Dipole polarizabilities of charged pions L.V. Filkov 1 , V.L. - PowerPoint PPT Presentation

Dipole polarizabilities of charged pions L.V. Fil’kov 1 , V.L. Kashevarov 1,2 , Th. Walcher 2 [1] Lebedev Physical Institute, Moscow [2] Institut fur Kernphysik, Mainz, Germany EMIN – 2015 XIV International Seminar on Electromagnetic Interactions of Nuclei

Outline 1.Introduction. 2. g + p -> g + p + + n (Mainz). 3. p - + Z -> g + p - + Z (Serpukhov). 4. p - + Z -> g + p - + Z ( COMPASS). 5 . g + g -> p + + p - . 6. Summary.

Pion polarizabilities characterize the behavior of the pion in an external electromagnetic field. The dipole ( a 1 , b 1 ) and quadrupole ( a 2 , b 2 ) pion polarizabilities are defined through the expansion of the non-Born helicity amplitudes of Compton scattering on the pion over t at s= m 2 s=(q 1 +k 1 ) 2 , u=(q 1 – k 2 ) 2 , t=(k 2 – k 1 ) 2 M ++ (s= μ 2 ,t ) = pm[ 2( a 1 - b 1 ) + t/6 ( a 2 - b 2 ) + O(t 2 )] M +- (s= μ 2 ,t ) = p/m [2 ( a 1 + b 1 ) + t/6 ( a 2 + b 2 ) + O(t 2 )] 15.5 x 10 -4 fm 3

Review of experimental data on ( a 1 – b 1 ) p ± ( a 1 - b 1 ) p ± Experiments g p gp + n MAMI (2005) 11.6 ± 1.5 stat ± 3.0 syst ± 0.5 mod g p gp + n Lebedev Phys. Inst. (1984) 40 ± 20 p - Z g p - Z Serpukhov (1983) 13.6 ± 2.8 ± 2.4 p - Z g p - Z COMPASS (2014) 4.0 ± 1.2 ± 1.4 38.2 ± 9.6 ± 11.4 D. Babusci et al. (1992) PLUTO gg  p + p - 34.4 ± 9.2 DM1 4.4 ± 3.2 E g < 700 MeV MARK II J.F. Donoghue, B. Holstein (1993) 5.4 gg  p + p - MARK II 5.25 ± 0.95 A. Kaloshin, V. Serebryakov (1994) gg  p + p - MARK II L. Fil’kov, V. Kashevarov (2005) gg  p + p - fit of all data from 13.0+2.6-1.9 threshold to 2.5 GeV R. Garcia-Martin, B. Moussallam 4.7 (2010), gg  p + p -

g + p → g + p + + n (MAMI) and s 1 = (k 2 + q 2 ) 2

where t = (p p – p n ) 2 = -2m p T, 537 MeV < E g <817 MeV The cross section of g p→ g p + n has been calculated in the framework of two different models: I. Contribution of all pion and nucleon pole diagrams. II. Contribution of pion and nucleon pole diagrams and D (1232), P 11 (1440), D 13 (1520), S 11 (1535) resonances, and σ -meson .

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 ( α 1 – β 1 ) p + =0. I. The kinematical region where the contribution of ( α 1 – β 1 ) p + is small: 1.5 m 2 < s 1 < 5 m 2 Model-1 Model-2 Fit of the experimental data

II. The kinematical region where the ( α 1 – β 1 ) p + contribution is substantial: 5 m 2 < s 1 < 15 m 2 , -12 m 2 < t < -2 m 2 ( α 1 – β 1 ) p + = (11.6 ± 1.5 st ± 3.0 sys ± 0.5 mod ) 10 -4 fm 3 ChPT (Gasser et al. (2006)) : ( α 1 –β 1 ) p+ = (5.7 ± 1.0) 10 -4 fm 3

p - + Z → p - + g + Z F eff ≈ 1 Width of the peak: Maximum of the Coulomb peak at Q 2 = 6.8 Serpukhov (1985) 4 × 10 -6 (GeV/c) 2 E beam =40 GeV , at w 1 = 600 MeV Coulomb amplitude dominates for Q 2 ≤ 2 × 10 -4 (GeV/c) 2 Q 2 ≤ 6 × 10 -4 (GeV/c) 2 = 13.6 ± 2.8 ± 2.4 Q 2 x 10 3 (GeV/c) 2

p - + Z -> p - + g + Z COMPASS Collaboration a 1 +b 1 = 0 E beam = 190 GeV Q 2 ≤ 15 × 10 -4 (GeV/c) 2 ( ( Serp) ) /( (COMP) ) ≈ 22.5 This value of Q 2 is very far from the Coulomb peak and therefore a contribution of an interference between the Coulomb and nuclear amplitudes should be taken into account . CN =2 × 10 -3 (GeV/c) 2 - interference Q 2 ( G. Faldt, U. Tangblad – (2007)) This distribution has maximum at Q≈10 - 2 GeV/c. The maximum of the Coulomb peak at Q ≤5× 10 -4 GeV/c. Much of the contribution from the Coulomb peak was not taken account (a 1 ) p ± =2.0 ± 0.6 ± 0.7 The bump in the nuclear cross section for Q 2 >1.5 × 10 -3 ( Gev/c) 2 is a puzzle.

Q 2 dependence for different Z N Q 2 /GeV 2

z ± = 1 ± cos Q cm X g = E g / E beam x g 0.4 0.5 0.6 0.7 0.8 0.9 x g Serpukhov COMPASS W ≤ 490 MeV, 0.15 > cos Q cm > -1

s Contribution of the s -meson z=co s q cm (J.A. Oller, L. Roca – 2008)

=4 - COMPASS result M s = 441 MeV, G s = 544 MeV, G sgg = 1.98 keV, g spp = 3.31 GeV, g 2 sgg = 16 p M s G sgg (1) - z= -1 ( 2) - z= -1 ÷ 0.15 (3) - COMPASS 10

Total cross section for the reaction g g → p + p - The cross section is particularly sensitive to at w ≤ 800 MeV. However, the values of the experimental cross section of the process under consideration in this region are very ambiguous. 280 MeV < w < 500 Mev Born term, dipole and quadrupole polarizabilities, s -meson M s = 441MeV, G s =544MeV, G sgg = 1keV , sgg =16 p M s G sgg , g 2 g pp =2.924 GeV (a 1 -b 1 ) p ± = 10

Summary 1.The values of (a 1 -b 1 ) p ± obtained in the Serpukhov, Mainz, and LPI experiments are at variance with the ChPT predictions. 2. In order to improve the result of the Mainz experiment it is necessary to use a better neutron detector and to take into account the contribution of the anomalous magnetic moments of the nucleons in the model-2. 3.The result of the COMPASS Collaboration is in agreement with the ChPT calculations. However, this result is very model dependent. It is necessary to correctly investigate the interference between Coulomb and nuclear amplitudes and to take into account the contribution of the s -meson. 4. New, more accurate experimental data on the process gg->p + p - in region W ≤ 800 MeV are needed to obtain reliable values of (a 1 -b 1 ) p ± .