Atoms, consisting of  +  -,  +  - or  -  +, as a tool to check precise "Low Energy QCD" predictions L. Nemenov KAON Kaon Physics International Conference University of Michigan, Ann Arbor April 29-May 1 on behalf of the DIRAC Collaboration

CERN Geneva, Switzerland Kyoto University Kyoto, Japan Bern University Bern, Switzerland KEK Tsukuba, Japan Santiago de Compostela University Santiago de Compostela, Spain University of Messina Messina, Italy IHEP Protvino, Russia INFN-Laboratori Nazionali di Frascati Frascati, Italy SINP of Moscow State University Moscow, Russia JINR Dubna, Russia Nuclear Physics Institute ASCR Rez, Czech Republic IFIN-HH Bucharest, Romania Institute of Physics ASCR Prague, Czech Republic Tokyo Metropolitan University Tokyo, Japan Czech Technical University Prague, Czech Republic Zurich University Zurich, Switzerland Kyoto Sangyou University Kyoto, Japan DIRAC collaboration

Contents 6. Search for long-lived  +  - atoms. 3. DIRAC setup. 4. Status of  +  - atom investigation. 5. Status of  +  -,  -  + atom investigation. 7. Atoms consisting of  +  Generation of  +  -,  -  + and  +  - atoms in p-nuclear interaction at proton beam momentum 24 GeV/c and 450 GeV/c. 1. Low-energy QCD precise predictions. 2. Method of  and K  atom investigation.

In ChPT the effective Lagrangian, which describes the  interaction, is an expansion in (even) terms: Colangelo et al. in 2001, using ChPT (2-loop) & Roy equations: These results (precision) depend on the low-energy constants (LEC) l 3 and l 4 : Lattice gauge calculations from 2006 provided values for these l 3 and l 4. Because l 3 and l 4 are sensitive to the quark condensate, precision measurements of a 0, a 2 are a way to study the structure of the QCD vacuum. (tree) (1-loop) (2-loop)  scattering lengths

Lattice calculations of l 3, l 4 J. Gasser, H. Leutwyler: Model calculation (1985) l 3 =2.6  2.5,  l 3 / l 3  1 Lattice calculations in near future will obtain  l 3 / l 3  0.1 or  l 3  To check the predicted values of l 3 the experimental relative errors of  -scattering lengths and their combinations must be at the level ( )% 2006: l 3, l 4 First lattice calculations 2012: 10 collaborations: 3 USA, 5 Europe, 2 Japan

 scattering ChPT predicts s-wave scattering lengths: The estimates indicate values in the range 0 < l 3 < 5 is the quark condensate, reflecting the property of QCD vacuum.where The expansion of M  2 in powers of the quark masses starts with the linear term: Measurement of l 3  improved the value of

 scattering lengths I. ChPT predicts s-wave scattering lengths: V. Bernard, N. Kaiser, U. Meissner. – 1991 J. Bijnens, P. Dhonte, P. Talavera. – April 2004 A. Roessl. – 1999 II. Roy-Steiner equations: P.Büttiker et al. − 2004

 scattering The measurement of the s- wave  scattering lengths would test our understanding of the chiral SU(3) L  SU(3) R symmetry breaking of QCD ( u, d and s quarks), while the measurement of  scattering lengths checks only the SU(2) L  SU(2) R symmetry breaking ( u, d quarks). What new will be known if  K scattering length will be measured? This is the principal difference between  and  scattering! Experimental data on the  low-energy phases are absent

Pionium lifetime The lifetime of  +  − atoms is dominated by the annihilation process into  0  0 : a 0 and a 2 are the  S-wave scattering lengths for isospin I=0 and I=2. Pionium (A 2  ) is a hydrogen-like atom consisting of  + and  - mesons: E B =-1.86 keV, r B =387 fm, p B ≈0.5 MeV If π+π+ ππ π0π0 π0π0 Gasser et al. – 2001

    and     atoms lifetime K+K+ ππ K0K0 π0π0 (**) J. Schweizer (2004) From Roy-Steiner equations: K  -atom (A K  ) is a hydrogen-like atom consisting of K + and  − mesons: E B = -2.9 keV r B = 248 fm p B ≈ 0.8 MeV The K  -atom lifetime (ground state 1S),  =1/  is dominated by the annihilation process into K 0  0 : ** If

