High-statistics data on the $e^+e^-\to π^+π^-$ cross section and the pion vector form factor have been obtained recently by several collaborations. Unfortunately, there are some tensions between different datasets, especially the most precise ones, which have not been resolved so far. Additional independent constraints on the data are therefore of interest. We consider a parametrization-free method of analytic extrapolation proposed recently, which is based on a mixed phase and modulus extremal problem and combines rigorous upper and lower bounds with numerical simulations to account for the statistical distributions of the input and output values. Spacelike data on the form factor and measurements of the modulus in the region $(0.65-0.71)$ GeV are used as input. In previous works, the formalism was applied for extrapolating the form factor to low energies. In the present work, we use it as a stringent and model-independent test of consistency with analyticity and unitarity for the high-statistics data around the $ρ$ resonance. The study reveals some inconsistencies, in particular below the $ρ$ peak the BABAR data are slightly higher than the band of extrapolated values, while above the $ρ$ peak all the data are situated at the lower edge of the band. The implications of the results on the two-pion vacuuum polarization contribution to the anomalous magnetic moment of the muon are briefly discussed.
We use unitarity and analyticity of scattering amplitudes to constrain fermionic operators in the standard model effective field theory. For four-fermion operators at mass dimension 8, we scatter flavor superpositions in fixed standard model representations and find the Wilson coefficients to be constrained so that their contraction with any pair of pure density matrices is positive. These constraints imply that flavor-violating couplings are upper-bounded by their flavor-conserving cousins. For instance, LEP data already appears to preclude certain operators in upcoming $μ\to 3e$ measurements…
Unitarity, analyticity, dispersion relations and resonances in strongly interacting $W_L W_L$, $Z_L Z_L$ and $hh$ scattering
如果电弱对称性破缺扇区被证明是强相互作用的，那么积极研究的纵向规范玻色子加希格斯玻色子的有效理论就可以有效地扩展到幺正性饱和的区域（微扰膨胀破裂的区域）。这是通过色散关系来实现的，色散关系的减法常数和左切贡献可以以不同的方式近似获得，从而产生不同的么正化过程。我们说明的想法与反振幅方法，一个版本的N/D方法和另一个改进版本的K矩阵。在这三种情况下，我们得到的分波是酉的，具有适当的左切和右切的解析的，在某些情况下，第二黎曼单中的极点可以被理解为动态产生的共振。此外，他们再现在次领先秩序（NLO）的微扰展开的五个分波不消失（J=2），他们是重整化尺度（$μ$）独立。此外，么正化形式主义的耦合通道的情况下进行了推广。然后，我们将结果应用于规范玻色子$V=W, Z$在高能下的纵向分量的弹性散射振幅。我们还计算了$h h \rightarrow h h$和非弹性过程$VV\rightarrow h h$，它们耦合到弹性$VV$通道中，用于保管同位旋$I=0$ .我们数值比较了三种方法的各种值的低能量耦合和解释的差异的原因发现在$I=J=1$分波。然后，我们研究了共振出现在不同的弹性和耦合通道的有效拉格朗日参数。
In this work we discuss in detail the non-perturbative determination of the momentum dependence of the form factors entering in semileptonic decays using unitarity and analyticity constraints. The method contains several new elements with respect to previous proposals and allows to extract, using suitable two-point functions computed non-perturbatively, the form factors at low momentum transfer $q^2$ from those computed explicitly on the lattice at large $q^2$, without any assumption about their $q^2$-dependence. The approach will be very useful for exclusive semileptonic $B$-meson decays, whe…
The physics motivation and the conceptual design of the PIONEER experiment, a next-generation rare pion decay experiment testing lepton flavor universality and CKM unitarity, are described. Phase I of the PIONEER experiment, which was proposed and approved at Paul Scherrer Institut, aims at measuring the charged-pion branching ratio to electrons vs.\ muons, $R_{e/μ}$, 15 times more precisely than the current experimental result, reaching the precision of the Standard Model (SM) prediction at 1 part in $10^4$. Considering several inconsistencies between the SM predictions and data pointing towa…
Pion beta decay, $π^+\to π^0 e^+ν(γ)$, provides a theoretically clean $\pm 0.3\%$ determination of the CKM matrix element $V_{\text{ud}}$. That value falls short of super-allowed nuclear beta decays where an order of magnitude better precision already exists. We advocate a new strategy for utilizing pion beta decay, based on its role in determining ${V_{\text{us}} / V_{\text{ud}}}$ via the ratio $R_V=Γ\left(K\to πl ν(γ)\right)/Γ\left(π^+\to π^0 e^+ν(γ)\right)$. $R_V$ measures $ { f_+^K(0) |V_{\text{us}}| / f_+^π(0) |V_{\text{ud}}| }$ and is insensitive to the Fermi constant and some radiative …
In this talk I briefly review the precision test of the first row CKM unitarity, focusing mainly on $V_{ud}$ and $V_{us}$ extracted from pion, kaon, neutron and superallowed nuclear beta decays. I will discuss the current status of several important Standard Model theory inputs to these processes, and the need for future improvements.
We consider the isospin one-half example system, with $D \,π, D\,η, D_s \bar K, D^* π, D^*η, D^*\bar K$ coupled channels in the $J^P = 1^-$ partial wave, chosen such that various phenomena that come with the opening of an anomalous threshold can be illustrated in a step-wise procedure by a suitable variation of up, down and strange quark masses. We use a set of LEC in the chiral Lagrangian that were adjusted to a large set of Lattice QCD results. The six phase shifts and inelasticity parameters are presented for various choices of the pion mass. For a pion mass of 150 MeV there are no anomalou…
Dark pion is a promising candidate for the strongly interacting massive particle dark matter. A large pion self-coupling $m_π/f_π$ tends to be required for correct relic abundance, and hence the partial-wave amplitudes can violate the perturbative unitarity even for the coupling within naïve perturbative regime. We improve the partial-wave amplitudes in order to satisfy the optical theorem. We demonstrate that the improvement is relevant only for semi-relativistic pions, and thus this does not affect the self-scattering cross section at the cosmic structures. We also discuss the impact of the …
