[PPT] - S- and p-wave structure of S = -1 meson- baryon scattering in the PowerPoint Presentation

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

Daniel Sadasivan Maxim Mai Michael Doring

Supported by NSF (PIF No.1415459, CAREER PHY-1452055), DE-AC05-06OR23177 & DE-SC0016582). HPC support by Forschungszentrum Julich 1

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Motivation

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What is a Resonance

Seen in peak at a certain energy in scattering cross

sections.

Described by certain quantum numbers.
Can be studied through analytic continuation
Useful to relate results to other theories like quark

models and lattice QCD.

1340 1360 1380 1400 1420 1440 0.5 0.0 0.5 1.0 1.5 WCMS MeV Re f fm 1340 1360 1380 1400 1420 1440 0.0 0.5 1.0 1.5 2.0 2.5 WCMS MeV Re f fm

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Resonances We Are Looking For

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Applications

Λ(1405) is dominated by KN interaction
A similar mechanism can be responsible for the generation of K−pp bound
states. See for example, S. Ajimura et al arXiv:1805.12275 [nucl-ex].
The equation of state of neutron stars is sensitive to the antikaon condensate and

thus to the propagation of antikaons in nuclear medium. In the era of high- precision measurements of neutron star properties with LIGO, this ultimately can lead to new interconnection between QCD and astrophysical observations

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Method

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Model

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. 7

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Possible Meson Baryon Interactions for S=-1

Possible data for S=-1 interactions. The data that exists in the energy region of interest is shown in red. 8

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1.0
0.5

0.0 0.5 1.0 0.0 0.5 1.0 1.5 2.0 Cos θ dσ dΩ (mb) K- p→K0 n (275 MeV) 0.0 0.5 1.0 1.5 2.0 dσ dΩ (mb) K- p→K0 n (235 MeV) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 dσ dΩ (mb) K- p→K0 n (265 MeV) 2 4 6 8 10 dσ dΩ (mb) K- p→K0 n (225 MeV) 1.0

0.5

0.0 0.5 1.0 Cos θ K- p→K0 n (285 MeV) K- p→K0 n (245 MeV) K- p→K0 n (275 MeV) K- p→K0 n (235 MeV) 1.0

0.5

0.0 0.5 1.0 Cos θ K- p→K0 n (295 MeV) K- p→K0 n (255 MeV) K- p→K0 n (285 MeV) K- p→K0 n (245 MeV) 1.0

0.5

0.0 0.5 1.0 Cos θ K- p→K0 n (265 MeV) K- p→K0 n (295 MeV) K- p→K0 n (255 MeV)

Data the Free Parameters Were Fit to

In addition, we fit to threshold data including data from the SIDDHARTA Experiment which uses Anti-Kaon Nucleon processes to produce kaonic deuterium. This measurement has a real and imaginary part. Below: Total cross sections fitted by the model. The dashed black line shows the contribution of the s-wave part of the amplitude only. Right: Differential cross sections fitted by the model. 9

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More Data

1.30 1.35 1.40 1.45 1.50 M [GeV] arbitrary units

1. 2. 3. d/dMinv [b/GeV] Wtot=2. GeV Wtot=2.1 GeV

00 +-

+

Wtot=2.2 GeV 0.5 1 d/dMinv [b/GeV] Wtot=2.3 GeV Wtot=2.4 GeV Wtot=2.5 GeV 1.35 1.4 1.45 0.2 0.4 0.6 Minv [GeV] d/dMinv [b/GeV] Wtot=2.6 GeV 1.35 1.4 1.45 Minv [GeV] Wtot=2.7 GeV 1.35 1.4 1.45 Minv [GeV] Wtot=2.8 GeV

Above: Fit of the generic couplingsK−p→Σ(1660)π−andΣ(1660)→(π−Σ+)π +to the invariant mass distribution in arbitrary units. Left: Fit (χ2pp= 1.07) to theπΣ invariant mass distribution (Minv) from γp→K+(πΣ) reaction 10

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Predictions

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8.
4.

0. 4. 8. 12. 16. fJ

I [GeV-1]

0(1/2-)

1.
2.

0.

1. 0(1/2+)

1.25 1.30 1.35 1.40 1.45

1.

0. 1. 2. 3. 4. W [GeV] fJ

I [GeV-1]

1(1/2-)

1.25 1.30 1.35 1.40 1.45

3.
1.
2.

0. 1. W [GeV]

1(1/2+)

PWA Amplitudes

Real (solid, blue) and imaginary (red, dashed) parts of ̄KN partial wave amplitudes with I(JP). The vertical dashed lines show the positions of the πΛ,π0Σ0,π+Σ−,π−Σ+,K−p, ̄K0n thresholds, and the dots over the plots represent the available data in the respective channel from top to bottom.

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Lambda(1405)

Left: Pole positions (black stars) for the 0(1/2−). The error ellipses are from a re-sampling procedure shown explicitly in the corresponding insets. The shaded squares show the prediction from

ther literature for the narrow

(blue) and broad (orange) pole of Λ(1405) Below: A plot of the amplitude in the complex plane that shows the two peaks.

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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.

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Analysis

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Possible Explanations of the Anomalous Structure

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.

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Lasso Test of Robustness

Above: Plot of Lasso (Least Absolute Shrinkage and Selection Operator) Method. This parametric plot shows how the χ2 components and distance of the pole are related to the penalty term. λcrit is the value for which the amplitude is no longer visible. λinit is when the amplitude is unpenalized. Right: The amplitude that is penalized. 17

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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.

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Σ(1385) Explicit Inclusion Test

1.0
0.5

0.0 0.5 1.0 0.0 0.5 1.0 1.5 2.0 Cos θ dσ/dΩ [mb] K-p→K 0n (w=265 MeV) 0.0 0.5 1.0 1.5 2.0 dσ/dΩ[mb] 2.0 2.5 3.0 3.5 4.0 4.5 5.0 dσ/dΩ[mb] K-p→K-p (w=265 MeV) 2 4 6 8 10 dσ/dΩ[mb] K-p→K-p (w=225 MeV) 1.0

0.5

0.0 0.5 1.0 Cos θ K-p→K 0n (w=275 MeV) K-p→K 0n (w=235 MeV) K-p→K-p (w=275 MeV) K-p→K-p (w=235 MeV) 1.0

0.5

0.0 0.5 1.0 Cos θ K-p→K 0n (w=285 MeV) K-p→K 0n (w=245 MeV) K-p→K-p (w=285 MeV) K-p→K-p (w=245 MeV) 1.0

0.5

0.0 0.5 1.0 Cos θ K-p→K 0n (w=295 MeV) K-p→K 0n (w=255 MeV) K-p→K-p (w=295 MeV) K-p→K-p (w=255 MeV)

Reversed Formula for the differential cross section The partial waves of the best fit are plotted as shown earlier but we additionally include a black line to show the best fit when the partial waves are reversed. Real Formula for the differential cross section

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Formula for explicitly including a resonance in a way that preserves unitarity. Best fit parameters and pole positions found when the Σ(1385) is explicitly included.

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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.

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Summary

The Mai-Meissner Model is fit to differential cross section as well

as older data.

Both poles of the Lambda(1405) were reproduced
A new anomalous structure was observed that didn’t have the right

parity for the Sigma(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.

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Thank You

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