The study of pentaquark states in the unitary chiral approach En Wang, Zhengzhou Univ. In collaboration with: H. X. Chen, L. S. Geng, J. X. Lu, W. H. Liang, D. M. Li, E. Oset and J. J. Xie RHIQCD workshop@Kyoto, Japan Nov. 28, 2016

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Outline Motivation The Cabibbo-suppressed process Λb→J/ψpπ- Search the pentaquarks with strangeness Summary

Motivation July 2015-The observation of two Pc states in LHCb

The masses and widthes of the two Pc 𝑀_𝑃𝑐 (4380)=4380±8±29 MeV Γ_𝑃𝑐 (4380)=205±18±86 MeV 𝑀_𝑃𝑐 (4450)=4449.8±1.7±2.5 MeV Γ_𝑃𝑐 (4450)=39±5±19 MeV

Theoretical works Many explanations: molecular state, triangle singularity, Multiquark. Talk given by Hua-Xing Chen in this workshop Nov. 28/29. More references: T. J. Burns, Eur. Phys. J. A 51, 152 (2015). R. Chen, X. Liu, S.L. Zhu, Nucl. Phys. A 954, 406 (2016). H.X. Chen, W. Chen, X. Liu, S.L. Zhu, Phys. Rep. 639, 1 (2016).

The Cabibbo-suppressed process Λb→J/ψpπ- First reported by LHCb in Jun. 2014. [JHEP1407 (2014) 103]. The branching fraction

The results of LHCb in 2014 What is the structure in the J/ψp mass distribution?

The strange structure Prior to the discovery of Pc states, the LHCb collaboration (2014) has reported on the observation of the Λb→J/ψpπ- decay, in which there is a strange structure around 4.4 GeV in J/ψp distribution. However, it is noted that there is no sign of exotic structures in mass J/ψp distribution in that paper, and even not discussed in the Pc discovery paper of LHCb2015.

The Cabibbo-suppressed process Λb→J/ψpπ- If more data about this process are collected, the Pc may be more clearly. The Pc may contribute differently to Λb→J/ψpπ- and Λb→J/ψpK.

Pc(4450) as a molecular state of D*Σc In Ref. Roca, the narrow peak of J/ψp distribution in Λb→J/ψK-p decay in LHCb2015, associated to Pc(4450), was interpreted as a molecular state of D*Σc interacting in S-wave. Pc(4450) decays into J/ψp also in S-wave. Ref. Roca: LHCb pentaquark as a D¯∗Σc−D¯∗Σ∗c molecular state - Roca, L. et al. Phys.Rev. D92 (2015) no.9, 094003 arXiv:1507.04249 [hep-ph]

The decay process Λb→J/ψpπ- First step-weak decay Assuming the initial ud pair acts as a spectator. I=0 S=0 J/ψp

The decay process First step-weak decay J/ψp

The decay process Second step-hadronization J/ψp

Could the d from b decay go to baryon? Λb decays to J/ψ and pπ- system with the invariant mass 1.5 GeV, and three-momentum of final state ~700 MeV. The π- should be emitted with a large momentum.

Could the d from b decay go to baryon? It is favored to create the π- from the d of weak decay, because the large mass of the b quark.

Could the d from b decay go to baryon? The above process is suppressed because d of the ud pair is required to form the π-, which need a large momentum transferred to the original d quark.

The hadronization J/ψpπ- is one of the possible final states, thus we have to consider the final state interaction of the pπ- and other meson-baryon pairs.

The final state interaction S-wave interaction of mesons with baryons in the strangeness S=0 was studied in a coupled channel unitary approach in Ref. Inoue. [Phys.Rev. C65 (2002) 035204] Bethe-Salpeter equation

Transition potential is obtained from the lowest order meson-baryon chiral Lagrangian The coupling fi is the pseudoscalar decay constants for i channel,

Cij reflect the SU(3) flavor symmetry, G function

Diagrams & amplitude Without the effect Pc(445), the amplitude,

amplitude Vp expresses the weak and hadronization strength, and it also contains the overall suppression factor Vcb*Vcd.

J/ψp interaction in S-wave The final J/ψp pair is in S-wave, and total spin J=1/2, which is one of the possible spins.

