1. Testing QCD Symmetries via Precision Measurements of Light Pseudoscalar Mesons Liping Gan University of North Carolina Wilmington Wilmington, NC, USA

2. 6/12/2015 Contents 1.Physics Motivation – Symmetries of QCD – QCD symmetries and Properties of π 0, η and η’ 2.Experiments at Jlab – Part I: Primakoff experiments – Part II: Rare decays of η and η’ 3.Summary 2

3. 6/12/2015 What is symmetry? Symmetry is an invariance of a physical system to a set of changes. Symmetries and symmetry breakings are fundamental in physics Noether’s theorem Symmetry Conservation Law 3

4. 6/12/2015 Continuous Symmetrys of QCD in the Chiral Limit chiral limit: is the limit of vanishing quark masses m q → 0. QCD Lagrangian with quark masses set to zero: QCD Lagrangian with quark masses set to zero: Large global symmetry group: 4

5. Fate of QCD symmetries Fate of QCD symmetries 6/12/20155

6. Discrete Symmetries of QCD Charge: C Parity: P Time-Reversal: T Combinations: CP, CT, PT, CPT 6

7. 6/12/2015 Lightest pseudoscalar mesons Chiral SU L (3)XSU R (3) spontaneously broken Goldstone mesons π 0, η 8Chiral SU L (3)XSU R (3) spontaneously broken Goldstone mesons π 0, η 8 Chiral anomalies Mass of η 0 →  ( P: π 0, η, η ׳ ) Chiral anomalies Mass of η 0 P →  ( P: π 0, η, η ׳ ) Quark flavor SU(3) breakingQuark flavor SU(3) breaking The mixing of π 0, η and η ׳ The mixing of π 0, η and η ׳ 7

8. Some Interesting η Rare Decay Channels ModeBranching RatioPhysics Highlight π0 π0π0 π0 <3.5 × 10 − 4 <3.5 × 10 − 4 CP, P π 0 2γ ( 2.7 ± 0.5 ) × 10 − 4 ( 2.7 ± 0.5 ) × 10 − 4 χPTh, Ο(p 6 ) π+ π−π+ π− <1.3 × 10 − 5 <1.3 × 10 − 5 CP, P π0 π0 γπ0 π0 γ <5 × 10 − 4 <5 × 10 − 4 C 3γ3γ <1.6 × 10 − 5 <1.6 × 10 − 5 C π0 π0 π0 γπ0 π0 π0 γ <6 × 10 − 5 <6 × 10 − 5 C π0 e+ e−π0 e+ e− <4 × 10 − 5 <4 × 10 − 5 C 4π04π0 <6.9 × 10 − 7 <6.9 × 10 − 7 CP, P 6/12/2015 The π 0, η and η’ system provides a rich laboratory to study the symmetry structure of QCD. 8

9. Part I: Part I: Primakoff Program at Jlab 6 & 12 GeV Precision measurements of electromagnetic properties of  0, ,  via Primakoff effect. Precision measurements of electromagnetic properties of  0, ,  via Primakoff effect. a)Two-Photon Decay Widths: 1)Γ(  0 →  ) @ 6 GeV 2)Γ(  →  ) 3)Γ(  ’ →  ) b) Transition Form Factors at lo w Q 2 (0.001-0.5 GeV 2 /c 2 ): F(  * →  0 ), F(  * →  ), F(  * →  ) Input to Physics:  precision tests of Chiral symmetry and anomalies  determination of light quark mass ratio   -  ’ mixing angle Input to Physics:   0,  and  ’ electromagnetic interaction radii  is the  ’ an approximate Goldstone boson? 6/12/20159

10. Status of Primakoff Experiments at JLab  PrimEx-I for Γ(  0  ) was performed in 2004 with 6 GeV beam. Published in PRL 106, 162303 (2011)  PrimEx-II for Γ(  0  ) was carried out in 2010. Analysis is in progress.  The 12 GeV part of program has was reviewed by 3 special high energy PACs. Included in Jlab 12 GeV upgrade White paper and CDR. PAC18 (2000) PAC23 (2003) PAC27 (2005)  The first 12 GeV Primakoff experiment on Γ(  →  ) in Hall D was approved by PAC35 in Jan 2010. 10

