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Hidalgo-Duque, C., Nieves, J., & Pavon Valderrama, M. (2013). Heavy quark spin symmetry and SU(3)-flavour partners of the X (3872). Nucl. Phys. A, 914, 482–487.
Abstract: In this work, an Effective Field Theory (EFT) incorporating light SU(3)-flavour and heavy quark spin symmetries is used to describe charmed meson-antimeson bound states. At Lowest Order (LO), this means that only contact range interactions among the heavy meson and antimeson fields are involved. Besides, the isospin violating decays of the X(3872) will be used to constrain the interaction between the D and a (D) over bar* mesons in the isovector channel. Finally, assuming that the X(3915) and Y(4140) resonances are D* (D) over bar* and D-s* (D) over bar (s)* molecular states, we can determine the four Low Energy Constants (LECs) of the EFT that appear at LO and, therefore, the full spectrum of molecular states with isospin I = 0, 1/2 and 1.
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Hidalgo-Duque, C., Nieves, J., & Pavon Valderrama, M. (2013). Light flavor and heavy quark spin symmetry in heavy meson molecules. Phys. Rev. D, 87(7), 076006–14pp.
Abstract: We propose an effective field theory incorporating light SU(3)-flavor and heavy quark spin symmetry to describe charmed meson-antimeson bound states. At lowest order the effective field theory entails a remarkable simplification: it only involves contact range interactions among the heavy meson and antimeson fields. We show that the isospin violating decays of the X(3872) can be used to constrain the interaction between the D and a (D) over bar* mesons in the isovector channel. As a consequence, we can rule out the existence of an isovector partner of the X(3872). If we additionally assume that the X(3915) and Y(4140) are D*(D) over bar* and D*(s)(D) over bar*(s) molecular states, we can determine the full spectrum of molecular states with isospin I = 0, 1/2 and 1.
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Nieves, J., & Pavon Valderrama, M. (2012). Heavy quark spin symmetry partners of the X(3872). Phys. Rev. D, 86(5), 056004–18pp.
Abstract: We explore the consequences of heavy quark spin symmetry for the charmed meson-antimeson system in a contact-range (or pionless) effective field theory. As a trivial consequence, we theorize the existence of a heavy quark spin symmetry partner of the X(3872), with J(PC) = 2(++), which we call X(4012) in reference to its predicted mass. If we additionally assume that the X(3915) is a 0(++) heavy spin symmetry partner of the X(3872), we end up predicting a total of six D-(*())(D) over bar (()*()) molecular states. We also discuss the error induced by higher order effects such as finite heavy quark mass corrections, pion exchanges and coupled channels, allowing us to estimate the expected theoretical uncertainties in the position of these new states.
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Pavon Valderrama, M. (2012). Power counting and perturbative one pion exchange in heavy meson molecules. Phys. Rev. D, 85(11), 114037–21pp.
Abstract: We discuss the possible power counting schemes that can be applied in the effective field theory description of heavy meson molecules, such as the X(3872) or the recently discovered Z(b)(10610) and Z(b)(10650) states. We argue that the effect of coupled channels is suppressed by at least two orders in the effective field theory expansion, meaning that they can be safely ignored at lowest order. The role of the one pion exchange potential between the heavy mesons, and, in particular, the tensor force, is also analyzed. By using techniques developed in atomic physics for handling power-law singular potentials, which have been also successfully employed in nuclear physics, we determine the range of center-of-mass momenta for which the tensor piece of the one pion exchange potential is perturbative. In this momentum range, the one pion exchange potential can be considered a subleading order correction, leaving at lowest order a very simple effective field theory consisting only of contact-range interactions.
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Pavon Valderrama, M. (2011). Perturbative renormalizability of chiral two-pion exchange in nucleon-nucleon scattering. Phys. Rev. C, 83(2), 024003–11pp.
Abstract: We study the perturbative renormalizability of chiral two-pion exchange for singlet and triplet channels within effective field theory, provided that the one-pion exchange piece of the interaction has been fully iterated. We determine the number of counterterms/subtractions needed to obtain finite results when the cutoff is removed, resulting in three counterterms for the singlet channel and six for the triplet. The results show that perturbative chiral two-pion exchange reproduce the data up to a center-of-mass momentum of k similar to 200-300 MeV in the singlet channel and k similar to 300-400 MeV in the triplet.
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