Exotic three-body states

Author(s)

Brenda Bertotto Malabarba

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2024-04-05

Examining board members

Alberto Martinez Torres; Luciano Melo Abreu; Diogo Rodrigues Boito; Bruno Omar El bennich; Fernando Silveira Navarra

• Advisor: Alberto Martinez Torres

Abstract

Historical records show that understanding the nature of matter and its constituents has been a research topic since 600 B.C, with Thales of Miletus (610 - 546 BC) being the first to raise relevant questions. Ever since, this field of research has been developing and it continues being one of the most important topic of investigation among the hadron physics community. But, even nowadays, understanding the inner structure of a hadron remains a challenge for modern physics. Over the past years, and with the development of experimental equipments, more and more states which cannot be explained as quark-antiquark states (q q) or three-quark states (qqq) are being found. Such states are called *exotic states*. In this thesis we investigate properties of different exotic states: First we present the N* states with hidden charm and molecular nature generated from three-body interactions of the N D D* system. Also continuing with the topic of generation of exotic states, we study the three-body systems K D, K D and K* D*, where three states were observed from the dynamics involved in the K D and K D systems for different isospin configurations. We also study the two-body interactions in the D subsystem, in which the formation of the state D(2420) is found. We also determine observables which can help in showing the exotic nature of these states. In particular, we show the results for the decay widths to two-body final states of the states (2170) and D(2900), with (2170) and D(2900) described as molecular states generated from the three-body interactions of the K K and D K K systems, respectively, and we compare the results with available experimental data. The study of the above mentioned N* states was inspired by the recent discovery of the LHCb collaboration, which observed the existence of pentaquark states P_c with masses around 4300-4500 MeV and whose quantum numbers are still unknown. It is interesting to notice that the system N D D*/N D D* has a threshold around 4814 MeV. Considering the attractive nature of the N D - N D* interactions, which generates a state with a binding energy of ~200 MeV, we could have formation of states around 4600 MeV, a value close to the masses found for the states P_c. Another characteristic of this system is the fact that the interactions in the D D* subsystem are attractive and can generate, for example, the states X(3872)/Z_c(3900). Because the interactions in the subsystems D D* and N D - N D* are attractive, the possibility that the system N D D*/N D D* has an attractive interaction seems quite plausible. These properties motivated us to study such systems. To investigate the possible formation of a state in the three-body system N D D*/N D D* we need to calculate the scattering matrix T for this system. To do this, we solve the Faddeev equations using the fixed center approximation (FCA), where the two-body amplitudes for the subsystems N D, N D*, N D and N D* are the kernel for solving these equations. The modulus squared of the three-body T matrix for the N D D*/N D D* system has peaks for isospin 1/2 and spin parity 1/2 and 3/2 around ~4400-4570 MeV with widths ~2 - 14 MeV, so we show the existence of N* states with spin parity 1/2 and 3/2 and isospin 1/2. We also consider the case where there is a generation of a state _c in 2600 MeV in the D N - D* N system with a small width and negative parity. When implementing such possibility we find signals of formation of states in the modulus squared of the three-body T matrix for isospin 3/2 and spin parity 1/2 and 3/2 with masses 4359-4514 MeV and widths of 1-4 MeV. The peaks observed can be identified as _c states with hidden charm. Continuing with the motivation behind the study of the different systems investigated in this thesis, the systems K D, K D and K* D* were considered to check if such dynamic could explain the nature of the X(2900) state observed by LHCb along with the X(2900) state. These states were observed in the decay of B K D K in the invariant mass of D K and have masses and widths given by: M_X = 2866 ± 7 MeV, _X = 57 ± 13 MeV, M_X = 2904 ± 5 MeV and _X = 110 ± 12 MeV. In addition, their quantum numbers of spin-parity are: J = 0 for X and J = 1 for X. Considering s-wave interactions the K D and K* D* systems have quantum numbers compatible with those of X(2900). Since the interactions in some of the corresponding subsystems are attractive (or, at least, not very repulsive) we can expect generation of a three-body bound state. It should be mentioned that the system K D, even though it does not have quantum numbers compatible with those of X(2900), presents interactions which are even more attractive in its subsystems when compared to K D. This fact drives us to study this system given the high probability of observing the generation of an exotic state arising from such three-body dynamics. In a similar way to what was done for the N D D* system, we obtain the three-body T-matrices for each of the systems by solving the Faddeev equations with the fixed center approximation. It should be noticed that to study, a three-body system, we first need to describe the two-body interactions between the particles constituting the system. To describe the K* D* subsystem we consider the study carried out in Ref., where three states are found: X, X and X. These states have I(J) = 0(0) and mass M = 2866 MeV with width ~ 57 MeV, I(J) = 0(1) with M = 2861 MeV and ~ 20 MeV and I(J) = 0(2) with M = 2775 MeV and ~ 38 MeV, respectively. It should be mentioned that the state X obtained in Ref. was identified as the X(2900) observed by the LHCb collaboration. In our case, we are especially interested in the X system because if we consider all interactions in s-wave it presents J = 1, which is compatible with the quantum numbers of X(2900). To describe the two-body system D ( D) we follow Ref., where a state with spin-parity 1/2 was observed and identified as D(2420). However, in the work of Ref. the state identified as