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

Chiral Expansion, Renormalization and the Nuclear Force

The renormalization of singular chiral potentials as applied to NN scattering and the structure of the deuteron is discussed. It is shown how zero range theories may be implemented non-perturbatively as constrained from known long range NN forces.Comment: Talk at International IUPAP Conference on Few-Body Problems in Physics (FB18), Santos-Sao Paulo (Brasil), 21-26 August 200

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

Gauge invariance in the presence of a cutoff

We use the method of gauging equations to construct the electromagnetic current operator for the two-nucleon system in a theory with a finite cutoff. The employed formulation ensures that the two-nucleon T-matrix and corresponding five-point function, in the cutoff theory, are identical to the ones formally defined by a reference theory without a cutoff. A feature of our approach is that it effectively introduces a cutoff into the reference theory in a way that maintains the long-range part of the exchange current operator; for applications to effective field theory (EFT), this property is usually sufficient to guarantee the predictive power of the resulting cutoff theory. In addition, our approach leads to Ward-Takahashi (WT) identities that are linear in the interactions. From the point of view of EFT's where such a WT identity is satisfied in the reference theory, this ensures that gauge invariance in the cutoff theory is maintained order by order in the expansion.Comment: 15 pages, 2 figure

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.Comment: 10 pages, 2 figures (updated version

Renormalization of NN-Scattering with One Pion Exchange and Boundary Conditions

A non perturbative renormalization scheme for Nucleon-Nucleon interaction based on boundary conditions at short distances is presented and applied to the One Pion Exchange Potential. It is free of off-shell ambiguities and ultraviolet divergences, provides finite results at any step of the calculation and allows to remove the short distance cut-off in a suitable way. Low energy constants and their non-perturbative evolution can directly be obtained from experimental threshold parameters in a completely unique and model independent way when the long range explicit pion effects are eliminated. This allows to compute scattering phase shifts which are, by construction consistent with the effective range expansion to a given order in the C.M. momentum $p$. In the singlet $^1S_0$ and triplet $^3S_1- ^3D_1$ channels ultraviolet fixed points and limit cycles are obtained respectively for the threshold parameters. Data are described satisfactorily up to CM momenta of about $p \sim m_\pi$.Comment: 22 pages, 10 figures, revte

Renormalization of the Deuteron with One Pion Exchange

We analyze the deuteron bound state through the One Pion Exchange Potential. We pay attention to the short distance peculiar singularity structure of the bound state wave functions in coordinate space and the elimination of short distance ambiguities by selecting the regular solution at the origin. We determine the so far elusive amplitude of the converging exponential solutions at the origin. All bound state deuteron properties can then be uniquely deduced from the deuteron binding energy, the pion-nucleon coupling constant and pion mass. This generates correlations among deuteron properties. Scattering phase shifts and low energy parameters in the 3S1-3D1 channel are constructed by requiring orthogonality of the positive energy states to the deuteron bound state, yielding an energy independent combination of boundary conditions. We also analyze from the viewpoint of short distance boundary conditions the weak binding regime on the light of long distance perturbation theory and discuss the approach to the chiral limit.Comment: 22 pages, 11 figure

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

Heavy quark spin symmetry and SU(3)-flavour partners of the X (3872)

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