Analytic continuation of the pion form factor from the spacelike to the timelike domain
Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 3, pp. 383-397 Cet article a éte moissonné depuis la source Math-Net.Ru

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We solve the problem of analytically continuing the electromagnetic pion form factor into the complex domain of transferred momenta. We treat the pion as a composite quark–antiquark system. We demonstrate that the analytic properties of the form factor calculated in the framework of relativistic quantum mechanics with direct interaction agree with the analytic properties following from the general principles of quantum field theory.
Keywords: form factor, analytic property, relativistic composite quark model.
Mots-clés : pion
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A. F. Krutov; M. A. Nefedov; V. E. Troitsky. Analytic continuation of the pion form factor from the spacelike to the timelike domain. Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 3, pp. 383-397. http://geodesic.mathdoc.fr/item/TMF_2013_174_3_a2/

[1] P. A. M. Dirac, Rev. Modern Phys., 21:3 (1949), 392–399 | DOI | MR | Zbl

[2] B. D. Keister, W. N. Polyzou, “Relativistic Hamiltonian dynamics in nuclear and particle physics”, Advances in Nuclear Physics, v. 20, Plenum Press, New-York, London, 1991, 225–479

[3] E. Gilman, F. Gross, J. Phys. G, 28:4 (2002), R37–R116, arXiv: nucl-th/0111015 | DOI

[4] G. R. Farrar, D. R. Jackson, Phys. Rev. Lett., 43:4 (1979), 246–249 | DOI

[5] G. P. Lepage, S. J. Brodsky, Phys. Lett. B, 87:4 (1979), 359–365 | DOI | MR

[6] A. V. Efremov, A. V. Radyushkin, Phys. Lett. B, 94:2 (1980), 245–250 | DOI

[7] G. M. Huber, H. P. Blok, T. Horn et al. [The Jefferson Lab. $F_{\pi}$ Collaboration], Phys. Rev. C, 78:4 (2008), 045203, 16 pp. | DOI

[8] A. V. Radyushkin, Nucl. Phys. A, 532:1–2 (1991), 141–154 | DOI

[9] V. Braguta, W. Lucha, D. Melikhov, Phys. Lett. B, 661:5 (2008), 354–259, arXiv: 0710.5461 | DOI

[10] S. R. Amendolia, M. Arik, B. Badelek et al., Nucl. Phys. B, 277 (1986), 168–196 ; S. R. Amendolia, B. Badelek, G. Batignani et al., Phys. Lett. B, 146:1–2 (1984), 116–120 | DOI | DOI

[11] F. Gross, Relativistic Quantum Mechanics and Field Theory, John Wiley Sons, New York, 1999 | MR

[12] A. V. Radyushkin, EChAYa, 20:1 (1989), 97–154

[13] H. A. Bethe, E. E. Salpeter, Phys. Rev., 82:2 (1951), 309–310 | DOI | MR

[14] M. Gell-Mann, F. E. Low, Phys. Rev., 84:2 (1951), 350–354 | DOI | MR | Zbl

[15] A. A. Logunov, A. N. Tavkhelidze, Nuovo Cimento. Ser. 10, 29:2 (1963), 380–399 | DOI | MR

[16] D. Ebert, R. N. Faustov, V. O. Galkin, Eur. Phys. J. C, 47:3 (2006), 745–755, arXiv: hep-ph/0511029 | DOI

[17] J. F. Donoghue, E. S. Na, Phys. Rev. D, 56:11 (1997), 7073–7076, arXiv: hep-ph/9611418 | DOI

[18] W. W. Buck, R. F. Lebed, Phys. Rev. D, 58:5 (1998), 056001, 12 pp., arXiv: hep-ph/9802369 | DOI

[19] B. V. Geshkenbein, Phys. Rev. D, 61:3 (2000), 033009, 7 pp., arXiv: hep-ph/9806418 | DOI

[20] D. Melikhov, O. Nachtmann, V. Nikonov, T. Paulus, Eur. Phys. J. C, 34:3 (2004), 345–360, arXiv: hep-ph/0311213 | DOI

[21] M. Belička, S. Dubnička, A. Z. Dubničková, A. Liptaj, Phys. Rev. C, 83:2 (2011), 028201, 4 pp., arXiv: 1102.3122 | DOI

[22] B. Ananthanarayan, I. Caprini, I. S. Imsong, Phys. Rev. D, 85:9 (2012), 096006, 10 pp., arXiv: 1203.5398 | DOI

