Real parts of πN forward amplitudes at high energies

Höhler, G.; Jakob, H.‐P.; Kaiser, Frieder

doi:10.1016/0370-2693(75)90671-1

Cited by 10 publications

(7 citation statements)

References 18 publications

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“…At that time, the derivative approach was strongly criticized by several authors [17,18,19,20], in the sense that it had no practical interest, for instance, because "the mathematical condition for the convergence of the series excludes all cases of physical interest" [17]. However, it should be noted that some of these criticisms were connected with the physical situation at that time, some directed to attempts to extend the method to low energies (for example, as in [32]) and/or to some possible excessive optimism about the derivative approach [33].…”

Section: Discussionmentioning

confidence: 99%

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Critical analysis of derivative dispersion relations at high energies

Ávila

Menon

2004

Nuclear Physics A

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We discuss some formal and fundamental aspects related with the replacement of integral dispersion relations by derivative forms, and their practical uses in high energy elastic hadron scattering, in particular $pp$ and $\bar{p}p$ scattering. Starting with integral relations with one subtraction and considering parametrizations for the total cross sections belonging to the class of entire functions in the logarithm of the energy, a series of results is deduced and our main conclusions are the following: (1) except for the subtraction constant, the derivative forms do not depend on any additional free parameter; (2) the only approximation in going from integral to derivative relations (at high energies) concerns to assume as zero the lower limit in the integral form; (3) the previous approximation and the subtraction constant affect the fit results at both low and high energies and therefore, the subtraction constant can not be disregarded; (4) from a practical point of view, for single-pole Pomeron and secondary reggeons parametrizations and center-of-mass energies above 5 GeV, the derivative relations with the subtraction constant as a free fit parameter are completely equivalent to the integral forms with finite (non-zero) lower limit. A detailed review on the conditions of validity and assumptions related with the replacement of integral by derivative relations is also presented and discussed.Comment: Revised version, 30 pages, 16 eps-figures, elsart.cls (included), to appear in Nucl Phys.

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Section: Discussionmentioning

confidence: 99%

“…The DDR, in the form introduced by Bronzan, Kane and Sukhatme (BKS), have been criticized by several authors [17,18,19,20] and analyzed and discussed in detail by Fischer, Kolář [21] and Vrkoč [22]. Despite all these works, we understand that two aspects related with the replacement of the IDR, Eqs.…”

Section: Historical Summary and Main Pointsmentioning

confidence: 99%

Critical analysis of derivative dispersion relations at high energies

Ávila

Menon

2004

Nuclear Physics A

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“…(6-7) and the CMSr, Eqs. (8)(9). We first present the fit procedure and then discuss all the obtained results.…”

Section: Practical Equivalences Between the Integral And The Dermentioning

confidence: 99%

“…Even if we can "reproduce" the experimental behavior by means of suitable analytical parameterizations, with statistical errors inferred for the free parameters, these errors should, in principle, be propagated too. In this case, the infinity series in both sDDR and EDDR have certainly limited usefulness (see for example [9,10] for the sDDR case). However, if error propagation from the fit results is not of interest or can be neglected, and, most importantly, one has a "correct" or acceptable model for the imaginary part of the amplitudes, then we are restricted only to the the formal conditions discussed above and the derivative approach becomes reliable, including the correction series (Theorem 1).…”

Section: B Eddrmentioning

confidence: 99%

“…Later on it was shown that, for hadronic forward elastic scattering * Electronic address: menon@ifi.unicamp.br in the region of high and asymptotic energies, these integral relations can be replaced by derivative forms [4][5][6]. Since then, the formal replacement of integral by derivative relations and their practical use have been widely discussed in the literature [7][8][9][10][11][12][13], mainly in the seminal papers by Kolář and Fischer [12,13]. See Ref.…”

Section: Introductionmentioning

confidence: 99%

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Derivative dispersion relations above the physical threshold

Ávila¹,

Menon²

2007

Braz. J. Phys.

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We discuss some formal and practical aspects related to the replacement of Integral Dispersion Relations (IDR) by derivative forms, without high-energy approximations. We first demonstrate that, for a class of functions with physical interest as forward scattering amplitudes, this replacement can be analytically performed, leading to novel Extended Derivative Dispersion Relations (EDDR), which, in principle, are valid for any energy above the physical threshold. We then verify the equivalence between the IDR and EDDR by means of a popular parametrization for total cross sections from proton-proton and antiproton-proton scattering and compare the results with those obtained through other representations for the derivative relations. Critical aspects on the limitations of the whole analysis, from both formal and practical points of view, are also discussed in some detail.Comment: Final version, published in Brazilian Journal of Physics, V. 37, 358 (2007

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H - N

Höhler¹

1983

Pion Nucleon Scattering. Part 2: Methods and Results of Phenomenological Analyses

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Real parts of πN forward amplitudes at high energies

Cited by 10 publications

References 18 publications

Critical analysis of derivative dispersion relations at high energies

Critical analysis of derivative dispersion relations at high energies

Derivative dispersion relations above the physical threshold

H - N

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