Renormalization of B-meson distribution amplitudes

We summarize a recent calculation of the evolution kernels of the two-particle B-meson distribution amplitudes $\phi_+$ and $\phi_-$ taking into account three-particle contributions. In addition to a few phenomenological comments, we give as a new result the evolution kernel of the combination of three-particle distribution amplitudes $\Psi_A-\Psi_V$ and confirm constraints on $\phi_+$ and $\phi_-$ derived from the light-quark equation of motion.Comment: 7 pages, 2 figures. Contribution to the proceedings of the Int. Workshop on Effective Field Theories: from the pion to the upsilon. Feb. 2009. Valencia, Spai

PoN-S : a systematic approach for applying the Physics of Notation (PoN)

Visual Modeling Languages (VMLs) are important instruments of communication between modelers and stakeholders. Thus, it is important to provide guidelines for designing VMLs. The most widespread approach for analyzing and designing concrete syntaxes for VMLs is the so-called Physics of Notation (PoN). PoN has been successfully applied in the analysis of several VMLs. However, despite its popularity, the application of PoN principles for designing VMLs has been limited. This paper presents a systematic approach for applying PoN in the design of the concrete syntax of VMLs. We propose here a design process establishing activities to be performed, their connection to PoN principles, as well as criteria for grouping PoN principles that guide this process. Moreover, we present a case study in which a visual notation for representing Ontology Pattern Languages is designed

Three-particle contributions to the renormalisation of B-meson light-cone distribution amplitudes

We study light-cone distribution amplitudes of heavy-light systems, such as a B-meson. By an explicit computation, we determine how two-parton distribution amplitudes mix with three-parton ones at one loop: \phi_+ is shown to mix only into itself, whereas \phi_- mixes with the difference of three-parton distribution amplitudes \Psi_A-\Psi_V. We determine the corresponding anomalous dimension and we check the gauge independence of our result by considering a general covariant gauge. Finally, we comment on some implications of our result for phenomenological models of these distribution amplitudes.Comment: 21 pages, 5 figures, some comments and 2 references added, except for typesetting matches version published in JHE

Resumming QCD vacuum fluctuations in three-flavour Chiral Perturbation Theory

Due to its light mass of order Lambda_QCD, the strange quark can play a special role in Chiral Symmetry Breaking (ChSB): differences in the pattern of ChSB in the limits N_f=2 (m_u,m_d->0, m_s physical) and N_f=3 (m_u,m_d,m_s->0) may arise due to vacuum fluctuations of s-bar s pairs, related to the violation of the Zweig rule in the scalar sector and encoded in particular in the O(p^4) low-energy constants L_4 and L_6. In case of large fluctuations, we show that the customary treatment of SU(3)xSU(3) chiral expansions generate instabilities upsetting their convergence. We develop a systematic program to cure these instabilities by resumming nonperturbatively vacuum fluctuations of s-bar s pairs, in order to extract information about ChSB from experimental observations even in the presence of large fluctuations. We advocate a Bayesian framework for treating the uncertainties due to the higher orders. As an application, we present a three-flavour analysis of the low-energy pi-pi scattering and show that the recent experimental data imply a lower bound on the quark mass ratio 2m_s/(m_u+m_d) > 14 at 95 % confidence level. We outline how additional information may be incorporated to further constrain the pattern of ChSB in the N_f=3 chiral limit.Comment: 58 pages, 8 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

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

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

Bs to l+ l- gamma as a Test of Lepton Flavor Universality

We discuss a number of strategies to reduce the $\mathcal B(B^0_s \to \ell^{+} \ell^{-} \gamma)$ theoretical error, and make such a measurement a new probe of the interactions that are interesting in the light of present-day flavor discrepancies. In particular, for low di-lepton invariant mass we propose to exploit the close parenthood between $\mathcal B(B^0_s \to \ell^{+} \ell^{-} \gamma)$ and the measured $\mathcal B(B^0_s \to \phi (\to K^+ K^-) \gamma)$. For high $q^2$, conversely, we exploit the fact that the decay is dominated by two form-factor combinations, plus contributions from broad charmonium that we model accordingly. We construct the ratio $R_\gamma$, akin to $R_K$ and likewise sensitive to lepton-universality violation. Provided the two rates in this ratio are integrated in a suitable region that minimises bremsstrahlung contributions while maximising statistics, the ratio is very close to unity and the form-factor dependence cancels to an extent that makes it a new valuable probe of lepton-universality violating contributions in the effective Hamiltonian. We finally speculate on additional ideas to extract short-distance information from resonance regions, which are theoretically interesting but statistically limited at present.Comment: 21 pages, 4 figures. v4: in appendix removed equation already present in main tex

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

Consistent Analysis of the B→πB\to\pi Transition Form Factor in the Whole Physical Region

In the paper, we show that the $B\to\pi$ transition form factor can be calculated by using the different approach in the different $q^2$ regions and they are consistent with each other in the whole physical region. For the $B\to\pi$ transition form factor in the large recoil regions, one can apply the PQCD approach, where the transverse momentum dependence for both the hard scattering part and the non-perturbative wavefunction, the Sudakov effects and the threshold effects are included to regulate the endpoint singularity and to derive a more reliable PQCD result. Pionic twist-3 contributions are carefully studied with a better endpoint behavior wavefunction for $\Psi_p$ and we find that its contribution is less than the leading twist contribution. Both the two wavefunctions $\Psi_B$ and $\bar\Psi_B$ of the B meson can give sizable contributions to the $B\to\pi$ transition form factor and should be kept for a better understanding of the B decays. The present obtained PQCD results can match with both the QCD light-cone sum rule results and the extrapolated lattice QCD results in the large recoil regions.Comment: 18pages, 6 figure