Fast computation of observed cross section for ψ'→PP decays

  • It has been conjectured that the relative phase between strong and electromagnetic amplitudes is universally -90° in charmonium decays. ψ' decaying into a pseudoscalar pair provides a possibility to test this conjecture. However, the experimentally observed cross section for such a process is depicted by the two-fold integral, which takes into account the initial state radiative (ISR) correction and energy spread effect. Using the generalized linear regression approach, a complex energy-dependent factor is approximated by a linear function of energy. Taking advantage of this simplification, the integration of ISR correction can be performed and an analytical expression with accuracy at the level of 1% is obtained. Then, the original two-fold integral is simplified into a one-fold integral, which reduces the total computing time by two orders of magnitude. Such a simplified expression for the observed cross section usually plays an indispensable role in the optimization of scan data taking, the determination of systematic uncertainty, and the analysis of data correlation.
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  • [1] Jousset J et al. (DM / collaboration). Phys. Rev. D, 1990, 41: 13892 Coffman D et al. (Mark 0 collaboration). Phys. Rev. D, 1988, 38: 26953 Suzuki M. Phys. Rev. D, 1999, 60: 0515014 López G, Lucio M J L, Pestieau J. hep-ph/99023005 Kpke L, Wermes N. Phys. Rep., 1989, 174: 676 Baldini R et al. Phys. Lett. B, 1998, 444: 1117 Suzuki M. Phys. Rev. D, 2001, 63: 0540218 Gérard J M, Weyers J. Phys. Lett. B, 1999, 462: 3249 YUAN C Z, WANG P, MO X H. Phys. Lett. B, 2003, 567: 7310 WANG P, YUAN C Z, MO X H. Phys. Rev. D, 2004, 69: 05750211 BAI J Z et al. (BES collaboration). Phys. Rev. Lett., 2004, 91: 05200112 WANG P, YUAN C Z, MO X H. Phys. Lett. B, 2003, 574: 4113 WANG P, MO X H, YUAN C Z. Int. J. Mod. Phys. A, 2006, 21: 516314 Ablikim M et al. (BES/ collaboration). Phys. Rev. D, 2004, 70: 07710115 WANG Y K, MO X H, YUAN C Z et al. Nucl. Instrum. Methods A, 2007, 583: 47916 WANG Y K, ZHANG J Y, MO X H, YUAN C Z et al. China Physic C, 2009, 33: 50117 Haber H E and Perrier J. Phys. Rev. D, 1985, 32: 296118 Chernyak V L and Zhitnitsky A R. Nucl. Phys. B, 1982, 201: 49219 WANG P, MO X H, YUAN C Z. Phys. Lett. B, 2003, 557: 19220 Kuraev E A, Fadin V S. Sov. J. Nucl. Phys., 1985, 41: 466-47221 Altarelli G and Martinelli G. CERN, 1986, 86-02: 4722 Berends F A, Burgers G, Neerven W L. Nucl. Phys. B, 1988, 297: 429; Berends F A, Burgers G, Neerven W L. Nucl. Phys. B, 1988, 304: 92123 Tsai Y S. SLAC-PUB-3129, 198324 Alexander P et al. Nucl. Phys. B, 1989, 320: 4525 Lee S Y. Accelerator Physics (2nd Edition). Shanghai: Fu- Dan University Press, 200626 Wille K. The Physics of Particle Accelerators. New York: Oxford University Press, 200027 CHEN F Z, WANG P, WU J M, ZHU Y S. HEP NP, 1990, 14: 585-595 (in Chinese)28 Cahn R N. Phys. Rev. D, 1987, 36: 266629 Amsler C et al. Phys. Lett. B, 2008, 667: 130 MO X H, ZHU Y S. HEP NP, 2001, 25: 1133-1139 (in Chinese)31 MO X H. (2S) Scan and Some Other Studies (Post-doctor report). Beijing, 2003
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WANG Bo-Qun, MO Xiao-Hu, WANG Ping and BAN Yong. Fast computation of observed cross section for ψ'→PP decays[J]. Chinese Physics C, 2011, 35(5): 411-418. doi: 10.1088/1674-1137/35/5/001
WANG Bo-Qun, MO Xiao-Hu, WANG Ping and BAN Yong. Fast computation of observed cross section for ψ'→PP decays[J]. Chinese Physics C, 2011, 35(5): 411-418.  doi: 10.1088/1674-1137/35/5/001 shu
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Received: 2010-08-12
Revised: 1900-01-01
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Fast computation of observed cross section for ψ'→PP decays

Abstract: It has been conjectured that the relative phase between strong and electromagnetic amplitudes is universally -90° in charmonium decays. ψ' decaying into a pseudoscalar pair provides a possibility to test this conjecture. However, the experimentally observed cross section for such a process is depicted by the two-fold integral, which takes into account the initial state radiative (ISR) correction and energy spread effect. Using the generalized linear regression approach, a complex energy-dependent factor is approximated by a linear function of energy. Taking advantage of this simplification, the integration of ISR correction can be performed and an analytical expression with accuracy at the level of 1% is obtained. Then, the original two-fold integral is simplified into a one-fold integral, which reduces the total computing time by two orders of magnitude. Such a simplified expression for the observed cross section usually plays an indispensable role in the optimization of scan data taking, the determination of systematic uncertainty, and the analysis of data correlation.

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