Determination of the hadronic width of the ground state in pionic hydrogen

In a new high-precision experiment at the Paul Scherrer Institut (PSI), the hadronic shift (ε _1s) and width (Γ_1s) of the ground state of pionic hydrogen, which are directly connected to the pion-nucleon isospin scattering lengths, were remeasured (PSI-Experiment R-98-01 Gotta et al. 1998). The results can be confronted with recent work of effective field theories defined in the low-energy limit of quantum chromodynamics (QCD), such as, e. g., chiral perturbation theory (ChPT). In addition, Γ_1s is connected to the pion-nucleon coupling constant f _πN. A precisely known value for f _πN allows an accurate determination of the Goldberger-Treiman discrepancy, which constitutes a measure of chiral symmetry breaking. This contribution is mainly devoted to describe a method for an accurate extraction of the hadronic width from the π ^??H data.     

A study of the centrally produced π+π−π0 system formed in the reactionpp→p f (π+π−π0)p s at 300 GeV/c

The reactionpp→p _f (π⁺π^?π⁰)p _s , where the π⁺π^?π⁰ system is centrally produced, has been studied at 300 GeV/c. The π⁺π^?π⁰ mass spectrum shows evidence for the η, ω anda ₂ (1320) as well as an enhancement in thea ₁ (1260) region. A Dalitz plot analysis of the π⁺π^?π⁰ system has been performed. Thea ₁ (1260) parameters coming from the fit of the 1⁺ S wave arem=1208±15 MeV and Γ=430±50 MeV. No evidence is found for theh ₁(1170) orh ₁(1380).     

Scattering lengths of pionic 3He and 4He

Scattering lengths of pionic ³He and ⁴He and the charge exchange contribution to the 1s width of pionic ³He are calculated within the fixed scatterer approximation of the multiple scattering formalism. Particular attention is focussed on the nuclear physics part and on πN p-wave contributions. For the first time triple scattering and double-spin-flip contributions have been included. We find significant deviations from previous estimates and calculations. Good agreement is achieved with the experimental π^?3He scattering length, whereas in the case of ⁴He a repulsive dispersion contribution is clearly needed. We propose to use the measured 1s level shift of pionic ³He as a constraint to deduce a precise value of the isoscalar πN scattering length. Furthermore, we find that multiple scattering reduces the impulse approximation value for Γ_1s(π^?3He → π^{0 3}H) by more thsn 20 %. This result casts some doubt on impulse approximation calculations of radiative pion capture as well.     

Pionic deuterium

The strong-interaction shift ε _1s ^πD and broadening Γ _1s ^πD in pionic deuterium have been determined in a high statistics study of the πD(3p-1s) X-ray transition using a high-resolution crystal spectrometer. The pionic deuterium shift will provide constraints for the pion-nucleon isospin scattering lengths extracted from measurements of shift and broadening in pionic hydrogen. The hadronic broadening is related to pion absorption and production at threshold. The results are ε _1s ^πD = (?2356 ± 31) meV (repulsive) and Γ _1s ^πD meV yielding for the complex πD scattering length a _πD = [?(24.99±0.33)+i(6.22 _?0.26 ^+0.12 )] × 10^?3 m _π ^?1 . From the imaginary part, the threshold parameter for pion production is obtained to be α = (251 _?11 ⁺⁵ ) μb. This allows, in addition, and by using results from pion absorption in ³He at threshold, the determination of the effective couplings g ₀ and g ₁ for s-wave pion absorption on isoscalar and isovector NN pairs.     

Chiral symmetry probed with pionic atoms

Study of pionic atom has been revisited by a recent discovery of deeply bound pionic states in the context of possible sensitivity to the partial chiral restoration in the nuclear medium. Precisely measured binding energies and widths of the deeply bound π^? Is states in ^115,119,123Sn in ^116,120,124Sn(d,³He) reactions at recoil-free conditions are used to deduce the medium-modified isovector scattering amplitude as b₁ = 0.115 ± 0.007m _π ^?1. The observed enhancement of b ₁ over the free πN value infers 34% reduction of $\left\langle {\bar qq} \right\rangle $ at the normal nuclear density, ρ = 0.17 fm^?3.     

The influence of inelastic πω channel on pion form factor at s<(mω + mπ)2

It is shown that F_π(s) can be calculated in a model independent way if one knows the phase δ₁ and the inelasticity η of the p-wave ππ scattering and also F_π and the form factor of the γ¹ → π°ω transition for s> (m_ω + m_π)². The correction on F_π(s) for s< (m_ω + m_π)² due to the πω state with a strong ?′(1250) allows to explain the discrepancy between ?-dominance predictions and the experimental data.     

