S- and p-wave structure of $S=-1$ meson-baryon scattering in the resonance region

We perform a simultaneous analysis of s- and p-waves of the $S=-1$ meson-baryon scattering amplitude using all low-energy experimental data. For the first time, differential cross section data are included for chiral unitary coupled-channel models. From this model s- and p-wave amplitudes are extracted and we observe both well-known $I(J^P)=0(1/2^-)$ s-wave states as well as a new $I(J^P)=1(1/2^+)$ state absent in quark models and lattice QCD results. Multiple statistical and phenomenological tests suggest that, while the data clearly require an $I=1$ p-wave resonance, the new state just accounts for the absence of the decuplet $\Sigma(1385)3/2^+$ in the model.

What is a Resonance • Seen in peak at a certain energy in scattering cross sections.
• Assigned to certain quantum numbers.
• Can be studied through analytic continuation • Useful to relate results to other theories like quark models and lattice QCD. • The equation of state of neutron stars is sensitive to the antikaon condensate and thus to the propagation of antikaons in nuclear medium.

T T V V
A depiction of the operator form of the Bethe Saltpeter Equation.
The bubble chain summation caused by iteration of the Bethe Salpeter Ansatz The chiral expansion of the driving term, V.

Possible Meson Baryon Interactions for S=-1
Possible channels for S=-1 interactions. The data that exists in the energy region of interest is shown in red.
Fit to the Data: New Data Differential cross sections fitted by the model.

2.
3.  Below: A plot of the amplitude in the complex plane that shows the two peaks.

An Anomalous Structure
Left: A representation of the position of a pole in the best fit of our model in the 1(1/2 + ) Channel.
Below: The amplitudes of the couplings for the poles observed in the best fit.

Analysis
When a structure is observed in a good fit to good data and does not have the quantum numbers of any known state, categorically speaking there are three possibilities.
1. It's present because the data demonstrate that there exists an undiscovered state in nature.
2. It's present because the data require the model to account for something it isn't currently accounting for.
3. It's completely arbitrary; it's existence does not improve the fit in any way.

Lasso Test of Robustness
Plot of Lasso (Least Absolute Shrinkage and Selection Operator) Method.

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The amplitude that is penalized.

Possible Explanations of the Anomalous Structure
When a structure is observed in a good fit to the data and does not have the quantum numbers of any known state, categorically speaking there are three possibilities.
1. It's present because the data demonstrate that there exists an undiscovered state in nature.
2. It's present because the data require the model to account for something it isn't currently accounting for.
3. It's completely arbitrary; it's existence does not improve the fit in any way.
Reversed Formula for the differential cross section The partial waves of the best fit. We additionally include a black line to show the best fit when the partial waves are reversed.
Real Formula for the differential cross section When a structure is observed in a good fit to the data and does not have the quantum numbers of any known state, categorically speaking there are three possibilities.
1. It's present because the data demonstrate that there exists an undiscovered state in nature.
2. It's present because the data require the model to account for something it isn't currently accounting for.
3. It's completely arbitrary; it's existence does not improve the fit in any way.

Summary
• The Mai-Meissner Model is fit to differential cross section as well as older data. This constitutes the first ever simultaneous fit of all data without explicit resonances.
• Both poles of the Λ(1405) were reproduced • A new anomalous structure was observed that didn't have the right parity for the Σ(1385).
• This statistically robust state likely exists because the differential cross section data demand a p-wave resonance and a NLO model cannot give it the right J.