Weinberg like sum rules revisited

Sergey S Afonin1,2
1V.A. Fock Department of Theoretical Physics, St. Petersburg State University, St. Petersburg, Russia
2Department of Physics and Astronomy, University of Bochum, Bochum, Germany

Tóm tắt

The generalized Weinberg sum rules containing the difference of isovector vector and axial-vector spectral functions saturated by both finite and infinite number of narrow resonances are considered. We give a historical survey and summarize the status of these sum rules analyzing their overall agreement with phenomenological Lagrangians, low-energy relations, parity doubling, hadron string models, and experimental data. PACS codes: 11.55.Hx, 11.30.Rd

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Tài liệu tham khảo

Weinberg S: Phys Rev Lett. 1967, 18: 507-

Das T, Mathur VS, Okubo S: Phys Rev Lett. 1967, 18: 761-

Glashow SL, Schnitzer HJ, Weinberg S: Phys Rev Lett. 1967, 19: 139-

Glashow SL, Schnitzer HJ, Weinberg S: Phys Rev Lett. 1967, 19: 205-

Schechter J, Venturi G: Phys Rev Lett. 1967, 19: 276-

Das T, Mathur VS, Okubo S: Phys Rev Lett. 1967, 19: 470-

Sakurai JJ: Phys Rev Lett. 1967, 19: 803-

Oakes RJ, Sakurai JJ: Phys Rev Lett. 1967, 19: 1266-

Das T, Guralnik GS, Mathur VS, Low FE, Young JE: Phys Rev Lett. 1967, 18: 759-

Das T, Mathur VS, Okubo S: Phys Rev Lett. 1967, 19: 859-

Dicus DA, Mathur VS: Phys Rev. 1973, 2: D 525-

Lee TD, Weinberg S, Zumino B: Phys Rev Lett. 1967, 18: 507-

Wilson KG: Phys Rev. 1969, 179: 1499-

Bég MAB: Phys Rev D. 1976, 13: 2266-

Gross DJ, Wilczek F: Phys Rev Lett. 1973, 30: 1343-

Politzer HD: Phys Rev Lett. 1973, 30: 1346-

Borchardt S, Mathur VS: Phys Rev D. 1974, 9: 2371-

Hagiwara T, Mohapatra RN: Phys Rev D. 1975, 8: 2223-

Bernard C, Duncan A, LoSecco J, Weinberg S: Phys Rev D. 1975, 12: 792-

Weisberger WI: Phys Rev D. 1976, 13: 961-

Prasad SC: Phys Rev D. 1974, 9: 1017-

Mohapatra RN: Phys Rev D. 1974, 9: 2355-

Bég MAB, Shei S-S: Phys Rev D. 1975, 12: 3092-

Auvil PR, Deshpe NG: Phys Lett B. 1974, 49: 73-

Broadhurst DJ: Nucl Phys B. 1975, 85: 189-

Shifman MA, Vainstein AI, Zakharov VI: Nucl Phys B. 1979, 147: 385-

Lucha W, Melikhov D, Simula S: Phys Rev D. 2007, 76: 036002-

Moussallam B: Nucl Phys B. 1997, 504: 381-

Kuzmin VA, Tavkhelidze AN, Chetyrkin KG: Pisma Zh Eksp Teor Fiz. 1977, 25: 456-

Chetyrkin KG, Krasnikov NV, Tavkhelidze AN: Phys Lett B. 1978, 76: 83-

Floratos EG, Narison S, de Rafael E: Nucl Phys B. 1979, 155: 115-

de Rafael E: *Les Houches. 1997, 1171-[hep-ph/9802448]

Peccei RD, Solà J: Nucl Phys B. 1987, 281: 1-

Albrecht H, (ARGUS Collaboration), et al: Z Phys C. 1986, 33: 7-

Dominguez CA, Solà J: Z Phys C. 1988, 40: 63-

Dominguez CA, Solà J: Phys Lett B. 1988, 208: 131-

Donoghue JF, Golowich E: Phys Rev D. 1994, 49: 1513-

Schael S, (ALEPH Collaboration), et al: Phys Rept. 2005, 421: 191-

Ackerstaff K, (OPAL Collaboration), et al: Eur Phys J C. 1999, 7: 571-

Davier M, Girla L, Hoecker A, Stern J: Phys Rev D. 1998, 58: 096014-

Peris S, Phily B, de Rafael E: Phys Rev Lett. 2001, 86: 14-

Ioffe BL, Zyablyuk KN: Nucl Phys A. 2001, 687: 437-

Zyablyuk KN: hep-ph/0404230

Bijnens J, Gamiz E, Prades J: JHEP. 2001, 0110: 009-

Cirigliano V, Golowich E, Maltman K: Phys Rev D. 2003, 68: 054013-

Rojo J, Latorre JI: JHEP. 2004, 0401: 055-

Friot S, Greynat D, de Rafael E: JHEP. 2004, 0410: 043-

Narison S: Phys Lett B. 2005, 624: 223-

Moussallam B: Eur Phys J C. 1999, 6: 681-

Dominguez CA, Schilcher K: Phys Lett B. 1999, 448: 93-

Ciulli S, Schilcher K, Sebu C, Spiesberger H: Phys Lett B. 2004, 595: 359-

Schilcher K, Spiesberger H: hep-ph/0612304

Bijnens J: Phys Rept. 1996, 265: 369-

Holdom B, Lewis R: Phys Rev D. 1995, 51: 6318-

Andrianov AA, Espriu D, Tarrach R: Nucl Phys B. 1998, 533: 429-

Klevansky SP, Lemmer RH: hep-ph/9707206

Andrianov AA, Andrianov VA: hep-ph/9705364

Andrianov AA, Andrianov VA: hep-ph/9911383

Broniowski W: hep-ph/9911204

Peris S, Perrottet M, de Rafael E: JHEP. 1998, 98: 011-

Andrianov AA, Andrianov VA, Afonin SS: hep-ph/0101245

Andrianov AA, Andrianov VA, Afonin SS: hep-ph/0209260

Andrianov VA, Afonin SS: Eur Phys J A. 2003, 17: 111-

Andrianov VA, Afonin SS: J Math Sci. 2005, 125: 99-[Translated from: Zap Nauchn Semin 2002, 291:5]

