Abstract.
By means of empirical fits to the differential cross section data on pp and \(\bar{p}p\) elastic scattering, above 10 GeV (center-of-mass energy), we determine the eikonal in the momentum-transfer space (q 2- space). We make use of a numerical method and a novel semi-analytical method, through which the uncertainties from the fit parameters can be propagated up to the eikonal in the q 2- space. A systematic study of the effect of the experimental information at large values of the momentum transfer is developed and discussed in detail. We present statistical evidence that the imaginary part of the eikonal changes sign in the q 2- space and that the position of the zero decreases as the energy increases; after the position of the zero, the eikonal presents a minimum and then goes to zero through negative values. We discuss the applicability of our results in the phenomenological context, outlining some connections with nonperturbative QCD. A short review and a critical discussion on the main results concerning “model-independent” analyses are also presented.
Similar content being viewed by others
References
Y. Dokshitzer, Philos. Trans. R. Soc. London A 359, 309 (2001)
V. Barone, E. Predazzi, High-Energy Particle Diffraction (Spring-Verlag, Berlin, 2002). E. Predazzi, in International Workshop on Hadron Physics 98, Florianópolis, 1998, edited by E. Ferreira, F.F.S. Cruz, S.S. Avancini (World Scientific, Singapore, 1999) p. 80
A. Martin, in Proceedings of the VIIIth Blois Workshop-International Conference on Elastic and Diffractive Scattering, Protvino, 1999, edited by V.A. Petrov, A.V. Prokudin (World Scientific, Singapore, 2000) p. 121
G. Matthiae, Rep. Prog. Phys. 57, 743 (1994)
P. Valin, Phys. Rep. 203, 233 (1991)
R.J. Glauber, in Lectures in Theoretical Physics, edited by W.E. Brittin et al. (Interscience, New York, 1959) Vol. I, p. 315; W. Czyż, L.C. Maximom, Ann. Phys. (New York) 52, 59 (1969); V. Franco, G.K. Varma, Phys. Rev. C 18, 349 (1978)
R. Henzi, P. Valin, Nucl. Phys. B 148, 513 (1979)
N. Byers, C.N. Yang, Phys. Rev. 142, 976 (1966); T.T. Chou, C.N. Yang, in High Energy Physics and Nuclear Structure, edited by G. Alexander (North-Holland, Amsterdam, 1967) p. 348; Phys. Rev. 170, 1592 (1968); Phys. Rev. Lett. 20, 1213 (1968); Phys. Rev. 175, 1832 (1968)
R.J. Glauber, J. Velasco, Phys. Lett. B 147, 380 (1984)
C. Bourrely, J. Soffer, T.T. Wu, Phys. Rev. D 19, 3249 (1979); Nucl. Phys. B 247, 15 (1984); Phys. Rev. Lett. 54, 757 (1985)
Y. Afek, C. Leroy, B. Margolis, P. Valin, Phys. Rev. Lett. 45, 85 (1980); L. Durand, H. Pi, Phys. Rev. D 38, 78 (1988)
M.M. Block, E.M. Gregores, F. Halzen, G. Pancheri, Phys. Rev. D 58, 017503 (1998); 60, 054024 (1999)
P.A.S. Carvalho e M.J. Menon, Phys. Rev. D 56, 7321 (1997)