Method of   observation and investigation

Method of  and  atoms observation and investigation

Coulomb pairs and atoms For the charged pairs from the short-lived sources and small relative momentum Q there is strong Coulomb interaction in the final state. This interaction increases the production yield of the free pairs with Q decreasing and creates atoms. There is precise ratio between the number of produced Coulomb pairs (N C ) with small Q and the number of atoms (N A ) produced simultaneously with these Coulomb pairs: Coulomb pairsAtoms  +  -  +  -  -  +   +  -  +  -  -  +  +  -  +  -  -  +   +  -  +  -  -  + 

Cross section calculation precision 0.6% Break-up probability Solution of the transport equations provides one-to-one dependence of the measured break-up probability (P br ) on pionium lifetime τ All targets have the same thickness in radiation lengths 6.7*10 -3 X 0 There is an optimal target material for a given lifetime

Experimental setup 1 Target station with Ni foil; 2 First shielding; 3 Micro Drift Chambers; 4 Scintillating Fiber Detector; 5 Ionization Hodoscope; 6 Second Shielding; 7 Vacuum Tube; 8 Spectrometer Magnet; 9 Vacuum Chamber; 10 Drift Chambers; 11 Vertical Hodoscope; 12 Horizontal Hodoscope; 13 Aerogel Čerenkov; 14 Heavy Gas Čerenkov; 15 Nitrogen Čerenkov; 16 Preshower; 17 Muon Detector

Experimental conditions SFD Coordinate precision  X = 60  m  Y = 60  m  W = 120  m Time precision  t X = 380 ps  t Y = 512 ps  t W = 522 ps DC Coordinate precision  = 85  m VH Time precision  = 100 ps Spectrometer Relative resolution on the particle momentum in L.S Precision on Q-projections  Q X =  Q Y = 0.5 MeV/c  Q L = 0.5 MeV/c (  )  Q L = 0.9 MeV/c (  ) Trigger efficiency 98 %for pairs with Q L < 28 MeV/c Q X < 6 MeV/c Q Y < 4 MeV/c

Published results on  atom: lifetime and scattering length * theoretical uncertainty included in systematic error DIRAC data  1s ( s) value stat syst theo* tot |a 0 -a 2 | value stat syst theo* tot Reference 2001 PL B 619 (2005) PL B 704 (2011) 24 NA48K-decay a 0 -a 2 value stat syst theo tot Reference 2009 K3K3 EPJ C64 (2009) K e4  & K 3  EPJ C70 (2010) 635

Run , statistics with low and medium background (2/3 of all statistics). Point-like production of all particles.  +  - atoms, run Analysis on Q L, Q T < 4 MeV/c P br ( ) =  The expected precision of |a 0 -a 2 | measurement using atomic pairs from runs and is 3%.

Break-up dependencies P br from atoms lifetime for  +  - atom (A  ) and    + atom (A  ) Probability of break-up as a function of lifetime in the ground state for A  (solid line) and A  atoms (dashed line) in Ni target of thickness 108  m. Average momentum of A  and A  are 6.4 GeV/c and 6.5 GeV/c accordingly. P br values corresponding to  1S th Atoms,  mP br P br -  P br +  A  A  A  A 

Run , statistics with low and medium background (2/3 of all statistics). Point-like production of all particles.  +  - and  +  - atoms, run Analysis on Q L, Q T < 4 MeV/c

    and     pairs analysis  +  - pairs  +  - pairs  +  - and  +  - pairs sum N A (Q L )200    49 n A (Q L )53  3745  5998  70 P br (Q L )0.27    P br theor  The data analysis using two dimentional distribution on Q L -Q T will decrease P br error on a factor 1.5.

