日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

The existence and properties of the sigma meson have been controversial for almost six decades, despite playing a central role in the spontaneous chiral symmetry of QCD or in the nucleon-nucleon attraction. This controversy has also been fed by the strong indications that it is not an ordinary quark-antiquark meson. Here we review both the recent and old experimental data and the model independent dispersive formalisms which have provided precise determinations of its mass and width, finally settling the controversy and leading to its new name: $f_0(500)$. We then provide a rather conservative average of the most recent and advanced dispersive determinations of its pole position $\sqrt{s_\sigma}=449^{+22}_{-16}-i(275\pm12)$. 
In addition, after comprehensive introductions, we will review within the modern perspective of effective theories and dispersion theory, its relation to chiral symmetry, unitarization techniques, its quark mass dependence, popular models, as well as the recent strong evidence, obtained from the QCD $1/N_c$ expansion or Regge theory, for its non ordinary nature in terms of quarks and gluons.

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From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance

We present improved nucleon-nucleon potentials derived in chiral effective field theory up to next-to-next-to-next-to-leading order. We argue that the nonlocal momentum-space regulator employed in the two-nucleon potentials of previous works (Nucl. Phys. A 747, 362 (2005) and Phys. Rev. C 68, 041001 (2003)) is not the most efficient choice, in particular since it affects the long-range part of the interaction. We are able to significantly reduce finite-cutoff artefacts by using an appropriate regularization in coordinate space which maintains the analytic structure of the amplitude. The new potentials do not require the additional spectral function regularization employed in (Nucl. Phys. A 747, 362 (2005)) to cut off the short-range components of the two-pion exchange and make use of the low-energy constants ci and di determined from pion-nucleon scattering without any fine tuning. We discuss in detail the construction of the new potentials and convergence of the chiral expansion for two-nucleon observables. We also employ a simple approach for estimating the theoretical uncertainty in few-nucleon calculations from the truncation of the chiral expansion that replaces previous reliance on cutoff variation.

Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order

We present improved nucleon-nucleon potentials derived in chiral effective field theory up to next-to-next-to-next-to-leading order. We argue that the nonlocal momentum-space regulator employed in the two-nucleon potentials of Refs. [E. Epelbaum, W. Gloeckle, U.-G. Mei{\ss}ner, Nucl. Phys. A747 (2005) 362], [D.R. Entem, R. Machleidt, Phys. Rev. C68 (2003) 041001] is not the most efficient choice, in particular since it affects the long-range part of the interaction. We are able to significantly reduce finite-cutoff artefacts by using an appropriate regularization in coordinate space which maintains the analytic structure of the amplitude. The new potentials do not require the additional spectral function regularization employed in Ref. [E. Epelbaum, W. Gloeckle, U.-G. Mei{\ss}ner, Nucl. Phys. A747 (2005) 362] to cut off the short-range components of the two-pion exchange and make use of the low-energy constants c_i and d_i determined from pion-nucleon scattering without any fine tuning. We discuss in detail the construction of the new potentials and convergence of the chiral expansion for two-nucleon observables. We also introduce a new procedure for estimating the theoretical uncertainty from the truncation of the chiral expansion that replaces previous reliance on cutoff variation.

From controversy to precision on the sigma meson: A review on the status of the non-ordinary f(0)(500) resonance

In this study, we construct a coordinate-space chiral potential, including Δ-isobar intermediate states in its two-pion-exchange component up to order Q3 (Q denotes generically the low momentum scale). The contact interactions entering at next-to-leading and next-to-next-to-next-to-leading orders (Q2 and Q4, respectively) are rearranged by Fierz transformations to yield terms at most quadratic in the relative momentum operator of the two nucleons. The low-energy constant multiplying these contact interactions are fitted to the 2013 Granada database, consisting of 2309 pp and 2982 np data (including, respectively, 148 and 218 normalizations) in the laboratory-energy range 0–300 MeV. For the total 5291 $pp$ and $np$ data in this range, we obtain a Χ2 /datum of roughly 1.3 for a set of three models characterized by long- and short-range cutoffs, RL and RS respectively, ranging from (RL,RS)=(1.2,0.8) fm down to (0.8,0.6) fm. The long-range (short-range) cutoff regularizes the one- and two-pion exchange (contact) part of the potential.

