Unitarized Chiral Perturbation Theory Research Articles

Can the two-pole structure of the D_{0}^{*}(2300) be understood from recent lattice data?

It was demonstrated in a series of papers employing unitarized chiral perturbation theory that the phenomenology of the scalar open-charm state, the D_0^*(2300), can be understood as the interplay of two poles, corresponding to two scalar-isospin doublet states with different SU(3) flavor content. Within this formalism the lightest open charm positive parity states emerge as being dynamically generated from the scattering of the Goldstone-boson octet off D mesons, a picture that at the same time solves various problems that the experimental observations posed. However, in recent lattice studies of Dpi scattering at different pion masses only one pole was reported in the D_0^* channel, while it was not possible to extract reliable parameters of a second pole from the lattice data. In this paper we demonstrate how this seeming contradiction can be understood and that imposing SU(3) constraints on the fitting amplitudes allows one to extract information on the second pole from the lattice data with minimal bias. The results may also be regarded as a showcase how approximate symmetries can be imposed in the K-matrix formalism to reduce the number of parameters.

The Ξ(1620) and Ξ(1690) molecular states from S = −2 meson-baryon interaction up to next-to-leading order

We have studied the meson-baryon interaction in the neutral S=−2 sector using an extended Unitarized Chiral Perturbation Theory, which takes into account not only the leading Weinberg-Tomozawa term (as all the previous studies in S=−2 sector), but also the Born terms and next-to-leading order contribution. Based on the SU(3) symmetry of the chiral Lagrangian we took most of the model parameters from the BCN model [1], where these were fitted to a large amount of experimental data in the neutral S=−1 sector. We have shown that our approach is able to generate dynamically both Ξ(1620) and Ξ(1690) states in very reasonable agreement with the data, and can naturally explain the puzzle with the decay branching ratios of Ξ(1690). Our results clearly illustrate the reliability of chiral models implementing unitarization in coupled channels and the importance of considering Born and NLO contributions for precise calculations.

Thermal hadron resonances in chiral and U(1)A restoration

We review recent work on thermal resonances and their connection with chiral symmetry and U(1)A restoration within the QCD phase diagram. In particular, the ƒ0 (500) and K∗ 0 (700) states generated from ππ and πK scattering within Unitarized Chiral Perturbation Theory (ChPT) at finite temperature allow one to describe scalar susceptibilities, which combined with Ward Identities yield interesting conclusions regarding the interplay between chiral and U(1)A restoration, key to understand the nature of the transition.

Systematizing and addressing theory uncertainties of unitarization with the Inverse Amplitude Method

Effective Field Theories (EFTs) constructed as derivative expansions in powers of momentum, in the spirit of Chiral Perturbation Theory (ChPT), are a controllable approximation to strong dynamics as long as the energy of the interacting particles remains small, as they do not respect exact elastic unitarity. This limits their predictive power towards new physics at a higher scale if small separations from the Standard Model are found at the LHC or elsewhere. Unitarized chiral perturbation theory techniques have been devised to extend the reach of the EFT to regimes where partial waves are saturating unitarity, but their uncertainties have hitherto not been addressed thoroughly. Here we take one of the best known of them, the Inverse Amplitude Method (IAM), and carefully following its derivation, we quantify the uncertainty introduced at each step. We compare its hadron ChPT and its electroweak sector Higgs EFT applications. We find that the relative theoretical uncertainty of the IAM at the mass of the first resonance encountered in a partial-wave is of the same order in the counting as the starting uncertainty of the EFT at near-threshold energies, so that its unitarized extension should a priori be expected to be reasonably successful. This is so provided a check for zeroes of the partial wave amplitude is carried out and, if they appear near the resonance region, we show how to modify adequately the IAM to take them into account.

The role of strangeness in chiral and U(1)_A restoration

We use recently derived Ward identities and lattice data for the light- and strange-quark condensates to reconstruct the scalar and pseudoscalar susceptibilities (chi _S^kappa , chi _P^K) in the isospin 1/2 channel. We show that chi _S^kappa develops a maximum above the QCD chiral transition, after which it degenerates with chi _P^K. We also obtain chi _S^kappa within Unitarized Chiral Perturbation Theory (UChPT) at finite temperature, when it is saturated with the K_0^*(700) (or kappa ) meson, the dominant lowest-energy state in the isospin 1/2 scalar channel of pi K scattering. Such UChPT result reproduces the expected peak structure, revealing the importance of thermal interactions, and makes it possible to examine the chi _S^kappa dependence on the light- and strange-quark masses. A consistent picture emerges controlled by the m_l/m_s ratio that allows one studying K-kappa degeneration in the chiral, two-flavor and SU(3) limits. These results provide an alternative sign for O(4)times U(1)_A restoration that can be explored in lattice simulations and highlight the role of strangeness, which regulated by the strange-quark condensate helps to reconcile the current tension among lattice results regarding U(1)_A restoration.