The strong interaction shift and width of the ground state of pionic hydrogen

The 3p-1s transition in pionic hydrogen was investigated with a high-resolution crystal spectrometer system. From the precisely measured transition energy, together with the (calculated) electromagnetic energy, the strong interaction shift of the 1s state was obtained as ϵ_1s = −7.127 ± 0.028(stat.)± 0.036(syst.) eV (attractive). From the natural line width, measured for the first time, we determine the decaywidth of the 1s state: Γ_1s^(decay) = 0.97 ± 0.10(stat.)± 0.05(syst.) eV. With the recently calculated electromagnetic corrections the s-wave scattering lengths of an isospin symmetric strong interaction are deduced. The scattering length for elastic scattering of a negative pion on a proton is a_{π⁻p→π⁻p}^h = 0.0885±0.00003(stat.)±0.0006(syst.)m_π⁻¹. The scattering lengthe for single charge exchange is found to be a_{π⁻p→π⁰n}^h = −0.136 ± 0.007(stat.) ± 0.003(syst.)m_π⁻¹.The experiment was performed at the Paul Scherrer Institute (PSI) in Switzerland. A focussing crystal spectrometer with an array of bent crystals, the cyclotron trap (a magnetic system designed to increase the particle stop density) and a CCD (charge-coupled device) detector system were employed. The results from the pionic hydrogen experiment — together with those from the pionic deuterium experiment — were used to test the isospin symmetry of the strong interaction. The present data are still consistent with isospin sysmmetry.     

The Pionic Hydrogen Experiment at PSI

The measurement of the strong-interaction effects in pionic hydrogen gives access to fundamental properties of the pion–nucleon interaction. Methods developed within the framework of Heavy-Baryon Chiral Perturbation Theory allow calculations with an accuracy of a few per cent, which should be tested by experiment. Techniques advanced for recent experiments on the precision spectroscopy of X-rays from antiprotonic and pionic atoms will be used in a new series of measurements for pionic hydrogen. The aim is to achieve finally an accuracy of 0.2% for the hadronic shift ∈_1s and most important of about 1% for the broadening Γ_1s . An essential part of the experimental program is an improved understanding of the atomic cascade. At first, the value of ∈_1s has to be proven not to be influenced by molecular formation. Secondly, a more accurate determination of Γ_1s requires a detailed study of Coulomb deexcitation. This revised version was published online in August 2006 with corrections to the Cover Date.     

The formation of the superheavy hydrogen isotope <Superscript>6</Superscript>H in the absorption of stopped π<Superscript>−</Superscript>-mesons by nuclei

An experimental search for the superheavy hydrogen isotope ⁶H was conducted through studying the absorption of stopped π^?-mesons by ⁹Be and ¹¹B nuclei. A structure in the missing mass spectrum caused by the resonance states of ⁶H was observed in three reaction channels, namely, ⁹Be(π^?, pd)X, ¹¹B(π^?, d³He)X, and ¹¹B(π^?, p⁴He)X. The parameters of the lowest state E_r=6.6±0.7 MeV and Γ=5.5±2.0 MeV (E_r is the resonance energy with respect to the disintegration into the triton and three neutrons) are evidence that ⁶H is a more weakly bound system than ⁴H and ⁵H. Three excited states of ⁶H were observed. Their resonance levels (E_1r=10.7±0.7 MeV, Γ_1r=4±2 MeV, E_2r=15.3±0.7 MeV, Γ _2r=3±2 MeV, and E_3r=21.3±0.4 MeV, Γ_3r=3.5±1.0 MeV) are energetically capable of disintegrating into six free nucleons.     

Pionic charge exchange on the proton from 40 to 250 MeV

The total cross sections for pionic charge exchange on hydrogen were measured using a transmission technique on thin CH₂ and C targets. Data were taken for π⁻${\pi }^{-}$ lab energies from 39 to 247 MeV with total errors of typically 2% over the Δ-resonance and up to 10% at the lowest energies. Deviations from the predictions of the SAID phase shift analysis in the 60–80 MeV region are interpreted as evidence for isospin-symmetry breaking in the s-wave amplitudes. The charge dependence of the Δ-resonance properties appears to be smaller than previously reported.     