D(2420) has a mass of 2526.47 MeV and a width of 31.6 MeV, the former value being about 100 MeV above the nominal mass of this state. In this case, in order to obtain a description in better agreement with the experimental data, we decided, before starting the three-body calculations, to update the study made in Ref.. This is done by considering other relevant t-mechanism contributing to the scattering between a and a D, which were ignored in Ref.. To be precise we consider the exchange of pseudoscalar mesons via box diagrams, implementing in this way the fact that . Adding such contributions to the kernel used in Ref. to solve the Bethe-Salpeter equation produces a pole with a mass of ~2428 MeV and width ~33 MeV, with J = 1, compatible with the experimental values determined for D(2420). To describe the K D and K D subsystems we follow Ref., while the interactions in the K* and D* subsystems were described following Refs.. Once the two-body t-matrices describing the interactions in the two-body subsystems are determined, we can use the former as kernel for solving the Faddeev equations and determine the three-body T-matrices for each system. This T-matrix is a function of the energy in the center of mass frame of the system and its modulus squared can show structures related to the formation of states where the three-body dynamics plays a major role. In particular, the modulus squared of the three-body T-matrix for the K D system presents a broad peak when considering total isospin 0 for the system. The mass related to this state is approximately 3074 MeV and its width is of 64 MeV, values which are incompatible with those of X(2900). However, our results show the formation of states at higher energy, for the case of isospin 1, in the K D system, no peak was observed. Turning our attention now to the K D system, peaks were observed for both isospin 0 and 1. In case of isospin 0 the mass related to the observed state is 2872 MeV, with a width of ~100 MeV. This state has quantum numbers I(J) = 0(1), mass and width compatible with those of the state D*_s1(2860). For total isospin 1, another peak related to a state with a mass of 2883 MeV and a width of 7 MeV is seen. This state, due to its quantum numbers, is manifestly exotic, that is: it cannot certainly be described as a q q state, needing q c s q as minimum quark content. No state with these properties has been observed so far and it could be a positive strangeness partner of the X_i states found by the LHCb collaboration. As for the system K* D*, no state is observed. Actually, we find peaks in the modulus squared of the three-body T-matrix above the three-body threshold of the system, an energy region where the fixed center approximation is not reliable and a more precise study needs to be done in order to claim the association of the signals found with new states. In addition to the generation of three-body states, we also study the decay properties of states obtained from a three-body dynamic. To be more specific, we investigate some of the two-body decay modes of (2170) and D(2900). In Ref. the BESIII collaboration reported the observation of a signal of (2170) when studying the process e e K K . In this work the values found for the partial decay widths of this state to the channels K(1460) K, K(1400) K and K(1270) K were obtained. In addition to these widths, the BESIII collaboration studied the processes e e and e e and determined the decay widths to these final states. Other collaborations, such as Belle and BaBar, also determined these widths. In this thesis, we calculate the decay widths of (2170) to the above mentioned channels considering (2170) as being generated from the interactions of the K K system as found in Ref.. In our model the state K(1460) is also considered as a three-body state which is generated from the K K K system when the K K subsystem forms f(980). To describe the properties of K(1400) and K(1270) three different models were used: 1) considering them as a mixture of states belonging to the axial nonet; 2) Assuming K(1270) to be a molecular state with two associated poles; 3) Using a phenomenological model based on the experimental data. To calculate the decay width of (2170) to the final states and within a f(980) description for (21700), we need to include and as coupled channels of and K K and solve the Bethe-Salpeter equation following the model of Ref.. Within the preceding formalism, we obtain the decay widths of (2170) to K_R K channels, with K_R representing the previously mentioned kaonic resonances, and show that the values found are compatible with the experimental results determined by the BESIII collaboration. Furthermore, by considering the molecular description for (2170) we are able to explain the strong decay suppression observed to the K*(895) K*(895) channel. As for the final states and , we show that the ratio of widths _ / _ found within our formalism is compatible with the experimental results. However, to be able to distinguish between the different models used to determine such quantities it is necessary to have better experimental data, to reduce uncertainties. We will finalize the discussions presented in this thesis by showing the results obtained for the two-body decay widths of the state D(2900). This study was inspired by a signal observed by the LHCb collaboration at ~3000 MeV in the mass spectrum of the D* , D and D systems. The structure observed in the D spectrum is compatible with an unnatural parity for the signal found whereas for D* and D it is compatible with a natural parity. Interestingly, in Ref. a D meson with mass around 2900 MeV, width of 55 MeV and unnatural parity was predicted. Such state was obtained from the three-body dynamics involved in the D K K system. Using this description we calculate the decay widths of D(2900) to the following two-body channels: D* , D* , D*_s K and D*_s0(2317) K. As a result we get that the channel with the greatest decay width is D*_s0(2317) K, with = 18.33 ± 7.25 MeV. So a state D(2900) of molecular nature has a greater chance of being observed in the D*_s0(2317) K channel. (AU)

• FAPESP's process: 20/00676-8 - Exotic three-hadrons states with strangeness
• Grantee: Brenda Bertotto Malabarba
• Support Opportunities: Scholarships in Brazil - Doctorate