Assessment of systematic theory uncertainties in IAM unitarization

Effective Field Theories (EFTs) for Goldstone Boson scattering at a low order allow the computation of near–threshold observables in terms of a few coefficients arranged by a counting. As a matter of principle they should make sense up to an energy scale E ∼ 4πF but the expansion in powers of momentum violates exact elastic unitarity and renders the derivative expansion unreliable at much lower energies. If new–physics deviations from the Standard Model are found and encoded in low-energy coefficients, perhaps at the LHC, it will be profitable to extend the reach of the EFT to regimes where partial waves are saturating unitarity. The methods known in hadron physics as “Unitarized Chiral Perturbation Theory” extend the EFT up to its nominal reach or up to the first new physics resonance or structure (if found below that energy reach) in the partial wave amplitude, but they usually have unknown uncertainties. We recapitulate our analysis of the systematic theory uncertainties of the well known Inverse Amplitude Method (IAM).

Precision dispersive approaches versus unitarized chiral perturbation theory for the lightest scalar resonances $$\sigma /f_0(500) $$ and $$\kappa /K_0^*(700) $$

For several decades, the $\sigma/f_0(500)$ and $\kappa/K_0^*(700)$ resonances have been subject to long-standing debate. Both their existence and properties were controversial until very recently. In this tutorial review we compare model-independent dispersive and analytic techniques versus unitarized Chiral Perturbation Theory, when applied to the lightest scalar mesons $\sigma/f_0(500)$ and $\kappa/K_0^*(700)$. Generically, the former have settled the long-standing controversy about the existence of these states, providing a precise determination of their parameters, whereas unitarization of chiral effective theories allows us to understand their nature, spectroscopic classification and dependence on QCD parameters. Here we review in a pedagogical way their uses, advantages and caveats.

Multi-particle systems on the lattice and chiral extrapolations: a brief review

The extraction of two- and three-body hadronic scattering amplitudes and the properties of the low-lying hadronic resonances from the finite-volume energy levels in lattice QCD represents a rapidly developing field of research. The use of various modifications of the L\"uscher finite-volume method has opened a path to calculate infinite-volume scattering amplitudes on the lattice. Many new results have been obtained recently for different two- and three-body scattering processes, including the extraction of resonance poles and their properties from lattice data. Such studies, however, require robust parametrizations of the infinite-volume scattering amplitudes, which rely on basic properties of $S$-matrix theory and -- preferably -- encompass systems with quark masses at and away from the physical point. Parametrizations of this kind, provided by unitarized Chiral Perturbation Theory, are discussed in this review. Special attention is paid to three-body systems on the lattice, owing to the rapidly growing interest in the field. Here, we briefly survey the formalism, chiral extrapolation, as well as finite-volume analyses of lattice data.

Chiral dynamics and S-wave contributions in {bar{B}}^0/D^0 rightarrow pi ^{pm }eta l^{mp } nu decays

In this work, we analyze the semi-leptonic decays bar{B}^0/D^0 rightarrow (a_0(980)^{pm }rightarrow pi ^{pm }eta ) l^{mp } nu within light-cone sum rules. The two and three-body light-cone distribution amplitudes (LCDAs) of the B meson and the only available two-body LCDA of the D meson are used. To include the finite-width effect of the a_0(980), we use a scalar form factor to describe the final-state interaction between the pi eta mesons, which was previously calculated within unitarized Chiral Perturbation Theory. The result for the decay branching fraction of the D^0 decay is in good agreement with that measured by the BESIII Collaboration, while the branching fraction of the {bar{B}}^0 decay can be tested in future experiments.

Two-meson form factors in unitarized chiral perturbation theory

We present a comprehensive analysis of form factors for two light pseudoscalar mesons induced by scalar, vector, and tensor quark operators. The theoretical framework is based on a combination of unitarized chiral perturbation theory and dispersion relations. The low-energy constants in chiral perturbation theory are fixed by a global fit to the available data of the two-meson scattering phase shifts. Each form factor derived from unitarized chiral perturbation theory is improved by iteratively applying a dispersion relation. This study updates the existing results in the literature and explores those that have not been systematically studied previously, in particular the two-meson tensor form factors within unitarized chiral perturbation theory. We also discuss the applications of these form factors as mandatory inputs for low-energy phenomena, such as the semi-leptonic decays Bs→ π+π−ℓ+ℓ− and the τ lepton decay τ → π−π0ντ, in searches for physics beyond the Standard Model.