11. Γ(  0 →  ) Experiments 6/12/201511

12. Axial Anomaly Determines π 0 Lifetime   0 →  decay proceeds primarily via the chiral anomaly in QCD.  The chiral anomaly prediction is exact for massless quarks:  Corrections to the chiral anomaly prediction: Calculations in NLO ChPT:  Γ(  0  ) = 8.10eV ± 1.0% (J. Goity, et al. Phys. Rev. D66:076014, 2002)  Γ(  0  ) = 8.06eV ± 1.0% (B. Ananthanarayan et al. JHEP 05:052, 2002) Calculations in NNLO SU(2) ChPT:  Γ(  0  ) = 8.09eV ± 1.3% (K. Kampf et al. Phys. Rev. D79:076005, 2009)  Precision measurements of  (  0 →  ) at the percent level will provide a stringent test of a fundamental prediction of QCD.  0 →   Calculations in QCD sum rule:  Γ(  0  ) = 7.93eV ± 1.5% (B.L. Ioffe, et al. Phys. Lett. B647, p. 389, 2007) is one of the few quantities in confinement region that QCD can  Γ(  0  ) is one of the few quantities in confinement region that QCD can calculate precisely to higher orders! calculate precisely to higher orders! 12 π k1k1 k2k2

13. 13 Primakoff Method ρ,ωρ,ω Challenge: Extract the Primakoff amplitude 12 C target Primakoff Nucl. Coherent Interference Nucl. Incoh. Requirement:  Photon flux  Beam energy   0 production Angular resolution

14. PrimEx-I (2004)  JLab Hall B high resolution, high intensity photon tagging facility  New pair spectrometer for photon flux control at high beam intensities 1% accuracy has been achieved  New high resolution hybrid multi-channel calorimeter (HyCal) 6/12/201514

15. We measure:  incident photon energy: E  and time  energies of decay photons: E  1, E  2 and time  X,Y positions of decay photons Kinematical constraints:  Conservation of energy;  Conservation of momentum;  m  invariant mass  0 Event selection 6/12/201515

16. Fit Differential Cross Sections to Extract Γ(  0  ) Theoretical angular distributions smeared with experimental resolutions are fit to the data on two nuclear targets: 6/12/201516

17. Verification of Overall Systematical Uncertainties   + e   +e Compton cross section measurement  e + e - pair-production cross section measurement: Systematic uncertainties on cross sections are controlled at 1.3% level. 17

18. PrimEx-I Result PRL 106, 162303 (2011)  (  0  ) = 7.82  0.14(stat)  0.17(syst) eV 2.8% total uncertainty 6/12/201518

19. Goal for PrimEx-II  PrimEx-I has achieved 2.8% precision (total) on  (  0  ) : 7.82 eV  1.8% (stat)  2.2% (syst.)  Task for PrimEx-II is to obtain 1.4% precision: Projected uncertainties:  0.5% (stat.)  1.3% (syst.) PrimEx-I 7.82eV  2.8% PrimEx-II projected  1.4% 6/12/201519

20. Estimated Systematic Uncertainties Type PrimEx-IPrimEx-II Photon flux1.0% Target number<0.1% Veto efficiency0.4%0.2% HYCAL efficiency0.5%0.3% Event selection1.7%0.4% Beam parameters0.4% Acceptance0.3% Model dependence0.3% Physics background 0.25% Branching ratio0.03% Total syst.2.2%1.3%  Improve Background Subtraction: Add timing information in HyCal (~500 chan.) Improve photon beam line Improve PID in HyCal (add horizontal veto ) More empty target data  Measure HyCal detection efficiency 6/12/201520

21. PrimEx-II Status PrimEx-II Status  Experiment was performed from Sep. 27 to Nov. 10 in 2010.  Physics data collected:  π 0 production run on two nuclear targets: 28 Si (0.6% statistics) and 12 C (1.1% statistics).  Good statistics for two well-known QED processes to verify the systematic uncertainties: Compton scattering and e + e - pair production. 6/12/201521

22. ~8K Primakoff events~20K Primakoff events ( E  = 4.4-5.3 GeV) Primakoff 6/12/201522

23. 6/12/201523 Γ(η →  ) Experiment

24. Physics Outcome from New  Experiment 2. Extract  -  ’mixing angle: 3. Determine Light quark mass ratio: H. Leutwyler Phys. Lett., B378, 313 (1996) 1.Resolve long standing discrepancy between collider and Primakoff measurements: Γ(  →3 π ) ∝ |A| 2 ∝ Q -4 24

