Charged Pion Mass Research Articles

Determination of the S-wave π π scattering lengths from a study of K ±→π ± π 0 π 0 decays

We report the results from a study of the full sample of ~ 6.031 10^7 K+- -> pi+- pi0 pi0 decays recorded by the NA48/2 experiment at the CERN SPS. As first observed in this experiment, the pi0 pi0 invariant mass M00 distribution shows a cusp-like anomaly in the region around M00 = 2m+, where m+ is the charged pion mass. This anomaly has been interpreted as an effect due mainly to the final state charge exchange scattering process pi+ pi- -> p0 p0 in K+- -> pi+- pi+ pi- decay. Fits to the M00 distribution using two different theoretical formulations provide the presently most precise determination of (a0 - a2), the difference between the pi pi S-wave scattering lengths in the isospin I=0 and I=2 states. Higher-order pi pi rescattering terms, included in the two formulations, allow also an independent, though less precise, determination of a2.

CUSPS IN THE KAON DECAYS

We consider two ways of the experimental determination of the S-wave ππ scattering lengths: from K → 3π decays and from Ke4 decays. In both cases the unitary cusps, which emerge due to the difference in the charged and neutral pion masses, play a crucial role. We construct a systematic effective field theory framework which can be used to describe decay amplitudes in the cusp region.

Precise determination of theI=2ππscattering length from mixed-action lattice QCD

The $I=2$ $\ensuremath{\pi}\ensuremath{\pi}$ scattering length is calculated in fully dynamical lattice QCD with domain-wall valence quarks on the asqtad-improved coarse MILC configurations (with fourth-rooted staggered sea quarks) at four light-quark masses. Two- and three-flavor mixed-action chiral perturbation theory at next-to-leading order is used to perform the chiral and continuum extrapolations. At the physical charged pion mass, we find ${m}_{\ensuremath{\pi}}{a}_{\ensuremath{\pi}\ensuremath{\pi}}^{I=2}=\ensuremath{-}0.043\text{ }30\ifmmode\pm\else\textpm\fi{}0.000\text{ }42$, where the error bar combines the statistical and systematic uncertainties in quadrature.

Observation of a cusp-like structure in the [formula omitted] invariant mass distribution from [formula omitted] decay and determination of the ππ scattering lengths

We report the results from a study of a partial sample of ∼2.3×107K±→π±π0π0 decays recorded by the NA48/2 experiment at the CERN SPS, showing an anomaly in the π0π0 invariant mass (M00) distribution in the region around M00=2m+, where m+ is the charged pion mass. This anomaly, never observed in previous experiments, can be interpreted as an effect due mainly to the final state charge exchange scattering process π+π−→π0π0 in K±→π±π+π− decay [N. Cabibbo, Phys. Rev. Lett. 93 (2004) 121801]. It provides a precise determination of a0−a2, the difference between the ππ scattering lengths in the isospin I=0 and I=2 states. A best fit to a rescattering model [N. Cabibbo, G. Isidori, JHEP 0503 (2005) 21] corrected for isospin symmetry breaking gives (a0−a2)m+=0.268±0.010(stat)±0.004(syst), with additional external uncertainties of ±0.013 from branching ratio and theoretical uncertainties. If the correlation between a0 and a2 predicted by chiral symmetry is taken into account, this result becomes (a0−a2)m+=0.264±0.006(stat)±0.004(syst)±0.013(ext).

Determination of the pion-nucleon coupling constant and scattering lengths

We critically evaluate the isovector GMO sum rule for forward pion-nucleon scattering using the recent precision measurements of negatively charged pion-proton and pion-deuteron scattering lengths from pionic atoms. We deduce the charged-pion-nucleon coupling constant, with careful attention to systematic and statistical uncertainties. This determination gives, directly from data a pseudoscalar coupling constant of 14.11+-0.05(statistical)+-0.19(systematic) or a pseudovector one of 0.0783(11). This value is intermediate between that of indirect methods and the direct determination from backward neutron-proton differential scattering cross sections. We also use the pionic atom data to deduce the coherent symmetric and antisymmetric sums of the negatively charged pion-proton and pion-neutron scattering lengths with high precision. The symmetric sum gives 0.0012+-0.0002(statistical)+-0.0008 (systematic) and the antisymmetric one 0.0895+-0.0003(statistical)+-0.0013(systematic), both in units of inverse charged pion-mass. For the need of the present analysis, we improve the theoretical description of the pion-deuteron scattering length.

