1 / 24

Dipole and quadrupole polarizabilities of the pion

Dipole and quadrupole polarizabilities of the pion. L.V. Fil’kov, V.L. Kashevarov Lebedev Physical Institute. NSTAR 2007. 1. Introduction 2. g g  p 0 p 0 3. g p  g p + n 4. g g  p + p - 5. p - A  g p - A 6. Discussion

micheal
Download Presentation

Dipole and quadrupole polarizabilities of the pion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Dipole and quadrupole polarizabilities of the pion L.V. Fil’kov, V.L. Kashevarov Lebedev Physical Institute NSTAR 2007

  2. 1. Introduction 2. g g  p0 p0 3.g p  g p+n 4. g g  p+ p- 5. p-A  g p- A 6. Discussion 7. Summary NSTAR 2007

  3. The dipole (a1, b1) and quadrupole (a2, b2) pion polarizabilities are defined through the expansion of the non-Born helicity amplitudes of the Compton scattering on the pion over t at s=m2 s=(q1+k1)2, u=(q1–k2)2, t=(k2–k1)2 M++(s=μ2,t)=pm[ 2(α1 - β1) + 1/6(α2 - β2)t ] + O(t2) M+-(s=μ2,t)=p/m[ 2(α1 + β1) + 1/6(α2+β2)t] + O(t2) (α1, β1 and α2, β2 in units 10-4 fm3 and 10-4 fm5, respectively)

  4. g g→p0p0 L. Fil’kov, V. Kashevarov, Eur. Phys. J. A5, 285 (1999); Phys. Rev. C72, 035211 (2005)

  5. s-channel: ρ(770), ω(782), φ(1020); t-channel: σ, f0(980), f0(1370), f2(1270), f2(1525) Free parameters: mσ, Γσ, Γσ→ gg, (α1-β1), (α1+β1), (α2-β2), (α2+β2) The σ-meson parameters were determined from the fit to the experimental data on the total cross section in the energy region 270 - 825 MeV. As a result we have found: mσ=(547± 45) MeV, Γσ=(1204±362) MeV, Γσ→ gg=(0.62±0.19) keV p0 meson polarizabilities have been determined in the energy region 270 - 2250 MeV. A repeated iteration procedure was used to obtain stable results.

  6. The total cross section of the reaction gg→p0p0 H.Marsiske et al., Phys.Rev.D 41, 3324 (1990) J.K.Bienlein, 9-th Intern. Workshop on Photon-Photon Collisions, La Jolla (1992) our best fit

  7. p0 meson polarizabilities [1] L .Fil’kov, V. Kashevarov, Eur.Phys.J. A 5, 285 (1999) [2] L. Fil’kov, V. Kashevarov, Phys.Rev. C 72, 035211 (2005) [3] J. Gasser et al., Nucl.Phys. B728, 31 (2005) [4] A. Kaloshin et al., Z.Phys. C 64, 689 (1994) [5] A. Kaloshin et al., Phys.Atom.Nucl. 57, 2207 (1994) Two-loop ChPT calculations predict a positive value of (α2+β2)p0, in contrast to experimental result. One expects substantial correction to it from three-loop calculations.

  8. g + p →g + p+ + n (MAMI) J. Ahrens et al., Eur. Phys. J. A 23, 113 (2005)

  9. where t = (pp –pn )2 = -2mp Tn The cross section of g p→ gp+ n has been calculated in the framework of two different models: • Contribution of all pion and nucleon pole diagrams. • Contribution of pion and nucleon pole diagrams and • D(1232), P11(1440), D13(1520), S11(1535) resonances, • and σ-meson.

  10. To decrease the model dependence we limited ourselves to kinematical regions where the difference between model-1 and model-2 does not exceed 3% when (α1 – β1)p+ =0. I. The kinematical region where the contribution of (α1 – β1)p+ is small: 1.5 m2 < s1 < 5 m2 Model-1 Model-2 Fit of the experimental data The small difference between the theoretical curves and the experimental data was used for a normalization of the experimental data.

