[SLAC] [SLAC Pubs and Reports] SLAC-PUB-7274On the Infrared Sensitivity of the Longitudinal Cross Section in e+ e- Annihilation Abstract We have calculated the contributions proportional to $\beta_0^n\alpha_s^{n+1}$ to the longitudinal fragmentation function in $e^+e^-$ annihilation to all orders of perturbation theory. We use this result to estimate higher-order perturbative corrections and nonperturbative corrections to the longitudinal cross section $\sigma_L$ and discuss the prospects of determining $\alpha_s$ from $\sigma_L$. The structure of infrared renormalons in the perturbative expansion suggests that the longitudinal cross section for hadron production with fixed momentum fraction $x$ receives nonperturbative contributions of order $1/(x^2Q^2)$, whereas the total cross section has a larger, $1/Q$ correction. This correction arises from very large longitudinal distances and is related to the behaviour of the Borel integral for the cross section with fixed $x$ at large values of the Borel parameter. (Equations render on Windows, Mac OS, AIX, Linux, Solaris, and IRIX with the techexplorer plug-in.) Full Text PDF slac-pub-7274 (155 KB) Compressed PostScript slac-pub-7274 (65.9 KB) Alternate download methods: old, ancient* *download methods - technical info techexplorer slac-pub-7274 (5.84 KB) More Information Full bibliographic data for this document, including its complete author list, is (or soon will be) available from SLAC's SPIRES-HEP Database. Please report problems with this file to posting@slac.stanford.edu. The SLAC preprint inventory is provided by the SLAC Technical Publications Department. Page generated 01 May 2001 @ 13:25 PDT by htmlme.pl
We have calculated the contributions proportional to $\beta_0^n\alpha_s^{n+1}$ to the longitudinal fragmentation function in $e^+e^-$ annihilation to all orders of perturbation theory. We use this result to estimate higher-order perturbative corrections and nonperturbative corrections to the longitudinal cross section $\sigma_L$ and discuss the prospects of determining $\alpha_s$ from $\sigma_L$. The structure of infrared renormalons in the perturbative expansion suggests that the longitudinal cross section for hadron production with fixed momentum fraction $x$ receives nonperturbative contributions of order $1/(x^2Q^2)$, whereas the total cross section has a larger, $1/Q$ correction. This correction arises from very large longitudinal distances and is related to the behaviour of the Borel integral for the cross section with fixed $x$ at large values of the Borel parameter. (Equations render on Windows, Mac OS, AIX, Linux, Solaris, and IRIX with the techexplorer plug-in.)
(Equations render on Windows, Mac OS, AIX, Linux, Solaris, and IRIX with the techexplorer plug-in.)
PDF slac-pub-7274 (155 KB) Compressed PostScript slac-pub-7274 (65.9 KB) Alternate download methods: old, ancient* *download methods - technical info techexplorer slac-pub-7274 (5.84 KB)
Full bibliographic data for this document, including its complete author list, is (or soon will be) available from SLAC's SPIRES-HEP Database.