Precision determination of pion mass using X-ray CCD spectroscopy

An experiment is described which aims to determine the charged pion mass to 1 ppm or better, from which a new determination of the upper limit of the muon neutrino mass is anticipated. The experimental approach uses a high-intensity negative pion beam (produced at the PSI 590 MeV proton cyclotron), injected into a cyclotron trap and stopped inside a gas-filled target chamber, to form highly excited exotic atoms of pionic nitrogen and muonic oxygen. The energy of photons, emitted during de-excitation, is directly proportional to the mass of the pion or muon. These soft X-ray emission spectra are measured using a high-precision crystal spectrometer, with an array of six, high quantum efficiency X-ray position resolving CCDs at the focus. To achieve sub-ppm accuracy, simultaneous calibration of the pionic nitrogen line is provided by measurement of an adjacent muonic oxygen line, whose energy is known to 0.3 ppm. The high precision of the experiment offers a new opportunity to determine the pion mass to the level of 1 ppm. This result, if achieved, will enable new upper limits to be placed on the rest mass of the muon neutrino, which may possibly be of cosmological significance in consideration of the neutrino mass contribution to dark matter.

New light on electromagnetic corrections to the scattering parameters obtained from experiments on pionium

We calculate the electromagnetic corrections needed to obtain isospin invariant hadronic pion–pion s-wave scattering lengths a 0, a 2 from the elements a cc , a 0 c of the s-wave scattering matrix for the ( π + π −, π 0 π 0) system at the π + π − threshold. The latter can be extracted from experiments on the π + π − atom (pionium). Our calculation uses energy-independent hadronic pion–pion potentials V 0 and V 2 that satisfactorily reproduce the low-energy phase shifts given by two-loop chiral perturbation theory, with the hadronic mass of the pion taken first as the charged-pion mass and then as the neutral-pion mass. We also take into account an important relativistic effect whose inclusion influences the corrections considerably.

Erratum: Relativistic effects in the pionium lifetime [Phys. Rev. D 58, 014011 (1998)

The pionium decay width is evaluated in the framework of chiral perturbation theory and the relativistic bound state formalism of constraint theory. Corrections of order O(\alpha) are calculated with respect to the conventional lowest-order formula, in which the strong interaction amplitude has been calculated to two-loop order with charged pion masses. Strong interaction corrections from second-order perturbation theory of the bound state wave equation are found to be of the order of 0.4%. Electromagnetic radiative corrections, due to pion-photon interactions, are estimated to be of the order of -0.1%. Electromagnetic mass shift insertions in internal propagators produce a correction of the order of 0.3%. The correction due to the passage from the strong interaction scattering amplitude evaluated with the mass parameter fixed at the charged pion mass to the amplitude evaluated with the mass parameter fixed at the neutral pion mass is found to be of the order of 6.4%.

Upper limit of the muon-neutrino mass and charged-pion mass from momentum analysis of a surface muon beam.

