Low energy reaction K - p → Λη and the negative parity Λ resonances Liye Xiao （肖立叶） tutor: Xianhui Zhong The Seventh International Symposium on Chiral Symmetry in Hadrons and Nuclei October 27th-October 30th, 2013, Beijing, China arXiv: Hunan Normal University

Outline ♣ Introduction ►Background ►A few words about the opportunity for this work ♣ Framework ♣ Result and analysis ►Λ-resonance properties from KN scattering ►Λ-resonance properties from strong decay ♣ Summary

Introduction Excited three quark states? Dynamically generated resonances? Three quark states containing mulit-quark components? or the other explanations?

The existing foundation for our research: ★ Recently, we systematically studied the reactions K - p→Σ 0 π 0,K 0 n,Λπ 0 ●Λ(1670) has a very weak coupling to KN ●Λ(1520) needs a strong coupling to KN Thats can't be well explained with the symmetry constituent quark model in the SU(6)× O(3) limit. ★ Crystal Ball Collaboration obtained the new data from the reaction K - p→Λη PRC 64, ● The poorly known strong coupling of Λ(1670) to Λη might be reliably obtained ● Only the Λ resonances contribute here due to the isospin selection rule ★ Strong decays in the chiral quark model approach is a good way to understand the natures of these strong coupling properties extracted from the KN scattering

k q PiPi PfPf k q PfPf PiPi k q PiPi PfPf kq PiPi PfPf k q PiPi PfPf Framework

Partial wave analysis for s-channel: A unified form for the transition amplitude where, T l± are the partial wave amplitudes with J=l±1/2 Thus, Due to spin-dependent forces in the quark-quark interaction, the symmetryt of SU(6)×O(3) is generally broken, then, configuration mixing would occur. So The deviation of C R from unity implies the SU(6)×O(3) symmetry breaking

Λ-resonance properties from KN scattering The results by exclusive cross sections for Λ(1405)S 01, Λ(1670)S 01, t-channel and u-channel K - p→ Λη total cross sections compared with the data The results by switching off the contributions of Λ(1405)S 01, Λ(1670)S 01, t-channel and u-channel Λ (1670)S 01 is responsible for the bump structure in the cross section around its threshold. No obvious contributions from the D-wave states, Λ (1520)and Λ (1690), are found in the reaction.

C R >>1 Thus, Λ(1670)S 01 should have a much stronger coupling to Λη than that derived from the symmetry quark model. These phenomenologies might be explained by the configuration mixing between the S-wave states Λ (1405)S 01, Λ (1670)S 01 and Λ (1800)S 01

Considering the differential cross section

★ Our theoretical results seem to slightly underestimate the DCS at both forward and backword angles in the beam momenta region of P K =730~742MeV/c ★ The dominant roles of Λ(1670)S 01 and u-, t-channel backgrounds are significant seen in the DCS. ● Switching off the contribution of Λ(1670)S 01, we find out the cross sections will be underestimated draftily. ● Without the u-channel contribution, the DCS will be significantly underes -timated around ηproduction threshold. ● Switching off t-channel contribution, we can see that the DCS are strongly overestimated at both forward and backword angles. ★ Slight contributions of Λ(1405)S 01 can be seen in the DCS around the η production threshold. ★ In the data around ηproduction threshold, a bowl structure seems to appear. ● In this energy region, the bowl structures might be caused by the interferences between Λ(1670)S 01 and Λ(1690)D 03. While, we can't obtain a bowl structure in the DCS for the too small contribution of Λ(1690)D 03 in this reaction. ● Liu and Xie had carefully studied these bowl structure in the DCS and need a exotic D-wave state Λ(1669) with Г=1.5MeV to reproduce the bowl structure. PRC 86, PRC 85,

Λ-resonance properties from strong decay S-wave states: Thus, as a pure state, the Λ (1670)S 01 strong decays can not be described at all Taking Λ (1670) as a mixed state with J=1/2 - : The total decay width for Λ (1405) is Г th ≈53MeV (Г=50±2MeV) With the configuratiion mixing the Λη branching ratio is enhanced obviously, while the NK branching ratio is suppressed. (1)

The strong decay properties of Λ (1800)S 01 : Our predicted strong decays are compatible with the data of ALSTON. As a result, we get that:

D-wave states: As pure states, the strong decay properties of Λ(1520)D 03 and Λ(1690)D 03 can't be understood reasonably.

The strong decay properties of as a counterpart of Λ(1690). It should be emphasized that Λ(1690)D 03 has a very weak coupling to Λη, alth- ough it has been draftily enhanced by considering the configuration mixing e- ffects, which gives an explanation why the contribution of Λ(1690)D 03 to the reaction K - p→Ληis tiny even though Λ(1690)D 03 has a large CR-factor. )

Interpretation of C R with configuration mixing: Stands for the relative strength of a single- resonance with configuration mixing effects Stands for the relative strength of a single-re- sonance without configuration mixing effects so, Firstly, taking them as pure states, we can derive the coupling of the transition amplitudes for these resonances, which can given by the η-η' mixing angle (2)

Considering the configuration mixing effects, the wave functions can be generally written as Then we can derive the coupling of the transition amplitudes for these mixed resonances, they are

With these extracted g R and g R ' parameters, it is found that C R is a function of η-η' mixing angle, which might be in the range 30 0 ~47 0. PRD 85, (2012) Eur.Phy.J.C 69, 133(2010) When taking a small η-η' mixing angle (=35 0 ), we can explanation the large C R which we get in the K - p→Λη scatting reaction

Summary ♣ In this work, we have studied the low energy reaction K - p→Λη with a chiral qu- ark model. A reasonable description of the measurements has been achieved A ★ Λ(1670)S 01 dominates the reaction around at the low energy regions; ★ The t- and u-channel backgrounds also play crucial roles; ★ Slight contributions of Λ(1405)S 01 are found, however, Λ(1405)S 01 does not obviously affect the shapes of the differential cross sections; ★ No obvious roles of the D-wave states Λ(1520)D 03 and Λ(1690)D 03 are found in the reaction. B ★ We found that a much large amplitude of Λ(1670)S 01 in the reaction is needed, which is about 34 times [C R ≈34] larger than that derived from the symmetry qu- ark model; ★ In our previous study, we got that Λ(1670)S 01 should have a much weaking co- upling to KN; ♣ To understand these strong interaction properties of Λ(1670)S 01, we further study the strong decay properties of the low-lying negative parity Λ-resonan- ces. It is found that the configuration mixing effects are crucial to understand the strong decay properties.Considering configuration mixing effects, we can reasonably explain the strong interaction properties of Λ(1670)S 01 extracted from the K - p→Λη.

♣ The data of the K - p → Λη process show that there seems to exist a bowl stru- cture in the DCS in a narrow energy region near the ηΛthreshold, which indi- cates a strong D-wave contribution there. However, the contribution of Λ(1690) D 03 to K - P → Λη process too small to give a bowl structure in the DCS. Altho- ugh with the configuration mixing effects in these D-wave states, the amplitude of Λ(1690)D 03 in the reaction could be enhanced a factor of ∼ 38, the contribut- ion of Λ(1690)D 03 is still tiny for the very weak coupling of Λ(1690)D 03 to ηΛ. To clarify whether there are contributions of a narrow D-wave state or not, more accurate measurements are needed. ♣ As a byproduct, we also have predicted the strong decay properties of the une- stablished D-wave state Λ(3/2 - ) 3. This resonance mainly decay into Σ(1385)π andΣπchannels. We hope the experimentalists can search this missing D-wave state in theΣ(1385)πandΣπchannels. Thank you!