At long distances interactions between neutral ground state atoms can be described by the Van der Waals potential V (r) = − P ∞ n=6 Cn/r n . In the ultra-cold regime atom-atom scattering is dominated by s-waves phase shifts given by an effective range expansion p cot δ0(p) = −1/α0 + r0p 2 /2 + . . . in terms of the scattering length α0 and the effective range r0. We show that while for these potentials the scattering length cannot be predicted, the effective range is given by the universal low energy theorem r0 = A + B/α0 + C/α 2 0 where A,B and C depend on the dispersion coefficients Cn and the reduced di-atom mass. We confront this formula to about a hundred determinations of r0 and α0 and show why the result is dominated by the leading dispersion coefficient C6. Universality and scaling extends much beyond naive dimensional analysis estimates. Van der Waals (VdW) forces appear ubiquitously in many contexts of atomic, molecular, nuclear and particle physics. They account for long range dipole fluctuations between charge neutral atomic and molecular systems [1] with implications on the production of Bose-Einstein condensates of ultra-cold atoms and molecules [2]. The intermediate range nucleon-nucleon interaction due to two pion exchange also exhibits this VdW behaviour based on chiral symmetry [3] providing a justification for the liquid drop model of nuclei [4]. The short distance gluon exchange interaction between (colour neutral) hadrons also display this kind of interaction [5,6]. Van der Waals forces, however, diverge when naively extrapolated to short distance scales [7,8]. The study of such problems in a variety of situations will certainly shed light on the usefulness of renormalization ideas within the specific context of quantum mechanics (see e.g. Ref.[9]).Fundamental work for neutral atoms was initiated in Refs. [10,11,12] (see also [13]),within a quantum-defect theoretical viewpoint. In this letter we systematically show that these simplified approaches work and analyze why they succeed. VdW forces are extremely simple in this case and are described by the potentialwhere C n are the VdW coefficients which are computed ab initio from intensive electronic orbital atomic structure calculations (see e.g. Ref.[14] for a compilation). Usually, only the terms with n = 6, 8, 10 are retained although the series is expected to diverge asymptotically, C n ∼ n! [15]. The impressive calculation in Hydrogen up to C 32 [16] exhibits the behaviour C n ∼ (1/2) n n! at relatively low n-values. The potential (1) holds for distances much larger than the ionization length l I = / √ 2m e I (I is the ionization potential) which usually is a few a.u. In the Born-Oppenheimer approximation the quantum mechanical problem consists of solving the Schrödinger equation for the two atoms apart a distance r,where U (r) = 2µV (r)/ 2 is the reduced potential, µ = m 1 m 2 /(m 1 + m 2 ) the reduced di-atom mass, k = p/ = 2π/λ the wavenumber, and u k (r) the reduced wave function. For our purposes, it is convenient to write the reduce...

The effective theory for baryons with combined 1/N c and chiral expansions is analyzed for non-

We analyze the One Boson Exchange Potential from the point of view of Renormalization theory. We show that the nucleon-meson Lagrangean while predicting the NN force does not predict the NN scattering matrix nor the deuteron properties unambiguously due to the appearance of short distance singularities. While the problem has traditionally been circumvented by introducing vertex functions via phenomenological strong form factors, we propose to impose physical renormalization conditions on the scattering amplitude at low energies. Working in the large Nc approximation with π,σ,ρ and ω mesons we show that, once these conditions are applied, results for low energy phases of proton-neutron scattering as well as deuteron properties become largely insensitive to the form factors and to the vector mesons yielding reasonable agreement with the data and for realistic values of the coupling constants.

The Serber force has relative orbital parity symmetry and requires vanishing NN interactions in partial waves with odd angular momentum. We illustrate how this property is well fulfilled for spin triplet states with odd angular momentum and violated for odd singlet states for realistic potentials but fails for chiral potentials. The analysis is carried out in terms of partial wave sum rules for NN phase shifts, r-space potentials at long distances, and V low k potentials. We analyze how Serber symmetry can be accommodated within a large-N c perspective when interpreted as a long-distance symmetry. A prerequisite for this is the numerical similarity of the scalar and vector meson resonance masses. The conditions under which the resonance exchange potential can be approximated by a Yukawa form are also discussed. Although these masses arise as poles on the second Riemann in ππ scattering, we find that within the large-N c expansion the corresponding Yukawa masses correspond instead to a well-defined large-N c approximation to the pole that cannot be distinguished from their location as Breit-Wigner resonances.

No abstract

In this contribution, baryon axial-vector couplings are studied in the framework of the combined 1/N c and chiral expansions [1]. This framework is implemented on the basis of the emergent spinflavor symmetry in baryons at large N c and HBChPT, and linking both expansions (ξ-expansion), where 1/N c is taken to be a quantity O(p). The study is carried out including one-loop contributions, which corresponds to O(ξ 3) for baryon masses and O(ξ 2) for the axial couplings. An analysis of the Lattice QCD results for the axial couplings of both N and ∆ is presented.

Wigner and Serber symmetries for the two-nucleon system provide unique examples of long distance symmetries in Nuclear Physics, i.e. symmetries of the meson exchange forces broken only at arbitrarily small distances. We analyze the large N c picture as a key ingredient to understand these, so far accidental, symmetries from a more fundamental viewpoint. A set of sum rules for NN phase-shifts, NN potentials and coarse grained V lowk NN potentials can be derived showing Wigner SU(4) and Serber symmetries not to be fully compatible everywhere. The symmetry breaking pattern found from the partial wave analysis data, high quality potentials in coordinate space at long distances and their V lowk relatives is analyzed on the light of large N c contracted SU(4) C symmetry. Our results suggest using large N c potentials as long distance ones for the two-nucleon system where the meson exchange potential picture is justified and known to be consistent with large N c counting rules. We also show that potentials based on chiral expansions do not embody the Wigner and Serber symmetries nor do they scale properly with N c . We implement the One Boson Exchange potential realization saturated with their leading N c contributions due to π, σ , ρ and ω mesons. The short distance 1/r 3 singularities stemming from the tensor force can be handled by renormalization of the Schrödinger equation. A good description of deuteron properties and deuteron electromagnetic form factors in the impulse approximation for realistic values of the meson-nucleon couplings is achieved. International Workshop on Effective Field Theories: from the pion to the upsilon

Wigner symmetry in nuclear physics provides a unique example of a nonperturbative medium and long distance symmetry, a symmetry strongly broken at short distances. We analyze the consequences of such a concept within the framework of one-boson exchange potentials in NN scattering and keeping the leading N c contributions. Phenomenologically successful relations between singlet 1 S 0 and triplet 3 S 1 scattering phase shifts are provided in the entire elastic region. We establish symmetry breaking relations among noncentral phase shifts which are successfully fulfilled by even-L partial waves and strongly violated by odd-L partial waves, in full agreement with large N c requirements.