An Effective Field Theory study of heavy meson-heavy antimeson molecules based on Heavy Quark Symmetries

The study of the low and intermediate energy hadronic interactions has experienced great advances in the last few years. The fact that low energy QCD dynamics can be described by means of effective theories, in which the degrees of freedom are mesons and baryons, has been widely exploited to explain the complex experimental observed spectrum. In this thesis, we have extended these ideas to the quark charm and bottom sectors. The whole new set of meson and baryon states with open charm and hidden charm found by the BABAR, CLEO, BELLE, BES or LHCb collaborations has stimulated a lot of theoretical work. Recently, several of these collaborations have discovered new exotic states with masses around 4000 MeV, which do not seem to have a simple quark-antiquark c-cbar structure. They have been called XYZ particles. Some of these states are the isoscalar resonances X(3872), X(3940), X(4160), Y(4260) and the isovector Z_c(3900), Z_c(4020). In addition, other observed states with explicit charm do not have either a simple interpretation within conventional quark models, such as the Ds(2317), Ds(2460) mesons or the Lambda_c(2595), Lambda_c(2625) baryons. In the bottom sector, exotic resonances have also been found, such as the mesonic states Z_b(10610) y Z'b(10650) and the baryon resonances Lambda_b(5912) and Lambda_b(5920). Among these discovered states, the X(3872), Zb(10610) and Z'b(10650) are of paramount relevance in this thesis. The X(3872) resonance was observed for the first time by the Belle Collaboration in 2003 with quantum numbers J^{PC} = 1^{++}. The isovector states Zb(10610) and Zb(10650), J^{PC} = 1^{+-}, were discovered more recently, also by the Belle Collaboration. These resonances can naturally be described as molecular states, composed by a loosely bound heavy meson-antimeson pair. To justify this description, we have studied the interaction between D^{(*)} Dbar^{(*)}$ mesons (and similarly in the quark bottom sector), incorporating the restrictions derived from the Heavy Quark Symmetry (HQS). HQS is a spin-flavour underlying symmetry of QCD that appears when the quark masses are much larger than the confinement scale Lambda_{QCD}. HQS predicts that spin interactions are negligible in the limit of infinite quark masses. For finite masses, such as that of the charm quark, there are some corrections of the order (Lambda_{QCD}/m_Q) but the symmetry is still quite precise. For instance, despite the D and D* mesons are not degenerate, the mass difference between the two mesons is less than a pion mass. This symmetry is specially useful to simplify the study of composite systems involving both light and heavy quarks. Owing to HQS, simple relationships among properties (such as masses or decay constants) of different spin states can be formulated. HQS also embodies a flavour symmetry that relates the charm and bottom sectors. Assuming an additional SU(3) flavour-symmetry in the light sector, we have deduced the most general contact (s-wave) interaction between P^{(*)} Pbar^{(*)} (P^{(*)} = D^{(*)}, B^{(*)}) mesons compatible with Heavy Quark Spin Symmetry (HQSS). We have also studied One Pion Exchange (OPE) and coupled channel effects on the potential, which turned out to be numerically small and suppressed in the counting. Bound states are dynamically generated by solving the Lippmann-Schwinger Equation (LSE), using the previous interactions as its kernel. Since the potential at leading order (LO) is a contact interaction, there are ultraviolet divergences in the theory, whose renormalization has also been discussed in detail. In this manner, meson-antimeson molecules predicted by our model appear as poles in the T-matrix. At LO, the effective theory depends on four undetermined Low Energy Constants (LECs). The values of these LECs are not restricted by any elementary model or further underlying symmetry and must be fitted to reproduce experimental observations. Hence, we identify some exotic resonances as molecular states to fix the LECs (as occurs in Chiral Perturbation Theory). Once these counter-terms are determined, we have predicted a whole family of molecular HQS partners of the resonances used as inputs. Thus, in Chapter 3, we describe an effective Lagrangian incorporating light SU(3)-flavour and heavy quark spin symmetries and it is used to describe hidden-charm meson-antimeson bound states. As mentioned above, at LO, the effective field theory entails a remarkable simplification and it only involves contact range interactions among the heavy meson and antimeson fields. In this context, we show that the isospin violating decays of the X(3872) can be used to constrain the interaction between the D and the Dbar^* mesons in the isovector channel. As a consequence, we can rule out the existence of an isovector partner of the X(3872). Next, and assuming that the X(3915) and Y(4140) are D*Dbar* and Ds*Dbar_s* molecular states, we determine the full spectrum of molecular states with isospin I=0, 1/2 and 1. The predicted spectrum includes open and hidden-strangeness sectors as well. One of the most relevant predictions in this chapter is the partner of the X(3872), called X_2. This resonance, a loosely bound D* Dbar* state with quantum numbers J^{PC} = 2^{++}, has the same dynamics as the X(3872). Next, in Chapter 4, we have studied the HQS EFT in a finite box. This analysis is interesting since the study of EFTs in lattice is increasing and further understanding of finite volume effects is mandatory. The procedure followed is the substitution of an infinite volume by a finite volume in the formalism. As the basic volume unit we have used a cube; but