Light- and strange-quark mass dependence of the \u03c1(770) meson revisited

Recent lattice data on ππ-scattering phase shifts in the vector-isovector channel, pseudoscalar meson masses and decay constants for strange-quark masses smaller or equal to the physical value allow us to study the strangeness dependence of these observables for the first time. We perform a global analysis on two kind of lattice trajectories depending on whether the sum of quark masses or the strange-quark mass is kept fixed to the physical point. The quark mass dependence of these observables is extracted from unitarized coupled-channel one-loop Chiral Perturbation Theory. This analysis guides new predictions on the ρ(770) meson properties over trajectories where the strange-quark mass is lighter than the physical mass, as well as on the SU(3) symmetric line. As a result, the light- and strange-quark mass dependence of the ρ(770) meson parameters are discussed and precise values of the Low Energy Constants present in unitarized one-loop Chiral Perturbation Theory are given. Finally, the current discrepancy between two- and three-flavor lattice results for the ρ(770) meson is studied.

Two-Pole Structures in QCD: Facts, Not Fantasy!

The two-pole structure refers to the fact that particular single states in the spectrum as listed in the PDG tables are often two states. The story began with the Λ ( 1405 ) , when in 2001, using unitarized chiral perturbation theory, it was observed that there are two poles in the complex plane, one close to the K ¯ p and the other close to the π Σ threshold. This was later understood combining the SU(3) limit and group-theoretical arguments. Different unitarization approaches that all lead to the two-pole structure have been considered in the mean time, showing some spread in the pole positions. This fact is now part of the PDG book, although it is not yet listed in the summary tables. Here, I discuss the open ends and critically review approaches that cannot deal with this issue. In the meson sector, some excited charm mesons are good candidates for such a two-pole structure. Next, I consider in detail the D 0 * ( 2300 ) , which is another candidate for this scenario. Combining lattice QCD with chiral unitary approaches in the finite volume, the precise data of the Hadron Spectrum Collaboration for coupled-channel D π , D η , D s K ¯ scattering in the isospin I = 1 / 2 channel indeed reveal its two-pole structure. Further states in the heavy meson sector with I = 1 / 2 exhibiting this phenomenon are predicted, especially in the beauty meson sector. I also discuss the relation of these two-pole structures and the possible molecular nature of the states under consideration.

Role of the thermal f0(500) in chiral symmetry restoration

We show that the $\sigma/f_0(500)$ state with finite-temperature $T$ corrections to its spectral properties included, plays an essential role for the description of the scalar susceptibility $\chi_S$, signaling chiral symmetry restoration. First, we use the $O(4)$ Linear Sigma Model as a testbed to derive the connection between $\chi_S$ and the $\sigma$ propagator and to check the validity and reliability of the approach where $\chi_S$ is saturated by the $\sigma/f_0(500)$ inverse self-energy, which we calculate at finite $T$ to one loop. A more accurate phenomenological description is achieved by considering the saturation approach as given by the thermal $f_0(500)$ state generated in Unitarized Chiral Perturbation Theory. Such approach allows to describe fairly well recent lattice data within the uncertainty range given by the UChPT parameters. Finally, we compare the UChPT saturated description with one based on the Hadron Resonance Gas, for which the hadron mass dependences are extracted from recent theoretical analysis. Several fits to lattice data are performed, which confirm the validity of the thermal $f_0(500)$ saturated approach and hence the importance of that thermal state for chiral symmetry restoration.

The role of isospin filtering reactions in the S = −1 sector

The present study reveals interesting constraining effects of isospin filtering reactions on the low energy constants present in meson-baryon chiral effective Lagrangian, particularly, on the next-to-leading order constants. Our model has been developed within the framework of Unitarized Chiral Perturbation Theory and has been fitted to two-body scattering data in the sector of S = −1. In addition, the model was further elaborated by means of the inclusion of high-spin hyperonic resonances.