25. 25 Measurement of Γ(  →  ) in Hall D at 12 GeV 75 m Counting House  Incoherent tagged photons  Pair spectrometer and a TAC detector for the photon flux control  30 cm liquid Hydrogen and 4 He targets (~3.6% r.l.)  Forward Calorimeter (FCAL) for  →  decay photons  CompCal and FCAL to measure well-known Compton scattering for control of overall systematic uncertainties.  Solenoid detectors and forward tracking detectors (for background rejection) CompCal FCAL Photon tagger 6/12/201525

26. 26 Advantages of the Proposed Light Targets  Precision measurements require low A targets to control:  coherency  contributions from nuclear processes Hydrogen: no inelastic hadronic contribution no nuclear final state interactions proton form factor is well known better separation between Primakoff and nuclear processes new theoretical developments of Regge description of hadronic processes J.M. Laget, Phys. Rev. C72, (2005) A. Sibirtsev, et al. arXiv:1001.0646, (2010) 4 He: higher Primakoff cross section the most compact nucleus form factor well known new theoretical developments for FSI S. Gevorkyan et al., Phys. Rev. C 80, (2009) 6/12/201526

27. Approved Beam Time Days Setup calibration, checkout 2 Tagger efficiency, TAC runs 1 4 He target run 30 LH 2 target run 40 Empty target run 6 Total 79 6/12/201527

28. Estimated Error Budget Estimated Error Budget Contributions Estimated Error Photon flux1.0% Target thickness0.5% Background subtraction2.0% Event selection1.7% Acceptance, misalignment0.5% Beam energy0.2% Detection efficiency0.5% Branching ratio (PDG) 0.66% Total Systematic3.02% Statistical1.0% Systematic3.02% Total3.2%  Systematical uncertainties (added quadratically):  Total uncertainty (added quadratically): 6/12/201528

29. 6/12/2015 Transition Form Factors at Low Q 2 Direct measurement of slopesDirect measurement of slopes – Interaction radii: F γγ*P (Q 2 )≈1-1/6 ▪ P Q 2 – ChPT for large N c predicts relation between the three slopes. Extraction of Ο(p 6 ) low-energy constant in the chiral Lagrangian Input for light-by-light scattering for muon (g-2) calculationInput for light-by-light scattering for muon (g-2) calculation Test of future lattice calculationsTest of future lattice calculations 29

30. 6/12/201530 Rare decays of η and η’ Part II: Rare decays of η and η’

31. Why Are η Decays Interesting for New Physics?  Due to the conservation of G and P in the strong interaction, the η decay width Γ η =1.3 KeV is extremely narrow (comparing to Γ ρ = 149 MeV) η decays have the dominant strong interaction filtered out, enhancing the branching ratios for other interactions by a factor of ~100,000. η decays provide a unique, flavor-conserving laboratory to search for new sources of C, P, and CP violation in the regime of EM and suppressed strong processes.  The heaviest member in the octet pseudoscalar mesons (547.9 MeV/c 2 )

32. Selection Rule Summary Table: η Decay to π’s and γ’s ηXηX 0π0π1π1π2π2π3π3π4π4π 0γ0γ P, CP 1γ1γ C, CP 2γ2γ 3γ3γ CCCCC 4γ4γ Gamma Column implicitly includes γ*  e + e - Key: C and P allowed, observed Forbidden by energy and momentum conservation. C and P allowed, upper limits only C violating, CP conserving, etc. L = 0 L = 1 L = even or odd (no parity constraint). C, CP

33. Some Interesting η Rare Decay Channels ModeBranching RatioPhysics Highlight π0 π0π0 π0 <3.5 × 10 − 4 <3.5 × 10 − 4 CP, P π 0 2γ ( 2.7 ± 0.5 ) × 10 − 4 ( 2.7 ± 0.5 ) × 10 − 4 χPTh, Ο(p 6 ) π+ π−π+ π− <1.3 × 10 − 5 <1.3 × 10 − 5 CP, P π0 π0 γπ0 π0 γ <5 × 10 − 4 <5 × 10 − 4 C 3γ3γ <1.6 × 10 − 5 <1.6 × 10 − 5 C π0 π0 π0 γπ0 π0 π0 γ <6 × 10 − 5 <6 × 10 − 5 C π0 e+ e−π0 e+ e− <4 × 10 − 5 <4 × 10 − 5 C 4π04π0 <6.9 × 10 − 7 <6.9 × 10 − 7 CP, P 6/12/201533

