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Symmetry Tests in Positronium Decay

Paul Vetter University of California, Berkeley Lawrence Berkeley National Laboratory

e- g1 g2 g3 g4 e+ g5

INT UW Seattle November, 2002 Positronium People Weak Interactions People Gammasphere People Paul Vetter Rod Clark Stuart Freedman Paul Fallon Michelle Cyrier (now Stanford student) Augusto Macchiavelli, Mario Cromaz, etc. States in Positronium The spectroscopic structure is the same as the Bohr (same Hamiltonian) except that the reduced mass is less:

æ 2 2 ö h 2 e (me-)(me+ ) 1 HY = ç - Ñ - ÷ Y M = = me ç 2m r ÷ m + m 2 è ø e- e+ Relativistic corrections are the same (except for factors of 2) New field retardation effects (“nucleus” moves)

Ground state has n =1, l = 0 and total = 0 or 1

ì y(1,+1) = e+ + 1 e- + 1 ï ( 2) ( 2) ï 1 ï y(1,0) = e+ + 1 e- - 1 + e+ - 1 e- + 1 ï 2 ( ( 2) ( 2) ( 2) ( 2)) y(Stot ,sz ) = í ï y(1,-1) = e+ - 1 e- - 1 ï ( 2) ( 2) ï 1 y(0,0) = e+ + 1 e- - 1 - e+ - 1 e- + 1 îï 2 ( ( 2) ( 2) ( 2) ( 2))

3 States y(1,x) are S1 = Orthopositronium (O-Ps) mean lifetime ~ 140 ns 1 State y(0,0) is S0 = Parapositronium (P-Ps) mean lifetime ~ 120 ps Charge Conjugation Symmetry in Positronium The charge symmetry operator changes to : C p = p - C + C reverses the sign of the “internal” quantum numbers of a particle (charge, number, number, strangeness, beauty…) C does not change mass, energy, momentum, spin... 2 Obviously, C = I so eigenvalues of C are +1, -1. - C + C -

Particles, in general, are not eigenstates of C. That would mean C p = p = ± p C True for , uncharged , (p0,r0, h, f, …), and uncharged bound states – like positronium. Positronium is an eigenstate of C and transforms like: 2S+1 l+S 2S+1 C Ps L J = (-1) Ps L J ( ) ( ) The is intrinsically C-odd, so for a state of n photons: C n g = (-1)n n g

So! if a given state of Ps annihilates by a C conserving process, the number of photons, n, is strictly odd or even by C symmetry: 1S ® 2g,4g,K 3S ® 3g,5g,K 0 1 Fundamental Physics Tests in Ps Decay e- g1 g2 QED tests at high orders of a at tree level: g3 e+ g4 Four photon decay of P-Ps: G(P - Ps ® 4g)= 0.0138957(4) ma7 (1-14.5(6) a / p + O(a2 ))=1.43´10-6 G.S. Adkins and E.D. Pfahl, Phys. Rev. A 59, R915 (1999).

Five photon decay of O-Ps: 2 G(O- Ps ® 5g)= GLO (3g) (0.0189(11) a ) = (2/ 9p)(p2 - 9) ma6 (0.0189(11) a2 )µ a8 = 0.959´10-6 G.S. Adkins and F.R. Brown, Phys. Rev. A 28, 1164 (1983). e- g1 g2 g3 Search for C violating, forbidden decay modes: g4 e+ g5 G(O - Ps ® 4g) RC/ = 3 4 O-Ps ( S1)-> 4 g G(O - Ps ® 3g)

C/ G(P - Ps ® 3,5g) P-Ps (1S )-> 3 g, 5g R = 0 3,5 G(P - Ps ® 2g) Outline of the Experiment

Goals • Search for O-Ps -> 4g (C violation) • Search for O-Ps -> 5g (QED allowed) • Search for P-Ps -> 5g (C violation) • Measure P-Ps -> 4g (QED allowed)

Make as much O-Ps as possible Minimize backgrounds • 68Ge source • BGO Compton suppression • Beta detector timing Count as long as possible Sort data • Identify unambiguous from scattering • Count N(2g), N(3g), N(4g), N(5g) Estimate detection efficiencies • Monte Carlo simulation of Gammasphere • Input Ps photons ... • Derive e(2g), e(3g), e(4g), e(5g) Estimate backgrounds • Monte Carlo different background mechanisms? Too slow! • mixing, use raw data Calculate N/e for all desired ratios for O-Ps and P-Ps populations Making Positronium

• Long-lived source -- low decay energy 22Na, 68Ge • Clean (no daughter g’s) • Stop in fine-grained insulator material • If : E(e+) < ionization potential of stopping material and E(e+) > ionization potential - binding energy of Ps (6.8 eV) Ps can be formed -- “Ore gap theory” • Pickoff in material (O-Ps -> e+e- -> 2 x 511 keV ) • Timing trigger when e+ is emitted The 68Ge aerogel Positronium source MARK I

Positronium Source inside Gammasphere Polarized O-Ps source (upward e+) MARK II in Gammasphere target chamber MARK II Three Photon O-Ps Decay Kinematics

k3 k Energy in (O-Ps -> 3g) decay derived from two angles a2 1 included between photon momenta in a plane. Probability for angles a1 and a2 calculable in closed form a1 a3