We have determined the momentum ${p}_{{\ensuremath{\mu}}^{+}}$ of muons from the decay ${\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}$ at rest, by analyzing a surface muon beam in a magnetic spectrometer equipped with a silicon microstrip detector. The result ${p}_{{\ensuremath{\mu}}^{+}}=(29.79200\ifmmode\pm\else\textpm\fi{}0.00011)$ MeV/c leads to a squared muon-neutrino mass of ${m}_{{\ensuremath{\nu}}_{\ensuremath{\mu}}}^{2}=(\ensuremath{-}0.016\ifmmode\pm\else\textpm\fi{}0.023)$ Me${\mathrm{V}}^{2}$, which corresponds to a "laboratory" upper limit of 0.17 MeV (C.L.=0.9) for the muon-neutrino mass. The cosmological upper limit of the neutrino mass (65 eV), the muon mass, and the new value of ${p}_{{\ensuremath{\mu}}^{+}}$ yield the pion mass ${m}_{{\ensuremath{\pi}}^{+}}=(139.57022\ifmmode\pm\else\textpm\fi{}0.00014)$ MeV. Alternatively, if one does not use the cosmological upper limit of ${m}_{{\ensuremath{\nu}}_{\ensuremath{\mu}}}$, then a combined fit including the new ${p}_{{\ensuremath{\mu}}^{+}}$ value, and the ${m}_{{\ensuremath{\mu}}^{+}}$ and ${m}_{{\ensuremath{\pi}}^{\ensuremath{-}}}$ values from other experiments and the $\mathrm{CPT}$ theorem (${m}_{{\ensuremath{\pi}}^{+}}={m}_{{\ensuremath{\pi}}^{\ensuremath{-}}}$) leads to ${m}_{{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}}=(139.57037\ifmmode\pm\else\textpm\fi{}0.00021)$ MeV. As a side result, the mean kinetic energy of the pions stopped in the production target, made of isotropic graphite, immediately before their decay is found to be $\stackrel{-}{{T}_{{\ensuremath{\pi}}^{+}}}=(0.425\ifmmode\pm\else\textpm\fi{}0.016)$ eV. This is consistent with the hypothesis that the pions are trapped in the potential well of a spherical harmonic oscillator, $V(r)={V}_{0}+\frac{1}{2}{k}_{s}{r}^{2}$, with ${k}_{s}=(1.144\ifmmode\pm\else\textpm\fi{}0.088)\ifmmode\times\else\texttimes\fi{}{10}^{17}$ eV/${\mathrm{cm}}^{2}$.

New precision measurement of the muon momentum in pion decay at rest

We have continued the measurement of the muon momentum p μ + in the decay π + → μ + v μ of pions at rest. The new result p μ + = 29.79179±0.00053 MeV/ c, and the assumption of a vanishing neutrino mass m νμ lead to a charged pion mass of 139.56996±0.00067 MeV/ c 2, 3.5 standard deviations higher than the current world average of the mass obtained from pionic X-rays. For m ν μ > 0 the discrepancy would be even larger.

Application of the Dashen-Frautschi method to the calculation of the difference between the nn and np singlet scattering lengths

The difference between the1S0 np and nn scattering lengths is calculated by a method due to Dashen and Frautschi. In the calculation the driving term used is the change in the one-pion exchange contribution between the two channels due to differences in the charged and neutral pion masses which are exchanged, in the charged and neutralπN coupling constants, and in the external proton and neutron masses. The split in the coupling constants is also estimated with the same formalism, and constitutes an independent result. The over-all result obtained isann−anp=−(3.8±3.4) fermi, if the elementary-particle physics definition of scattering length is used. This is in qualitative agreement with recent experimental findings.

Effect of Electromagnetic Corrections to Low-Energy Nucleon-Nucleon Scattering on Charge Independence

The low-energy nucleon-nucleon scattering lengths are calculated, taking into account the electric charge and magnetic-moment distributions of the nucleons. Corrections in the one-pion exchange part of the effective nuclear interaction due to the charged and uncharged pion mass difference are also included. The singlet proton-proton, proton-neutron, and neutron-neutron scattering lengths are calculated and compared with experiment. These corrections reduce the discrepancy to be explained by other effects in order to maintain charge independence. We conclude that recent measurements of the neutron-neutron scattering length do not contradict the hypothesis of charge independence.

Possible charge dependence of nucleon-nucleon phase shifts

Phase shifts were calculated in a semi-theoretical model setting the quantum mass sequentially equal to the neutral pion mass and the charged pion mass. The results show that analysis under the assumption of charge independence may give false p-p phase values. (D.C.W.)