Power Counting of Contact-Range Currents in Effective Field Theory

We analyze the power counting of two-body currents in nuclear effective field theories (EFTs). We find that the existence of non-perturbative physics at low energies, which is manifest in the existence of the deuteron and the 1S0 NN virtual bound state, combined with the appearance of singular potentials in versions of nuclear EFT that incorporate chiral symmetry, modifies the renormalization-group flow of the couplings associated with contact operators that involve nucleon-nucleon pairs and external fields. The order of these couplings is thereby enhanced with respect to the naive-dimensional-analysis estimate. Consequently, short-range currents enter at a lower order in the chiral EFT than has been appreciated up until now, and their impact on low-energy observables is concomitantly larger. We illustrate the changes in the power counting with a few low-energy processes involving external probes and the few-nucleon systems, including electron-deuteron elastic scattering and radiative neutron capture by protons.Comment: 5 pages. Minor revisions. Conclusions unchanged. Version to appear in Physical Review Letter

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.Comment: 21 pages, 1 figur

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.Comment: 18 pages; final version accepted for publicatio

Kohn-Sham calculations combined with an average pair-density functional theory

A recently developed formalism in which Kohn-Sham calculations are combined with an ``average pair density functional theory'' is reviewed, and some new properties of the effective electron-electron interaction entering in this formalism are derived. A preliminary construction of a fully self-consitent scheme is also presented in this framework.Comment: submitted to Int. J. Mod. Phys. B (proceedings of the 30th International Workshop on Condensed Matter Theories

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.Comment: 20 pages, 8 figures, a section has been added discussing cut-off dependence. Accepted for publication in PR

Deriving the existence of BBˉ∗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.Comment: 21 pages, 3 figures; a sign error in the potential has been corrected and new predictions have been compute

Deuteron form factors in chiral effective theory: regulator-independent results and the role of two-pion exchange

We evaluate the deuteron charge, quadrupole, and magnetic form factors using wave functions obtained from chiral effective theory ($\chi$ET) when the potential includes one-pion exchange, chiral two-pion exchange, and genuine contact interactions. We study the manner in which the results for form factors behave as the regulator is removed from the $\chi$ET calculation, and compare co-ordinate- and momentum-space approaches. We show that, for both the LO and NNLO chiral potential, results obtained by imposing boundary conditions in co-ordinate space at $r=0$ are equivalent to the $\Lambda \to \infty$ limit of momentum-space calculations. The regulator-independent predictions for deuteron form factors that result from taking the $\Lambda \to \infty$ limit using the LO $\chi$ET potential are in reasonable agreement with data up to momentum transfers of order 600 MeV, provided that phenomenological information for nucleon structure is employed. In this range the use of the NNLO $\chi$ET potential results in only small changes to the LO predictions, and it improves the description of the zero of the charge form factor

Renormalization of NN Interaction with Relativistic Chiral Two Pion Exchange

The renormalization of the NN interaction with the Chiral Two Pion Exchange Potential computed using relativistic baryon chiral perturbation theory is considered. The short distance singularity reduces the number of counter-terms to about a half as those in the heavy-baryon expansion. Phase shifts and deuteron properties are evaluated and a general overall agreement is observed.Comment: 13 pages, 4 figures. Reference included. Typos corrected. Appendix and discussion adde

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.Comment: 15 pages, 6 figure