Pion mass

FIGURE 11.8 Experimental spectrum of the relativistic Ml transition in He-like chlorine fitted with the profile described in the text. The line width (FWHM) is equal to 0.4 eV. 

FIGURE 11.9 Spectrum of the 5 4 transitions in pionic nitrogen and muonic oxygen. 

A new experiment was thus done, using the improvement described in Sections 1 and 2 which lead to a statistical accuracy in the comparison between the pionic and muonic line, compatible with a final uncertainty below 2 ppm [7]. To reach such an accuracy, the CCD detector characterization described in [16] was required. 

Previous tests of the Klein-Gordon equation has been obtained from the observation of pionic titanium transitions [29] with an accuracy of 2%, and from the observation of pionic nitrogen transitions [5]. 

FIGURE H.10 Spectrum of the 3p — Is transition in pionic hydrogen with a H2 target at a pressure P = 2 bar and temperature T = 20 K (equivalent to a pressure of 28 bar at room temperature). The crystal used is a quartz (101). 

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The muon mass is only slightly lower than the pion mass, and we should expect that insertion of hadronic vacuum polarization in the radiative photon in Fig. 7.13 will give a contribution to the anomalous magnetic moment comparable with the contribution induced by insertion of the muon vacuum polarization. 

Recently, serious progress was made in pionic and antiprotonic atoms and that gave new results about scattering lengths and the pion mass. The work with... 

Charged Pion Mass Determination and Energy — Calibration Standards Based on Pionic X-ray Transitions... 

Abstract. Recent experiments are aiming at an accuracy of 1 ppm for the mass of the charged pion using the characteristic X-rays from exotic atoms. Once the pion mass is established with that precision, the narrow lines from medium Z pionic atoms can be used as a calibration standard in the few keV range. The precision of this new standard is not limited by the large natural line width of fluorescence X-rays and their complex structure due to multi-hole excitations. 

Fig. 1. Principle of the set-up for the pion mass experiment consisting of the cyclotron trap with a gas cell and a curved-crystal spectrometer equipped with a two-dimensional position-sensitive X-ray detector. The focusing condition for a wave length A reflected under the Bragg angle Ob is R-sin B, where R is the (horizontal) radius of curvature. Typical values for R and the diameter of the spherically bent crystals are 3 m and 100 mm...

The experiments aiming at the determination of the charged pion mass use X-ray transitions from the intermediate part of the atomic cascade, where the influence of the hadronic interaction can be neglected. The two most recent experiments both measured the (5from different elements. In one case, a solid state Mg target was taken [15,16], whereas the most recent experiment used an N2 gas target [12,17]. 

The recent high-precision measurement of the pion mass was performed in... 

Having once established a precise value for the pion mass, the X-ray transitions from pionic atoms can be used to produce a set of calibration lines in the few keV range. 

The paper is organized as follows. In Section 2, we describe in more detail the spectrometer and its characterization. In Section 3, we describe the present status of the pion mass measurement and the test of the Klein-Gordon equation. In Section 4, we describe the present status of the pionic hydrogen experiment. In Section 5 we present preliminary results on transition energies in highly-charged ions, and Section 6 is our conclusion. 

FIGURE 11.4 Surface mapping of the 2.9 m spherically bent (220) Si crystal that was used for the measurement of the pion mass, with a two-wave interferometer, with respect to a 2 m reference lens. Deviation from a perfect sphere are smaller than 3.5 laser wavelength (640 nm). 

In this work, we have presented the present status of the pion mass measurement from light exotic atoms, and as well as preliminary results for the pionic hydrogen strong interaction shift and width measurement. We have shown that such high accuracy measurements can only be performed in conjunction with highly-charged ion measurements, that provide the necessary spectrometer characterization. As... 

K. Assamagan, C. Bronnimann, M. Daum, H. Forrer, R. Frosch, P. Gheno, R. Horisberger, M. Janousch, P. Kettle, T. Spirig, C. Wigger, Upper limit of the muon-neutrino mass and charged-pion mass from momentum analysis of a surface muon beam, Phys. Rev. D 53 (1996) 6065-6077. 

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