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Register a new userLow-energy theorems for nucleon-nucleon scattering at $M_{pi}=450$ MeV
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We apply the low-energy theorems to analyze the recent lattice QCD results for the two-nucleon system at a pion mass of $M_pisimeq 450$ MeV obtained by the NPLQCD collaboration. We find that the binding energies of the deuteron and dineutron are inconsistent with the low-energy behavior of the corresponding phase shifts within the quoted uncertainties and vice versa. Using the binding energies of the deuteron and dineutron as input, we employ the low-energy theorems to predict the phase shifts and extract the scattering length and the effective range in the $^3S_1$ and $^1S_0$ channels. Our results for these quantities are consistent with those obtained by the NPLQCD collaboration from effective field theory analyses but are in conflict with their determination based on the effective-range approximation.
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The interactions between two octet baryons are studied at low energies using lattice QCD (LQCD) with larger-than-physical quark masses corresponding to a pion mass of $m_{pi}sim 450$ MeV and a kaon mass of $m_{K}sim 596$ MeV. The two-baryon systems that are analyzed range from strangeness $S=0$ to $S=-4$ and include the spin-singlet and triplet $NN$, $Sigma N$ ($I=3/2$), and $XiXi$ states, the spin-singlet $SigmaSigma$ ($I=2$) and $XiSigma$ ($I=3/2$) states, and the spin-triplet $Xi N$ ($I=0$) state. The $s$-wave scattering phase shifts, low-energy scattering parameters, and binding energies when applicable, are extracted using Luschers formalism. While the results are consistent with most of the systems being bound at this pion mass, the interactions in the spin-triplet $Sigma N$ and $XiXi$ channels are found to be repulsive and do not support bound states. Using results from previous studies at a larger pion mass, an extrapolation of the binding energies to the physical point is performed and is compared with experimental values and phenomenological predictions. The low-energy coefficients in pionless EFT relevant for two-baryon interactions, including those responsible for $SU(3)$ flavor-symmetry breaking, are constrained. The $SU(3)$ symmetry is observed to hold approximately at the chosen values of the quark masses, as well as the $SU(6)$ spin-flavor symmetry, predicted at large $N_c$. A remnant of an accidental $SU(16)$ symmetry found previously at a larger pion mass is further observed. The $SU(6)$-symmetric EFT constrained by these LQCD calculations is used to make predictions for two-baryon systems for which the low-energy scattering parameters could not be determined with LQCD directly in this study, and to constrain the coefficients of all leading $SU(3)$ flavor-symmetric interactions, demonstrating the predictive power of two-baryon EFTs matched to LQCD.
We analyze the peripheral structure of the nucleon-nucleon interaction for LAB energies below 350 MeV. To this end we transform the scattering matrix into the impact parameter representation by analyzing the scaled phase shifts $(L+1/2) delta_{JLS} (p)$ and the scaled mixing parameters $(L+1/2)epsilon_{JLS}(p)$ in terms of the impact parameter $b=(L+1/2)/p$. According to the eikonal approximation, at large angular momentum $L$ these functions should become an universal function of $b$, {it independent} on $L$. This allows to discuss in a rather transparent way the role of statistical and systematic uncertainties in the different long range components of the two-body potential. Implications for peripheral waves obtained in chiral perturbation theory interactions to fifth order (N5LO) or from the large body of NN data considered in the SAID partial wave analysis are also drawn from comparing them with other phenomenological high-quality interactions, constructed to fit scattering data as well. We find that both N5LO and SAID peripheral waves disagree more than $5 sigma$ with the Granada-2013 statistical analysis, more than $ 2 sigma$ with the 6 statistically equivalent potentials fitting the Granada-2013 database and about $1 sigma $ with the historical set of 13 high-quality potentials developed since the 1993 Nijmegen analysis.
We calculate the lambda-nucleon scattering phase shifts and mixing angles by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory. Scattering amplitudes are obtained by solving the corresponding coupled-channel integral equations that have a milder ultraviolet behavior compared to their non-relativistic analogs. This allows us to consider the removed cutoff limit in our leading-order calculations also in the $^3P_0$ and $^3P_1$ partial waves. We find that, in the framework we are using, at least some part of the higher-order contributions to the baryon-baryon potential in these channels needs to be treated nonperturbatively and demonstrate how this can be achieved in a way consistent with quantum field theoretical renormalization for the leading contact interactions. We compare our results with the ones of the non-relativistic approach and lattice QCD phase shifts obtained for non-physical pion masses.
Energy-dependent and single-energy fits to the existing nucleon-nucleon database have been updated to incorporate recent measurements. The fits cover a region from threshold to 3 GeV, in the laboratory kinetic energy, for proton-proton scattering, with an upper limit of 1.3 GeV for neutron-proton scattering. Experiments carried out at the COSY-WASA and COSY-ANKE facilities have had a significant impact on the partial-wave solutions. Results are discussed in terms of both partial-wave and direct reconstruction amplitudes.
We examine the results of Chiral Effective Field Theory ($chi$EFT) for the scalar- and spin-dipole polarisabilities of the proton and neutron, both for the physical pion mass and as a function of $m_pi$. This provides chiral extrapolations for lattice-QCD polarisability computations. We include both the leading and sub-leading effects of the nucleons pion cloud, as well as the leading ones of the $Delta(1232)$ resonance and its pion cloud. The analytic results are complete at N$^2$LO in the $delta$-counting for pion masses close to the physical value, and at leading order for pion masses similar to the Delta-nucleon mass splitting. In order to quantify the truncation error of our predictions and fits as $68$% degree-of-belief intervals, we use a Bayesian procedure recently adapted to EFT expansions. At the physical point, our predictions for the spin polarisabilities are, within respective errors, in good agreement with alternative extractions using experiments and dispersion-relation theory. At larger pion masses we find that the chiral expansion of all polarisabilities becomes intrinsically unreliable as $m_pi$ approaches about $300;$MeV---as has already been seen in other observables. $chi$EFT also predicts a substantial isospin splitting above the physical point for both the electric and magnetic scalar polarisabilities; and we speculate on the impact this has on the stability of nucleons. Our results agree very well with emerging lattice computations in the realm where $chi$EFT converges. Curiously, for the central values of some of our predictions, this agreement persists to much higher pion masses. We speculate on whether this might be more than a fortuitous coincidence.
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