Highly resolved electronic spectra and electronic structure of benzo[f]quinoxaline

Vibrational analysis of highly resolved phosphorescence (P), flourescence (F) and absorption spectra of benzo[f]quinoxaline (BQ) in Shpolskii matrices, at 77 K, was carried out. The spectra were dominated by phenanthrene-type fundamental vibrations. The appearance of several out-of-plane (op) modes in the P spectrum as well as the P lifetime, much shortened relative to that of the parent hydrocarbon, point to the proximity of the lowest n, π¹ and π, π¹ states of the BQ molecule. High activity of op modes in the F spectrum and complex structure of the absorption spectrum onset have been explained in terms of the pseudo-Jahn-Teller interaction between close-lying S₁ (π, π¹)and S₂(n, π¹) states.According to calculations of the BQ electronic structure, performed using a modified INDO CI method, the T₁(π, π¹)-T₂(n, π¹) and S₁(π, π¹-S₂(n, π¹) energy gaps are about 1200 and 700 cm^-1, respectively.     

Pions in the light-cone nucleon and electromagnetic form factors

The light-cone Fock-state decomposition of the nucleon involves pion-quark core (π′N′ andπ′Δ′) components. The size of the quark core is at present of special importance for the analysis of the onset of colour transparency in the A(e,e′p) reactions. With the light-coneNπ′N′ andNπ′Δ′ vertex functions deduced from experimental data on high-energy proton fragmentation into nucleons and isobars, we evaluate the effect of the pionic cloud on the electromagnetic form factors of nucleons. We find the quark core radius to be about 10% smaller than the nucleon's radius. Analysis of the renormalization of the total nucleon-nucleon cross section for the presence of the pionic cloud suggests a similar core radius.     

Highly resolved electronic absorption and luminescence spectra of some phenanthrolines in Shpolskii matrices: Part II. Fluorescence and S1←S0 absorption spectra

Highly resolved fluorescence and S₁←S₀ absorption spectra of some phenanthrolines in n-alkane matrices were obtained at 77 K. The vibrational analysis of the spectra was carried out. Mirror symmetry distortions of the fluorescence and absorption spectra were attributed to vibronic coupling between ¹(π, π¹) states. It was shown that vibronic mixing of S₁(π, π¹) and S₂(π, π¹) states occurs in phenanthroline molecules with S₁-S₂ energy gap not exceeding 3000 cm^-1 (i.e., 4,7-, 1,7- and 1,10-Phen), whereas in other phenanthrolines the coupling of S₁ and S₃(π, π¹) plays a dominant role. Fluorescence quantum yields of phenanthroline liquid solutions were measured. Changes of luminescence efficiencies due to the change of the polarity of the media point to a weak coupling of the lowest ¹(π, π¹) and ¹(n, π¹) states.     

Structural dynamics of 4‐cyanobenzaldehyde in S2(ππ*) state

The excited state structural dynamics of 4‐cyanobenzaldehyde (p‐CNB) were studied by using the resonance Raman spectroscopy and the quantum mechanical calculations. The experimental A‐ and B‐band absorptions were, respectively, assigned to the major n_O → π₃* and π₂ → π₃* transitions according to the B3LYP‐TD/6‐31G(d) and CIS/6‐31G(d) computations, and the resonance Raman spectra. It was determined that the actual S₂(π₂π₃) state was in energy lower than S₃(π₁π₃), which was just opposite to the B3LYP‐TD/6‐31G(d) calculated order of the S₂(π₁π₃) and S₃(π₂π₃). The vibrational assignments were carried out for the A‐ and B‐band resonance Raman spectra. The B‐band resonance Raman intensities of p‐CNB were dominated by the C2–C3/C5–C6 symmetric stretch mode ν₈, the overtones nν₈ and their combination bands with the ring C–H bend mode ν₁₇, the C9–N10 stretch mode ν₆, the C7–O8 stretch mode ν₇ and the remaining modes. The conical intersection between S₁(n_Oπ₃) and S₂(π₂π₃) states of p‐CNB was determined at complete active space self‐consistent field (CASSCF)(8,7)/6‐311G(d,p) level of theory. The B‐band short‐time structural dynamics and the corresponding decay dynamics of p‐CNB were obtained by analysis of the resonance Raman intensity pattern and CASSCF computations. The resonance Raman spectra indicated that CI[S₁(n_Oπ₃)/S₂(π₁π₂π₃π₄)] located nearby the Franck–Condon region. The excited state decay dynamics evolving from the S_{2, FC}(π₂π₃) to the S₁(n_Oπ₃) state was proposed. Copyright © 2013 John Wiley & Sons, Ltd.     

