A review on partial-wave dynamics with chiral effective field theory and dispersion relation

Abstract

The description of strong interaction physics of low-lying resonances is out of the valid range of perturbative QCD. Chiral effective field theories (EFTs) have been developed to tackle the issue. Partial wave dynamics is the systematic tool to decode the underlying physics and reveal the properties of those resonances. It is extremely powerful and helpful for our understanding of the non-perturbative regime, especially when dispersion techniques are utilized simultaneously. Recently, plenty of exotic/ordinary hadrons have been reported by experiment collaborations, e.g. LHCb, Belle, and BESIII, etc. In this review, we summarize the recent progress on the applications of partial wave dynamics combined with chiral EFTs and dispersion relations, on related topics, with emphasis on ππ, πK, πN and KN scatterings.

Scrutinizing $ππ$ scattering in light of recent lattice phase shifts

“…Furthermore, the factorization of the cuts and various poles leads to a novel feature of the phase shifts from the cuts and poles, which makes it much convenient and powerful when analyzing the phase-shift data without being troubled by the contribution of possible "spurious" poles generated by some unitarization approaches [30]. The PKU representation has been successfully applied to extracting the pole positions of σ and κ [6,27], and later on it is also extended to the πN scattering and predicts the novel N * (890) resonance in S 11 channel [8,31].…”

“…The ππ phase shift in the IJ = 00 channel rises smoothly from the elastic threshold and reaches π/2 at about 1.0 GeV, which does not exhibit a typical resonance lineshape [2][3][4]. Such an observation raises a long time debate about whether the σ resonance exists or not until the σ pole is simultaneously determined by several model-independent approaches such as Roy equation or those dispersive methods respecting the unitarity, analyticity, and the crossing symmetry of the scattering amplitude [5][6][7][8][9]. For further details, see the mini review of scalar resonances provided by PDG [10].…”

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

“…( 46) we see that φ 4 /φ 2 ∼ s 2 , so that if s 3 /π |RC(t 1 )|(s) scales as s 2 (a typical NLO ChPT contribution), then ∆(s)G(s) for the four-body intermediate contribution scales as s 4 (a three-loop effect). Therefore, this uncertainty to the mass of the resonances scales as (m resonance /Λ U ) 8 , with Λ U the unitarity cutoff the theory, 4π f π for hadron physics and 4πv for HEFT. Then, the influence of this uncertainty is very much diminished for m resonance < Λ U , though it raises strongly for higher energies.…”

“…We have used, for I = J = 1, the amplitude t(s) from Ref. [43], 8 where the ππ S and P waves are parameterized analytically in the physical region based on the the GKPY equation [2] and reproduce ππ scattering data up to s = 2 GeV. The integral |I 2 [G + t 1 ]| evaluates to 0.08, of the same size but on the larger side of the first estimate.…”

“…More generically, a widely used strategy in hadron physics [8] is to construct "unitarized" amplitudes that extrapolate to those higher energy regimes satisfying unitarity exactly (for elastic processes). Popular ones are the K-matrix method, that is already being incorporated into the Monte Carlo simulations of high-energy processes at the LHC; the N /D method [9,10]; or variations of the Bethe-Salpeter equation [7,11].…”