1. Prague 05-10/07/2004Marialaura Colantoni1 Advance Study Institute SYMMETRY and SPIN Marialaura Colantoni* on behalf of the COMPASS coll. *Universita’ del Piemonte Orientale and INFN-To Measurement of electric and magnetic pion polarizabilities with Primakoff reaction at Compass spectrometer

2. Prague 05-10/07/2004Marialaura Colantoni2 Compass physics program

3. Prague 05-10/07/2004Marialaura Colantoni3 The polarizability The polarizability (electric  and magnetic  ) relates the average dipole (electric and magnetic ) moment to an external electromagnetic field. q+q+ q-q- The polarizability is a quantity which characterizes a particle like its charge, radius ….

4. Prague 05-10/07/2004Marialaura Colantoni4 Chirality What is the chiral symmetry? Nambu, Quarks frontiers in elementary particle in the limit of zero quark masses SU(3) L  SR(3) R exact chiral symmetry

5. Prague 05-10/07/2004Marialaura Colantoni5 Chirality Nambu, Quarks frontiers in elementary particle The inclusion of quark mass introduces a small breaking of chiral symmetry  perturbative expansion in energy

6. Prague 05-10/07/2004Marialaura Colantoni6 Pion polarizabilities Chiral dynamics describes: properties production decay amplitude low energy interactions Goldstone bosons of the Goldstone bosons ( , , K) among themselves and with  ’s The pion polarizabilities can be described in the framework of the Chiral Perturbation Theory (  PT) based on the chiral symmetry of QCD and Goldstone theorem

7. Prague 05-10/07/2004Marialaura Colantoni7 The  PT L QCD (quark,gluon)  at low energy  L eff ( , , ,p,n..) The  PT provide a rigorous way to determine  ,   via the effective chiral lagrangian The numerical values are: Consistent with the chiral simmetry U. Burgi, Phys.Lett. B 377 (1996) 147

8. Prague 05-10/07/2004Marialaura Colantoni8 Measurements of pion polarizabilities Photon-Photon Collision: f(1270) From the results of MARK II group (1990) [1] with the reaction:  +  - +  +   =(2.2  1.6 stat+sys )10 -4 fm 3  +  - +  + the value of   =(2.2  1.6 stat+sys )10 -4 fm 3 was deduced [2] [1] J.Boyer et al., Phys. Rev. D42, 1350 (1990) [2] P.Babusci et al., Phys. Lett. B 277, 158 (1992)

9. Prague 05-10/07/2004Marialaura Colantoni9 Measurements of pion polarizabilities Pion Photoproduction: A test made by the Lebedev group (1986) with the reaction  + p   +  + + n   = (20±12 stat ) · 10 –4 fm 3  + p   +  + + n showed the feasibility   = (20±12 stat ) · 10 –4 fm 3 [3]. High precision measurement made @ MAMI (A2 coll.)  n ++ p  ++ Data analysis is in progress [3] T.A. Aibergenov et al., Cezch J. Phys B36, 948 (1986)

10. Prague 05-10/07/2004Marialaura Colantoni10 Measurements of pion polarizabilities Primakoff reaction: The Serpukhov group (1985) with the reaction  + 12 C   +  + 12 C  + 12 C   +  + 12 C at 40 GeV gives:   = (6.8 ± 1.4 stat ± 1.2 sys ) · 10 –4 fm 3   = (6.8 ± 1.4 stat ± 1.2 sys ) · 10 –4 fm 3 [4] with the hypothesis (   +   )=0   = (-7.1 ± 2.8 stat ± 1.8 sys ) · 10 –4 fm 3   = (-7.1 ± 2.8 stat ± 1.8 sys ) · 10 –4 fm 3 [5] (   +   )= (1.4±1.4 stat ±1.2 sys ) · 10 –4 fm 3 (   +   )= (1.4±1.4 stat ±1.2 sys ) · 10 –4 fm 3 [5] ** Z  Z  [4] Yu M. Antipov et al., Phys. Lett. 121 B (1985) 445 [5] Yu M. Antipov et al., Z. Phys. C 26 (1985) 495

11. Prague 05-10/07/2004Marialaura Colantoni11 The Primakoff reaction For the reaction  + Z   ’ + Z +  one measures the Primakoff cross section:  photon energy in the antilab system  real photon scattering angle , p 1  ’, p 1 ’ s 1 = ( p 1 ’ + k’ ) 2 , k’  *, k Z, p 2 Z, p 2 ’ t = ( p 2 ’ – p 2 ) 2 Electric & Magnetic polarizabilities 

12. Prague 05-10/07/2004Marialaura Colantoni12 The goals P beam =190 GeV/c to increase the ratio of the coulombian/nuclear cross section and less multiple scattering effect GOALS:  measure independently (   +   ),  ,    enough statistics: to get the statistical errors negligible versus the systematic one evaluate systematic errors due to different cuts more complete angular distribution   t ~ 5 · 10-4 (GeV/c) 2