[23] H. R. Grigoryan, A. V. Radyushkin, Phys. Rev. D, 76:11 (2007), 115007, 12 pp., arXiv: 0709.0500 | DOI

[24] H. R. Grigoryan, A. V. Radyushkin, Phys. Rev. D, 76:9 (2007), 095007, 8 pp., arXiv: 0706.1543 | DOI

[25] S. J. Brodsky, G. F. de Téramond, Phys. Rev. D, 77:5 (2008), 056007, 20 pp., arXiv: 0707.3859 | DOI

[26] H. J. Kwee, R. F. Lebed, JHEP, 01 (2008), 027, 17 pp., arXiv: 0708.4054 | DOI

[27] S. N. Sokolov, TMF, 36:2 (1978), 193–207 | DOI | MR

[28] H. Leutwyler, J. Stern, Ann. Phys., 112:1 (1978), 94–164 | DOI | MR

[29] F. Coester, Progr. Part. Nucl. Phys., 29 (1992), 1–32 | DOI

[30] W. N. Polyzou, Ch. Elster, W. Glöckle, J. Golak, Y. Huang, H. Kamada, R. Skibiński, H. Witala, Few-Body Systems, 49:1–4 (2011), 129–147 | DOI

[31] B. Bakamjan, L. H. Thomas, Phys. Rev., 92:5 (1953), 1300–1310 | DOI

[32] W. N. Polyzou, Phys. Rev. C, 82:6 (2010), 064001, 9 pp., arXiv: 1008.5222 | DOI | MR

[33] V. E. Troitskii, Yu. M. Shirokov, TMF, 1:2 (1969), 213–221 | DOI

[34] A. F. Krutov, V. E. Troitsky, Eur. Phys. J. C, 20:1 (2001), 71–76, arXiv: hep-ph/9811318 | DOI

[35] A. F. Krutov, V. E. Troitsky, N. A. Tsirova, Phys. Rev. C, 80:5 (2009), 055210, 5 pp., arXiv: 0910.3604 | DOI

[36] A. F. Krutov, V. E. Troitskii, TMF, 116:2 (1998), 215–224 | DOI | DOI | Zbl

[37] A. F. Krutov, V. E. Troitsky, Phys. Rev. C, 65:4 (2002), 045501, 17 pp., arXiv: hep-ph/0101327 | DOI

[38] A. A. Cheshkov, Yu. M. Shirokov, ZhETF, 44 (1963), 1982–1992 | MR

[39] A. F. Krutov, V. E. Troitsky, Phys. Rev. C, 68:1 (2003), 018501, 4 pp., arXiv: hep-ph/0210046 | DOI

[40] V. A. Matveev, R. M. Muradyan, A. N. Tavkhelidze, Lett. Nuovo Cimento. Ser. 2, 7:15 (1973), 719–723 | DOI

[41] S. J. Brodsky, G. R. Farrar, Phys. Rev. Lett., 31:18 (1973), 1153–1156 | DOI

[42] V. A. Matveev, L. A. Slepchenko, A. N. Tavkhelidze, Phys. Lett. B, 100:1 (1981), 75–78 | DOI

[43] P. L. Chung, F. Coester, B. D. Keister, W. N. Polyzou, Phys. Rev. C, 37:5 (1988), 2000–2015 | DOI

[44] P. L. Chung, F. Coester, W. N. Polyzou, Phys. Lett. B, 205:4 (1988), 545–548 | DOI

[45] W. Jaus, Phys. Rev. D., 44:9 (1991), 2851–2859 | DOI

[46] F. Schlumpf, Phys. Rev. D, 50:11 (1994), 6895–6898, arXiv: hep-ph/9406267 | DOI

[47] F. Cardarelli, I. L. Grach, I. M. Narodetskii, E. Pace, G. Salmè, S. Simula, Phys. Rev. D, 53:1 (1996), 6682–6685, arXiv: nucl-th/9507038 | DOI

[48] C. Bruch, A. Khodjamirian, J. H. Kühn, Eur. Phys. J. C, 39:1 (2005), 41–54, arXiv: hep-ph/0409080 | DOI

[49] D. V. Shirkov, V. V. Serebryakov, V. A. Mescheryakov, Dispersionnye teorii silnykh vzaimodeistvii pri nizkikh energiyakh, Nauka, M., 1967