Integrating out the heaviest quark in N--flavour ChPT

We extend a known method to integrate out the strange quark in three flavour chiral perturbation theory to the context of an arbitrary number of flavours. As an application, we present the explicit formulae to one--loop accuracy for the heavy quark mass dependency of the low energy constants after decreasing the number of flavours by one while integrating out the heaviest quark in N--flavour chiral perturbation theory.Comment: 18 pages, 1 figure. Text and references added. To appear in EPJ

Analysis of the B→K2∗(1430),a2(1320),f2(1270)B \to K^*_2(1430), a_2(1320), f_2(1270) form-factors with light-cone QCD sum rules

In this article, we study the $B \to K^*_2(1430)$, $a_2(1320)$, $f_2(1270)$ form-factors with the light-cone QCD sum rules, where the $B$-meson light-cone distribution amplitudes are used. In calculations, we observe that the line-shapes of the $B$-meson light-cone distribution amplitude $\phi_+(\omega)$ have significant impacts on the values of the form-factors, and expect to obtain severe constraints on the parameters of the $B$-meson light-cone distribution amplitudes from the experimental data in the future.Comment: 19 pages, 6 figures, slight revisio

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

Probing Lepton Flavor Violation in Meson Decays with LHC Data

In this letter, we use LHC data from the Drell-Yan processes $pp\to\ell_i\ell_j$ (with $i\neq j$) to derive model-independent upper limits on lepton-flavor-violating meson decays. Our analysis is based on an Effective Field Theory (EFT) approach and it does not require a specific assumption regarding the basis of effective operators. We find that current LHC data (140~$\mathrm{fb}^{-1}$) already provides competitive limits on $B(B\to \pi e \tau)$ and $B(B\to \pi \mu \tau)$ with respect to the ones obtained through experimental searches at the $B$-factories. Moreover, we derive upper limits on several decays that have not been searched for experimentally yet, such as $D^0\to e\tau$ in the charm sector, and various semileptonic decays such as $B\to \rho \mu\tau$, $B_s\to K \mu\tau$ and $B_s\to\phi\mu\tau$. Lastly, we discuss the validity of the EFT description of LHC data and the impact of loop corrections in our analysis.Comment: 11 pages, 2 tables, 4 figs; typos corrected, published in EPJ

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

Implications from clean observables for the binned analysis of B -> K*ll at large recoil

We perform a frequentist analysis of q^2-dependent B-> K*(->Kpi)ll angular observables at large recoil, aiming at bridging the gap between current theoretical analyses and the actual experimental measurements. We focus on the most appropriate set of observables to measure and on the role of the q^2-binning. We highlight the importance of the observables P_i exhibiting a limited sensitivity to soft form factors for the search for New Physics contributions. We compute predictions for these binned observables in the Standard Model, and we compare them with their experimental determination extracted from recent LHCb data. Analyzing b->s and b->sll transitions within four different New Physics scenarios, we identify several New Physics benchmark points which can be discriminated through the measurement of P_i observables with a fine q^2-binning. We emphasise the importance (and risks) of using observables with (un)suppressed dependence on soft form factors for the search of New Physics, which we illustrate by the different size of hadronic uncertainties attached to two related observables (P_1 and S_3). We illustrate how the q^2-dependent angular observables measured in several bins can help to unravel New Physics contributions to B-> K*(->Kpi)ll, and show the extraordinary constraining power that the clean observables will have in the near future. We provide semi-numerical expressions for these observables as functions of the relevant Wilson coefficients at the low scale.Comment: 50 pages, 21 figures. Improved form factor analysis, conclusions unchanged. Plots with full resolution. Version published in JHE

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

Size of Isospin Breaking in Charged K(L4) Decay

We evaluate the size of isospin breaking corrections to form factors $f$ and $g$ of the $K_{\ell 4}$ decay process $K^+\to\pi^+\pi^-\ell^+\nu_{\ell}$ which is actually measured by the extended NA48 setup at CERN. We found that, keeping apart the effect of Coulomb interaction, isospin breaking does not affect modules. This is due to the cancelation between corrections of electromagnetic origin and those generated by the difference between up and down quark masses. On the other hand, electromagnetism affects considerably phases if the infrared divergence is dropped out using a minimal subtraction scheme. Consequently, the greatest care must be taken in the extraction of $\pi\pi$ phase shifts from experiment.Comment: 29 pages, LaTeX, 7 postscript figure