34. 6/12/2015 Study of η →  0  0 Reaction  The Origin of CP violation is still a mystery  CP violation is described in SM by the phase in the Cabibbo- Kobayashi-Maskawa quark mixing matrix. A recent SM calculation predicts BR(η →  0  0 )<3x10 -17  The η →  0  0 is one of a few available flavor-conserving reactions listed in PDG to test CP violation.  Unique test of P and PC symmetries, and search for new physics beyond SM 34

35. Aug 26, 2011 Study of the η →  0  Decay  A stringent test of the χPTh prediction at Ο(p 6 ) level  Tree level amplitudes (both Ο(p 2 ) and Ο(p 4 )) vanish;  Ο(p 4 ) loop terms involving kaons are suppressed by large mass of kaon  Ο(p 4 ) loop terms involving pions are suppressed by G parity  The first sizable contribution comes at Ο(p 6 ) level  A long history that experimental results have large discrepancies with theoretic predictions.  Current experimental value in PDG is BR(η →  0  )=(2.7±0.5)x10 -4 35

36. 6/12/2015 Theoretical Status on η →  0  Average of χPTh 0.42 By E. Oset et al. 36

37. 6/12/2015 History of the η →  0  Measurements A long standing “η” puzzle is still un-settled. After 1980 37

38. High Energy η Production GAMS Experiment at Serpukhov D. Alde et al., Yad. Fiz 40, 1447 (1984)  Experimental result was first published in 1981  The η’s were produced with 30 GeV/c  - beam in the  - p → ηn reaction  Decay  ’s were detected by lead- glass calorimeter Major Background Major Background   - p →  0  0 n  η →  0  0  0 Final result: Final result:  (η →  0   (η →  0  ) = 0.84±0.17 eV η →  0  events 40 η →  0  events 38

39. Low energy η production CB experiment at AGS Low energy η production CB experiment at AGS S. Prakhov et al. Phy.Rev.,C78,015206 (2008)  The η’s were produced with 720 MeV/c  - beam through the  - p → ηn reaction  Decay  ’s energy range: 50-500 MeV Final result: Final result:  (η →  0  ) = 0.285±0.031±0.061 eV η →  0  events 92±23 η →  0  events 6/12/2015 η →  0  0  0 NaI(T1) 39

40. Major background in CB-AGS experiment 6/12/201540 data MC

41. 6/12/2015 CB Data Analysis II N. Knecht et al. phys. Lett., B589 (2004) 14 Final result Final result  (η →  0 γγ)=0.32±0.15 eV 41

42. 6/12/2015 Low Energy η Production Continue KLOE experiment B. Micco et al., Acta Phys. Slov. 56 (2006) 403  Produce Φ through ee collision at √s~1020 MeV  Produce Φ through e + e - collision at √s~1020 MeV  The decay η→  0 γγ proceeds through: Φ→  η, η→  0 γγ,  0 →γγ Final result: Final result:  (η →  0 γγ)=0.109±0.035±0.018 eV η →  0  events 42

43. 6/12/2015 What can be improved at 12 GeV Jlab?  High energy tagged photon beam to reduce the background from η → 3  0  Lower relative threshold for  -ray detection  Improve calorimeter resolution  Tag η by recoiled particles to reduce non-resonance  p →  0  0 p background  High resolution, high granularity PbWO 4 Calorimeter  Higher energy resolution → improve invariance mass  Higher energy resolution → improve  0   invariance mass  Higher granularity → better position resolution and less overlap clusters to reduce background from η → 3  0  Fast decay time → less pile-up clusters  Large statistics to provide a precision measurement of Dalitz plot 43

44. 44 Suggested Experiments in Hall D at Jlab 75 m Counting House 6/12/201544 GlueX FCAL Simultaneously measure the η →  0 , η →  0  0 :  η produced on LH 2 target with 11 GeV tagged photon beam γ+p → η+p  Tag η by measuring recoil p with GlueX detector to reduce the  p →  0  0 p background  Forward calorimeter (upgraded with high resolution, high granularity PbWO 4 ) to detect multi-photons from the η decays

45. Kinematics of Recoil Proton Polar angle ~55 o -80 oPolar angle ~55 o -80 o Momentum ~200-1200 MeV/cMomentum ~200-1200 MeV/c Angle θ η (Deg) Recoil θ p vs θ η (Deg) Recoil Pp (GeV) vs θp (Deg) 45 Recoil θp (Deg) Recoil Pp (GeV)

