On the phase of ϵ

Abstract We evaluate the ππ phase shifts δ I l =0.1 to one loop in chiral perturbation theory and determine the phase of the parameter ϵ ′, which measures direct CP violation in K→2 π decays. The result is φ ( ϵ ′)=45°±6°.

[1]  J. Roberts,et al.  Pion pion phase shift and form-factors in the decays k+- ---> pi+ pi- e+- nu(e) , 1973 .

[2]  P. Weilhammer,et al.  Measurement and analysis of the π+π+ system produced at small momentum transfer in the reaction π+p→π+π+n at 12.5 GeV , 1977 .

[3]  R. Dashen,et al.  Soft pions, chiral symmetry, and phenomenological lagrangians , 1969 .

[4]  P. Weilhammer,et al.  ππ Phase-shift analysis from 600 to 1900 MeV , 1973 .

[5]  N. Biswas,et al.  pi-pi+-->pi-pi+ interactions below 0.7 GeV from pi-p-->pi-pi+n data at 5 GeV/c , 1975 .

[6]  R. Ruchti,et al.  Determination of the S Wave $I = 0$ $\pi \pi$ Phase Shifts From Threshold to 0.96-{GeV} , 1981 .

[7]  H. Pagels Departures from chiral symmetry , 1975 .

[8]  Valencia,et al.  Spectrum of QCD and chiral Lagrangians of the strong and weak interactions. , 1989, Physical review. D, Particles and fields.

[9]  T. Devlin,et al.  Weak Hadronic Decays: K ---> 2 pi and K ---> 3 pi , 1979 .

[10]  A. Pich,et al.  The Role of Resonances in Chiral Perturbation Theory , 1989 .

[11]  S. Weinberg Pion scattering lengths , 1966 .

[12]  T. Ferbel,et al.  Study of $pi$$pi$ scattering in the isotopic-spin-2 channel , 1973 .

[13]  C. Yang,et al.  Phenomenological Analysis of Violation of CP Invariance in Decay of K0 and anti-K0 , 1964 .

[14]  A. N. Kamal,et al.  Amplitude analysis for D to Kπ decays , 1986 .

[15]  M. Losty,et al.  A study of π−π− scattering from π−p interactions at 3.93 GeV/c , 1974 .

[16]  S. Bunyatov,et al.  The ππ-scattering phases from the analysis of the reaction π - p→π - π + n near the threshold , 1979 .

[17]  Alan D. Martin,et al.  pi pi Phase Shift Analysis Below the K anti-K Threshold , 1974 .

[18]  M. Sigelle,et al.  Comments on the low-energy ππ P-wave , 1975 .

[19]  T. Truong Unitarity and chiral perturbation theory , 1991 .

[20]  Hai-Yang Cheng Isospin breaking effects on the ΔI = 32 K→ππ amplitudes☆ , 1988 .

[21]  Valencia,et al.  pi - pi scattering and chiral Lagrangians. , 1988, Physical review. D, Particles and fields.

[22]  G. Bunce,et al.  Experimental Study of 30,000 K(e4) Decays , 1977 .

[23]  Heinrich Leutwyler,et al.  Chiral Perturbation Theory: Expansions in the Mass of the Strange Quark , 1985 .

[24]  J. Basdevant,et al.  Construction of phenomenological ππ amplitudes , 1974 .

[25]  P. Langacker,et al.  Chiral perturbation theory , 1973 .

[26]  C. Froggatt,et al.  Phase-shift analysis of π+π− scattering between 1.0 and 1.8 GeV based on fixed momentum transfer analyticity (II) , 1975 .

[27]  A. Dobado,et al.  Unitarized chiral perturbation theory for elastic pion-pion scattering , 1990 .

[28]  M. Baubillier,et al.  Study of the I=2 ππ scattering from the reaction π−d → π−π−psp at 9.0 GeV/c , 1973 .

[29]  S. Roy Exact integral equation for pion-pion scattering involving only physical region partial waves , 1971 .

[30]  H. Pagels,et al.  PERTURBATION THEORY ABOUT A GOLDSTONE SYMMETRY. , 1971 .

[31]  A. Pich,et al.  Chiral lagrangians for massive spin-1 fields , 1989 .

[32]  Heinrich Leutwyler,et al.  Chiral perturbation theory to one loop , 1984 .

[33]  R. Ruchti,et al.  Study of. pi. -. pi. scattering amplitudes in the reaction. pi. /sup +/p. --> delta. /sup + +/. pi. /sup 0/. pi. /sup 0/ at 8. 0 GeV , 1983 .