J/ψp interaction With the effect of Pc(4450), the amplitude,

J/ψp interaction The amplitude for J/ψp to J/ψp transition from Ref. Roca. [Phys. Rev. D92, 094003(2015)] Thus, the decay width,

P and D wave in π-p scattering In LHCb2014, the signals of the two resonances [N(1440) and N(1520)] are found in π-p mass distribution.

Results and discussion Fit the data of LHCb2014, three free parameters, Vp, Vp^P, Vp^D.

Results Our results showed that the Pc structure of a peak followed by a dip can be clearly seen on top of the background, which agrees with the data of LHCb2014.

LHCb2016 In 2016, a full amplitude analysis of this process is performed by LHCb, and a better description of the data is achieved. [Phys.Rev.Lett. 117 (2016) no.8, 082003]

LHCb2016 The effects of Pc(4380) and Pc(4450) in this process is supported by the data of LHCb2016.

LHCb2016 The structure of Pc(4450) with a peak followed by a dip is also seen in the LHCb2016. More data around 4.4 GeV is needed.

The pentaquarks with strangeness In the unitary chiral approach of Ref. Wu, in addition to an isospin 1/2 and strangeness zero state, two more states are predicted in the isospin zero and strangeness -1.

The pentaquarks with strangeness If the Pc(4450) corresponds to the non-strange one, its strange counterparts should also be exist.

The pentaquarks with strangeness We propose to study the decays of Ξb→J/ψK-Λ and Λb→J/ψKΛ to search the strange counterparts of Pc. Basing on the works: J. X. Lu, E. Wang, J. J. Xie, L. S. Geng, and E. Oset, Phys.Rev. D93 (2016) 094009. H. X. Chen, L. S. Geng, W. H. Liang, E. Oset, E. Wang, and J. J. Xie, Phys.Rev. C93 (2016) no.6, 065203

The process of Λb→J/ψKΛ The amplitude M=4650 MeV, Γ=10 MeV

The process of Λb→J/ψKΛ The contribution of N(1895) (1/2-) will add coherently to the above one. The contribution of N(1900) (3/2+) will add incoherently as,

The process of Λb→J/ψKΛ One observes a clear peak around 4650 MeV, associated to the hidden-charm strange resonances.

Case of J/ψΛ in 3/2- The contribution of JP=3/2- J/ψΛ final state interaction, [more details PRD93, 094009(2016)] Finally, the amplitude,

Results for the case of J/ψΛ in 3/2- Instead of a peak, there is now a dip structure, coming from the interference of the P wave Ttree and T3/2-.

Results for the case of J/ψΛ in 3/2- The dip structure is common in hadron physics, for example in f0(980) in π+π- invariant mass of the J/ψ→ϕ π+π- and Bs → J/ψ π+π- . Refs: hep-ex/0104050, Nucl. Phys. B320, 1 (1989), Phys. Lett. B 698, 115 (2011), 1510.00653.

The process of Ξb→J/ψK-Λ J/ψΛ in 1/2- J/ψΛ in 3/2-

The results for J/ψΛ in ½- A peak structure is clearly seen in the J/ψΛ distribution.

The results for J/ψΛ in 3/2- A dip structure is clearly seen in the J/ψΛ distribution, the same as the Λb→J/ψKΛ with J/ψΛ system in 3/2-.

Summary Motivated by the data of LHCb2014 and LHCb2015, we studied the decay of Λb→J/ψpπ- to investigate the hidden-charm pentaquark state within the unitary chiral approach, assuming the J/ψp system in J=1/2, a structure of a peak followed by a dip can be clearly seen, which agrees with the low statistics data LHCb2014. This structure is also seen in the high statistics data LHCb2016.

Summary We propose to search the strange counterparts of Pc in the decays of Ξb→J/ψK-Λ and Λb→J/ψKΛ. For the case of J/ψΛ system in J=1/2, a peak is clear seen, and for the case of J/ψΛ system in J=3/2, there is a dip structure. We strongly encourage our experimental colleagues to study these two processes, which is helpful to test the existence of the pentaquark states with strangeness and to understand their nature.

Thanks for your attention!