Model-independent analysis of the ππ phase shifts from πN → ππN data

Патаракин, О.О.; Tikhonov, V. N.; Mukhin, K.N.

doi:10.1016/0375-9474(95)00473-4

Cited by 12 publications

(10 citation statements)

References 38 publications

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“…The uncertainties in the values of a 0 0 and a 2 0 are reexamined in refs. [24]. In recent years, it has become increasingly clear, however, that a new analysis of the ππ scattering amplitude at low energies is urgently needed.…”

Section: Introductionmentioning

confidence: 99%

Roy equation analysis of ππ scattering

et al. 2001

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We analyze the Roy equations for the lowest partial waves of elastic ππ scattering. In the first part of the paper, we review the mathematical properties of these equations as well as their phenomenological applications. In particular, the experimental situation concerning the contributions from intermediate energies and the evaluation of the driving terms are discussed in detail. We then demonstrate that the two S-wave scattering lengths a 0 0 and a 2 0 are the essential parameters in the low energy region: Once these are known, the available experimental information determines the behaviour near threshold to within remarkably small uncertainties. An explicit numerical representation for the energy dependence of the S-and P -waves is given and it is shown that the threshold parameters of the Dand F -waves are also fixed very sharply in terms of a 0 0 and a 2 0 . In agreement with earlier work, which is reviewed in some detail, we find that the Roy equations admit physically acceptable solutions only within a band of the (a 0 0 ,a 2 0 ) plane. We show that the data on the reactions e + e − → π π and τ → π π ν reduce the width of this band quite significantly. Furthermore, we discuss the relevance of the decay K → π π e ν in restricting the allowed range of a 0 0 , preparing the grounds for an analysis of the forthcoming precision data on this decay and on pionic atoms. We expect these to reduce the uncertainties in the two basic low energy parameters very substantially, so that a meaningful test of the chiral perturbation theory predictions will become possible.

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Section: Introductionmentioning

confidence: 99%

Roy equation analysis of ππ scattering

et al. 2001

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“…All necessary pion-pion crosssections in the c.m. energy √ s = 0.2−1 GeV (see fig.2) we take from [5], while for √ s > 1 GeV we take the sum of cross-sections σ i = j σ ij as constant of order 20 mb. Variation of σ i for √ s > 1 GeV leads to slight variations of the slope in the dependence of free path length on the energy of the pion.…”

Section: Quark Gluon and Pion Free Path Lengths In The Mediummentioning

confidence: 99%

“…A sensitivity of our results to variation of the quark and gluon free path lengths in QGP is shown in fig.13. Lines marked by circles correspond to evaluation using the values calculated in section 2.1 for quark and gluon free path lengths (5). Lines marked by stars correspond to evaluation with free path lengths twice larger then (5).…”

Section: Stability To Variation Of Parametersmentioning

confidence: 99%

“…Lines marked by circles correspond to evaluation using the values calculated in section 2.1 for quark and gluon free path lengths (5). Lines marked by stars correspond to evaluation with free path lengths twice larger then (5). We see that in the case of larger free path length, and thus lower emission rate of quarks and gluons (see (9)), the multiplicity of direct pions from QGP decreases, and (as a result of energy conservation) the multiplicity of direct pions from pionic gas and freeze-out pions increases.…”

Section: Stability To Variation Of Parametersmentioning

confidence: 99%

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Direct hadron production in ultrarelativistic heavy-ion collisions

Peressounko

Pokrovsky

1997

Nuclear Physics A

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“…Second, one can establish at this point contact with CHPT, that will allow one [1,21] to gain insight into the structure of the underlying theory, the Standard Model. First steps in this program have already been performed [22,23]. Of course, this enterprise requires that one understands the structure of the Roy equations in all details.…”

Section: Introductionmentioning

confidence: 99%

One-channel Roy equations revisited

Gasser¹,

Wanders²

1999

Eur. Phys. J. C

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The Roy equation in the single channel case is a nonlinear, singular integral equation for the phase shift in the low-energy region. We first investigate the infinitesimal neighborhood of a given solution, and then present explicit expressions for amplitudes that satisfy the nonlinear equation exactly. These amplitudes contain free parameters that render the nonuniqueness of the solution manifest. They display, however, an unphysical singularity at the upper end of the interval considered. This singularity disappears and uniqueness is achieved if one uses analyticity properties of the amplitudes that are not encoded in the Roy equation.

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Model-independent analysis of the ππ phase shifts from πN → ππN data

Cited by 12 publications

References 38 publications

Roy equation analysis of ππ scattering

Roy equation analysis of ππ scattering

Direct hadron production in ultrarelativistic heavy-ion collisions

One-channel Roy equations revisited

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