Study of the π+π+π-π- system centrally 0 produced by incident π+ andp beams at 85 GeV/c

The reactions π⁺ p→π⁺(π⁺π⁺π^-π^-)p andpp→p(π⁺π⁺π^-π^-)p, where the (π⁺ π⁺ π^- π^-) system is centrally produced have been studied at 85 GeV/c. The π⁺π⁺π^-π^- mass spectrum shows evidence for thef ₁ (1285) meson with a mass of 1278±2 MeV and width 41±12 MeV which decays mainly through ρ⁰(770)π⁺π^-. Thef ₁(1285) is also observed in the ηπ⁺π^- channel. There is no significant evidence for ηππ or 4π decay modes of thef ₁(1420). The ρ⁰ρ⁰ production is found to be small. A Dalitz plot analysis of the 3π system shows evidence fora ₂ (1320) production and for a large contribution of theJ ^PC=1⁺⁺ ρπ wave.     

Study of the ηπ+π− system centrally producedin the reactionpp→p f (ηπ+π−)p s at 300 GeV/c

The reactionpp→p _f (ηπ⁺π^?)p _s where the ηπ⁺π^? system is centrally produced has been studied at 300 GeV/c incident momentum at the CERN Ω spectrometer. The ηπ^± mass spectrum shows a strong δ/a ₀(980) signal having a mass of 984±4 and Γ=95±14 MeV. The ηπ⁺π^? mass spectrum shows η′ andf ₁(1285) signals over little background. A spin-parity analysis of the ηπ⁺π^? system shows evidence for aJ ^PC =1⁺⁺ peak at thef ₁(1285) mass but no evidence for the pseudoscalar states η(1270) andl/η(1440). No evidence is found for the ηππ decay of theE/f ₁(1420) meson for which we set an upper limit BR(E/f ₁(1420)→ηππ)<0.1 at 95% cl.     

Study of process e + e − → π+π−π0π0 at energies √s < 1 GeV with the spherical neutral detector

The cross section for the process e ⁺ e ^? → π⁺π^?π⁰π⁰ has been measured in an experiment with a spherical neutral detector, with the cross section at energies √s < 920 MeV having been measured for the first time. The model of vector dominance describes well the data obtained if the ρ, ρ′, and ρ″ resonances are taken into account. The probability of the decay ρ → π⁺π^?π⁰π⁰ is B(ρ → π⁺π^?π⁰π⁰) = (1.60 ± 0.74 ± 0.18) × 10^?5. The upper limit for the decay ω → π⁺π^?π⁰π⁰ has been improved by two orders of magnitude compared to previous measurements and is B(ω → π⁺π^?π⁰π⁰) < 2 × 10^?4 at a 90% confidence level.     

On mesonic interference phenomena in deep inelastic scattering

Possible effects of a π′ contribution to lepton deep-inelastic scattering (DIS) are analyzed. The exchange of the first radial excitation of the pion (π′(0^?)) has been advocated recently to solve the notorious problem of hard vertex form factors innucleon-nucleon scattering. The π′-meson exchange contribution is calculated in addition to the well known pionic (Sullivan) contribution. Interference between π and π′ contributions and their possible influence on the cut-off mass parameter of the πNN form factor extracted from DIS on the nucleon are examined. It is shown that the orthogonality relation between the π and π′ wave functions, in conjunction with number and momentum sum rules, put strong restrictions on the size of the interference effect. The interference effect between π and π′ is found to be negligible for the nucleon quark distributions and to modify only higher moments of the quark distributions. The interference effects of a pionic contribution with other mesons are discussed.     

A search for deeply bound pionic states of xenon produced in the 136Xe(d, 3He)135Xeπ-bound reaction

A search for deeply bound pionic states of xenon produced in the ¹³⁶Xe(d, ³He)¹³⁵Xe_π-bound reaction at E _d = 500 MeV is reported. The population of the 1s pionic-atom state of ¹³⁵Xe is observed on the predicted level of the cross section ～ 40 μb/sr. The binding energy of the 1s state, B = 2.9 ± 0.5 MeV, however, is lower than theoretically predicted.     

Measurement of the K S mean lifetime from π+π− and π0π0 decays using K L decays to determine the acceptance

A precision measurement of the K _S mean lifetime has been performed by comparing, in the same experimental setup, the distributions of two-pion decays of neutral kaons produced by high energy proton-beryllium interactions in two targets at a relative distance variable between 112 and 160 m. The value obtained combining the results from π⁺π^? and π⁰π⁰ decays is τ_s = (0.8971 ± 0.0021) 10^?10 s.