arXiv subjects

M. Pavon Valderrama

Publications and source records attributed to M. Pavon Valderrama.

At least 19 recordsLinked to original sources

arXiv2024

Limits on an improved action for contact effective field theory in two-body systems

We consider a possible resummation of subleading effects in two-body systems with a large scattering length as described by a short-range effective field theory (EFT). In particular, we investigate the consequences of a resummation of part of the range corrections. Explicit calculations of the two-body phase shifts and charge form factor indicate that, except for extreme choices, resummations do not alter the convergence of the EFT expansion and are often beneficial at lowest orders. We have considered the expansion when the regulator cutoff is removed as well as when it is finite, and find that the cutoff is not an important factor for resummations. Our results connect with other works where the partial resummation is induced by potentials with finite cutoffs or interaction ranges.

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arXiv2018

The $Ω(2012)$ as a hadronic molecule

Recently the Belle collaboration has discovered a narrow $S=-3$ baryon, the $Ω(2012)$. We explore the possibility that the $Ω(2012)$ is a $Ξ(1530)\,\bar K$ molecule, where the binding mechanism is the coupled channel dynamics with the $Ω\,η$ channel. The characteristic signature of a molecular $Ω(2012)$ will be its decay into the three body channel $Ξπ\bar{K}$, for which we expect a partial decay width of $2-3\,{\rm MeV}$. The partial decay width into the $Ξ\bar{K}$ channel should lie in the range of $1-11\,{\rm MeV}$, a figure compatible with experiment and which we have deduced from the assumption that the coupling involved in this decay is of natural size. For comparison purposes the decay of a purely compact $Ω(2012)$ into the $Ξ\bar{K}$ and $Ξπ\bar{K}$ channels is of the same order of magnitude as and one order of magnitude smaller than in the molecular scenario, respectively. This comparison indicates that the current experimental information is insufficient to distinguish between a compact and a molecular $Ω(2012)$ and further experiments will be required to determine its nature. A molecular $Ω(2012)$ will also imply the existence of two- and three-body molecular partners. The two-body partners comprise two $Λ$ hyperons located at $1740$ and $1950\,{\rm MeV}$ respectively, the first of which might correspond to the $Λ(1800)$ while the second to the $Λ(2000)$ or the $Λ(2050)$. The three-body partners include a $Ξ(1530) K\bar{K}$ and a $Ξ(1530) η\bar{K}$ molecule, with masses of $M = 2385-2445\,{\rm MeV}$ and $M = 2434-2503\,{\rm MeV}$ respectively. We might be tempted to identify the first with the $Ξ(2370)$ and the latter with the $Ω(2470)$ listed in the PDG.

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arXiv2015

Decay widths of the spin-2 partners of the X(3872)

We consider the $X(3872)$ resonance as a $J^{PC}=1^{++}$ $D\bar D^*$ hadronic molecule. According to heavy quark spin symmetry, there will exist a partner with quantum numbers $2^{++}$, $X_{2}$, which would be a $D^*\bar D^*$ loosely bound state. The $X_{2}$ is expected to decay dominantly into $D\bar D$, $D\bar D^*$ and $\bar D D^*$ in $d$-wave. In this work, we calculate the decay widths of the $X_{2}$ resonance into the above channels, as well as those of its bottom partner, $X_{b2}$, the mass of which comes from assuming heavy flavor symmetry for the contact terms. We find partial widths of the $X_{2}$ and $X_{b2}$ of the order of a few MeV. Finally, we also study the radiative $X_2\to D\bar D^{*}γ$ and $X_{b2} \to \bar B B^{*}γ$ decays. These decay modes are more sensitive to the long-distance structure of the resonances and to the $D\bar D^{*}$ or $B\bar B^{*}$ final state interaction.

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arXiv2014

Hidden charm and bottom molecular states

We investigate heavy quark symmetries for heavy light meson-antimeson systems in a contact-range effective field theory. In the SU(3) light flavor limit, the leading order Lagrangian respecting heavy quark spin symmetry contains four independent counter-terms. Neglecting $1/m_Q$ corrections, three of these low energy constants can be determ1ined by theorizing a molecular description of the $X(3872)$ and $Z_b(10610)$ states. Thus, we can predict new hadronic molecules, in particular the isovector charmonium partners of the $Z_b(10610)$ and the $Z_b(10650)$ states. We also discuss hadron molecules composed of a heavy meson and a doubly-heavy baryon, which would be related to the heavy meson-antimeson molecules thanks to the heavy antiquark-diquark symmetry. Finally, we also study the $X(3872) \to D^0\bar D^0π^0$ decay, which is not only sensitive to the short distance part of the $X(3872)$ molecular wave function, as the $J/ψππ$ and $J/\psi3π$ $X(3872)$ decay modes are, but it is also affected by the long-distance structure of the resonance. Furthermore, this decay might provide some information on the interaction between the $D\bar D$ charm mesons.