13. Prague 05-10/07/2004Marialaura Colantoni13 Second Spectrometer: SAS Geometrical Acceptance:  <30 mrad Gap: 200  100 cm 2 Integral field: 4.4 Tm Analyzed momentum: p>10 GeV/c First Spectrometer: LAS Geometrical Acceptance:  >30 mrad Gap: 172  229 cm 2 Integral field: 1 Tm Analyzed momentum: p<60 GeV/c The COMPASS hadron setup 2004

14. Prague 05-10/07/2004Marialaura Colantoni14 Typical reconstructed event:

15. Prague 05-10/07/2004Marialaura Colantoni15 The generator Target 208 Pb t < 850 MeV 2 1.05 · m 2  <s1<30 · m 2  E  > 90 GeV

16. Prague 05-10/07/2004Marialaura Colantoni16 Pion reconstruction p  [GeV]  p/p Pion momentum distribution GeneratedReconstructed Pion momentum resolution ~0.35%

17. Prague 05-10/07/2004Marialaura Colantoni17 Photon reconstruction: E  [GeV]  E/E GeneratedReconstructed Photon distribution energy Photon energy resolution ~ 2.5%

18. Prague 05-10/07/2004Marialaura Colantoni18  final state reconstruction: Resolution of transversal components of the four-momentum transfer to (  ): ~3 · 10 -4 (GeV/c) 2 t[GeV 2 ] t MC -t RC [GeV 2 ] GeneratedReconstructed Four momentum transfer

19. Prague 05-10/07/2004Marialaura Colantoni19 The efficiency = N rec / N gen t[GeV 2 ] Efficiency

20. Prague 05-10/07/2004Marialaura Colantoni20 Polarizabilities statistics With 10 7  /s, the spill structure is 5 s beam every 16 s  2.2·10 11  /day The interaction probability R =  N T = 5·10 -6 assuming:  = 0.5 mbarn N T = A  l/N A = 10 22 cm -2 The global efficiency is estimated to be  = 24 % due to: tracking efficiency ~92% gamma detection ~58% combined acceptance of COMPASS and SPS 60% analysis to reduce background ~75% 2.2 · 10 11  5 · 10 -6  0.24 = 2.64 · 10 5 Events/day

21. Prague 05-10/07/2004Marialaura Colantoni21 Primakoff summary Different target  Z 2 dependence in the the cross section Possible comparison with point like particle via the reaction:  + Z   + Z +  Constant efficiency on t t resolution  3 · 10 -4 (GeV/c) 2 Error on polarizabilities   0.4 · 10 -4 fm 3 (  theory ) kaon polarizabilities Also kaon polarizabilities can be measured

22. Prague 05-10/07/2004Marialaura Colantoni22 Kaon polarizability The K cross section scales down as m -1  3 times smaller compared to the  one. The polarizability goes as Assuming : 3 · 10 5 Kaon/s @ 190 GeV/c 10 3 Events/day we expect 10 3 Events/day

23. Prague 05-10/07/2004Marialaura Colantoni23 F 3  measurement  - + Z  - +  0 + Z useful to access  3  F 3  allows to verify the low energy theorem: F 3  = (12.9 ± 0.9 ± 0.5) GeV -3 [1] F 3  = (9.7 ± 0.2) GeV -3 [2] Expected ~ 5 · 10 3 events/day VS 200 Serpukov events in total [1] Antipov et al., Phys Rev D36 21 (1987) [2] Moinester et al., Proc Conference on Physics with GeV Particle beam, Julic, Germany 1994, Miskimen et al., Theory and Experiment, MIT, 1994

24. Prague 05-10/07/2004Marialaura Colantoni24 Conclusion Using the COMPASS spectrometer one can: test the  PT measuring the pion polarizabilities via the Primakoff reaction.test the  PT measuring the pion polarizabilities via the Primakoff reaction. measure the kaon polarizabilities for the first timemeasure the kaon polarizabilities for the first time measure the chiral anomaly amplitude for  3 measure the chiral anomaly amplitude for  3  and more…and more… this is only a part of the wide research program

25. Prague 05-10/07/2004Marialaura Colantoni25 Trigger y x beam  --  -beam z SM2 ECal2 (128  256)cm 2 SM1 Hodoscope (96  80)cm 2 Beam Counter Target Veto system Trigger:Hodoscope  ECal2 Trigger: Hodoscope  ECal2 ----

26. Prague 05-10/07/2004Marialaura Colantoni26 Comparison with the Serpukhov data @ Serpukhov @COMPASS beam momentum40 GeV/c190 GeV/c beam intensity 10 6   /spill 10 7   /spill targetBe, C, Cu, FeC, Cu, Pb scattered pion    1.2· 10 -4 rad    4 · 10 -5 rad  p /p  1%  p /p  (0.3  1)% outgoing photon    1.5· 10 -4 rad    3.1· 10 -5 rad  E /E  3.5%@27GeV  E /E  (5.5/  E + 1.5)% total flux10 11 10 13  /day Primakoff events~6·10 3 in total6.4 · 10 4 /day