Extracting the σ-term from low-energy pion-nucleon scattering

Abstract

Abstract. We present an extraction of the pion-nucleon (πN ) scattering lengths from low-energy πN scattering, by fitting a representation based on RoySteiner equations to the low-energy data base. We show that the resulting values confirm the scattering-length determination from pionic atoms, and discuss the stability of the fit results regarding electromagnetic corrections and experimental normalization uncertainties in detail. Our results provide further evidence for a large πN σ-term, σ πN = 58(5) MeV, in agreement with, albeit less precise than, the determination from pionic atoms.

Direct detection rate of heavy Higgsino-like and Wino-like dark matter

“…7. There is tension between the lattice result [42] ΣπN = 40(4) MeV, and phenomenological extractions ΣπN = 59.1(3.5) MeV and ΣπN = 58(5) MeV from pionic atoms[49] and low energy pion-nucleon scattering[50]. Since the scalar matrix elements of u and d quarks represent a small contribution to the total cross section[16], our results would be essentially unchanged if a larger value, ΣπN ≈ 60 MeV, were used.…”

Evaluation of pion-nucleon sigma term in Dyson-Schwinger equation approach of QCD

“…Notably we get f π = 93 MeV with DSE1 and Eq. ( 10). In DSE4, we take the same parameter values as in DSE1.…”

“…One can notice easily from Fig. 3 [8][9][10], from chiral perturbation theory (red) [13][14][15], from Lattice QCD (magenta ) [18][19][20]22], from various other models (blue) [25,26,28] and from the DSE(green) approach [24].…”

“…Especially Refs. [9,10] give the value around 60 MeV with quite small error bars. Theoretically the pion-nucleon sigma term could be calculated in chiral perturbation theory [13][14][15][16], lattice QCD [17][18][19][20][21][22], Dyson-Schwinger Equations(DSE) approach of QCD [23,24] and various other models [25][26][27][28].…”

“…Recently, special attentions have been paid to the σ πN , since it is also significant in searching for the Higgs boson, supersymmetric particles and cold dark matter [5][6][7]. σ πN can be obtained indirectly in experiments, such as the pion-nucleon scattering or pionic atom experiments [8][9][10]. Several recent analysis [9][10][11] give 50 MeV < σ πN < 70 MeV, which is relatively larger than the widely used value σ πN ≃ 45 MeV [12].…”