Testing QCD Symmetries via Precision Measurements of Light

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

Contents 1. Physics Motivation – Symmetries of QCD – QCD symmetries and Properties of π0, η and η’ 2. Experiments at Jlab – – Part I: Primakoff experiments Part II: Rare decays of η and η’ • Summary 3/16/2018 2

What is symmetry? Symmetry is an invariance of a physical system to a set of changes. Noether’s theorem S ym m e t r y C o n s e r va t i o n L a w Symmetries and symmetry breakings are fundamental in physics 3/16/2018 3

Continuous Symmetrys of QCD in the Chiral Limit chiral limit: is the limit of vanishing quark masses mq→ 0. QCD Lagrangian with quark masses set to zero: Large global symmetry group: 3/16/2018 4

Fate of QCD symmetries 3/16/2018 5

Discrete Symmetries of QCD Charge: Parity: Time-Reversal: Combinations: 3/16/2018 C P T CP, CT, PT, CPT 6

Lightest pseudoscalar mesons • Chiral SUL(3)XSUR(3) spontaneously broken Goldstone mesons 0, η π 8 • Chiral anomalies Mass of η 0 P→ ( P: π0, η, η )׳ • Quark flavor SU(3) breaking The mixing of π0, η and η ׳ 3/16/2018 7

Some Interesting η Rare Decay Channels Mode Branching Ratio Physics Highlight π0 π0 <3. 5 × 10 − 4 CP, P π0 2γ ( 2. 7 ± 0. 5 ) × 10 − 4 χPTh, Ο(p 6) π+ π− <1. 3 × 10 − 5 CP, P π0 π0 γ <5 × 10 − 4 C 3γ <1. 6 × 10 − 5 C π0 π0 π0 γ <6 × 10 − 5 C π0 e + e − <4 × 10 − 5 C 4π0 <6. 9 × 10 − 7 CP, P The π0, η and η’ system provides a rich laboratory to study the symmetry structure of QCD. 3/16/2018 8

Part I: Primakoff Program at Jlab 6 & 12 Ge. V Precision measurements of electromagnetic properties of 0, , via Primakoff effect. a) Two-Photon Decay Widths: 1) 2) 3) Γ( 0→ ) @ 6 Ge. V Γ( → ) Γ( ’→ ) Input to Physics: Ø precision tests of Chiral symmetry and anomalies Ø determination of light quark mass ratio Ø - ’ mixing angle 3/16/2018 b) Transition Form Factors at low Q 2 (0. 001 -0. 5 Ge. V 2/c 2): F( *→ 0), F( * → ) Input to Physics: Ø 0, and ’ electromagnetic interaction radii Ø is the ’ an approximate Goldstone boson? 9

Status of Primakoff Experiments at JLab q Prim. Ex-I for Γ( 0 ) was performed in 2004 with 6 Ge. V beam. Published in PRL 106, 162303 (2011) q Prim. Ex-II for Γ( 0 ) was carried out in 2010. Analysis is in progress. q The 12 Ge. V part of program has was reviewed by 3 special high energy PACs. Included in Jlab 12 Ge. V upgrade White paper and CDR. PAC 18 (2000) PAC 23 (2003) PAC 27 (2005) q The first 12 Ge. V Primakoff experiment on Γ( → ) in Hall D was approved by PAC 35 in Jan 2010. 3/16/2018 10

Γ( 0→ ) Experiments 3/16/2018 11

Axial Anomaly Determines π0 Lifetime q 0→ decay proceeds primarily via the chiral anomaly in QCD. q The chiral anomaly prediction is exact for massless quarks: k 1 π k 2 q Γ( 0 ) is one of the few quantities in confinement region that QCD can calculate precisely to higher orders! Calculations in NLO Ch. PT: qΓ( 0 ) = 8. 10 e. V ± 1. 0% (J. Goity, et al. Phys. Rev. D 66: 076014, 2002) qΓ( 0 ) = 8. 06 e. V ± 1. 0% (B. Ananthanarayan et al. JHEP 05: 052, 2002) Calculations in NNLO SU(2) Ch. PT: qΓ( 0 ) = 8. 09 e. V ± 1. 3% (K. Kampf et al. Phys. Rev. D 79: 076005, 2009) Ø Calculations in QCD sum rule: 0→ Ø Corrections to the chiral anomaly prediction: q Γ( 0 ) = 7. 93 e. V ± 1. 5% (B. L. Ioffe, et al. Phys. Lett. B 647, p. 389, 2007) q Precision measurements of ( 0→ ) at the percent level will provide 12 a stringent test of a fundamental prediction of QCD.