Dorokhov AE, Broniowski W: Eur Phys J C. 2003, 32: 79-

Dorokhov AE: Phys Rev D. 2004, 70: 094011-

Andrianov AA, Espriu D: JHEP. 1999, 10: 022-

Weinberg S: Phys Rev. 1968, 16: 1568-

Harada M, Yamawaki K: Phys Rev Lett. 2001, 86: 757-

Afonin SS: Phys Lett B. 2006, 639: 258-

Afonin SS: Mod Phys Lett A. 2007, 22: 1359-

Shifman M, Vainshtein A: arXiv:07100863 [hep-ph]

Beane S: Phys Rev D. 2001, 64: 116010-

Afonin SS, Andrianov AA, Andrianov VA, Espriu D: JHEP. 2004, 0404: 039-

Shifman M: hep-ph/0507246

Chiu CB, Pasupathy J, Wilson SL: Phys Rev D. 1985, 32: 1786-

Afonin SS: Nucl Phys B. 2007, 779: 13-

Jaffe RL, Pirjol D, Scardicchio A: Phys Rept. 2006, 435: 157-

Glozman LYa: Phys Rept. 2007, 444: 1-

Afonin SS: Int J Mod Phys A. 2007, 22: 4537-

Andrianov AA, Espriu D: arXiv:08034104 [hep-ph]

't Hooft G: Nucl Phys B. 1974, 72: 461-

Witten E: Nucl Phys B. 1979, 160: 57-

Coleman S, Witten E: Phys Rev Lett. 1980, 45: 100-

Knecht M, de Rafael E: Phys Lett B. 1998, 424: 335-

Golterman M, Peris S: Phys Rev D. 2003, 67: 096001-

Gasiorowicz S: Phys Rev. 1966, 146: 1067-

Sakurai JJ: Currents and Mesons. 1969, The University of Chicago Press, Chicago London

Adler SL, Dashen RF: Current Algebras and Applications to Particle Physics. 1968, Benjamin WA, INC, New York – Amsterdam

Ecker G, Gasser J, Pich A, de Rafael E: Nucl Phys B. 1989, 321: 311-

Gasser J, Leutwyler H: Nucl Phys B. 1985, 250: 465-

Yao W-M, et al: J Phys G. 2006, 33: 1-

Pich A: Rept Prog Phys. 1995, 58: 563-

Kawarabayashi K, Suzuki M: Phys Rev Lett. 1966, 16: 255-

Riazuddin , Fayyazuddin : Phys Rev. 1966, 147: 1071-

Sakurai JJ: Phys Rev Lett. 1966, 17: 552-

Geffen DA: Phys Rev Lett. 1967, 19: 770-

Brown SG, West GB: Phys Rev Lett. 1967, 19: 812-

Brown LS, Goble RG: Phys Rev Lett. 1968, 20: 346-

Schnitzer HJ: Phys Rev Lett. 1970, 24: 1384-

Schnitzer HJ: Phys Rev D. 1970, 2: 1621-

Harada M, Tanabashi M, Yamawaki K: Phys Lett B. 2003, 568: 103-

Andrianov VA, Afonin SS: Phys Atom Nucl. 2002, 65: 1862-[Translated from: Yad Fiz 2002, 65:1913]

Afonin SS, Espriu D: JHEP. 2006, 0609: 047-

Ademollo M, Veneziano G, Weinberg S: Phys Rev Lett. 1969, 22: 83-

Afonin SS: Phys Lett B. 2003, 576: 122-

Forkel H, Beyer M, Frederico T: JHEP. 2007, 0707: 077-

Afonin SS: Phys Rev C. 2007, 76: 015202-

Afonin SS: Mod Phys Lett A. 2008, 23: 3159-

Afonin SS: arXiv:0709.4444 [hep-ph] (to be published in Int J Mod Phys A)

Bugg DV: Phys Rept. 2004, 397: 257-

Golterman M, Peris S: JHEP. 2001, 01: 028-

Arriola ER, Broniowski W: Phys Rev D. 2006, 73: 097502-

Andrianov AA, Andrianov VA, Afonin SS: arXiv:hep-ph/0212171

Afonin SS: Int J Mod Phys A. 2006, 21: 6693-

Sanz-Cillero JJ: Nucl Phys B. 2006, 732: 136-

Andrianov AA, Afonin SS, Espriu D, Andrianov VA: Int J Mod Phys A. 2006, 21: 885-

Andrianov AA, Afonin SS, Espriu D, Andrianov VA: Nucl Phys Proc Suppl. 2007, 164: 296-

Andrianov AA, Afonin SS, Espriu D, Andrianov VA: AIP Conf Proc. 2008, 1030: 177-

Mondejar J, Pineda A: arXiv:0704.1417 [hep-ph]

Arriola ER, Broniowski W: Eur Phys J A. 2007, 31: 739-