Experimental Evidence on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mo>−</mml:mo><mml:mi>π</mml:mi></mml:math>Scattering Near the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ρ</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>Resonances, from<m

Hagopian, V.; Selove, W.

doi:10.1103/physrevlett.10.533

Cited by 69 publications

(20 citation statements)

References 5 publications

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“…u It has been suggested that this asymmetry could be due to an interference with an S and D wave (7 = 0) background. 11 (D) Production of/ 0 mesons. -As shown by Figs.…”

Section: (4)mentioning

confidence: 99%

Production of Multimeson Resonances byπ+pInteraction and Evidence for aπωResonance

et al. 1963

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“…u It has been suggested that this asymmetry could be due to an interference with an S and D wave (7 = 0) background. 11 (D) Production of/ 0 mesons. -As shown by Figs.…”

Section: (4)mentioning

confidence: 99%

Production of Multimeson Resonances byπ+pInteraction and Evidence for aπωResonance

et al. 1963

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“…Two possible explanations were proposed [4] to account for the behavior of the asymmetry A (a-a+ ): (1) a strong isoscalar S wave or (2) the existence of an isoscalar resonance 0'' near o0 mass. Early models of pion production invoking both alternatives described well the n--ao and a-a+ unpolarized data [8] and later [9] the data on a polarized target in n--pt +n--a+n.…”

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confidence: 99%

Evidence for a scalar stateI=0 0++(750)from measurements ofπ

1992

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Measurements of the reactions a + n 7 -a+a-p at 5.98 and 11.85 GeV/c and a-p +a-n'n at 17.2 GeV/c enable model-independent amplitude analyses which yield two solutions for moduli and cosines of certain relative phases of the two S-wave and six P-wave production amplitudes describing the pion production process below the dipion mass of 1000 MeV. We obtain four solutions for the S-and P-wave intensities in the physical region of the TN-+a+a-N reaction. The results for the S-wave intensity provide solution-independent evidence for a new resonant state I = 0 0++(750). Its a+a-decay width depends on the solution and is estimated to be in the range of 100-250 MeV. The I Z 0 0++(750) meson is best understood as the lowest-mass scalar gluonium O++(gg). Our results emphasize the need for a systematic study of pion production on the level of amplitudes in a new generation of dedicated experiments with spin at the recently proposed high-intensity hadron facilities. PACS number(s1: 14.40.Cs, 13.75.Gx, 13.85.Hd, 13.88.+e The isoscalar meson o with a mass near mass has a long and still controversial history. Following the discovery in 1961 of the p meson in aN +an-N reactions [I], large and energy-independent differences were observed [2-41 in the a-n-O and a-a+ angular distributions over a broad region [5-71 of the dipion mass m. The T-.no forward-backward asymmetry changes sign [7] as it goes through the p-mass while the n--a+ distribution shows a maximum [7] at the mass in its large forwardbackward asymmetry.he forward-backward asymmetry A -Repo, measures S-and P-wave interference.The behavior of A ( n--TO corresponds to a large and resonating P wave interfering with a nonresonant and essentially real S wave. Two possible explanations were proposed [4] to account for the behavior of the asymmetry A (a-a+ ): (1) a strong isoscalar S wave or (2) the existence of an isoscalar resonance 0'' near o0 mass. Early models of pion production invoking both alternatives described well the n--ao and a-a+ unpolarized data [8] and later [9] the data on a polarized target in n--pt +n--a+n. Experiments on unpolarized targets do not measure enough observables to isolate the two contributing S-wave amplitudes, and thus are not selective.An alternative is to search for resonances in an--+an-reactions. In the absence of colliding pion beams, model-dependent extrapolations of the unpolarized data on aN-n-n-N into the unphysical region of -t were used to obtain estimates of the phase shifts in n-a-n-n-scattering. Two solutions [lo-131 similar to the alternatives (1) and (2) were invariably produced for the I = 0 S-wave phase shift 6; in n--n-++n--a+. In principle, a solution can be selected from the study of n--n-++son-o where the S wave can be determined without P-wave interference. Originally, the nonresonating solution was selected [12] by a comparison with voao mass spectrum from n--p +n-Oa0n at 8 GeV/c (Ref. [14]). A more recent study of a-n-+ -n-OaO based on measurement of a+p+noao A + + at 8 GeV/c (Ref.[15]) prefers the resonating solution...