Primakoff Method ρ, ω 12 C target Primakoff Nucl. Coherent Interference Nucl. Incoh. Challenge: Extract the Primakoff amplitude Requirement: ØPhoton flux ØBeam energy Ø 0 production Angular resolution 13

Prim. Ex-I (2004) q JLab Hall B high resolution, high intensity photon tagging facility q New pair spectrometer for photon flux control at high beam intensities 1% accuracy has been achieved q New high resolution hybrid multi-channel calorimeter (Hy. Cal) 3/16/2018 14

0 Event selection We measure: Ø incident photon energy: E and time Ø energies of decay photons: E 1, E 2 and time Ø X, Y positions of decay photons Kinematical constraints: Ø Conservation of energy; Ø Conservation of momentum; Ø m invariant mass 3/16/2018 15

Fit Differential Cross Sections to Extract Γ( 0 ) Theoretical angular distributions smeared with experimental resolutions are fit to the data on two nuclear targets: 3/16/2018 16

Verification of Overall Systematical Uncertainties q + e +e Compton cross section measurement q e+e- pair-production cross section measurement: Systematic uncertainties on cross sections are controlled at 1. 3% level. 17

Prim. Ex-I Result PRL 106, 162303 (2011) ( 0 ) = 7. 82 0. 14(stat) 0. 17(syst) e. V 2. 8% total uncertainty 3/16/2018 18

Goal for Prim. Ex-II Ø Prim. Ex-I has achieved 2. 8% precision (total) on ( 0 ) : 7. 82 e. V 1. 8% (stat) 2. 2% (syst. ) Prim. Ex-I 7. 82 e. V 2. 8% Prim. Ex-II projected 1. 4% Ø Task for Prim. Ex-II is to obtain 1. 4% precision: Projected uncertainties: 0. 5% (stat. ) 1. 3% (syst. ) 3/16/2018 19

Estimated Systematic Uncertainties Type Prim. Ex-II Photon flux 1. 0% Target number <0. 1% Veto efficiency 0. 4% 0. 2% HYCAL efficiency 0. 5% 0. 3% Event selection 1. 7% 0. 4% Beam parameters 0. 4% Acceptance 0. 3% Model dependence 0. 3% Physics background 0. 25% Branching ratio 0. 03% Total syst. 2. 2% 1. 3% 3/16/2018 § Improve Background Subtraction: üAdd timing information in Hy. Cal (~500 chan. ) üImprove photon beam line üImprove PID in Hy. Cal (add horizontal veto ) ü More empty target data § Measure Hy. Cal detection efficiency 20

Prim. Ex-II Status § Experiment was performed from Sep. 27 to Nov. 10 in 2010. § Physics data collected: v π0 production run on two nuclear targets: and 12 C (1. 1% statistics). 28 Si (0. 6% statistics) v Good statistics for two well-known QED processes to verify the systematic uncertainties: Compton scattering and e +e- pair production. 3/16/2018 21

Prim. Ex-II Experimental Yield (preliminary) ( E = 4. 4 -5. 3 Ge. V) Primakoff 12 C ~8 K Primakoff events 3/16/2018 Primakoff 28 Si ~20 K Primakoff events 22

Γ(η→ ) Experiment 3/16/2018 23

Physics Outcome from New Experiment 1. Resolve long standing discrepancy between collider and Primakoff measurements: 3. Determine Light quark mass ratio: Γ( → 3π) ∝ 2. |A|2 ∝ Q-4 Extract - ’mixing angle: H. Leutwyler Phys. Lett. , B 378, 313 (1996) 24

Measurement of Γ( → ) in Hall D at 12 Ge. V Counting House 75 m Comp. Cal Photon tagger ØIncoherent tagged photons Ø Pair spectrometer and a TAC detector for the photon flux control Ø 30 cm liquid Hydrogen and 4 He targets (~3. 6% r. l. ) Ø Forward Calorimeter (FCAL) for → decay photons Ø Comp. Cal and FCAL to measure well-known Compton scattering for control of overall systematic uncertainties. ØSolenoid detectors and forward tracking detectors (for background rejection) 3/16/2018 FCAL 25 25

Advantages of the Proposed Light Targets q Precision measurements require low A targets to control: Ø coherency Ø contributions from nuclear processes Hydrogen: ü no inelastic hadronic contribution ü no nuclear final state interactions ü proton form factor is well known ü better separation between Primakoff and nuclear processes ü new theoretical developments of Regge description of hadronic processes J. M. Laget, Phys. Rev. C 72, (2005) A. Sibirtsev, et al. ar. Xiv: 1001. 0646, (2010) 4 He: ü higher Primakoff cross section ü the most compact nucleus ü form factor well known ü new theoretical developments for FSI S. Gevorkyan et al. , Phys. Rev. C 80, (2009) 3/16/2018 26 26