other more complex geometries could be used (e.g., rectangular boxes). This replacement imposes that the momentum-space integrals have to be substituted by a sum over a discrete set of three-momenta (as can be seen in the infinite square potential in quantum mechanics). Within this formalism, first the energy levels in the box are evaluated, and from them some synthetic data are generated. These data are then employed to study the inverse problem of getting the energies of the bound states and phase shifts for D Dbar or D*Dbar*. Different strategies are investigated and we conclude that a method based on the fit to the data by means of a potential and a conveniently regularized loop function, is the most efficient and allows us to produce accurate results in the infinite volume starting from levels of the box with errors far larger than the uncertainties obtained in the final results. Finally, in this chapter, the regularization method based on Gaussian wave functions is discussed and shown to be rather efficient in the finite box analysis and, as a byproduct, a practical and fast method to calculate the L\"uscher function with high precision is presented. In Chapter 5, we extend the EFT formalism outlined in Chapter 3 to the bottom sector taking advantage of Heavy Flavour Symmetry (HFS). This symmetry basically states that for quarks heavy enough (as the charm and bottom quarks), dynamics are flavour-independent, up to corrections of the order O(Lambda_{QCD}/m_Q). Thanks to this symmetry, one could also use possible exotic states discovered in the bottom sector to determine the LECs. In this chapter, we use as an input the X(3872) resonance and one of the Zb(10610)/Z'b(10650) states. We are thus able to fix three of the four LECs and obtain a set of states whose experimental determination would be again a test of the molecular assumptions used. From the X(3872) state, we have re-obtained the X_2 state but, we have also found the equivalent states in the bottom sector, the Xb and X_{b2} states. We have also obtained partners of the Zb(10610) and Z'b(10650) states in the charm sector, these Zc/Z'c states appear in our scheme as virtual states. These states were (likely) experimentally observed and we are convinced that they probably correspond to the recently reported Zc(3900) and Zc(4025) resonances by the BESIII Collaboration. The OPE effects in the bottom sector have been numerically computed as well. We have analyzed in detail the isoscalar sector (the OPE potential in the isoscalar sector is three times larger than in the isovector sector), where small deviations from the previous results have been found. This result allows us to keep neglecting the OPE effects in the following analyses. In Chapter 6, a similar EFT analysis is used to predict the possible existence of exotic (pentaquark) baryons. This has been accomplished by means of the Heavy Antiquark-Diquark Symmetry (HADS). This symmetry relates the dynamics of a heavy diquark with that of a heavy antiquark (because both systems have the same 3bar colour configuration). Thus, the doubly heavy baryons have approximately the same light-quark structure as the heavy antimesons. As a consequence, the existence of a heavy meson-antimeson molecule implies the possibility of a partner composed of a heavy meson and a doubly heavy baryon. In this regard, the D Dbar* molecular nature of the X(3872) hints at the existence of several baryonic partners with isospin I=0 and J^P=5/2^- or 3/2^-. Moreover, assuming that the Zb(10650) is a B*Bbar^* bound state, the existence of Xi_{bb}^* Bbar^* hadronic molecules with quantum numbers I(J^P)=1(1/2^-)$ and I(J^P)=1(3/2^-) have been predicted. These states are of special interest since they can be considered to be triply heavy pentaquarks. In Chapter 7, a parallel analysis of these molecular states has been carried out using a formalism based on two point Green functions, in the strict heavy quark limit. To that end, some suited interpolating currents have been defined for the different spin-parity-charge conjugation sectors. They can be used in sum rule or LQCD studies of these exotic molecular states. The isospin mixing of the X(3872) has been also discussed from this perspective. In chapters 8 and 9 we analyze certain decays of some of the molecular states studied in the previous chapters. Chapter 8 is devoted to the study of the hadron decay X(3872) to D^0 Dbar^0 pi^0. This process is of special interest because it is sensitive to the long-distance structure of the $X(3872)$. Indeed, we have argued that a precise experimental determination of this width might shed some light on the inner nature of the resonance. Moreover, it can also serve to further constrain the LECs because the final state interactions (FSI) between the final D Dbar states might significantly affect the decay width. Finally, in Chapter 9, we have studied the decays of the J^{PC} = 2^{++} molecular partner of the X(3872) state (X_{2} state) in both the charm and bottom sectors. We first analyze the hadron decays X_2 to P Pbar and X_2 to P Pbar*. These decays represent the largest contribution to the total decay width of the state and turn out to be of the order of few MeV. Next, we have also studied the X_2 to P Pbar* gamma radiative decays. The decay width is predicted to be tens of keV and it is discussed how this process, as the X(3872) to D^0 Dbar^0 pi^0 hadronic decay studied in Chapter 8, is sensitive to the long-distance details of the D* Dbar* wave function and, therefore, might reveal the nature of the studied resonance. The radiative decay is also affected by the FSI of the outgoing P Pbar* meson pair, what might provide additional constrains on the counter-terms that appear in the EFT at LO.