$C. This work will enable us to choose the in-flight configuration that will make the best compromise between the science performance and the in-flight operability of ECLAIRs. We will show some highlights of this work.Comment: 15 pages, 12 figures, Proceeding SPIE - Montreal 201

Corrections to the SU(3)×SU(3){\bf SU(3)\times SU(3)} Gell-Mann-Oakes-Renner relation and chiral couplings L8rL^r_8 and H2rH^r_2

Next to leading order corrections to the $SU(3) \times SU(3)$ Gell-Mann-Oakes-Renner relation (GMOR) are obtained using weighted QCD Finite Energy Sum Rules (FESR) involving the pseudoscalar current correlator. Two types of integration kernels in the FESR are used to suppress the contribution of the kaon radial excitations to the hadronic spectral function, one with local and the other with global constraints. The result for the pseudoscalar current correlator at zero momentum is $\psi_5(0) = (2.8 \pm 0.3) \times 10^{-3} GeV^{4}$, leading to the chiral corrections to GMOR: $\delta_K = (55 \pm 5)$. The resulting uncertainties are mostly due to variations in the upper limit of integration in the FESR, within the stability regions, and to a much lesser extent due to the uncertainties in the strong coupling and the strange quark mass. Higher order quark mass corrections, vacuum condensates, and the hadronic resonance sector play a negligible role in this determination. These results confirm an independent determination from chiral perturbation theory giving also very large corrections, i.e. roughly an order of magnitude larger than the corresponding corrections in chiral $SU(2) \times SU(2)$. Combining these results with our previous determination of the corrections to GMOR in chiral $SU(2) \times SU(2)$, $\delta_\pi$, we are able to determine two low energy constants of chiral perturbation theory, i.e. $L^r_8 = (1.0 \pm 0.3) \times 10^{-3}$, and $H^r_2 = - (4.7 \pm 0.6) \times 10^{-3}$, both at the scale of the $\rho$-meson mass.Comment: Revised version with minor correction

The cusp effect in eta' --> eta pi pi decays

Strong final-state interactions create a pronounced cusp in eta' --> eta pi0 pi0 decays. We adapt and generalize the non-relativistic effective field theory framework developed for the extraction of pi pi scattering lengths from K --> 3 pi decays to this case. The cusp effect is predicted to have an effect of more than 8% on the decay spectrum below the pi+ pi- threshold.Comment: 11 pages, 8 figures; comment added, typos corrected, version published in Eur. Phys. J.

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

The epsilon expansion at next-to-next-to-leading order with small imaginary chemical potential

We discuss chiral perturbation theory for two and three quark flavors in the epsilon expansion at next-to-next-to-leading order (NNLO) including a small imaginary chemical potential. We calculate finite-volume corrections to the low-energy constants $\Sigma$ and $F$ and determine the non-universal modifications of the theory, i.e., modifications that cannot be mapped to random matrix theory (RMT). In the special case of two quark flavors in an asymmetric box we discuss how to minimize the finite-volume corrections and non-universal modifications by an optimal choice of the lattice geometry. Furthermore we provide a detailed calculation of a special version of the massless sunset diagram at finite volume.Comment: 21 pages, 5 figure

Strong Interactions at Low Energy

The lectures review some of the basic concepts relevant for an understanding of the low energy properties of the strong interactions: chiral symmetry, spontaneous symmetry breakdown, Goldstone bosons, quark condensate. The effective field theory used to analyze the low energy structure is briefly sketched. As an illustration, I discuss the implications of the recent data on the decay $K\to \pi\pi e\nu$ for the magnitude of the quark condensate.Comment: Lectures given at the school of physics "Understanding the structure of hadrons", Prague, July 2001, 20 p

The Wide-Field X and Gamma-Ray Telescope ECLAIRs aboard the Gamma-Ray Burst Multi-Wavelength Space Mission SVOM

The X and Gamma-ray telescope ECLAIRs is foreseen to be launched on a low Earth orbit (h=630 km, i=30 degrees) aboard the SVOM satellite (Space-based multi-band astronomical Variable Objects Monitor), a French-Chinese mission with Italian contribution. Observations are expected to start in 2013. It has been designed to detect and localize Gamma-Ray Bursts (GRBs) or persistent sources of the sky, thanks to its wide field of view (about 2 sr) and its remarkable sensitivity in the 4-250 keV energy range, with enhanced imaging sensitivity in the 4-70 keV energy band. These characteristics are well suited to detect highly redshifted GRBs, and consequently to provide fast and accurate triggers to other onboard or ground-based instruments able to follow-up the detected events in a very short time from the optical wavelength bands up to the few MeV Gamma-Ray domain.Comment: Proccedings of the "2008 Nanjing GRB Conference", June 23-27 2008, Nanjing, Chin

Assessing the conservation value of waterbodies: the example of the Loire floodplain (France)

In recent decades, two of the main management tools used to stem biodiversity erosion have been biodiversity monitoring and the conservation of natural areas. However, socio-economic pressure means that it is not usually possible to preserve the entire landscape, and so the rational prioritisation of sites has become a crucial issue. In this context, and because floodplains are one of the most threatened ecosystems, we propose a statistical strategy for evaluating conservation value, and used it to prioritise 46 waterbodies in the Loire floodplain (France). We began by determining a synthetic conservation index of fish communities (Q) for each waterbody. This synthetic index includes a conservation status index, an origin index, a rarity index and a richness index. We divided the waterbodies into 6 clusters with distinct structures of the basic indices. One of these clusters, with high Q median value, indicated that 4 waterbodies are important for fish biodiversity conservation. Conversely, two clusters with low Q median values included 11 waterbodies where restoration is called for. The results picked out high connectivity levels and low abundance of aquatic vegetation as the two main environmental characteristics of waterbodies with high conservation value. In addition, assessing the biodiversity and conservation value of territories using our multi-index approach plus an a posteriori hierarchical classification methodology reveals two major interests: (i) a possible geographical extension and (ii) a multi-taxa adaptation