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 3/16/2018 79 27

Estimated Error Budget q Systematical uncertainties (added quadratically): Contributions Estimated Error Photon flux 1. 0% Target thickness 0. 5% Background subtraction 2. 0% Event selection 1. 7% Acceptance, misalignment 0. 5% Beam energy 0. 2% Detection efficiency 0. 5% Branching ratio (PDG) 0. 66% Total Systematic 3. 02% q Total uncertainty (added quadratically): Statistical Systematic 3. 02% Total 3/16/2018 1. 0% 3. 2% 28

Transition Form Factors at Low Q 2 • Direct measurement of slopes – Interaction radii: Fγγ*P(Q 2)≈1 -1/6▪PQ 2 – Ch. PT for large Nc 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) calculation • Test of future lattice calculations 3/16/2018 29

Part II: Rare decays of η and η’ 3/16/2018 30

Why Are η Decays Interesting for New Physics? q. The heaviest member in the octet pseudoscalar mesons (547. 9 Me. V/c 2) q. Due to the conservation of G and P in the strong interaction, the η decay width Γη =1. 3 Ke. V is extremely narrow (comparing to Γρ= 149 Me. V) 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.

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

Some Interesting η Rare Decay Channels Mode Branching Ratio Physics Highlight π0 π0 <3. 5 × 10 − 4 CP, P π0 2γ ( 2. 7 ± 0. 5 ) × 10 − 4 χPTh, Ο(p 6) π+ π− <1. 3 × 10 − 5 CP, P π0 π0 γ <5 × 10 − 4 C 3γ <1. 6 × 10 − 5 C π0 π0 π0 γ <6 × 10 − 5 C π0 e + e − <4 × 10 − 5 C 4π0 <6. 9 × 10 − 7 CP, P 3/16/2018 33

Study of η→ 0 0 Reaction q The Origin of CP violation is still a mystery q 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)<3 x 10 -17 q The η→ 0 0 is one of a few available flavor-conserving reactions listed in PDG to test CP violation. q Unique test of P and PC symmetries, and search for new physics beyond SM 3/16/2018 34

Study of the η→ 0 Decay q A stringent test of the χPTh prediction at Ο(p 6) level Ø Tree level amplitudes (both Ο(p 2) and Ο(p 4)) vanish; Ø Ο(p 4) loop terms involving kaons are suppressed by large mass of kaon Ø Ο(p 4) loop terms involving pions are suppressed by G parity Ø The first sizable contribution comes at Ο(p 6) level q A long history that experimental results have large discrepancies with theoretic predictions. q Current experimental value in PDG is BR(η→ 0 )=(2. 7± 0. 5)x 10 -4 Aug 26, 2011 35

Theoretical Status on η→ 0 By E. Oset et al. Average of χPTh 3/16/2018 0. 42 36

History of the η→ 0 Measurements After 1980 A long standing “η” puzzle is still un-settled. 3/16/2018 37

High Energy η Production GAMS Experiment at Serpukhov D. Alde et al. , Yad. Fiz 40, 1447 (1984) Ø Experimental result was first published in 1981 Ø The η’s were produced with 30 Ge. V/c - beam in the -p→ηn reaction Ø Decay ’s were detected by leadglass calorimeter Final result: Major Background Ø - p → 0 0 n Ø η → 0 0 0 (η→ 0 ) = 0. 84± 0. 17 e. V 40 η→ 0 events 38

Low energy η production CB experiment at AGS S. Prakhov et al. Phy. Rev. , C 78, 015206 (2008) Na. I(T 1) η → 0 0 0 Ø The η’s were produced with 720 Me. V/c - beam through the -p→ηn reaction Ø Decay ’s energy range: 50500 Me. V 3/16/2018 Final result: (η→ 0 ) = 0. 285± 0. 031± 0. 061 e. V 92± 23 η→ 0 events 39

Major background in CB-AGS experiment MC data MC MC 3/16/2018 40

CB Data Analysis II N. Knecht et al. phys. Lett. , B 589 (2004) 14 Final result (η→ 0γγ)=0. 32± 0. 15 e. V 3/16/2018 41

Low Energy η Production Continue KLOE experiment B. Micco et al. , Acta Phys. Slov. 56 (2006) 403 Ø Produce Φ through e+e- collision at √s~1020 Me. V Ø The decay η→ 0γγ proceeds through: Φ→ η, η→ 0γγ, 0→γγ Final result: (η→ 0γγ)=0. 109± 0. 035± 0. 018 e. V η→ 0 events 3/16/2018 42

