Chiral Amplitude Research Articles

Two-loop superstring five-point amplitudes. Part III. Construction via the RNS formulation: even spin structures

The contribution from even spin structures to the genus-two amplitude for five massless external NS states in Type II and Heterotic superstrings is evaluated from first principles in the RNS formulation. Using chiral splitting with the help of loop momenta this problem reduces to the evaluation of the corresponding chiral amplitude, which is carried out using the same techniques that were used for the genus-two amplitude with four external NS states. The results agree with the parity-even NS components of a construction using chiral splitting and pure spinors given in earlier companion papers [29] and [33].

Where Is the Lightest Charmed Scalar Meson?

The lightest charmed scalar meson is known as the D_{0}^{*}(2300), which is one of the earliest new hadron resonances observed at modern B factories. We show here that the parameters assigned to the lightest scalar D meson are in conflict with the precise LHCb data of the decay B^{-}→D^{+}π^{-}π^{-}. On the contrary, these data can be well described by an unitarized chiral amplitude containing a much lighter charmed scalar meson, the D_{0}^{*}(2100). We also extract the low-energy S-wave Dπ phase of the decay B^{-}→D^{+}π^{-}π^{-} from the data in a model-independent way, and show that its difference from the Dπ scattering phase shift can be traced back to an intermediate ρ^{-} exchange. Our work highlights that an analysis of data consistent with chiral symmetry, unitarity, and analyticity is mandatory in order to extract the properties of the ground-state scalar mesons in the singly heavy sector correctly, in analogy to the light scalar mesons f_{0}(500) and K_{0}^{*}(700).

Compression and shear behaviour of graded chiral auxetic structures

Graded chiral auxetic cellular metal structures were produced from copper alloy powder using Selective Electron Beam Melting (SEBM) technique and tested under compressive and shear loading conditions. The predesigned geometry of chiral structures has a variable chiral amplitude through the length of the specimens, which results in graded porosity of the analyzed auxetic structures. The deformation mechanisms and mechanical response were evaluated with compression and shear testing at two loading velocities. The infrared thermography has been used to track the evolution of plastic deformation in the specimens. The deformation process under compression loading starts in the area with the largest chiral amplitude and then continues through the whole height of the specimen. The shear loading shows two significantly different groups of responses, which are affected by local defects causing the start of failure in different parts of structure. The results of experimental testing were further used for validation of developed finite element models of chiral structures. The influence of graded porosity on the mechanical response of chiral structures was evaluated with parametric computational simulations and compared to the non-graded structure with constant chiral amplitude and same weight. The non-graded auxetic structure offers a stiffer response due to deformation uniformly distributed through the height of the specimens but fails abruptly at lower strains.

Effect ofZbstates onϒ(3S)→ϒ(1S)ππdecays

Within the framework of dispersion theory, we analyze the dipion transitions between the lightest $\Upsilon$ states, $\Upsilon(nS) \rightarrow \Upsilon(mS) \pi\pi$ with $m < n \leq 3$. In particular, we consider the possible effects of two intermediate bottomoniumlike exotic states $Z_b(10610)$ and $Z_b(10650)$. The $\pi\pi$ rescattering effects are taken into account in a model-independent way using dispersion theory. We confirm that matching the dispersive representation to the leading chiral amplitude alone cannot reproduce the peculiar two-peak $\pi\pi$ mass spectrum of the decay $\Upsilon(3S) \rightarrow \Upsilon(1S) \pi\pi$. The existence of the bottomoniumlike $Z_b$ states can naturally explain this anomaly. We also point out the necessity of a proper extraction of the coupling strengths for the $Z_b$ states to $\Upsilon(nS)\pi$, which is only possible if a Flatt\'e-like parametrization is used in the data analysis for the $Z_b$ states.

MODEL DEPENDENT ANALYSES ON THE Nc DEPENDENCE OF THE σ POLE TRAJECTORY

We explore the nature of the σ or f0(600) meson using large Nc technique, assuming that the σ pole dominates low energy physics in the IJ =00 channel. We trace the Nc dependence of the σ pole position using [1,1] Padé approximation of SU(3) chiral amplitude, [1,2] Padé approximation of SU(2) chiral amplitudes, and the PKU parametrization form. We find that in all 3 cases the σ pole moves to the real axis of the complex s-plane. Finally we construct a pedagogical example using the SU(2) Padé amplitude to show that when the analyticity property of the scattering amplitude is violated, it is possible that the σ pole resides on the complex s plane when Nc is large.

