1. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 1  and  K atoms as a tool to check precise low energy QCD International Workshop “Exotic hadronic atoms, deeply bound kaonic nuclear states and antihydrogen: present results, future challenges” Trento, June 19 to 23, 2006

2. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 2Outline High-energy and low-energy QCD Precise predictions of low-energy QCD Experimental check of low-energy QCD predictions First lifetime measurement of the π + π – -atom The new experiment on the investigation of π + π – -atom and observation of πK-atoms at PS CERN Potentials of the DIRAC setup at SPS CERN, GSI and J-PARC

3. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 3 Theoretical motivation QCD Standard ModelQ>>Q<< LOW energy HIGH energy Spontaneous chiral symmetry breaking (1967 – Weinberg) perturbative QCD QCD Lagrangian in presence of quark masses: L QCD(q,g) = L sym + L break-sym  high energy (small distance)  “weak” interaction (asymptotic freedom)  expansion in coupling L eff ( ,K,  ) = L sym + L break-sym  low energy (large distance)  strong interaction (confinement)  expansion in momentum & mass M, for large Q, depends only on: L sym L sym and L break-sym and q-condensate M, for small Q, depends on both: At low energies, QCD is replaced by an effective quantum field theory (ChPT) formulated in terms of asymptotically observable fields like , K,  1979,Weinberg 1984,Gasser & Leutwyler

4. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 4 A  and A  K observation and lifetime measurement Main features of the DIRAC set-up Thin targets: ~ 7  10 –3 X 0, Nuclear efficiency: 3  10 −4 Magnetic spectrometer Proton beam ~ 10 11 proton/spill Resolution on Q: Q x ≈ Q y ≈ Q L ≈ 0.5 MeV/c  (A πK ) too small to be measured directly e. m. interaction of A πK in the target A πK  π + K - A Kπ  K + π - Q < 3MeV/c,,  lab < 3 mrad Coulomb from short-lived sources non-Coulomb from long-lived sources “atomic pairs” “free pairs” Target Ni 98  m AπKAπK p 24 GeV/c p π π K K

5. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 5 Theoretical limitations ( A  ) 1. A 2π lifetime π+π+ ππ π0π0 π0π0 H. Jalloul, H.Sazdjian 1998 M.A. Ivanov et al. 1998 A. Gashi et al. 2002 J. Gasser et al. 2001 Current accuracy from the A 2π lifetime calculation 2. A 2π interaction with matter (break-up) L.Afanasyev, G.Baur, T.Heim, K.Hencken, Z.Halabuka, A.Kotsinyan, S.Mrowczynski, C.Santamarina, M.Schumann, A.Tarasov, D.Trautmann, O.Voskresenskaya from Basel, JINR and CERN Current accuracy from break-up probability P br To be reduced by factor 2

6. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 6 Theoretical limitations ( A  K ) K+K+ ππ K0K0 π0π0 J. Schweizer (2004) Current accuracy from the A Kπ lifetime calculations

7. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 7 Energy splitting Energy Splitting between np - nsstates in A 2  atom Energy Splitting between np - ns states in A 2  atom For n = 2 eV from QED calculations eV estimate from ChPT a 0 = 0.220 ± 0.005, a 2 =  0.0444 ± 0.0010 (2001) G. Colangelo, J. Gasser and H. Leutwyler s  E 2 ≈  0.56 eV  (1979) A. Karimkhodzhaev and R. Faustov (1999) A. Gashi et al. (1983) G. Austen and J. de Swart (2000) D. Eiras and J. Soto (1986) G. Efimov et al. Measurement of  and  E allows one to obtain a 0 and a 2 separately Lifetime: A 2    0  0

8. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 8 Metastable atoms A2A2 * is a metastable atom small angle     + + External beam p For p A = 5.6 GeV/c and  = 20  1s = 2.9  10  15 s, 1s = 1.7  10  3 cm  2s = 2.3  10  14 s, 2s = 1.4  10  2 cm  2p = 1.17  10  11 s, 2p = 7 cm 3p  23 cm 4p  54 cm Target Z Thicknessm Br  (l ≥1) 2p 0 3p 0 4p 0  (l =1, m = 0) 041004.45%5.86%1.05%0.46%0.15%1.90% 06505.00%6.92%1.46%0.51%0.16%2.52% 13205.28%7.84%1.75%0.57%0.18%2.63% 2859.42%9.69%2.40%0.58%0.18%3.29% 78218.8%10.5%2.70%0.54%0.16%3.53% Probabilities of the A 2π breakup (Br) and yields of the long-lived states for different targets provided the maximum yield of summed population of the long-lived states:  (l ≥1)

9. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 9 Atomic pairs

10. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 10 DIRAC analysis Improvements on systematics in P Br CC backgroundno improvement± 0.007 signal shapeno improvement± 0.002 Multiple scatteringmeasured to ±1% (DONE)+ 0.002 /-0.002 K + K  /pp bar admixturesto be measured * + 0.000 /-0.023 Finite size effectsto be measured ** + 0.000 /-0.017 Total+ 0.008 /-0.030 * To be measured in 2007/2008 with new PID ** To be measured in 2006/2008 with new trigger for identical particles at low Q Improvements on data quality by fine tuning Adjustments of drift characteristics almost run-by-run B-field adjustment and alignment tuning with  -mass  New pre-selection for all runs (DONE) Comments on analysis strategies Using only downstream detectors (Drift chambers) and investigating only Q L causes less sensitivity to multiple scattering and to the signal shape. Studies are under way and very promising.

11. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 11 Finite-size effects characteristic scale |a| = 387 fm (Bohr radius of  system) average value of r* ~ 10 fm range of  ~ 30 fm range of  ' ~ 900 fm critical region of r* ~ |a| is formed by  and  ' pairs UrQMD simulation pNi 24 GeV: ● ~15%  pairs  ● < 1%  ' pairs  shift in P br mainly due to  pairs '' 

12. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 12 Finite-size effects Simulation vs fit of DIRAC      CF simulation N  (      ) = 19.2% fit result N  (      ) = 21±7%  good description of  pairs by UrQMD In π + π  system finite-size effect induces shift in P br UrQMD simulation N   π + π    = 15%   P br ~ 2%   ~ 5% upper limit at 1  of     fitN  (π + π  )  = 20%   P br ~ 3%   ~ 7.5%  Systematic shift in  measurement from finite-size effect < 10% i.e. less then present DIRAC statistical error in . Expected shift with multi-layer target in future DIRAC five times less     corr. Function (CF), arbitrary units

13. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 13 Dual Target Method Single/Multilayer target comparison: –Same amount of multiple scattering –Same background (CC, NC, ACC) –Same number of produced A 2 , but lower number of dissociated pairs

14. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 14 ππ scattering lengths Results from E865/BNL (S.Pislak et al., Phys. Rev. Lett. 87 (2001) 221801) : K  π + π  e + v e (K e4 ) Present low energy QCD predictions: using Roy eqs. using Roy eqs. and ChPT constraints a 2 = f ChPT (a 0 ) Upgraded DIRAC (DIRAC II) Results from NA48/2 (J.R.Batley et al., Phys. Lett. B633 (2006) 173) : K +  π 0 π 0 π + First result (L. Rosselet et al., Phys. Rev. D15 (1977) 574) : DIRAC, 2001data (Phys. Lett. B 619 (2005) 50) DIRAC expected results, 2001–2003 data

15. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 15 Trajectories of π − and K + from the A πK break-up π  and K + momenta in GeV/c A πK, π - and K + momenta P atom (GeV/c) P π (GeV/c) P K (GeV/c) 5.131.134.0 5.771.274.5 6.411.415.0 10.262.268.0

16. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 16 Upgraded DIRAC experimental set-up description

17. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 17 V. Bernard, N. Kaiser, U. Meissner. – 1991 πK scattering I. ChPT predicts s-wave scattering lengths: J. Bijnens, P. Talaver. – April 2004 A. Rossel. – 1999 II. Roy-Steiner equations: III. A  K lifetime: J. Schweizer. – 2004 L (2), L (4) and 1-loop L (2), L (4), L (6) and 2-loop

18. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 18 What new will be known when  K scattering length will be measured? The measurement of s-wave πK scattering length would test our understanding of chiral SU(3) L  SU(3) R symmetry breaking of QCD (u, d and s), while the measurement of ππ scattering length checks only SU(2) L  SU(2) R symmetry breaking (u, d). This is the main difference between ππ and πK scattering!

19. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 19 Time scale for the A 2π and A πK experiment 2006 Manufacture and installation of new detectors and electronics: 6 months Test of the Upgraded setup and calibration: 3 months 2007 and 2008 Measurement of A 2π lifetime: 12 months In this time 86000 ππ atomic pairs will be collected to measure A 2π lifetime with precision of: At the same time we also should observe A πK and, if so, detect 5000 πK atomic pairs to estimate A πK lifetime with precision of: This estimation of the beam time is based on the A 2π statistics collected in 2001 and on the assumption of having 2.5 spills per supercycle during 20 hours per day.

20. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 20 Expected accuracy for ππ-scattering Estimates of relative errors (  |a 0 - a 2 | / |a 0 - a 2 | ) based on data taken with the upgraded DIRAC setup during 12 months (20h/day), single-layer target Number of atomic pairs n A Statistical error Theoretical error from  = f (a 0 - a 2 ) Theoretical error from P br =  (  ) (*) Error from non point-like production PS CERN 24 GeV/c 850002%0.6%1.2%  1% J-PARC 50 GeV/c 4.1  10 5 0.9%0.6%1.2% GSI 90 GeV/c 1.2  10 6 0.6% 1.2% SPS CERN 450 GeV/c 1.26  10 6 0.5%0.6%1.2% (*) Precision on P br =  (  ) can be increased and the error will be less than 0.6% private communication by D. Trautmann

21. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 21 Expected accuracy for πK-scattering Estimates of relative errors (  |a 1/2 - a 3/2 | / |a 1/2 - a 3/2 | ) based on data taken with the upgraded DIRAC setup during 12 months (20h/day), single-layer target Number of atomic pairs n A Statistical error Theoretical error from  = f (a 1/2 - a 3/2 ) Theoretical error from P br =  (  ) (*) Error from non point-like production PS CERN 24 GeV/c 700010%1.1%1.2%  1% J-PARC 50 GeV/c 1.7  10 4 7%1.1%1.2% GSI 90 GeV/c 1.4  10 5 2.5%1.1%1.2% SPS CERN 450 GeV/c 1.26  10 5 2.5%1.1%1.2% (*) Precision on P br =  (  ) can be increased and the error will be less than 0.6% private communication by D. Trautmann

22. Trento, June 20, 2006Leonid Nemenov, CERN (presented by L. Tauscher) 22 DIRAC collaboration 75 Physicists from 18 Institutes INFN Laboratori Nazionali di Frascati Frascati, Italy Trieste University and INFN-Trieste Trieste, Italy University of Messina Messina, Italy Basel University Basel, Switzerland Bern University Bern, Switzerland Zurich University Zurich, Switzerland Santiago de Compostela University Santiago de Compostela, Spain SINP of Moscow State University Moscow, Russia IHEP Protvino, Russia JINR Dubna, Russia IFIN-HH Bucharest, Romania Czech Technical University Prague, Czech Republic Institute of Physics ASCR Prague, Czech Republic KEK Tsukuba, Japan Kyoto Sangyou University Kyoto, Japan Tokyo Metropolitan University Tokyo, Japan CERN Geneva, Switzerland