Long-lived  +  - atoms The observation of  atom long-lived states opens the future possibility to measure the energy difference between ns and np states ΔE(ns-np) and the value of  scattering lengths |2a 0 +a 2 |. If a resonance method can be applied for the ΔE(ns-np) measurement, then the precision of  scattering length measurement can be improved by one order of magnitude relative to the precision of other methods.

Method for observing long-lived A 2  with breakup Pt foil QYQY l(2p) = 5.7 cm, l(3p) = 19 cm, l(4p) = 44 cm, l(5p) = 87 cm l(2s) = 0.14 mm, l(3s) = 0.46 mm, l(4s) = 1.1 mm for  =17

Simulation of long-lived A 2  observation From the experimental Coulomb pair analysis the expected number of atomic pairs will be n A =190  18. The expected atomic pairs signal obtained after background subtraction should be better than 6 . Atomic pairs from long-lived atoms (light area) above background (hatched area) produced in Beryllium target with criteria |Q X | < 1 MeV/c.

2010 data: distribution of pairs on (t + +t - )/2 for P=(1800, 2000) MeV/c (t + +t - )/2

2010 data: results for kaons and K + K - pairs in low momenta Total number of K + K - pairs in low momenta MeV/c is sse(K + ), sse(K - ), sse(K + K - ) – standard statistic error for K +, K -, K + K - pairs accordingly. Total number of K + K - pairs in high momenta MeV/c is The sum of low and high energy kaon pairs is 9800.

K + K - Coulomb pairs and K + K - atoms For the charged pairs from the short-lived sources and small relative momentum Q there is strong Coulomb interaction in the final state. There is precise ratio between the number of produced Coulomb pairs (N C ) with small Q and the number of atoms (N A ) produced simultaneously with these Coulomb pairs: Coulomb pairsAtoms +-+-  +  -  From K + K - pair analysis the Coulomb pair distribution on Q will be obtained, allowing to extract the total number of produced K + K - atoms.

 +  - atom and its lifetime τ (A 2K → ππ,πη)K + K - interaction 1.2× s [1]Coulomb-bound 8.5× s [3]momentum dependent potential 3.2× s [2]+ one-boson exchange (OBE) 1.1× s [2]+ f 0 ’ (I=0) + πη-channel (I=1) 2.2× s [4]ChPT [1] S. Wycech, A.M. Green, Nucl. Phys. A562 (1993), 446; [2] S. Krewald, R. Lemmer, F.P. Sasson, Phys. Rev. D69 (2004), ; [3] Y-J Zhang, H-C Chiang, P-N Shen, B-S Zou, PRD74 (2006) ; [4] S.P. Klevansky, R.H. Lemmer, PLB702 (2011) 235. K + K - interaction complexity The A 2  lifetime is strongly reduced by strong interaction (OBE, scalar meson f 0 and a 0 ) as compared to the annihilation of a purely Coulomb-bound system (K + K - ). References:

A  and A  production

Yield of A K  dependence as a function of the atoms angle production and momentum in L. S. Bin = 9.6 MeV/c. Yield of A K  per one p-Ni interaction

Yield of A  dependence as a function of the atoms angle production and momentum in L. S. Bin = 9.6 MeV/c. Yield of A  per one p-Ni interaction

Yield of A 2  per one p-Ni interaction Yield of A 2  dependence as a function of the atoms angle production and momentum in L. S. Bin = 15 MeV/c.

A  and A  production on PS and SPS at CERN Yield ratio     atoms35     atoms27     atoms17 The ratio of    ,     and     atom yields at the proton momentum 450 GeV/c and angle 4  to the yields at the proton momentum 24 GeV/c and angle 5.7 .

Thank you for your attention!