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arXiv2014

Long-distance structure of the X(3872)

We investigate heavy quark symmetries for heavy meson hadronic molecules, and explore the consequences of assuming the X(3872) and $Z_b(10610)$ as an isoscalar $D\bar D^*$ and an isovector $B\bar B^*$ hadronic molecules, respectively. The symmetry allows to predict new hadronic molecules, in particular we find an isoscalar $1^{++}$ $B\bar B^*$ bound state with a mass about 10580 MeV and the isovector charmonium partners of the $Z_b(10610)$ and the $Z_b(10650)$ states. Next, we study the $X(3872) \to D^0 \bar D^0π^0$ three body decay. This decay mode is more sensitive to the long-distance structure of the X(3872) resonance than its $J/ψππ$ and $J/\psi3π$ decays, which are mainly controlled by the short distance part of the X(3872) molecular wave function. We discuss the $D^0 \bar D^0$ final state interactions, which in some situations become quite important. Indeed in these cases, a precise measurement of this partial decay width could provide precise information on the interaction strength between the $D^{(*)}\bar D^{(*)}$ charm mesons.

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arXiv2013

Heavy Quark Symmetries: Molecular Partners of the X(3872) and $Z_{b}(10610)/Z_{b}'(10650)$

In this work, we have used an Effective Field Theory (EFT) framework based on Heavy Quark Spin (HQSS), Heavy Flavour (HFS) and Heavy Antiquark-Diquark symmetries (HADS). Using a standard lagrangian for the heavy meson-heavy antimeson system, we fit the counter-terms of the model to predict some promising experimental data that can be interpreted as heavy meson-heavy antimeson molecules, that is, the X(3872) and the $Z_{b}(10610)/Z'_{b}(10650)$. Next, and, taking advantage of HADS, we use the same lagrangian to explore the consequences for heavy meson-doubly heavy baryon molecules, which can also be interpreted as triply heavy pentaquarks.

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arXiv2013

Light Flavour and Heavy Quark Spin Symmetry in Heavy Meson Molecules

We propose an effective field theory incorporating light SU(3)-flavour 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 constraint the interaction between the $D$ and a $\bar{D}^*$ mesons in the isovector channel. As a consequence, we can rule out the existence of a isovector partner of the X(3872). If we additionally assume that the X(3915) and Y(4140) are $D^*\bar{D}^*$ and $D_s^*\bar{D}_s^*$ molecular states, we can determine the full spectrum of molecular states with isospin I=0, 1/2 and 1.

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arXiv2012

The Heavy Quark Spin Symmetry Partners of the X(3872)

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 $D^{(*)}\bar{D}^{(*)}$ 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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arXiv2012

Power Counting and Perturbative One Pion Exchange in Heavy Meson Molecules

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 Zb(10610) and Zb(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 on contact-range interactions.

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arXiv2012

Are there three Xi(1950) states?

Different experiments on hadron spectroscopy have long suspected the existence of several cascade states in the $1900-2000 {\rm MeV}$ region. They are usually labeled under the common name of $Ξ(1950)$. As we argue here, there are also theoretical reasons supporting the idea of several $Ξ(1950)$ resonances. In particular, we propose the existence of three $Ξ(1950)$ states: one of these states would be part of a spin-parity $(1/2)^{-}$ decuplet and the other two probably would belong to the $(5/2)^{+}$ and $(5/2)^{-}$ octets. We also identify which decay channels are the more appropriate for the detection of each of the previous states.

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arXiv2011

Perturbative Renormalizability of Chiral Two Pion Exchange in Nucleon-Nucleon Scattering: P- and D-waves

We study the perturbative renormalizability of chiral two pion exchange in nucleon-nucleon scattering for p- and d-waves within the effective field theory approach. The one pion exchange potential is fully iterated at the leading order in the expansion, a choice generating a consistent and well-defined power counting that we explore in detail. The results show that perturbative chiral two pion exchange reproduces the data up to a center-of-mass momentum of k_cm ~300 MeV at NNLO and that the effective field theory expansion convergences up to k_cm ~ 350 MeV.