What can be improved at 12 Ge. V Jlab? q High energy tagged photon beam to reduce the background from η→ 3 0 Ø Lower relative threshold for -ray detection Ø Improve calorimeter resolution q Tag η by recoiled particles to reduce non-resonance p→ 0 0 p background q High resolution, high granularity Pb. WO 4 Calorimeter Ø Higher energy resolution → improve 0 invariance mass Ø Higher granularity→ better position resolution and less overlap clusters to reduce background from η→ 3 0 Ø Fast decay time → less pile-up clusters q Large statistics to provide a precision measurement of Dalitz plot 3/16/2018 43

Suggested Experiments in Hall D at Jlab Counting House Glue. X FCAL 75 m Simultaneously measure the η→ 0 , η → 0 0: q η produced on LH 2 target with 11 Ge. V tagged photon beam γ+p → η+p q Tag η by measuring recoil p with Glue. X detector to reduce the p→ 0 0 p background q Forward calorimeter (upgraded with high resolution , high granularity Pb. WO 4) to detect multi-photons from the η decays 3/16/2018 44 44

Kinematics of Recoil Proton Recoil θp vs θη (Deg) Angle θη (Deg) Recoil θp (Deg) Recoil Pp (Ge. V) • Polar angle ~55 o-80 o • Momentum ~200 -1200 Me. V/c Recoil Pp (Ge. V) vs θp (Deg) 45

Detection of recoil p by Glue. X 3/16/2018 46

Reconstructed missing mass and efficiency 3/16/2018 47

Invariant Mass Resolution σ=3. 2 Me. V σ=6. 9 Me. V PWO M σ=6. 6 Me. V M 3/16/2018 Pb glass M 0 σ=15 Me. V M 0 48

S/N Ratio vs. Calorimeter Granularity PWO Pb Glass dmin=4 cm dmin=8 cm S/N=1. 4 η S/N=0. 024 η Background is from MC only Aug 26, 2011 49

Rate Estimation The +p→η+p cross section ~70 nb (θη=1 -6 o) Photon beam intensity Nγ~1. 5 x 107 Hz • The η→ 0 detection rate: BR(η→ 0 )~3 x 10 -4 , detection efficiency ~24% In order to get 10% precision on BR measurement, we need ~12 days beam time 50

Statistical Error on dΓ/d. Mγγ for η π02γ Prakhov et al. , PRC 78, 015206 (2008). This figure gives a very rough idea how statistics limits our ability to probe the dynamics of the η π02γ decay. Assumptions are 8. 3 accepted events per live day, negligible background, and 7 bins spanning 0. 025 -0. 375. 12 days 112 days

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 where BR upper limit ≈ 2*sqrt(fbkg*NMε)/NMε = 2*sqrt(fbkg/NMЄ) NM= number of mesons decaying into the experimental acceptance Є = efficiency for detecting products from the signal branch fbkg = fraction of NM which remains in the signal box after all cuts The figure of merit for experiments is therefore NMЄ /fbkg. This means that to reduce the BR upper limit by one order of magnitude, one must either • Increase NMЄ by TWO orders of magnitude, or • Decrease fbkg 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.

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 LH 2 target, 70 nb cross section, and 1. 5 E 7 gammas/second, we can produce 1. 3 E 7 η’s per year. The number of accepted η decays per year would be ~1/3 this, or ~4 E 6 per year. η production is conservatively similar to KLOE

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

Budget vs. Acceptance Cost per crystal is $250, we have already 1200 crystals and PMTs from Prim. Ex , $300 per PMT, $281 per ADC channel Size of #crystals # crystal Cal. (cm 2) needed Crystal Cost PMTs ADC Total 118 x 118 3481 2281 $0. 57 M $0. 68 M $0. 98 M $2. 23 M 150 x 150 5625 4425 $1. 1 M $1. 33 M $1. 55 M $5. 08 M Beam energy (Ge. V) Accp. (%) (118 x 118 cm 2) Acc. (%) (150 x 150 cm 2) 9 9. 1 27. 0 10 15. 8 36. 0 11 23. 8 44. 5 12 31. 1 51. 1 3/16/2018 Z=600 cm, Center hole size is 10 x 10 cm 2 56

Summary q A comprehensive Primakoff program has been developed at Jlab to study fundamental QCD symmetries at low energy. Ø Two experiments on Γ( 0 → ) were performed. Prim. Ex-I: Γ( 0 ) 7. 82 0. 14(stat. ) 0. 17(syst. ) e. V (2. 8% tot) Phys. Rev. Lett. , 106, 162302 (2011) Prim. Ex-II was performed analysis is in progress. The 0 lifetime at level of 1. 4% precision is expected. Ø A new precision experiment on Γ(η→ ) has been planned to run in Hall D at 12 Ge. V. q 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. q New collaboration at any levels will be strongly encouraged! 3/16/2018 57