SLIDE 1
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.
Dipole polarizabilities of charged pions L.V. Filkov 1 , V.L. - - PowerPoint PPT Presentation
Dipole polarizabilities of charged pions L.V. Filkov 1 , V.L. - - PowerPoint PPT Presentation
Dipole polarizabilities of charged pions L.V. Filkov 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
SLIDE 2
SLIDE 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
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Review of experimental data on (a1 – b1)p±
Experiments
(a1 - b1)p±
gpgp+ 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 p+p-
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)
gg p+p-
MARK II 5.25 ± 0.95
- L. Fil’kov, V. Kashevarov (2005)
gg p+p- fit of all data from
threshold to 2.5 GeV 13.0+2.6-1.9
- R. Garcia-Martin, B. Moussallam
(2010), gg p+p-
4.7
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g + p → g + p+ + n (MAMI)
and s1 = (k2 + q2)2
SLIDE 6
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: I. Contribution of all pion and nucleon pole diagrams.
- II. Contribution of pion and nucleon pole diagrams and
D(1232), P11(1440), D13(1520), S11(1535) resonances,
and σ-meson.
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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
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- 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
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p- + Z → p- + g + Z
Feff≈ 1 Maximum of the Coulomb peak at Width of the peak:
Q2 x 103(GeV/c)2
Serpukhov (1985)
Ebeam=40 GeV, 4 ×10-6 (GeV/c)2
Coulomb amplitude dominates for Q2≤ 2 ×10-4(GeV/c)2
Q2 ≤ 6 × 10-4 (GeV/c)2 = 13.6 ± 2.8 ± 2.4 Q2 = 6.8 at w1= 600 MeV
SLIDE 10
p- + Z -> p- + g + Z COMPASS Collaboration
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 and therefore a contribution of an interference between the Coulomb and nuclear amplitudes should be taken into account.
(a1)p±=2.0 ± 0.6 ±0.7
This distribution has maximum at Q≈10-2GeV/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 The bump in the nuclear cross section for Q2>1.5×10-3 (Gev/c)2 is a puzzle.
Q2
CN=2×10-3(GeV/c)2 - interference
( G. Faldt, U. Tangblad – (2007))
a1+b1= 0
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N
Q2/GeV2
Q2 dependence for different Z
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0.4 0.5 0.6 0.7 0.8 0.9 xg Serpukhov COMPASS Xg =Eg / Ebeam
z±= 1 ± cos Qcm W ≤ 490 MeV, 0.15 > cosQcm > -1
xg
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Contribution of the s-meson s
z=cosqcm
(J.A. Oller, L. Roca – 2008)
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=4 -COMPASS result
(1) - z= -1
(2) - z= -1 ÷ 0.15
(3) - COMPASS
10
Ms= 441 MeV, Gs = 544 MeV, Gsgg= 1.98 keV, gspp = 3.31 GeV, g2sgg = 16p Ms Gsgg
SLIDE 15
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
(a1-b1)p± = 10
Ms= 441MeV, Gs=544MeV, Gsgg= 1keV,
g2
sgg=16pMsGsgg,
gpp=2.924 GeV
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Summary
1.The values of (a1-b1)p± obtained in the Serpukhov, Mainz, and LPI experiments are at variance with the ChPT predictions. 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 (a1-b1)p± .
- 2. In order to improve the result of the Mainz experiment it is necessary to