Indications of partial chiral symmetry restoration from pionic atoms

Friedman, E.

doi:10.1016/s0370-2693(01)01326-0

Cited by 40 publications

(56 citation statements)

References 24 publications

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“…The combined isoscalar parameter, b 0 + 0.215 ReB 0 = −0.0274 ± 0.0002, is in good agreement with that obtained in the analysis of the 205 Pb [28]. The imaginary part, ImB 0 = 0.0472 ± 0.0013, is consistent with the global-fit value of 0.055 ± 0.003 by Batty et al [26] and Friedman [29,30], considering that they included the angle-transformation (AT) term, which causes an appreciable decrease in the width [27]. In fact, the best-fit value in our analysis with the AT term included is: ImB 0 = 0.058 ± 0.003.…”

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confidence: 88%

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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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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“…This model which was shown [14,15] to explain the anomaly in pionic atoms, is denoted here by W. An alternative approach which was also shown to explain the anomaly in pionic atoms [21] is to replace E by E − V c by imposing the minimal substitution requirement [22], which is effective through the energy dependence of the isoscalar parameter b 0 . This model is denoted here by E. Finally, applying both mechanisms we have the EW model.…”

Section: Discussionmentioning

confidence: 99%

“…Large scale fits to pionic atom data encompassing the whole of the periodic table showed [14,15] that indeed the density-dependence of the pion decay constant [9] which causes the isosvector scattering amplitude to become density dependent, is capable of removing the anomaly. Similar conclusions were also presented [16,4,17,5] on the basis of very restricted data sets, consisting mainly of the recently observed 'deeply bound' states of pionic atoms.…”

Section: Introductionmentioning

confidence: 99%

Elastic scattering of low energy pions by nuclei and the in-medium isovectorπNamplitude

et al. 2005

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Measurements of elastic scattering of 21.5 MeV π ± by Si, Ca, Ni and Zr were made using a single arm magnetic spectrometer. Absolute calibration was made by parallel measurements of Coulomb scattering of muons. Parameters of a pion-nucleus optical potential were obtained from fits to all eight angular distributions put together. The 'anomalous' s-wave repulsion known from pionic atoms is clearly observed and could be removed by introducing a chiral-motivated density dependence of the isovector scattering amplitude, which also greatly improved the fits to the data. The empirical energy dependence of the isoscalar amplitude also improves the fits to the data but, contrary to what is found with pionic atoms, on its own is incapable of removing the anomaly.

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“…[10], appears to be remarkably successful [11,12] but has been debated [13,14]. Clearly, this concept needs further justification.…”

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confidence: 99%

“…An interpretation of the "missing repulsion" in terms of a possible in-medium change of the pion decay constant, as suggested in ref. [10], appears to be remarkably successful [11,12] but has been debated [13,14]. Clearly, this concept needs further justification.…”

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Chiral Dynamics of Deeply Bound Pionic Atoms

2003

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We present and discuss a systematic calculation, based on two-loop chiral perturbation theory, of the pion-nuclear s-wave optical potential. A proper treatment of the explicit energy dependence of the off-shell pion self-energy together with (electromagnetic) gauge invariance of the Klein-Gordon equation turns out to be crucial. Accurate data for the binding energies and widths of the 1s and 2p levels in pionic 205 Pb and 207 Pb are well reproduced, and the notorious "missing repulsion" in the pion-nuclear s-wave optical potential is accounted for. The connection with the in-medium change of the pion decay constant is clarified.PACS numbers: 36.10Gv Keywords: pionic atoms, nuclear matter Recent accurate data on 1s and 2p states of negatively charged pions bound to Pb nuclei [1] have set new standards and constraints for the detailed analysis of s-wave pion-nucleus interactions. This subject has a long history [2,3,4,5,6,7,8], culminating in various attempts to understand the notorious "missing repulsion": the standard ansatz for the s-wave pion-nucleus optical potential in terms of the empirical threshold πN -amplitudes times the proton and neutron densities ρ p,n , supplemented by sizeable double-scattering corrections, still misses the empirically required repulsive interaction by a large amount. On purely phenomenological grounds, this problem can be fixed by simply introducing a sufficiently large negative real part, ReB 0 , in the ρ 2 term of the pion-nuclear optical potential [6]. The arbitrariness of this procedure is of course unsatisfactory, also in view of the fact that ReB 0 cannot be calculated microscopically with sufficient accuracy, and that the high precision measurements of the real part of the pion deuteron scattering length [9] suggests a very small net ReB 0 by analogy.In the meantime, this issue has been revived in a variety of ways. An interpretation of the "missing repulsion" in terms of a possible in-medium change of the pion decay constant, as suggested in ref.[10], appears to be remarkably successful [11,12] but has been debated [13,14]. Clearly, this concept needs further justification. In the present paper we show that a key to the understanding of low-energy pion-nucleus s-wave interactions lies in its distinct energy dependence imposed by chiral symmetry, in combination with the "accidental" approximate vanishing of the isospin-even threshold πN -amplitude. Another important feature, generally ignored in previous analyses, is the systematic incorporation of gauge invariance at all places where the pion energy ω appears explicitly, when solving the Klein-Gordon equation in the presence of electromagnetic interactions.Our framework will be in-medium chiral perturbation theory at two-loop order [16]. But before going into technical details, the following simplified treatment may be useful to illustrate driving mechanisms.Consider a zero-momentum π − interacting with nuclear matter at low proton and neutron densities, ρ p and ρ n . The in-medium pion polarization operator to leading ord...

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Indications of partial chiral symmetry restoration from pionic atoms

Cited by 40 publications

References 24 publications

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

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

Elastic scattering of low energy pions by nuclei and the in-medium isovectorπNamplitude

Chiral Dynamics of Deeply Bound Pionic Atoms

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