  11. II. The kinematical region where the (α1 – β1)p+ contribution is substantial: 5m2 < s1 < 15m2, -12m2 < t < -2m2 (α1 – β1)p+= (11.6 ± 1.5st ± 3.0sys ± 0.5mod) 10-4 fm3 ChPT (Gasser et al. (2006)): (α1 –β1)p+ = (5.7±1.0) 10-4 fm3

  12. gg→p+p- L.V. Fil’kov, V.L. Kashevarov, Phys. Rev. C 73, 035210 (2006) Old analyses: energy region 280 - 700 MeV (α1-β1)p±= 4.4 - 52.6 Our analysis: energy region 280 - 2500 MeV, DRs at fixed t with one subtraction at s=m2, DRs with two subtraction for the subtraction functions, subtraction constants were defined through the pion polarizabilities. s-channel: ρ(770), b1(1235), a1(1260), a2(1320) t-channel: σ, f0(980), f0(1370), f2(1270), f2(1525) Free parameters: (α1-β1)p±, (α1+β1)p±, (α2-β2)p±, (α2+β2)p±

  13. Charged pion polarizabilities [1] L. Fil’kov, V. Kashevarov, Phys. Rev. C 72, 035211 ( 2005). [2] J. Gasser et all., Nucl. Phys. B 745, 84 (2006).

  14. Total cross section of the process gg→p+p- our best fit calculations with α1 and β1 from ChPT Born contribution fit with α1 and β1 from ChPT

  15. Angular distributions of the differential cross sections Mark II – 90 CELLO - 92 VENUS - 95 ╬ ds/d(|cosQ*|<0.6) (nb) Calculations using our fit a1, b1: Bürgi-97, a2, b2 : our fit a1, b1, a2, b2: Gasser-06 |cosQ*|

  16. p- A→ p- g A t  10-4(GeV/c)2 dominance of Coulomb bremsstrahlung t  10-3 Coulomb and nuclear contributions are of similar size t  102  dominance of nuclear bremsstrahlung Serpukhov (1983): Yu.M. Antipov et al., Phys.Lett. B121, 445(1983) E1=40 GeV Be, C, Al, Fe, Cu, Pb w = w2/E1 |t| < 6x10-4 (GeV/c)2 (a1 + b1)=0: (a1 - b1)= 13.6  2.8  2.4

  17. Charged pion dipole polarizabilities

  18. Dispersion sum rules for the pion polarizabilities

  19. The DSR predictions for the charged pions polarizabilities in units 10-4 fm3 for dipole and 10-4 fm5 quadrupole polarizabilities. The DSR predictions for the p0 meson polarizabilities

  20. Contribution of vector mesons DSR ChPT

  21. Discussion • (α1 - β1)p± The σ meson gives a big contribution to DSR for (α1 –β1). However, it was not taken into account in the ChPT calculations. Different contributions of vector mesons to DSR and ChPT. 2. one-looptwo-loopsexperiment (α2-β2)p± = 11.9 16.2 [21.6] 25 +0.8-0.3 The LECs at order p6are not well known. The two-loop contribution is very big (~100%). • (α1,2+β1,2)p± Calculations at order p6 determine only the leading order term in the chiral expansion. Contributions at order p8could be essential.

  22. Summary • The values of the dipole and quadrupole polarizabilities of p0 have been found from the analysis of the data on the process gg→p0p0. • The values of (α1± β1)p0 and (α2 –β2)p0 do not conflict within the errors with the ChPT prediction. 3.Two-loop ChPT calculations have given opposite sign for (α2+β2)p0. 4. The value of (α1 –β1)p± =13.0+2.6-1.9 found from the analysis of the data on the process gg→ p+p - is consisted with results obtained at MAMI (2005) (g p→ g p+ n), Serpukhov (1983) (p-Z → g p-Z), and Lebedev Phys. Inst. (1984) (g p→ g p+ n). 5. However, all these results are at variance with the ChPT predictions. One of the reasons of such a deviation could be neglect of the σ- meson contribution in the ChPT calculations. 6. The values of the quadrupole polarizabilities (α2 ±β2 )p± disagree with the present two-loop ChPT calculations. 7. All values of the polarizabilities found agree with the DSR predictions.

  23. pp and rr contributions to (a1– b1) D(a1b1)p± - 1.88

  24. rr contribution to DSR

More Related