Extension of “Analysis ofO(p2)corrections to〈ππ|Q7,8|K〉”

We extend in several respects our earlier work on $\mathcal{O}{(p}^{2})$ corrections to the matrix elements of the electroweak penguin operator ${\mathcal{O}}_{\mathrm{ewp}}.$ First, to facilitate comparison with certain lattice studies we calculate $\mathcal{O}{(p}^{2})$ corrections to $〈\ensuremath{\pi}|{\mathcal{O}}_{\mathrm{ewp}}|K〉$ in the SU(3) limit of equal light quark masses. Next, we demonstrate how an apparent disagreement in the literature regarding whether higher order chiral contributions increase or decrease $〈(\ensuremath{\pi}\ensuremath{\pi}{)}_{\mathrm{I}=2}|{\mathcal{O}}_{\mathrm{ewp}}|K〉$ is simply a consequence of how the leading order chiral amplitude is defined. Finally, we address an aspect of the ${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}$ problem by estimating $\mathcal{O}{(p}^{2})$ corrections to recent determinations of $〈(\ensuremath{\pi}\ensuremath{\pi}{)}_{\mathrm{I}=2}|{\mathcal{Q}}_{7,8}|K〉$ which were carried out in the chiral limit.

A Critical Examination to the Unitarized IJ=20ππ Scattering Chiral Amplitude

We discuss the Padé approximation to the ππ scattering amplitudes in one-loop chiral perturbation theory.The approximation restores unitarity and can reproduce the correct resonance poles, but the approximation violates crossing symmetry and produces spurious poles on the complex s plane and therefore plagues its predictions in some cases.However we find that one virtual state in the IJ=20 channel may have physical relevance.

Determination of two-loop ππ scattering amplitude parameters

The chiral expansion of the ππ amplitude to the order of two loops was expressed in terms of six independent parameters in a previous paper: four of these are shown here to satisfy sum rules. Their derivation, where crossing symmetry plays a key role, is explained. Their convergence properties are studied and their practical evaluation, in terms of the available data on ππ phase shifts above 0.5 GeV, is discussed. Below 0.5 GeV the chiral amplitude itself is employed, such that the parameters are determined in a self-consistent way. Some care is devoted to the estimate of the errors.

Photon-photon scattering, pion polarizability, and chiral symmetry.

Recent attempts to detect the pion polarizability via analysis of $\gamma\gamma\rightarrow\pi\pi$ measurements are examined. The connection between calculations based on dispersion relations and on chiral perturbation theory is established by matching the low energy chiral amplitude with that given by a full dispersive treatment. Using the values for the polarizability required by chiral symmetry, predicted and experimental cross sections are shown to be in agreement.

Quantization of massive chiral electrodynamics reexamined.

We show that the models considered by Andrianov et al. [Phys. Rev. Lett. 63, 1554 (1989); and Phys. Rev. D 44, 2602 (1991)] are equivalent to other models where it is easily proved that the anomaly decouples and consequently the value of the chiral triangles amplitude is irrelvant for the unitarity of the S matrix.

Vector-meson contributions to the processes gamma gamma --> pi 0 pi 0, pi + pi -, KL--> pi 0 gamma gamma, and K+--> pi + gamma gamma.

We implement standard chiral perturbation theory to O(${p}^{4}$) by adding vector mesons. We show that it leads to a good agreement of the prediction for \ensuremath{\sigma}(\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}${\ensuremath{\pi}}^{0}$${\ensuremath{\pi}}^{0}$) with experiments and the vector mesons unitarize the chiral amplitude in an effective way. We also consider ${K}_{L}$\ensuremath{\rightarrow}${\ensuremath{\pi}}^{0}$\ensuremath{\gamma}\ensuremath{\gamma}, including the effect of vector mesons, and obtain a very distinct spectrum for two photons. Also, their effects on \ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}${\ensuremath{\pi}}^{+}$${\ensuremath{\pi}}^{\mathbf{\ensuremath{-}}}$ and ${K}^{+}$\ensuremath{\rightarrow}${\ensuremath{\pi}}^{+}$\ensuremath{\gamma}\ensuremath{\gamma} are briefly discussed.

CHIRAL SUPERSTRING AMPLITUDES AND THE GSO PROJECTION

Chirally symmetric amplitudes for the scattering of bosonic massless particles at fixed spin structures are shown to split into the absolute values squared of a chiral amplitude at fixed internal momenta. Chiral amplitudes are holomorphic in supermoduli and chiral polarization tensors, meromorphic in vertex operators insertion points. They may be recast in terms of intrinsic complex supergeometric objects. Amplitudes of opposite chirality may be endowed with independent spin structures so that the GSO projection can be enforced to construct the superstring.