====== TTP98-33 Positronium hyperfine splitting: analytical value at m*alpha^6 ======
 
 
   <hidden TTP98-33  Positronium hyperfine splitting: analytical value at m*alpha^6 > We present an analytic calculation of the m*alpha^6 recoil corrections to 
 the hyperfine splitting (HFS) of the ground state energy levels in 
 positronium. We find \Delta E_{\rm rec} = m alpha^6 (-1/6 ln(alpha) 
 + 331/432 -ln(2)/4 - 17 Zeta(3)/(8pi^2) + 5/(12 pi^2)) \approx m alpha^6 
 (- 1/6 ln(alpha) + 0.37632), confirming Pachucki's numerical result 
 \cite{Ph}. We present a complete analytic formula for the
 m*alpha^6 HFS of the positronium ground state and, including
 m*alpha^7*ln^2(alpha) effects, find E(1^3S_1)-E(1^1S_0))_{theory} = 203 392(1)
 MHz. This differs from the experimental results by about 
 3 standard deviations. 
 </hidden>
|**A. Czarnecki, K. Melnikov, A. Yelkhovsky**  | 
|** Phys. Rev. Lett. 82 311-314 1999  **  |
| {{preprints:1998:ttp98-33.pdf|PDF}} {{preprints:1998:ttp98-33.ps|PostScript}} [[http://arxiv.org/abs/hep-ph/9809341|arXiv]]   |
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