scholarly journals Unitarization Technics in Hadron Physics with Historical Remarks

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1114
Author(s):  
José Antonio Oller
Keyword(s):  
Effective Range Expansion ◽  
Chiral Perturbation ◽  
Final State ◽  
Hadron Physics ◽  
Coupled Channels ◽  
Inverse Amplitude Method ◽  
Final State Interactions ◽  
Historical Remarks ◽  
K Matrix ◽  
Inverse Amplitude

We review a series of unitarization techniques that have been used during the last decades, many of them in connection with the advent and development of current algebra and later of Chiral Perturbation Theory. Several methods are discussed like the generalized effective-range expansion, K-matrix approach, Inverse Amplitude Method, Padé approximants and the N / D method. More details are given for the latter though. We also consider how to implement them in order to correct by final-state interactions. In connection with this some other methods are also introduced like the expansion of the inverse of the form factor, the Omnés solution, generalization to coupled channels and the Khuri-Treiman formalism, among others.

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

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Alexandre Salas-Bernárdez ◽  
Felipe Llanes-Estrada ◽  
Juan Escudero-Pedrosa ◽  
José Antonio Oller
Keyword(s):  
Perturbation Theory ◽  
Partial Wave ◽  
Chiral Perturbation Theory ◽  
A Priori ◽  
Resonance Region ◽  
New Physics ◽  
Effective Field ◽  
Chiral Perturbation ◽  
Inverse Amplitude Method ◽  
Inverse Amplitude

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.

scholarly journals MESON2006 SUMMARY: THEORY

2007 ◽  
Vol 22 (02n03) ◽  
pp. 495-501
Author(s):  
TED BARNES
Keyword(s):  
B Mesons ◽  
Low Energy ◽  
Medium Effects ◽  
Final State ◽  
Hadron Physics ◽  
The Status ◽  
Recent Developments ◽  
Hadronic Production ◽  
Final State Interactions ◽  
Pion Nucleon

This is a summary of theoretical plenary contributions to the biennial hadron physics conference Meson2006, which was the ninth in this series. The topics covered in the meeting include low energy pion-pion and pion-nucleon interactions, photoproduction and hadronic production of light mesons and baryons, in-medium effects, recent developments in charmed mesons, charmonia and B mesons, the status of exotica, and some related topics such as final state interactions. In this contribution we review and summarize the plenary talks presented by theorists at the meeting, and emphasize some of the main points of their presentations. Where appropriate we will add brief comments on some aspects of QCD spectroscopy. Finally, following tradition, we conclude with a new Feynman story.

DALITZ PLOT ANALYSES FROM FOCUS

2005 ◽  
Vol 20 (02n03) ◽  
pp. 482-492 ◽  
Author(s):  
◽  
PAOLO DINI
Keyword(s):  
Matrix Model ◽  
Dalitz Plot ◽  
Decay Amplitude ◽  
Meson Decay ◽  
Charm Meson ◽  
Final State ◽  
Isobar Model ◽  
Plot Analysis ◽  
Final State Interactions ◽  
K Matrix

Charm meson decay-dynamics has been extensively studied in the last decade. Dalitz plot analysis has revealed as a powerful tool for investigating effects of resonant substructures, interference patterns and final-state-interactions in the charm sector. Recent results from FOCUS on D+ and Ds decays will be presented with particular emphasis on the decay amplitude formalism; Isobar model and K-matrix model results will be compared and discussed.

ELEMENTS OF RELATIVISTIC QUANTUM MECHANICS FOR FINAL STATE INTERACTIONS

2003 ◽  
Vol 18 (03) ◽  
pp. 411-420
Author(s):  
M. A. Pichowsky
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Baryon Resonance ◽  
Resonance Region ◽  
Thomas Jefferson ◽  
Relativistic Quantum Mechanics ◽  
Final State ◽  
Accelerator Facility ◽  
Coupled Channels ◽  
Final State Interactions

In the baryon resonance region the likelihood that electroproduction reactions will lead to multiple hadron production either in the final-state or in intermediate states requires a framework capable of describing the non-perturbative, coupled-channels nature of hadron scattering. For applications in the energy region accessible to the Thomas Jefferson National Accelerator Facility, such a framework must be Poincaré covariant, electromagnetic gauge invariant and unitary. These aspects of final-state interactions and how they have been implemented into frameworks based on the instant-form of relativistic quantum mechanics are briefly outlined.

FINAL-STATE INTERACTIONS IN COUPLED CHANNELS OF PHYSICAL HADRONS RESULTING IN A SIZABLE, DIRECT CP-VIOLATION IN $B^0(\bar B^0)\to\pi^+\pi^-$

2003 ◽  
Vol 18 (40) ◽  
pp. 2887-2894 ◽  
Author(s):  
SAUL BARSHAY ◽  
GEORG KREYERHOFF
Keyword(s):  
Cp Violation ◽  
Strong Interaction ◽  
Essential Role ◽  
Belle Collaboration ◽  
Final State ◽  
Elastic Interactions ◽  
Coupled Channels ◽  
Final State Interactions ◽  
Unusual Situation

We show that the large, direct CP-violation parameter Aππ=-Cππ, reported by the BELLE collaboration in the decays [Formula: see text], implies an unusual situation in which the presence of a very large difference between two strong-interaction phases (~ -110°) plays an essential role. We make the demonstration within a model of strong, two-body quasi-elastic interactions between physical hadrons. The model can accommodate a large difference between two strong-interaction phases, for which it provides a natural enhancement.

Sign in / Sign up

Export Citation Format

Share Document