1. Coherent Pion Production
E. A. Paschos
Coherent Pion Production 1

2. Papers over the past year 1) Paschos and Schalla: arXiv:0903.0451
Coherent pions production by neutrinos
2 ) Paschos and Rakshit: (arXiv: )
Pion spectra in the production of resonances
Both articles use helicity cross sections for W+ Target scattering
Both articles are follow ups of previous articles.
I will also use the article Gounaris, Kartavtsev and EAP (Phys. Rev D74, (2006)‏ 2

3. 3

4. ------> replace W +target by pion +target.
(i) It is argued thet for Q²= a few mπ² , i.e. Q² < 0.12 to 0.15 GeV² the reaction is determined by PCAC (Long tradition Adler, Faissner-Rein-Sehgal,...)‏
(ii) For ν²>> Q² the lepton current takes the divergence of the hadronic current
------> replace W +target by
pion +target.
The two conditions give the following formulas 4

5. I must emphazise we do not include only the pion pole, but all the contributions for Q²<0.15GeV².
The pion poles are shown explicitly and are smaller. For the neutral current there are no pion-poles. 5

6. 6

7. Original groups observed in NC reactions a sharp peak in t-dependence, which they called coherent scattering. The peak in neutrino scattering is a manifestation (reflection) of the diffractive peak in pion-nucleus elastic scattering. 7

8. Sparkle-chamber experiment
Faissner Figure 2
Sparkle-chamber experiment
Eν ≈ 2 GeV 8

9. Marage 1984 Figure
BEBC
Eν ≈ 20 GeV 9

10. Marage 1989 Figure 4 10

11. This contribution must always be there
This contribution must always be there. Additional terms are incoherent (other regions of phase space, other polarizations etc.) so that our calculation is a lower bound for this reaction. We study the extended kinematic regions in order to see how large are the extrapolations. 11

12. to first diffractive minimum
Calculation
Use data for elastic pion- nucleus scattering and integrate over the variables
Range of t from
to first diffractive minimum 12

13. Paschos & Schalla
model: 13

14. Paschos & Schalla 14

15. Berger & Sehgal 15

16. We define regions of phase space with a number ξ; no parameter of the theory!16

17. Charged current differential cross section17

18. 18

19. charged current neutral current
Top to bottom: ξ =1,2,3
charged current neutral current 19

20. The ratio of charged to neutral current is less model dependent
The ratio of charged to neutral current is less model dependent. We also define regions of phase space with the number xi; no parameter of the theory! 20

21. I must emphazise we do not include only the pion pole, but all the contributions for Q²<0.15GeV².
The pion poles are shown explicitly and are smaller. For the neutral current there are no pion-poles. 21

23. Bottom to top: Eν = 1.0 , 5.0 and 10.0 GeV
charged current neutral current 23

24. 24

25. Conclusions
1)The cross section is predicted as a function of Q^2,ν and t .When the experiments introduce appropriate cuts it will be possible to check the cross section dependence on various variables.
2) Expected accuracy 20%
3) The difference in the past came from the inappropriate use of data.
4) Up to now the agreement with the experimental results is very good.
5) The ratio of charged to neutral current reactions is predicted with the main difference coming from the kinematics. 25

26. Outlook MUCHAS GRACIAS!
The synergy of Neutrino Oscillation Physics and Precision Measurements of cross sections at low and medium low energies will elucidate many open issues.
It will clarify the dynamics of the neutrino interactions.
It will better determine the masses and mixing parameters:θe3,CP-phases,…. and open the road for discoveries.
Coherent scattering is a good benchmark.
MUCHAS GRACIAS!

27. Faissner Figure 3 27