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

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

Deconstructing 1S0 nucleon-nucleon scattering

A distorted-wave method is used to analyse nucleon-nucleon scattering in the 1S0 channel. Effects of one-pion exchange are removed from the empirical phase shift to all orders by using a modified effective-range expansion. Two-pion exchange is then subtracted in the distorted-wave Born approximation, with matrix elements taken between scattering waves for the one-pion exchange potential. The residual short-range interaction shows a very rapid energy dependence for kinetic energies above about 100 MeV, suggesting that the breakdown scale of the corresponding effective theory is only 270MeV. This may signal the need to include the Delta resonance as an explicit degree of freedom in order to describe scattering at these energies. An alternative strategy of keeping the cutoff finite to reduce large, but finite, contributions from the long-range forces is also discussed.Comment: 10 pages, 2 figures (introduction revised, references added; version to appear in EPJA

Causality bounds for neutron-proton scattering

We consider the constraints of causality and unitarity for the low-energy interactions of protons and neutrons. We derive a general theorem that non-vanishing partial-wave mixing cannot be reproduced with zero-range interactions without violating causality or unitarity. We define and calculate interaction length scales which we call the causal range and the Cauchy-Schwarz range for all spin channels up to J = 3. For some channels we find that these length scales are as large as 5 fm. We investigate the origin of these large lengths and discuss their significance for the choice of momentum cutoff scales in effective field theory and universality in many-body Fermi systems.Comment: 36 pages, 10 figures, 7 tables, version to appear in Eur. Phys. J.

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

Nuclear forces from chiral EFT: The unfinished business

In spite of the great progress we have seen in recent years in the derivation of nuclear forces from chiral effective field theory (EFT), some important issues are still unresolved. In this contribution, we discuss the open problems which have particular relevance for microscopic nuclear structure, namely, the proper renormalization of chiral nuclear potentials and sub-leading many-body forces.Comment: 16 pages, 3 figures; contribution to J. Phys. G, Special Issue, Focus Section: Open Problems in Nuclear Structur

Active commuting is associated with a lower risk of obesity, diabetes and metabolic syndrome in Chilean adults

Background: There is limited evidence on how active commuting is associated with health benefits in developing countries. The aim of this study therefore was to investigate the associations between active commuting and markers of adiposity and cardiometabolic risk in the Chilean adult population. Methods: In total, 5157 participants from the Chilean National Health Survey 2009–10 were included in this cross-sectional study. Active commuting was measured using the Global Physical Activity Questionnaire (GPAQ v2). Body mass index (BMI) and waist circumference (WC) were measured and used to define obesity and central obesity. Type 2 diabetes (T2D) and metabolic syndrome were determined using WHO and updated ATPIII-NCEP criteria, respectively. Results: The main finding of this study is that a 30 min increase in active commuting is associated with lower odds for BMI > 25.0 kg m−2 (0.93 [95% CI: 0.88–0.98, P = 0.010]). Similarly, the odds for central obesity was 0.87 [0.82–0.92, P < 0.0001]. Similar associations were found for T2D (0.81 [0.75–0.88], P < 0.0001) and metabolic syndrome (OR: 0.86 [0.80–0.92], P < 0.0001). Conclusion: Our findings show that active commuting is associated with lower adiposity and a healthier metabolic profile including lower risk for obesity, diabetes and metabolic syndrome

Joint effect of physical activity and sedentary behaviour on cardiovascular risk factors in Chilean adults

Background: To investigate the associations between combined categories of moderate-to-vigorous physical activity (MVPA) and sedentary behaviour (SB) with markers of adiposity and cardiovascular risk in adults. Methods: Overall, 5040 participants (mean age 46.4 years and 59.3% women) from the cross-sectional Chilean National Health Survey 2009–2010 were included in this study. MVPA and SB were measured using the Global Physical Activity questionnaire. Four categories were computed using MVPA- and SB-specific cut-offs (‘High-SB & Active’, ‘Low-SB & Active’, ‘High-SB & Inactive’ and ‘Low-SB & Inactive’). Results: Compared to the reference group (‘High-SB & Inactive’), those in ‘High-SB & Active’ and ‘Low-SB & Active’ were less likely to have an obese BMI (OR: 0.67 [0.54; 0.85], P = 0.0001 and 0.74 [0.59; 0.92] P = 0.0007, respectively) and less likely to have metabolic syndrome (OR: 0.63 [0.49; 0.82], P < 0.0001 and 0.72 [0.57; 0.91], P = 0.007), central obesity (OR: 0.79 [0.65; 0.96], P = 0.016 and 0.71 [0.59; 0.84], P < 0.0001), diabetes (OR: 0.45 [0.35; 0.59], P < 0.0001 and 0.44 [0.34; 0.56], P < 0.0001) and hypertension (OR: 0.52 [0.43; 0.63], P < 0.0001 and 0.60 [0.50; 0.72], P < 0.0001), respectively. Conclusions: Being physically active and spending less time in SBs was associated with lower adiposity and improvements in cardiovascular risk factors

The Inverse Amplitude Method in ππ\pi\pi Scattering in Chiral Perturbation Theory to Two Loops

The inverse amplitude method is used to unitarize the two loop $\pi\pi$ scattering amplitudes of SU(2) Chiral Perturbation Theory in the $I=0,J=0$, $I=1,J=1$ and $I=2,J=0$ channels. An error analysis in terms of the low energy one-loop parameters $\bar l_{1,2,3,4,}$ and existing experimental data is undertaken. A comparison to standard resonance saturation values for the two loop coefficients $\bar b_{1,2,3,4,5,6}$ is also carried out. Crossing violations are quantified and the convergence of the expansion is discussed.Comment: (Latex, epsfig) 30 pages, 13 figures, 8 table

Towards a high precision calculation for the pion-nucleus scattering lengths

We calculate the leading isospin conserving few-nucleon contributions to pion scattering on $^2$H, $^3$He, and $^4$He. We demonstrate that the strong contributions to the pion-nucleus scattering lengths can be controlled theoretically to an accuracy of a few percent for isoscalar nuclei and of 10% for isovector nuclei. In particular, we find the $\pi$-$^3$He scattering length to be $(62 \pm 4\pm 7)\times 10^{-3} m_{\pi}^{-1}$ where the uncertainties are due to ambiguities in the $\pi$-N scattering lengths and few-nucleon effects, respectively. To establish this accuracy we need to identify a suitable power counting for pion-nucleus scattering. For this purpose we study the dependence of the two-nucleon contributions to the scattering length on the binding energy of $^2$H. Furthermore, we investigate the relative size of the leading two-, three-, and four-nucleon contributions. For the numerical evaluation of the pertinent integrals, aMonte Carlo method suitable for momentum space is devised. Our results show that in general the power counting suggested by Weinberg is capable to properly predict the relative importance of $N$-nucleon operators, however, it fails to capture the relative strength of $N$- and $(N+1)$-nucleon operators, where we find a suppression by a factor of 5 compared to the predicted factor of 50. The relevance for the extraction of the isoscalar $\pi$-N scattering length from pionic $^2$H and $^4$He is discussed. As a side result, we show that beyond the calculation of the $\pi$-$^2$H scattering length is already beyond the range of applicability of heavy pion effective field theory.Comment: 24 pages, 14 figures, 10 table