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“…This is in contradiction to Chew's suggestion. In this Letter we will suggest an alternative phase shift which is in the spirit of Chew's conjecture and which (1) leads to the forward asymmetry of the p°, (2) is not inconsistent with the experimental phase shifts, and (3) will lead to a marked enhancement of the 7r + ir~ invariant-mass distribution at low energies.…”

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confidence: 69%

Conjecture for theT=0,S-Wave,π−πPhase Shift

Cook

1966

Phys. Rev. Lett.

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Recently Chew 1 has suggested that the T = 0, S-wave, 71-71 phase shift is a decreasing function of energy, being TI at threshold and dropping to ~7r/2 at the position of the p resonance. If such a behavior were indeed verified, this would not only allow one to understand the persistent forward asymmetry 2 in the decay of the p°, but (as Chew points out) would also provide rather persuasive evidence for the socalled "ghost states." Unfortunately, an admittedly crude examination of the data by Jacobs and Selove 3 shows that the phase shift is between 35 and 55° in the range 400-500 MeV. This is in contradiction to Chew's suggestion. In this Letter we will suggest an alternative phase shift which is in the spirit of Chew's conjecture and which (1) leads to the forward asymmetry of the p°, (2) is not inconsistent with the experimental phase shifts, and (3) will lead to a marked enhancement of the 7r + ir~ invariant-mass distribution at low energies.Rather than Chew's conjecture, we suggest that the phase shift drops through -377/2 as the energy increases from threshold to the p resonance. One may pursue Chew's arguments here and take this to mean that there are two ghost states. Thus the phase shift is 2TT at threshold and drops to ~TT/2 at the position of the p resonance. However, we will consider this as a completely ad hoc suggestion which has some rather interesting properties. Actually it is easy to obtain an analytic expression for such a phase shift by very crude (and of course not very convincing) arguments as follows: Since the scattering is supposedly very attractive, let us assume an extremely deep, finiterange potential of range R. As is well known, this leads to an expression for the energy dependence of the phase shift which we may express by writing 4(This is of course related to Wigner's remarks on the rapidity with which phase shifts may decrease; Wigner obtained 5 d6/dk > -R for a well of finite depth.) We may include some relativistic effects in this by performing a Lo-rentz contraction on R, i.e., R-+R(k 2 + 1) *, and obtainwhere s is the square of the invariant mass of the 77-7T system measured in units of the square of the pion mass. The range has been replaced by the T = 0, S-wave, TT-TI scattering length, i.e., R = -<2 0 <0), measured in units of the pion Compton wavelength. The phase shift is then taken to be 2TT at threshold in the spirit of Chew's remarks (i.e., there are two ghost states). We will use this expression for the calculations that follow, but Eq. (1) should be viewed as simply a set of possible phase shifts characterized by a single parameter, a 0 (0) . There is of course little reason to believe that the S-wave phase shift can be so characterized over the energy range in question, but considering its crudeness it has some surprising properties. Figure 1 shows 6 0 i0) (s) for a 0 (0) = -1.0, -2.2, -2.8. Chew's conjecture is reproduced by a 0 (0) --1.0. The conjecture proposed here is given by -2.8£a 0 (0) £-2.2. We see that if -2.8^0<°><-2.2, then TT/2 :S 6Q {0) {m 2 ) ~ 577/6...

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Experimental Evidence onπ−πScattering Near theρandf0Resonances, from

Cited by 69 publications

References 5 publications

Production of Multimeson Resonances byπ+pInteraction and Evidence for aπωResonance

Production of Multimeson Resonances byπ+pInteraction and Evidence for aπωResonance

Evidence for a scalar stateI=0 0++(750)from measurements ofπ

Conjecture for theT=0,S-Wave,π−πPhase Shift

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