M. Kawasaki, T. Maehara, M. Yonezawa, Phys. Rev. D 57, 1822 (1998)
M. Kawasaki, T. Maehara, M. Yonezawa, Phys. Rev. D 67, 012013 (2003)
F. Pereira, E. Ferreira, Phys. Rev. D 59, 014008 (1998); Phys. Rev. D 61, 077507 (2000)
A.F. Martini, M.J. Menon, D.S. Thober, Phys. Rev. D 57, 3026 (1998)
M.M. Islam, Nucl. Phys. B 104, 511 (1976)
L. Durand III, R. Lipes, Phys. Rev. Lett. 20, 637 (1968)
V. Franco, Phys. Rev. D 11, 1837 (1975)
S. Dubnicka, V.A. Meshcheryakov, Nucl. Phys. B 83, 311 (1974)
C. Bourrely, J. Soffer, T.T. Wu, Z. Phys. C 5, 159 (1980)
T. Maehara, T. Yanagida, M. Yonezawa, Prog. Theor. Phys. 57, 1097 (1977)
C. Bourrely, J. Soffer, T.T. Wu, Eur. Phys. J. C 28, 97 (2003)
S. Sanielevici, P. Valin, Phys. Rev. D 29, 52 (1984)
U. Amaldi, K.R. Schubert, Nucl. Phys. B 166, 301 (1980)
C. Furget, M. Buenerd, P. Valin, Z. Phys. C 47, 377 (1990)
K.R. Schubert, Landolt-Börnstein, Numerical Data and Functional Relationships in Science and Technology, New Series, Vol. I/9a (Springer-Verlag, Berlin, 1979)
A.S. Carrol et al. , Phys. Lett. B 61, 303 (1976); G. Fidecaro et al. , Phys. Lett. B 105, 309 (1981)
L.A. Fajardo et al. , Phys. Rev. D 24, 46 (1981); D.S. Ayres et al. , Phys. Rev. D 15, 3105 (1977); A.S. Carrol et al. , Phys. Lett. 80, 423 (1979); C.W. Akerlof et al. , Phys. Rev. D 14, 2864 (1976); R. Rubinstein et al. , Phys. Rev. D 30, 1413 (1984)
C. Augier et al. Phys. Lett. B 316, 448 (1993); N. Amos et al. , Phys. Lett. B 128, 343 (1983); G. Carboni et al. , Nucl. Phys. B 254, 697 (1985); N. Amos et al. , Phys. Lett. B 120, 460 (1983); M. Ambrosio et al. , Phys. Lett. B 115, 495 (1982); M. Bozzo et al. , Phys. Lett. B 147, 392 (1984); N.A. Amos et al. , Phys. Rev. Lett. 68, 2433 (1992); N.A. Amos et al. , Phys. Lett. B 243, 158 (1990); A. Breakstone et al. , Nucl. Phys. B 248, 253 (1984); M. Bozzo et al. , Phys. Lett. B 147, 385 (1984); A. Breakstone et al. , Phys. Rev. Lett. 54, 2180 (1985); M. Bozzo et al. , Phys. Lett. B 155, 197 (1985); D. Bernard et al. , Phys. Lett. B 171, 142 (1986)
R.J. Lombard, C. Wilkin, J. Phys. G 3, L5 (1977)
T.T. Chou, Found. Phys. 8, 319 (1978)
H.M. França, Y. Hama, Phys. Rev. D 19, 3261 (1979);
H.M. França, G.C. Marques, A.J. Silva, Il Nuovo Cimento A 59, 53 (1980)
C. Bourrely, P. Chiappetta, J. Soffer, T.T. Wu, Phys. Lett. B 132, 191 (1983)
T. Fearnley, CERN-EP/85-137, 1985 (unpublished)
R. Lombard, in Proceedings of the First International Workshop on Elastic and Diffractive Scattering, Blois, 1985, edited by B. Nicolescu, J. Tran Thanh Van (Editions Frontieres, Gif-Sur-Yvette, 1986) p. 231
H.M. França, Phys. Lett. B 392, 475 (1997)
B.Z. Kopeliovich, I.K. Potashnikova, B. Povh, E. Predazzi, Phys. Rev. D 63, 054001 (2001)
A. Donnachie, P.V. Landshoff, Z. Phys. C 2, 55 (1979); Phys. Lett. B 387, 637 (1996)
