Determination of the πN scattering lengths from pionic hydrogen

Schröder, H.-Ch.; Badertscher, A.; Goudsmit, P.F.A.; Janousch, M.; Leisi, H.J.; Matsinos, E.; Sigg, D.; Zhao, Z.G.; Chatellard, D.; Egger, J.‐P.; Jeannet, E.; Gabathuler, K.; Hauser, Peter C.; Simons, L. M.; Hassani, A.

doi:10.1016/s0370-2693(99)01237-x

Cited by 83 publications

(55 citation statements)

References 19 publications

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“…The discrepancy of our number with the experimental one of Ref. [24] possibly points toward a too conservative error assignment of the low energy phase-shifts in Ref. [22].…”

Section: A Fitting Procedurescontrasting

confidence: 90%

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S11−N(1535)and−N(1650)resonances

2001

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The s−wave meson-baryon scattering is analyzed for the strangeness S = 0 sector in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry. Four channels have been considered: πN , ηN , KΛ, KΣ. The needed two particle irreducible matrix amplitude is taken from lowest order Chiral Perturbation Theory in a relativistic formalism and low energy constants are fitted to the elastic πN phase-shifts and the π − p → ηn and π − p → K 0 Λ cross section data. The position of the complex poles in the second Riemann sheet of the scattering amplitude determine masses and widths of the S 11 − N (1535) and −N (1650) resonances, in reasonable agreement with experiment. A good overall description of data, from πN threshold up to 2 GeV, is achieved keeping in mind that the two pion production channel has not been included.

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“…The discrepancy of our number with the experimental one of Ref. [24] possibly points toward a too conservative error assignment of the low energy phase-shifts in Ref. [22].…”

Section: A Fitting Procedurescontrasting

confidence: 90%

“…This value should be compared both to the recent experimental one 0.252±0.006 fm of Ref. [24] and to the HBChPT result to third order of Ref. [14] 0.19 ± 0.05 fm.…”

Section: A Fitting Proceduresmentioning

confidence: 67%

S11−N(1535)and−N(1650)resonances

2001

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“…The lowest energy excitation modes of the condensate, so called Nambu-Goldstone bosons, are identified as pions. Their s-wave interaction with nucleons is predicted to vanish in its isoscalar part, and determined by the pion decay constant, f 2 π , in its isovector part [5,6] which is consistent with recent experimental values [7,8]. The f 2 π is also the order parameter of chiral symmetry breaking and directly connected to the magnitude of qq through the Gell-Mann-OaksRenner relation [4].…”

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confidence: 83%

Precision Spectroscopy of Pionic1sStates of Sn Nuclei and Evidence for Partial Restoration of Chiral Symmetry in the Nuclear Medium

et al. 2004

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Deeply bound 1s states of π − in 115,119,123 Sn were preferentially observed using the Sn(d, 3 He) pion-transfer reaction under the recoil-free condition. The 1s binding energies and widths were precisely determined, and were used to deduce the isovector parameter of the s-wave pion-nucleus potential to be b1 = −0.115 ± 0.007 m −1 π . The observed enhancement of |b1| over the free πN value (b free 1 /b1 = 0.78 ± 0.05) indicates a reduction of the chiral order parameter, f * π (ρ) 2 /f 2 π ≈ 0.64, at the normal nuclear density, ρ = ρ0.PACS numbers: 36.10. Gv,13.75.Gx,14.40.Aq,25.45.Hi Our work deals with characteristic properties of strongly interacting bound sytems, hadrons, consisting of light quarks (u and d). Their masses are nearly two orders of magnitude smaller (m u ≃ 5MeV, m d ≃ 8MeV) than typical hadron masses of ≈ 1 GeV. This extraordinary phenomenon is proposed to be produced by spontaneous breaking of chiral symmetry for massless quarks subject to the strong interaction [1,2,3]. It results in a ground state, the vacuum state, with a finite expectation value of quark-antiquark pairs, qq 0 ≈ −(250 MeV) 3 [4]. In such a scenario the hadrons are considered as quasi particle excitations of the condensate, qq , separated by an energy gap of ∼ 1 GeV. The lowest energy excitation modes of the condensate, so called Nambu-Goldstone bosons, are identified as pions. Their s-wave interaction with nucleons is predicted to vanish in its isoscalar part, and determined by the pion decay constant, f 2 π , in its isovector part [5,6] which is consistent with recent experimental values [7,8]. The f 2 π is also the order parameter of chiral symmetry breaking and directly connected to the magnitude of qq through the Gell-Mann-OaksRenner relation [4].We examine this chiral symmetry scenario by implanting a π − in a nuclear medium of density ρ [9, 10], where a new vacuum state with a reduced condensate, qq ρ , is proposed to be created [2]. This is the most basic case of a large effort to study the density and temperature dependence of the qq in relativistic heavy ion collisions.The density dependence of the quark condensate is expressed in the leading order by the pion-nucleon σ-term (σ N ≈ 45 MeV) in the following form [11]:which yields a reduction of about 0.65 for the normal nuclear density, ρ = ρ 0 = 0.17 fm −3 . Likewise, the pion decay constant in a medium (identified as the time component of the axial current) is reduced as [12],where the parameter α is predicted to be αρ 0 ≈ 0.45 from the chiral dynamics [13]. This reduction of the ratio is associated with the free and the in-medium isovector πN scattering length (b free 1 and b * 1 , respectively) as [14]Our program aims at measuring the isovector πN interaction parameter in the pion-nucleus potential (b * 1 (ρ)) [15] by studying deeply bound 1s states of π − in heavy N > Z nuclei [16,17,18,19,20]. Such states were predicted to be produced as discrete states by nuclear reactions [21,22,23,24,25] and to provide unique information on the s-wave interaction, where...

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“…The experimental data from where (b 0 , b 1 ) are usually extracted are the shift and width of pionic hydrogen and deuterium atoms. From the recent measurements at PSI one deduces the elastic π − p plus the π − p → π 0 n transition scattering lengths [1,2,3,4]. Using in addition the measured a π − d amplitude [4,5] in order to determine the isospin even and odd combinations…”

Section: Introductionmentioning

confidence: 99%

s-wave pion nucleon scattering lengths fromπN, pionic hydrogen, and deuteron data

2004

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The isoscalar and isovector scattering lengths (b0, b1) are determined using a unitarized coupled channel approach based on chiral Lagrangians. Using experimental values of pionic hydrogen and deuterium as well as low energy πN scattering data, the free parameters of the model are calculated. Isospin violation is incorporated to a certain extent by working with physical particle masses. For the deuterium scattering length a π − d new significant corrections concerning real and imaginary parts are evaluated, putting new constraints from π − d scattering on the values of (b0, b1). In particular, dispersion corrections, the influence of the ∆(1232) resonance, crossed terms and multiple scattering in a Faddeev approach are considered.

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Determination of the πN scattering lengths from pionic hydrogen

Cited by 83 publications

References 19 publications

S11−N(1535)and−N(1650)resonances

S11−N(1535)and−N(1650)resonances

Precision Spectroscopy of Pionic1sStates of Sn Nuclei and Evidence for Partial Restoration of Chiral Symmetry in the Nuclear Medium

s-wave pion nucleon scattering lengths fromπN, pionic hydrogen, and deuteron data

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