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

Motivation: Why a precise determination of  scattering ? Pions  Goldstone Bosons of the spontaneous chiral symmetry breaking In massless QCD, pions also massless Massless GB non interacting at low energies!! Quark masses  massive pseudo-GB. M q = quark mass If B 0 large: NO free parameters!! But How the QCD vacuum behaves (ferromagnet or antiferromagnet or what)? A precise determination of  scattering checks how big is B 0, and tells us... DIRAC has been a CERN experiment to measure the  scattering lengths

Roy Equations: results Recent Revival : Using  “data” from  N + ”Regge” + old K l4 : Fig.14. Ananthanarayan, Colangelo,Gasser & Leutwyler (2001) Adding ChPT+ Other, non ChPT, inputs (F s...): Colangelo,Gasser & Leutwyler (2001) TINY ERRORS CENTRAL VALUE LOWERED AGAIN NO NEW DATA CGL  Set of coupled integral equations relating all  channels used to analyse scattering data. 70’s: Using  data from  N+Regge+ old K l4 : Basdevant, Froggat, Petersen (74-77) We have recently questioned this high precision J. R. Peláez and F.J. Ynduráin. PRD68:074005,2003 They also give tiny errors for phase shifts and the  mass and width

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

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 Consistency checks Amplitude nedded only at t=0 or t=4M 2 Olsson sum rule: Froissart-Gribov: Unsubtracted, OF COURSE, to have an independent check from Roy eqs. We do not extract the low energy from here. We use the low energy from CGL and check the consistency with standard Regge.

Example: D-wave scattering length a +0 from Froissart-Gribov Sum S2 and P waves up to 820 MeV -a 0+ 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) sigma mismatch. Also 4 sigma for a 00, b 1 and 2.5 sigma for Olsson Sum Rules Low energy Pomeron >1420 MeV = (0.68 ±0.07)10 -4 We used a standard Pomeron residue  P =3.0 ±0.3 generous error!! We will see... I=2 Regge >1420 MeV = (-0.06 ±0.02) =(0.36±0.09)10 -4 High energy

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 Caprini, Colangelo, Gasser & Leutwyler...

Regge Analysis of ,  N and NN J. R. Peláez and F.J. Ynduráin. hep-ph/ 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 f N R (t)/ f  R (t) from  N and NN scattering.

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

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

Regge description of ,  N, NN cross sections Best Values f N P /f  P 1.406±0.007  0.366±0.010  0.94 ±0.10 ±0.10 PP 2.56 ±0.03  P’ 1.05 ±0.05 Veneziano model ~0.95 Rho dominance model ~0.84  : Excellent fit above 2 GeV Has to be used above >1.42 GeV Quark-model value =3/2 Respects QCD factorization Remarkable description of  K Within 20% of SU(3) limit= 0.82 f N P /f K P 0.67±0.01 J. R. Peláez and F.J. Ynduráin. hep-ph/ Impressive description of  N, NN OUR DESCRIPTION Drammatic improvement in Pomeron

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

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

Crossing sum rules to improve the rho residue The crossing sum rule At low energy, the S wave cancels and the well known P wave dominates. At high energy is purely Regge rho exchange.   = 0.94 ±0.10(Stat.) ±0.10(Syst.) J. R. Peláez and F.J. Ynduráin. hep-ph/ 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

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

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. ChPT + Roy Equations. Uncertainties on the matching point. Combined with  11 =108.9 ±2 o they arrive at: 23.4 ±4 o CERN-Munich Analysis B 24.8 ±3.8 o Estabrooks & Martin, “s-channel” 30.3 ±3.4 Estabrooks & Martin, “t-channel” 26.5 ±4.2 Protopopescu VI 26.6±3.7 o  11 -  00 =26.6±2.8 o  00 =82.3 ±3.4 o Still, ACGL choose at 800 MeV: Estabrooks & Martin: “...systematic changes in  00 of the order of 10 o ” The CERN-Munich experiment has 5 analysis with  10 o systematic error BUT

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 ~ 4 o statistical errors in  00, but disagree between themselves and the Berkeley data by ~ 10 o systematic errors throughout the whole low energy region. The differences at 800 are not oscillations of statistical nature that can be averaged but systematic errors of the different procedures to extract the phases

ChPT + Roy Equations. Uncertainties on the matching point. 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. Combined with  11 =108.9 ±2 o they arrive at: 23.4 ±4 o CERN-Munich Analysis B 24.8 ±3.8 o Estabrooks & Martin, “s-channel” 30.3 ±3.4 Estabrooks & Martin, “t-channel” 26.5 ±4.2 Protopopescu VI 26.6±3.7 o  11 -  00 =26.6±2.8 o  00 =82.3 ±3.4 o Still, ACGL choose at 800 MeV: Estabrooks & Martin: “...systematic changes in  00 of the order of 10 o ” The CERN-Munich experiment has 5 analysis with  10 o systematic error Protopopescu also gives  11 -  00 =19 ±4 again  10 o of systematic error One of their largest sources of error is subestimated by a factor of 3 BUT

CONCLUSIONS 2) Neglects systematic errors in  data from  N: Most relevant input, phases at matching point (800MeV), assumed error 3.4 o, is too small by a factor up to 3 F.J. Ynduráin. hep-ph/ ) Other non-ChPT input: Pion scalar radius needed for l 3. S = fm 2 Dispersive estimate model dependent. S. Descotes et al. EJPC24,469(2002) Estimate with recent data S = fm 2 Bound: S >= fm 2 F.J. Yndurain, Phys.Lett.B578:99-108,2004 Donoghue, Gasser, Leutwyler.NPB343,341(1990) 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 The recent chiral dispersive  scattering calculations by Colangelo Gasser & Leutwyler 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.

Using  “data” from  N +”Regge” +new K l4 ( E865 (01)) Descotes et al.Kaminski et al. Larger central values Larger errors Despite using incorrect Regge, other recent Roy analysis safer due to larger central values and errors All numbers from Colangelo, Gasser and Leutwyler: scattering lengths,  scattering phases, and the mass and width of the  (f 0 (600)) should be taken cautiously, since the uncertainties are largely underestimated