W. Faissler et al. , Phys. Rev. D 23, 33 (1981); E. Nagy et al. , Nucl. Phys. B 150, 221 (1979)
F. James, M. Roos, Minuit-Function Minimization and Error Analysis, CERN D506 (CERN, Geneva, 1992);
P.R. Bevington, D.K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 1992)
R. Castaldi, G. Sanguinetti, Ann. Rev. Nucl. Part. Sci. 35, 351 (1985)
A. Martin, Phys. Lett. B 404, 137 (1997)
NAG Fortran Library Manual, Mark 16 (1993)
M.J. Menon, Phys. Rev. D 48, 2007 (1993); A.F. Martini, M.J. Menon, D.S. Thober, Phys. Rev. D 54, 2385 (1996)
A.F. Martini, M.J. Menon, Phys. Lett. B 570, 53 (2003);
H.G. Dosch, Phys. Lett. B 190, 177 (1987); H.G. Dosch, Yu.A. Simonov, Phys. Lett B 205, 339 (1988), Yu.A. Simonov, Nucl. Phys. B 307, 512 (1998)
A. Di Giacomo, E. Meggiolaro, H. Panagopoulos, Nucl. Phys. B 483, 371 (1997); M. D’Elia, A. Di Giacomo, E. Meggiolaro, Phys. Lett. B 408, 315 (1997)
A. Krämer, H.G. Dosch, Phys. Lett. B 252, 669 (1990); H.G. Dosch, E. Ferreira, A. Krämer, Phys. Rev. D 50, 1992 (1994)
B. Carreras, J.N. J. White, Nucl. Phys. B 42, 95 (1972); J.N. J. White, Nucl. Phys. B 51, 23 (1973); J. Bellandi et al. , Hadronic J. 10, 95 (1987); 10, 149 (1987); T.T. Chou, C.N. Yang, Phys. Lett. B 244, 113 (1990)
J. Bellandi, R.J.M. Covolan, M.J. Menon, B.M. Pimentel, Hadronic J. 11, 17 (1988)
M.J. Menon, Doctoral Thesis, Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, 1988; Nucl. Phys. B (Proc. Suppl.) 25, 94 (1992); Canadian J. Phys. 74, 596 (1996)
R.J.M. Covolan, L.L. Jenkovszky, E. Predazzi, Z. Phys. C, 51, 459 (1991); R.J.M. Covolan, P. Desgrolard, M. Giffon, L.L. Jenkovszky, E. Predazzi, Z. Phys. C 58, 109 (1993)
M.N. Rosenbluth, Phys. Rev. 79, 615 (1950)
R.C. Walker et al. , Phys. Rev. D 49, 5671 (1994)
M.K. Jones et al. , Phys. Rev. Lett. 84, 1398 (2000)
O. Gayou et al. , Phys. Rev. C 64, 038202 (2001)
O. Gayou et al. , Phys. Rev. Lett. 88, 092301 (2002)
M. Guidal, M.V. Polyakov, A.V. Radyushkin, M. Vanderhaeghen, hep-ph/0410251
M.E. Christy et al. , Phys. Rev. C 70, 015206 (2004)
I.A. Qattan et al. , nucl-ex/0410010
P.A.S. Carvalho, A.F. Martini, M.J. Menon, A.E. Motter, in: International Workshop on Hadron Physics 98, Florianópolis, 1998, edited by E. Ferreira, F.F. de Souza Cruz, S.S. Avancini (World Scientific, Singapore, 1999), p. 326
Author information
Authors and Affiliations
Corresponding author
Additional information
Received: 19 August 2004, Revised: 12 November 2004, Published online: 14 January 2005
PACS:
13.85.Dz, 13.85.-t
Rights and permissions
About this article
Cite this article
Carvalho, P.A.S., Martini, A.F. & Menon, M.J. Eikonal representation in the momentum-transfer space. Eur. Phys. J. C 39, 359–376 (2005). https://doi.org/10.1140/epjc/s2004-02096-7
Issue Date:
DOI: https://doi.org/10.1140/epjc/s2004-02096-7