Status of charmed meson spectroscopy

The discovery of the ground state positive-parity charm-strange and charm-nonstrange mesons $ D_{s0}^* $(2317), Ds1(2460), $ D_0^* $(2400) and D1(2430) in 2003 and 2004 brought up several mysteries related to their masses. Here I briefly review recent progresses from lattice calculations and analysis of the precise LHCb measurements of the B−→ D+π−π− in the framework of unitarized chiral perturbation theory. It turns out that all the mysteries can be understood in a picture consistent with both lattice results and the LHCb measurements. In this picture, the main components of $ D_{s0}^* $(2317) and Ds1(2460) are DK and D∗K hadronic molecules, respectively. Furthermore, the resonance parameters of the ground state 0+ and 1+ charm-nonstrange mesons take values very different from the known ones of the $ D_0^* $(2400) and D1(2430), which were obtained by using an improper resonance parameterization. It is pointed out that there should be two $ D_0^* $ and two D1 broad states in region relevant to the $ D_0^* $ (2400) and D1(2430). Suggestions towards identifying the higher nonstrange resonances are given.

Quark-mass dependence in omega rightarrow 3pi decays

We study the quark-mass dependence of omega rightarrow 3pi decays, based on a dispersion-theoretical framework. We rely on the quark-mass-dependent scattering phase shift for the pion–pion P-wave extracted from unitarized chiral perturbation theory. The dispersive representation then takes into account the final-state rescattering among all three pions. The described formalism may be used as an extrapolation tool for lattice QCD calculations of three-pion decays, for which omega rightarrow 3pi can serve as a paradigm case.

Two-pole structure of the

We study the interaction of the Dπ, Dη and DsK̄ channels in JP = 0+ in the framework of unitarized chiral perturbation theory in finite volume, predicting the volume dependence of the energy levels. The results succesfully describe the energy levels provided in a recent lattice QCD calculation of the same system. We find two poles in the energy region of the resonance, with masses MeV and half-widths MeV respectively. We study their evolution in the light-flavor SU(3) limit, which allows us to identify the resonance and the pole with lower mass as partners of the same SU(3) multiplet. The mass of the higher pole is obtained between the Dη and DsK̄ threshold energies, strongly coupled to the latter channel, thus we expect it to influence the DsK̄ invariant mass distribution.

Chiral Extrapolations of the ρ(770) Meson in Nf = 2 + 1 Lattice QCD Simulations

Several lattice QCD simulations of meson-meson scattering in p-wave and Isospin = 1 in Nf = 2 + 1 flavours have been carried out recently. Unitarized Chiral Perturbation Theory is used to perform extrapolations to the physical point. In contrast to previous findings on the analyses of Nf = 2 lattice data, where most of the data seems to be in agreement, some discrepancies are detected in the Nf = 2 + 1 lattice data analyses, which could be due to different masses of the strange quark, meson decay constants, initial constraints in the simulation, or other lattice artifacts. In addition, the low-energy constants are compared to the ones from a recent analysis of Nf = 2 lattice data.

Chiral dynamics, S-wave contributions and angular analysis in Drightarrow pi pi ell bar{nu }

We present a theoretical analysis of the D^-rightarrow pi ^+pi ^- ell bar{nu } and bar{D}^0rightarrow pi ^+pi ^0 ell bar{nu } decays. We construct a general angular distribution which can include arbitrary partial waves of pi pi . Retaining the S-wave and P-wave contributions we study the branching ratios, forward–backward asymmetries and a few other observables. The P-wave contribution is dominated by rho ^0 resonance, and the S-wave contribution is analyzed using the unitarized chiral perturbation theory. The obtained branching fraction for Drightarrow rho ell nu , at the order 10^{-3}, is consistent with the available experimental data. The S-wave contribution has a branching ratio at the order of 10^{-4}, and this prediction can be tested by experiments like BESIII and LHCb. Future measurements can also be used to examine the pi –pi scattering phase shift.

Two-pole structure of the [formula omitted

The so far only known charmed non-strange scalar meson is dubbed as D0⁎(2400) in the Review of Particle Physics. We show, within the framework of unitarized chiral perturbation theory, that there are in fact two (I=1/2,JP=0+) poles in the region of the D0⁎(2400) in the coupled-channel Dπ, Dη and DsK¯ scattering amplitudes. With all the parameters previously fixed, we predict the energy levels for the coupled-channel system in a finite volume, and find that they agree remarkably well with recent lattice QCD calculations. This successful description of the lattice data is regarded as a strong evidence for the two-pole structure of the D0⁎(2400). With the physical quark masses, the poles are located at (2105−8+6−i102−12+10) MeV and (2451−26+36−i134−8+7) MeV, with the largest couplings to the Dπ and DsK¯ channels, respectively. Since the higher pole is close to the DsK¯ threshold, we expect it to show up as a threshold enhancement in the DsK¯ invariant mass distribution. This could be checked by high-statistic data in future experiments. We also show that the lower pole belongs to the same SU(3) multiplet as the Ds0⁎(2317) state. Predictions for partners in the bottom sector are also given.