46. Detection of recoil p by GlueX 6/12/201546

47. Reconstructed missing mass and efficiency 6/12/201547

48. 6/12/2015 Invariant Mass Resolution PWO Pb glass σ=15 MeV σ=6.9 MeV σ=3.2 MeV σ=6.6 MeV  M   0 M  0  M  48

49. Aug 26, 2011 S/N Ratio vs. Calorimeter Granularity PWO d min =4cm S/N=1.4 Pb Glass d min =8cm S/N=0.024 49 Background is from MC only

50. Rate Estimation The  +p → η+p cross section ~70 nb (θ η =1-6 o ) The  +p → η+p cross section ~70 nb (θ η =1-6 o ) Photon beam intensity N γ ~1.5x10 7 Hz Photon beam intensity N γ ~1.5x10 7 Hz The η →  0  detection rate: BR(η →  0  )~3x10 -4, detection efficiency ~24%The η →  0  detection rate: BR(η →  0  )~3x10 -4, detection efficiency ~24% In order to get 10% precision on BR measurement, we need ~12 days beam time 50

51. Statistical Error on dΓ/dM γγ for η  π 0 2γ 112 days 12 days This figure gives a very rough idea how statistics limits our ability to probe the dynamics of the η  π 0 2γ decay. Assumptions are 8.3 accepted events per live day, negligible background, and 7 bins spanning 0.025-0.375. Prakhov et al., PRC 78, 015206 (2008).

52. Experiment Figure of Merit for “Forbidden Branch” Searches In C and CP violation searches in η decays to date, it’s been true that Bkg Events >> Signal Events. Since the background fluctuations are sqrt(N), the upper limit for the branching ratio at ~95% CL is then approximately BR upper limit ≈ 2*sqrt(f bkg *N M ε)/N M ε = 2*sqrt(f bkg /N M Є) where N M = number of mesons decaying into the experimental acceptance Є = efficiency for detecting products from the signal branch f bkg = fraction of N M which remains in the signal box after all cuts The figure of merit for experiments is therefore N M Є /f bkg. This means that to reduce the BR upper limit by one order of magnitude, one must either Increase N M Є by TWO orders of magnitude, or Decrease f bkg by TWO orders of magnitude. While maintaining a competitive η production rate, Jlab would reduce BR upper limits by one order of magnitude using background reduction alone.

53. How Many η’s Can We Make? A year of Jlab operations is about 32 weeks. Assuming 50% efficiency for the accelerator and end-station, that is 112 live days. With a 30 cm LH2 target, 70 nb cross section, and 1.5E7 gammas/second, we can produce 1.3E7 η’s per year. The number of accepted η decays per year would be ~1/3 this, or ~4E6 per year. η production is conservatively similar to KLOE

55. Comparison of different crystals (From R. Y. Zhu) 55

56. Budget vs. Acceptance 6/12/2015 Size of Cal.(cm 2 ) #crystals# crystal needed Crystal Cost PMTsADCTotal 118x11834812281$0.57 M$0.68 M$0.98 M$2.23 M 150x15056254425$1.1 M$1.33 M$1.55 M$5.08 M Beam energy (GeV) Accp. (%) (118x118cm 2 ) Acc. (%) (150x150cm 2 ) 99.127.0 1015.836.0 1123.844.5 1231.151.1 Cost per crystal is $250, we have already 1200 crystals and PMTs from PrimEx, $300 per PMT, $281 per ADC channel Z=600 cm, Center hole size is 10x10 cm 2 56

57. Summary  A comprehensive Primakoff program has been developed at Jlab to study fundamental QCD symmetries at low energy.  Two experiments on Γ(  0 →  ) were performed. PrimEx-I: Γ(  0  )  7.82  0.14(stat.)  0.17(syst.) eV (2.8% tot) Phys. Rev. Lett., 106, 162302 (2011) Phys. Rev. Lett., 106, 162302 (2011) PrimEx-II was performed and analysis is in progress. The  0 lifetime at level of 1.4% precision is expected.  A new precision experiment on Γ(η →  ) has been planned to run in Hall D at 12 GeV.  New proposal on rare decays of η and η’ to test the χPTh prediction, P, C and PC symmetries is under development. The goal is to significantly improve the precision of B.R. or reduce the upper limits of B.R. in PDG by one order of magnitude.  New collaboration at any levels will be strongly encouraged! 6/12/201557