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On the precision of  scattering from chiral dispersive calculations

Departamento de Física Teórica II. Universidad Complutense de Madrid. On the precision of  scattering from chiral dispersive calculations. José R. Peláez. J. R. Peláez and F.J. Ynduráin. PRD 68:074005,2003 F.J. Ynduráin. ‘QCD@Work’, hep-ph/0310206

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On the precision of  scattering from chiral dispersive calculations

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  1. Departamento de Física Teórica II. Universidad Complutense de Madrid On the precision of  scattering from chiral dispersive calculations José R. Peláez J. R. Peláez and F.J. Ynduráin. PRD68:074005,2003 F.J. Ynduráin. ‘QCD@Work’, hep-ph/0310206 J. R. Peláez and F.J. Ynduráin. hep-ph/0312187. To appear in Phys. Rev. D.

  2. Motivation: Why a precise determination of  scattering ? A precise determination of  scattering checks how big is B0, and tells us... Quark massesmassive pseudo-GB. Mq = quark mass If B0 large: But NO free parameters!! Pions Goldstone Bosons of the spontaneous chiral symmetry breaking In massless QCD, pions also massless Massless GB non interacting at low energies!! How the QCD vacuum behaves (ferromagnet or antiferromagnet or what)? DIRAC has been a CERN experiment to measure the  scattering lengths

  3. Recent Revival : Using “data” from N + ”Regge” + old Kl4: Fig.14. Ananthanarayan, Colangelo,Gasser & Leutwyler (2001) Adding ChPT+ Other, non ChPT, inputs (Fs...): Colangelo,Gasser & Leutwyler (2001) TINY ERRORS CENTRAL VALUE LOWERED AGAIN NO NEW DATA CGL We have recently questioned this high precision J. R. Peláez and F.J. Ynduráin. PRD68:074005,2003 Roy Equations: results Set of coupled integral equations relating all  channels used to analyse scattering data. 70’s:Using  data from N+Regge+ old Kl4: Basdevant, Froggat, Petersen (74-77) They also give tiny errors for phase shifts and the  mass and width

  4. QUESTIONS ON THE CGL CALCULATION Inconsistent with other sum rules, high energy data, and Regge Theory Inconsistent with other sum rules, high energy data, and Regge Theory Ignores systematic errors in data Input from scalar factor model dependent and challenged

  5. Olsson sum rule: Amplitude nedded only at t=0 or t=4M2 Froissart-Gribov: We do not extract the low energy from here. We use the low energy from CGL and check the consistency with standard Regge. Unsubtracted, OF COURSE, to have an independent check from Roy eqs. Consistency checks 1) Inconsistency with High energy data and Regge: When using correct Regge behavior (as from QCD) in the Olsson and Froissart-Gribov sum rules there is a 2.5 to 4 sigma mismatch (even more now). J. R. Peláez and F.J. Ynduráin. PRD68:074005,2003

  6. Example: D-wave scattering length a+0 from Froissart-Gribov Sum High energy generous error!! We will see... We used a standard Pomeron residue P=3.0 ±0.3 (0.68 ±0.07)10-4 = Pomeron >1420 MeV (-0.06 ±0.02)10-4 = I=2 Regge >1420 MeV 0=(0.36±0.09)10-4 Low energy S2 and P waves up to 820 MeV -a0+ from Roy-CGL = (-2.10 ±0.01)10-4 Other waves up to 1420 S2 and P waves from 820 to 1420 MeV from CERN-Munich data & CGL. (1.84±0.05)10-4 = 4 sigma mismatch. Also 4 sigma for a00, b1 and 2.5 sigma for Olsson Sum Rules

  7. Caprini, Colangelo, Gasser & Leutwyler... Suggested our Regge behavior was incorrect due to crossing symmetry sum rules violations noticed in the 70’s (Pennington.) when used with CERN-Munich data. They claimed that FACTORIZATION did not apply to  scattering

  8. J. R. Peláez and F.J. Ynduráin. hep-ph/0312187 Regge Analysis of , N and NN At high energy, the amplitudes are governed by the exchange of Regge poles related to resonances that couple in the t channel. Regge Pole In QCD the f’s only depend on t and the initial hadrons (like structure functions)factorize(Gell-Mann, Gribov, DGLAP), that is So that we get the pole and fNR(t)/ fR(t) from N and NN scattering.

  9. J. R. Peláez and F.J. Ynduráin. hep-ph/0312187 Regge parameters of N and NN Fit to 270 data points of N , KN and NN total cross sections for kinetic energy between 1 and 16.5 GeV

  10. Regge description of  ,N, NN cross sections +- (mb) s(GeV) Results between total  data and CERN- Munich for 1.4< s<2GeV Matches CERN- Munich at 1.4 GeV. Pomeranchuk theorem: Same  13.2±0.3 mb. CGL use 5±3 mb J. R. Peláez and F.J. Ynduráin. hep-ph/0312187 4 EXPERIMENTS, ‘67, ’73, ’76,’80: IGNORED by Colangelo, Gasser & Leutwyler Excelent fit above 2 GeV -- (mb) 0- (mb)

  11. Regge description of  ,N, NN cross sections J. R. Peláez and F.J. Ynduráin. hep-ph/0312187 Impressive description of N, NN OUR DESCRIPTION :Excellent fit above 2 GeV Has to be used above >1.42 GeV Quark-model value =3/2 Veneziano model ~0.95 Rho dominance model ~0.84 Drammatic improvement in Pomeron Respects QCD factorization Remarkable description of K Within 20% of SU(3) limit= 0.82

