1. Dipole polarizabilities of π±-mesons
L.V. Fil’kov1, V.L. Kashevarov1,2
[1] Lebedev Physical Institute, Moscow
[2] Institut für Kernphysik, Mainz, Germany

2. Outline Introduction. 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-.
DSRs and ChPT
Summary

3. Pion polarizabilities characterize the behavior of the pion in an external electromagnetic field.
The dipole (a1, b1) and quadrupole (a2, b2) pion polarizabilities are defined through the expansion of the non-Born helicity amplitudes of 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(a1 - b1) + t/6 (a2 - b2) + O(t2)]
M+-(s=μ2,t) = p/m[2(a1 + b1) + t/6 (a2 + b2) + O(t2)]
15.5x10-4 fm3

4. Review of experimental data on (a1 – b1)p±
Experiments
(a1 - b1)p±
gpgp+ n MAMI (2005)
11.6 ± 1.5stat ± 3.0syst ± 0.5mod
gp 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
D. Babusci et al. (1992) PLUTO
gg  + DM1
Eg< 700 MeV MARK II
38.2 ± 9.6 ± 11.4
34.4 ± 9.2
4.4 ± 3.2
J.F. Donoghue, B. Holstein (1993)
gg  p+p MARK II
5.4
A. Kaloshin, V. Serebryakov (1994)
5.25 ± 0.95
L. Fil’kov, V. Kashevarov (2005)
gg  p+p- fit of all data from
threshold to 2.5 GeV
R. Garcia-Martin, B. Moussallam (2010), gg  p+p-
4.7

5. g + p → g + p+ + n
( MAMI, Eur. Phys. J. A 23, 113 (2005) )

6. D(1232), P11(1440), D13(1520), S11(1535) resonances,
where t = (pp –pn )2 = -2mp T,
537 MeV < Eg <817 MeV
The cross section of g p→ g p+ 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.

7. 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 to the experimental data

8. (α1 – β1)p+= (11.6 ± 1.5st ± 3.0sys ± 0.5mod) 10-4 fm3
II. The kinematical region where the (α1 – β1)p+ contribution
is substantial:
5m2 < s1 < 15m2, m2 < 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

9. p- + Z → p- + g + Z
Feff≈ 1
Width of the peak:
Maximum of the Coulomb peak at
Q2 = 6.8
Serpukhov (Phys. Lett. B 121, 445 (1983) )
Ebeam=40 GeV,
4 ×10-6 (GeV/c)2
at w1= 600 MeV
Coulomb amplitude dominates for Q2≤ 2 ×10-4(GeV/c)2
Q2 ≤ 6 × 10-4 (GeV/c)2
Q2≈2-8×10-3(GeV/c)2 –estimation of strong background
= 13.6 ± 2.8 ± 2.4
Q2 x 103(GeV/c)2

10. p- + Z -> p- + g + Z COMPASS Collaboration (Phys. Rev. Lett
Ebeam = 190 GeV (
(Serp)) /(
(COMP)) ≈ 22.5
Q2 ≤ 15 × 10-4 (GeV/c)2
This value of Q2 is very far from the Coulomb peak
5×10-4≤Q2≤15×10-4(GeV/c)2 -the interference with the nuclear amplitude is very important.
The authors could not describe the bumps in the nuclear cross section at Q>0.04 (GeV/c).
At high energies the elastic multiple scattering of hadrons in nuclei is important. (Glauber model) (G.Fäldt, U.Tengblad)
Without a real fit to the data it is impossible to estimate the effect of model dependence of the diffractive background.
(a1)p±=2.0 ± 0.6 ±0.7

11. Q2 dependence for different Z (Serpukhov)
Z2 dependence –an estimation of a contribution of the nuclear background N
Q2/GeV2

12. xg Serpukhov z±= 1 ± cos Qcm W ≤ 490 MeV, 0.15 > cosQcm > -1
Xg =Eg / Ebeam xg xg
Serpukhov
COMPASS
W ≤ 490 MeV, > cosQcm > -1

13. Contribution of the s-meson
z=cosqcm
(J.A. Oller, L. Roca – 2008)

14. 10 (1) - z= -1 (3) - COMPASS =4 - COMPASS result
(J.A. Oller, L. Roca)
Ms= 441 MeV, Gs = 544 MeV,
Gsgg= 1.98 keV, gspp = 3.31 GeV,
g2sgg = 16p Ms Gsgg
(1) - z= -1
(2) - z= -1 ÷ 0.15
(3) - COMPASS 10
Serpukhov: D(a1-b1)p±≈2.7

15. Total cross section for the reaction 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.
Ms= 441MeV, Gs=544MeV,
Gsgg= 1.298keV,
g2sgg=16pMsGsgg,
gpp=3.31 GeV
Result of our fit:
(a1-b1)p± = 10
(a1+b1)p±= 0.107
(a2-b2)p±=30
(a2+b2)p±=0.151
280 MeV < w < 500 MeV:
Born term, dipole and quadrupole polarizabilities,
s-meson

16. The s-meson is only partialy including in ChPT.
DSRs and ChPT
The s-meson is only partialy including in ChPT.
Different methods of vector mesons calculatios in DSRs and ChPT
DSR
ChPT
(Mv/m)2

17. Summary
1.The values of (a1-b1)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 consider other models to fit to the
cross section of the process under consideration.
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 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 (a1-b1)p± .
5. Reasons of the discrepancy between the predictions of DSRs and ChPT
for (a1-b1)π± are due to the difference in the results of the calculations of
the contributions of vector- and s- mesons using these models.
6. It should be noted that the most model independent result was obtained
in the Serpukhov experiment.