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Höhler, G.

doi:10.1007/10201161_87

Cited by 24 publications

(53 citation statements)

References 178 publications

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“…One way would be to fit to threshold and subthreshold parameters. Up to date, only the Karlsruhe (KA) analysis gives these consistently with the phase shifts [28]. From the point of the chiral expansion, this expansion around the center of the Mandelstam triangle together with the threshold parameters should provide the best data to fix the LECs.…”

Section: The Fitting Proceduresmentioning

confidence: 93%

“…We find (we only give the formulas for the subthreshold parameters not already given in [11]): Notice that d + 0n = a + 0n for any n. The resulting values are given in table 4. The "empirical" values based on a dispersion-theoretical continuation into the unphysical region are taken from [28]. For the VPI SP98 analysis, we have in addition [32] d + 00 = −1.…”

Section: E Subthreshold Parametersmentioning

confidence: 99%

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Pion-nucleon scattering in chiral perturbation theory (I): Isospin-symmetric case

1998

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We construct the complete effective chiral pion-nucleon Lagrangian to third order in small momenta based on relativistic chiral perturbation theory. We then perform the so-called heavy baryon limit and construct all terms up-to-and-including order 1/m 2 with fixed and free coefficients. As an application, we discuss in detail pionnucleon scattering. In particular, we show that for this process and to third order, the 1/m expansion of the Born graphs calculated relativistically can be recovered exactly in the heavy baryon approach without any additional momentum-dependent wave function renormalization. We fit various empirical phase shifts for pion laboratory momenta between 50 and 100 MeV. This leads to a satisfactory description of the phase shifts up to momenta of about 200 MeV. We also predict the threshold parameters, which turn out to be in good agreement with the dispersive analysis. In particular, we can sharpen the prediction for the isovector S-wave scattering length, 0.083We also consider the subthreshold parameters and give a short comparison to other calculations of πN scattering in chiral perturbation theory or modifications thereof.

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Section: The Fitting Proceduresmentioning

confidence: 93%

Section: E Subthreshold Parametersmentioning

confidence: 99%

Pion-nucleon scattering in chiral perturbation theory (I): Isospin-symmetric case

1998

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“…The value of a 1/2 − a 3/2 is more uncertain. The KH analysis leads to 0.274 ± 0.005 M −1 π [5] whereas the VPI group has recently given a larger value [6]. Their analysis was critically reexamined by Höhler [7].…”

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confidence: 99%

Chiral corrections to the S-wave pion-nucleon scattering lengths

Bernard¹,

Kaiser

Meißner

1993

Physics Letters B

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We calculate the chiral corrections to Weinberg's prediction for the S-wave πN scattering lengths up-to-and-including order O(M 3 π ) making use of heavy baryon chiral perturbation theory. For the isospin-odd scattering length a − these corrections are small and bring the prediction closer to the empirical value. In the case of the isospineven a + large cancellations appear so that the O(M 3 π ) result depends sensitively on certain resonance parameters which enter the calculation of the contact terms present at next-to-leading order.

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“…Other contributions to the nucleon mass come from the chromo-electric and chromo-magnetic gluon pieces and the sea terms due to the s quarks. Experimentally this matrix element has been measured from low energy π-N scattering, [1]. A delicate extrapolation to the chiral limit [2] gives a result for the isospin even amplitude of Σ/f 2 π with Σ = σ πN , from which the πN sigma term may be found.…”

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confidence: 99%

The πN sigma term — an evaluation using staggered fermions

Altmeyer

Göckeler

Horsley

et al. 1994

Nuclear Physics B - Proceedings Supplements

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A lattice calculation of the πN sigma term is described using dynamical staggered fermions. Preliminary results give a sea term comparable in magnitude to the valence term. Theoretical DiscussionPreprint HLRZ 93-70 November 1993 The πN sigma term, σ πN , is defined as that part of the mass of the nucleon coming from the expectation value of the up (u) and down (d) quark mass terms in the QCD Hamiltonian,where we have taken these quarks to have equal current mass (= m). Other contributions to the nucleon mass come from the chromo-electric and chromo-magnetic gluon pieces and the sea terms due to the s quarks. Experimentally this matrix element has been measured from low energy π-N scattering, [1]. A delicate extrapolation to the chiral limit [2] gives a result for the isospin even amplitude of Σ/f 2 π with Σ = σ πN , from which the πN sigma term may be found. The precise value obtained this way has been under discussion for many years. For orientation we shall just quote a range of results from later analyses of σ πN ≈ 56MeV, [3], down to 45MeV, [4].To estimate valence and sea contributions to σ πN , classical current algebra analyses assume octet dominance and make first order perturbation theory about the SU F (3) flavour symmetric Hamiltonian. This gives where we have first assumed that the nucleon wavefunction does not change much around the symmetric point. We then subtract and add a strange component. At the symmetric point the u and d quarks each have equal valence and sea part, while the s quark matrix element only has a sea component. Thus in the first term the sea contribution cancels, justifying the definitions given in eq. (2). Using first order perturbation theory for the baryon mass splittings σ val πN may be calculated to give σ val πN ≈ 25MeV and so σ sea πN ≈ 31 ∼ 20MeV. This in turn means that m s N |ss|N ≈ 400 ∼ 250MeV, which would indicate a sizeable portion of the nucleon mass (938MeV) comes from the strange quark contribution. Measuring σ πNWe now turn to our lattice calculation. We have generated configurations using dynamical staggered fermions on a 16 3 × 24 lattice at β = 5.35, m = 0.01 (plus some larger masses), [5]. Practically there are several possibilities open to us for the evaluation of the matrix element. The easiest is simply to differentiate the shift operator S 4 giving(the Feynman-Hellmann theorem). Thus we need to measure M N for different masses m and numerically estimate the gradient. This leads to σ πN ≈ 11.9(8)m| m=0.01 ≈ 0.12(1),

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C - H

Cited by 24 publications

References 178 publications

Pion-nucleon scattering in chiral perturbation theory (I): Isospin-symmetric case

Pion-nucleon scattering in chiral perturbation theory (I): Isospin-symmetric case

Chiral corrections to the S-wave pion-nucleon scattering lengths

The πN sigma term — an evaluation using staggered fermions

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