  12. “non standard Regge” used in recent dispersive calculations. s(GeV) The “non standard Regge” of CGL lies systematically BELOW the DATA (despite the large compensates a bit the too small Pomeron) 0- (mb) -- (mb) +- (mb)

  13. Regge description of  ,N, NN cross sections J. R. Peláez and F.J. Ynduráin. hep-ph/0312187 For us, a description up to ~15 GeV is enough, but at higher energies hadronic cross sections RAISE. We improve: s The  <15 GeV description is unaffected s

  14. Crossing sum rules to improve the rho residue J. R. Peláez and F.J. Ynduráin. hep-ph/0312187 The crossing sum rule At low energy, the S wave cancels and the well known P wave dominates. At high energy is purelyRegge rho exchange. =0.94 ±0.10(Stat.)±0.10(Syst.) Crossing sum rules satisfied if Regge is used down to ~1.42 MeV Conclusion The Regge used by CGL does NOT describe the data. The updated analysis confirms the mismatch in their analysis

  15. QUESTIONS ON THE CGL CALCULATION Ignores systematic errors in data Inconsistent with other sum rules, high energy data, and Regge Theory Ignores systematic errors in data Input from scalar factor model dependent and challenged

  16. ChPT + Roy Equations. Uncertainties on the matching point. Still, ACGL chooseat 800 MeV: 23.4 ±4o CERN-Munich Analysis B 24.8 ±3.8o Estabrooks & Martin, “s-channel” 30.3 ±3.4 Estabrooks & Martin, “t-channel” 26.5 ±4.2 Protopopescu VI 26.6±3.7o 11-00 =26.6±2.8o 00=82.3 ±3.4o Combined with 11=108.9 ±2othey arrive at: BUT One of their main sources of error is the matching phase at 800 MeV. CGL consider 11-00 “in the hope” that some errors would cancel in that combination. NOWHERE the experimentalistsclaim that such cancellation occurs at 800 MeV. Experimentalists NEVER give such a difference. Estabrooks & Martin: “ ...systematic changes in 00 of the order of 10o” The CERN-Munich experiment has 5 analysis with 10o systematic error

  17. ChPT + Roy Equations. Uncertainties on the matching point. One of the largest sources of uncertainty is the matching phase at  s = 800 MeV The five CERN Munich analysis yield ~ 4o statistical errors in 00, but disagree between themselves and the Berkeley data by ~ 10o systematic errors throughout the whole low energy region. The differences at 800 are not oscillations of statistical nature that can be averaged but systematicerrors of the different procedures to extract the phases

  18. ChPT + Roy Equations. Uncertainties on the matching point. Still, ACGL chooseat 800 MeV: 23.4 ±4o CERN-Munich Analysis B 24.8 ±3.8o Estabrooks & Martin, “s-channel” 30.3 ±3.4 Estabrooks & Martin, “t-channel” 26.5 ±4.2 Protopopescu VI 26.6±3.7o 11-00 =26.6±2.8o 00=82.3 ±3.4o Combined with 11=108.9 ±2othey arrive at: BUT Ananthanarayan, Colangelo Gasser & Leutwyler consider 11-00 “in the hope” that some errors would cancel in that combination. NOWHERE the experimentalists claim that such cancellation occurs at 800 MeV. They NEVER give such a difference. Estabrooks & Martin: “ ...systematic changes in 00 of the order of 10o” The CERN-Munich experiment has 5 analysis with 10o systematic error Protopopescu also gives 11-00=19 ±4 again 10o of systematic error One of their largest sources of error is subestimated by a factor of 3

  19. CONCLUSIONS 1) Inconsistent with High energy data and Regge: When using correct Regge behavior (as from QCD) in the Olsson and Froissart-Gribov sum rules there was a 2 to 4 sigma mismatch (even more now). J. R. Peláez and F.J. Ynduráin. PRD68:074005,2003 With our most recent description of DATA, the mismatch persists. Several sum-rules OFF by 2.5 to 4 sigmas. Factorization & crossing can be accomodated simultaneously in a Regge description of  scattering data J. R. Peláez and F.J. Ynduráin. PRD in press. 2) Neglects systematic errors in  data from N: Most relevant input, phases at matching point (800MeV),assumed error 3.4o, is too small by a factor up to 3 F.J. Ynduráin. ‘QCD@Work’, hep-ph/0310206 3) Other non-ChPT input: Pion scalar radius needed for l3.<r2>S=0.61+-0.04 fm2 Dispersive estimate model dependent. Donoghue, Gasser, Leutwyler.NPB343,341(1990) S. Descotes et al. EJPC24,469(2002) Estimate with recent data <r2>S= 0.75+-0.06 fm2 Bound: <r2>S>=0.70+-0.06 fm2 F.J. Yndurain, Phys.Lett.B578:99-108,2004 The recent chiral dispersive  scattering calculations by Colangelo Gasser & Leutwyler

  20. Using “data” from N +”Regge” +newKl4 (E865 (01)) Despite using incorrect Regge, other recent Roy analysis safer due to larger central values and errors Larger central values Larger errors Descotes et al. Kaminski et al. All numbers from Colangelo, Gasser and Leutwyler: scattering lengths,  scattering phases, and the mass and width of the  (f0(600)) should be taken cautiously, since the uncertainties are largely underestimated

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