Experimental conditions (run ) Primary proton beam24 GeV/c Beam intensity(10.5÷12)·10 10 proton/spill Single count of one IH plane(5÷6)·10 6 particle/spill Spill duration450 ms Ni target Purity99.98% Target thickness (year)98±1 μm (2008)108 ±1 μm ( ) Radiation thickness6.7·10 -3 X 0 7.4·10 -3 X 0 Probability of inelastic proton interaction 6.4· ·10 -4

Experimental conditions Secondary particles channel (relative to the proton beam) 5.7° Angular divergence in vertical and horizontal planes ± 1° Solid angle sr Dipole magnetB max = 1.65 T, BL = 2.2 Tm Time resolution [ps] VHIHSFD plane11234XYW

 +  - data Statistics for measurement of |a 0 -a 2 | scattering length difference and expected precision YearnAnA δ stat (%)Δ syst (%)δ syst (%)MSδ tot (%) * * There is 30% of the data with a higher background whose implication will be investigated.

Analysis of multiple scattering in Ni (100 μm) Run Analysis of multiple scattering in Ni (100 µm). Only events with one track in each projection were analyzed. δθ/θ ~ 0.7 %. After including in the analysis of all available events the statistics will be doubled and the expected value will be less than 0.5 %.

Probability of break-up as a function of Ni target thickness for A  (solid line) and A  atoms (dashed line),  1S = s. Average momentum of A  and A  are 6.4 GeV/c and 6.5 GeV/c accordingly. Break-up dependencies P br from the target thickness for  +  - atom (A  ) and    + atom (A  )

Q L distribution  +  - pairs

Q L distribution  +  - pairs

Simulation of  +  - pairs from Beryllium target and “ atomic pairs ” from Platinum foil Distributions of reconstructed values of Q T for non-Coulomb, Coulomb pairs and pairs from metastable atom

Magnet was designed and constructed in CERN (TE/MCS/MNC) Layout of the dipole magnet (arrows indicate the direction of magnetization) Opera 3D model with surface field distribution Integrated horizontal field homogeneity inside the GFR X х Y = 20 mm х 30 mm: ∆∫Bxdz/ ∫Bx(0,0,z)dz [%] Horizontal field distribution along z-axis at X=Y=0 mm ∫Bx(0,0,z)dz = 24.6 x [T x m]

Q Y distribution for e + e - pair

2010 data: results for K + K - and pp pairs in high momenta Total number of K + K - pairs in high momenta is The sum of low and high energy kaon pairs is 9806.

 +  - atom and its lifetime Interests in KK physics? General: non-understood KK interplay with the scalar mesons f 0 [0 + (0 ++ )] and a 0 [1 - (0 ++ )] & kaonium, the only double-mesonic atom with hidden strangeness, is decaying via strangeness annihilation DIRAC experiment: study of low-energy K + K - scattering  estimate number of produced atoms A 2K Kaonium decay width or lifetime “expected”: Decay width  ( A 2K ) = [  ( A 2K )] -1 = -  3 m K 2 Im(a KK ) … A 2K structure dependent: strong effects enter through the complex scattering length a KK. DIRAC experiment: search for “atomic pairs” K + K - from A 2K ionization  upper limit on  ( A 2K )  info about scattering length a KK !

Life time τ in 10 –18 s Ionization Probability  +  - atoms ionization probability  +  - atoms Lorentz factor is  =  m Pt x

Impact on atomic beam by external magnetic field B lab and Lorentz factor  …. relative distance between  + and   in A 2  system …. laboratory magnetic field …electric field in A 2  system →E→E → B lab →A→A →pA→pA    v/c → B lab →E→E →A→A Lamb shift measurement with external magnetic field → | E | =  B lab ≈  B lab L. Nemenov, V. Ovsiannikov, Physics Letters B 514 (2001) 247

Resonant enhancement of the annihilation rate of A  L. Nemenov, V. Ovsiannikov, E. Tchaplyguine, Nucl. Phys. (2002)

Resonant enhancement

Resonant method 00 00 00 00 00 00 -- ++ A* 2   A*   A*  Charged secondary Proton beam Resonators  res1  res2  res3  res4 Pt foil