/pdf/minimally-nonlocal-nucleon-nucleon-potentials-with-chiral-2fmt4vm521.pdf

Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange including Δ resonances

Using the delta-shell representation we present a successful fit to neutron-proton and proton-proton scattering data below pion production threshold. A detailed overview of the theory necessary to calculate observables with this potential is presented. A new data selection process is used to obtain the largest mutually consistent data base. The analysis includes data within the years 1950 to 2013. Using 46 parameters we obtain chi^2/Ndata = 1.04 with Ndata = 6713 including normalization data. Phase shifts with error bars are provided.

Coarse-grained potential analysis of neutron-proton and proton-proton scattering below the pion production threshold

Using the δ -shell representation we present a successful fit to neutron-proton and proton-proton scattering data below pion production threshold. A detailed overview of the theory necessary to calculate observables with this potential is presented. A new data selection process is used to obtain the largest mutually consistent data base. The analysis includes data within the years 1950 to 2013. Using 46 parameters we obtain χ/Ndata = 1.04 with Ndata = 6713 including normalization data. Phase shifts with error bars are provided.

/pdf/coarse-grained-potential-analysis-of-neutron-proton-and-11q978vanz.pdf

Nucleon-nucleon potentials are common in nuclear physics and are determined from a finite number of experimental data with limited precision sampling the scattering process. We study the statistical assumptions implicit in the standard least-squares ${\ensuremath{\chi}}^{2}$ fitting procedure and apply, along with more conventional tests, a tail-sensitive quantile-quantile test as a simple and confident tool to verify the normality of residuals. We show that the fulfillment of normality tests is linked to a judicious and consistent selection of a nucleon-nucleon database. These considerations prove crucial to a proper statistical error analysis and uncertainty propagation. We illustrate these issues by analyzing about 8000 proton-proton and neutron-proton scattering published data. This enables the construction of potentials meeting all statistical requirements necessary for statistical uncertainty estimates in nuclear structure calculations.

/pdf/statistical-error-analysis-for-phenomenological-nucleon-34c23ggd3a.pdf

Statistical error analysis for phenomenological nucleon-nucleon potentials

We undertake a simultaneous partial wave analysis of proton-proton and neutron-proton scattering data below the pion production threshold up to laboratory energies of $350\phantom{\rule{4.pt}{0ex}}\text{MeV}$. We represent the interaction as a sum of $\ensuremath{\delta}$ shells in configuration space below $3\phantom{\rule{4.pt}{0ex}}\text{fm}$ and a charge dependent one pion exchange potential above $3\phantom{\rule{4.pt}{0ex}}\text{fm}$ together with electromagnetic effects. We obtain a chi square value of 2813, for pp, and 3985, for nn, with a total of 2747 and 3691 pp and nn data, respectively, obtained till 2013 and a total number of 46 fitting parameters yielding a chi square value by degree of freedom of ${\ensuremath{\chi}}^{2}/\mathrm{d}.\mathrm{o}.\mathrm{f}=1.06$. Special attention is payed to estimate the errors of the phenomenological interaction as well as the derived effects on the phase shifts and scattering amplitudes.

/pdf/partial-wave-analysis-of-nucleon-nucleon-scattering-below-36777d5olt.pdf

R. Navarro Pérez

Papers

Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange including Δ resonances

Coarse-grained potential analysis of neutron-proton and proton-proton scattering below the pion production threshold

Coarse-grained potential analysis of neutron-proton and proton-proton scattering below the pion production threshold

Statistical error analysis for phenomenological nucleon-nucleon potentials

Partial-wave analysis of nucleon-nucleon scattering below the pion-production threshold