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arXiv2011

Deriving the existence of $B\bar{B}^*$ bound states from the X(3872) and Heavy Quark Symmetry

We discuss the possibility and the description of bound states between $B$ and $\bar{B}^*$ mesons. We argue that the existence of such a bound state can be deduced from (i) the weakly bound X(3872) state, (ii) certain assumptions about the short range dynamics of the $D\bar{D}^*$ system and (iii) heavy quark symmetry. From these assumptions the binding energy of the possible $B\bar{B}^*$ bound states is determined, first in a theory containing only contact interactions which serves as a straightforward illustration of the method, and then the effects of including the one pion exchange potential are discussed. In this latter case three isoscalar states are predicted: a positive and negative C-parity $^3S_1-{}^3D_1$ state with a binding energy of $20\,{\rm MeV}$ and $6\,{\rm MeV}$ below threshold respectively, and a positive C-parity $^3P_0$ shallow state located almost at the $B\bar{B}^*$ threshold. However, large uncertainties are generated as a consequence of the $1/m_Q$ corrections from heavy quark symmetry. Finally, the newly discovered isovector $Z_b(10610)$ state can be easily accommodated within the present framework by a minor modification of the short range dynamics.

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arXiv2011

Renormalization of chiral two pion exchange NN interactions with delta excitations: correlations in the partial wave expansion

In this work we consider the renormalization of the chiral two-pion exchange potential with explicit delta-excitations for nucleon-nucleon scattering at next-to-leading (NLO) and next-to-next-to-leading order (N2LO). Due to the singular nature of the chiral potentials, correlations between different partial waves are generated. In particular we show that two-body scattering by a short distance power like singular attractive interaction can be renormalized in all partial waves with a single counterterm, provided the singularities are identical. A parallel statement holds in the presence of tensor interactions when the eigenpotentials in the coupled channel problem also coincide. While this construction reduces the total number of counterterms to eleven in the case of nucleon-nucleon scattering with chiral two-pion exchange interactions with delta degrees of freedom, the differences in the scattering phases as compared to the case with the uncorrelated partial wave renormalization become smaller as the angular momentum is increased in the elastic scattering region.

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arXiv2011

Perturbative renormalizability of chiral two pion exchange in nucleon-nucleon scattering

We study the perturbative renormalizability of chiral two pion exchange for the 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 in order to obtain finite results when the cut-off is removed, resulting in three counterterms for the singlet channel and six for the triplet. The results show that chiral two pion exchange can be treated perturbatively up to a center-of-mass momentum of k ~ 200-300 MeV in the singlet channel and k ~ 300-400 in the triplet.

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arXiv2010

Nucleon-Nucleon interaction, charge symmetry breaking and renormalization

We study the interplay between charge symmetry breaking and renormalization in the NN system for s-waves. We find a set of universality relations which disentangle explicitly the known long distance dynamics from low energy parameters and extend them to the Coulomb case. We analyze within such an approach the One-Boson-Exchange potential and the theoretical conditions which allow to relate the proton-neutron, proton-proton and neutron-neutron scattering observables without the introduction of extra new parameters and providing good phenomenological success.

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arXiv2010

Perturbative Renormalizability of Chiral Two Pion Exchange and Power Counting in Nucleon-Nucleon Scattering

We show how to renormalize chiral two pion exchange perturbatively if one pion exchange has already been fully iterated at leading order. This particular choice corresponds to the implementation of the counting proposal of Nogga, Timmermans and van Kolck at subleading orders. We illustrate why the perturbative treatment of the two pion exchange contributions is mandatory in order to avoid certain inconsistencies in Weinberg's counting. In addition, renormalizability implies modifications of the power counting which we explore for the particular case of the singlet channel.

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arXiv2009

A Two Potential Formula and its Application to Proton-Proton Scattering

Within the framework of potential scattering theory we derive an analytical two-potential formula for the on-shell partial wave scattering amplitude. This formula embodies a large number of possible applications, including long range Coulomb forces as well as short distance singular potentials. As an example illustrating the use of the formula we analyze the determination of the strong proton-proton scattering s-wave phase shift from the experimentally determined Coulomb phase when the one pion exchange and two pion exchange chiral potentials are taken into account and analyze the relevant scales of the problem.

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arXiv2009

Renormalization of chiral two-pion exchange NN interactions with Delta-excitations: Central Phases and the Deuteron

The renormalization of the chiral np interaction with Delta-excitations in intermediate states is considered at next-to-leading order (NLO) and next-to-next-to-leading order (N2LO) for central waves. The inclusion of the Delta-excitation as an explicit degree of freedom improves the convergence properties of the effective field theory results for np scattering with respect to Delta-less theory, and allows the existence of a deuteron bound state in the infinite cut-off limit. The 1S_0 singlet and 3S_1 triplet phase shifts reproduce data for p ~ m_pi. The role of spectral function regularization is also discussed.

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