2 sinai P(a ,a ,a ) = 1-cosa k2 1 2 3 åi( i) 3 (åi sinai) 0.05 0.1 0.1 0.15 0.2 0.2 150 0.15 0.05 0.2 0.15 Calculated 3g spectrum 0.1 Allowed phase volume spectrum 1.5

100

1.0 (degrees) 1 q

0.5 50 Angular distribution probability Relative Probability per energy interval for O-Ps 3 photon decay (Probability to have angles a1 and a2) 0.0 0 100 200 300 400 500 Photon Energy (keV) 0 0 50 100 150 q2 (degrees) 4 and 5 photon decays: No closed form for spectra. Four Photon Decay Kinematics Event generating software 1.0

GRACE/BASES/SPRING (KEK) 0.8 QED allowed diagrams calculate allowed phase space 0.6

Generate Random events (phase space weighted) Probability 0.4 Feed to GEANT simulation of Gammasphere 0.2 Monte-Carlo calculated Determine detection efficiency energy spectrum of 4 g decay photons

0.0 0 100 200 300 400 500 Energy (keV) Five Photon Decay Kinematics 1.0

0.8

0.8 0.6 e- g1

0.6 Probability 0.4 g2 Monte-Carlo calculated angular separation of 4 g photons 0.4 g3 0.2 Probability e+ g4 0.0 0.2 Monte-Carlo calculated energy spectrum of 5g decay photons 0 50 100 150 Angular Separation (degrees) 0.0 0 100 200 300 400 500 Energy (keV) 1.0 0.8

0.8 0.6 e- g1 0.6 g2 0.4 Monte-Carlo calculated g3 Probability Planarity of 4g events (distance from origin to plane of 3 photon directions)

Probability 0.4 g4 0.2 Monte-Carlo calculated e+ g5 0.2 angular separation of 5g decay photons 0.0 0 20 40 60 80 100 0.0 Planarity (%) 0 50 100 150 Angular separation (degrees) Sorted Data

Live : 0.98 x 106 7 2 10 3 Data: 0.8 TB 6 4 10 5 Raw events: 1 x 1011 5 10 4 Annihilation Event Selection criteria: 10 3 1. Sum Energy = 1022 keV +/- 5 keV 10 2. Prompt photons 102 Counts per channel 3. Vector Momentum Sum < 100 keV/c t = 20 ns 101 t = -20 ns 4. Distance of decay plane to origin 100 5. Colinearity -100 0 100 200 300 Time after b trigger (ns)

Valid Ps annihilation events passing all cuts 150 511 keV ]

O-Ps decays after 20 ns (late), P-Ps decays early ( < 20ns) 3

100

EventEvent Totals Totals Counts [10 (Passing(Passing all all cuts): cuts): 50 N -20 < T < 20 ns T > 20 ns N -20 < T < 20 ns T > 20 ns 0 0 100 200 300 400 500 9 9 22 g g 3.01013.0101 x x 10 109 5.31145.3114 x x 10 109 Energy (keV) 7 7 33gg 1.09071.0907 x x 10 107 4.03024.0302 x x 10 107 44gg 1616 44 Energy spectrum of valid 3g annihilation events. 55gg 11 22 Angular resolution of Gammasphere for correlated photons. Backgrounds

288 d 68Ge 68 m 68Ga 100% E.C.

2 2mec

b+ 1.3% E.C. 1.5%

1.077 MeV b+ 89%, 1.89 MeV E.C. 1.5% 68Zn

Background contributions to the 4 and 5 photon counts estimated with an “event-mixing” technique on raw data. Events with two or three hits are combined. Simulated or 1077 keV photons. -- Run synthetic data through sort code. Four and Five Photon Branching Ratio Results

-6 (O(O-Ps-Ps - >-> 4 4gg)/(O)/(O-Ps-Ps - >-> 3 3gg) )< < 3.7 3.7 x x 10 10-6 (90%(90% C.L.) C.L.)

-6 C Symmetry Tests PreviousPrevious limit limit (1996) (1996) < < 2.6 2.6 x x 10 10-6 (90%(90% C.L.) C.L.) (90% Confidence level limits) [Yang[Yang et et al al.,., Phys. Phys. Rev. Rev. A A 54 54, ,1952 1952 (1996)] (1996)]

-7 (P(P-Ps-Ps - >-> 5 5gg)/(P)/(P-Ps-Ps - >-> 2 2gg) ) < < 2.7 2.7 x x 10 10-7 (90%(90% C.L.) C.L.) (no(no previous previous limit) limit)

-6 (O(O-Ps-Ps - >-> 5 5gg)/(O)/(O-Ps-Ps - >-> 3 3gg) ) = = 1.67(99)(37) 1.67(99)(37) x x 10 10-6

-6 QEDQED value(tree) value(tree) == 0.9591 0.9591 x x 10 10-6 -6 PreviousPrevious mmt mmt.(1.(1 event, event, ‘95) ‘95) = = 2.2(2.2) 2.2(2.2) x x 10 10-6 [Matsumoto[Matsumoto et et al. al., ,Phys. Phys. Rev. Rev. A A 54 54, ,1947(1996)] 1947(1996)]

QED Tests (1 s errors) -6 (P(P-Ps-Ps - >-> 4 4gg)/(O)/(O-Ps-Ps - >-> 2 2gg) ) == 1.14(33)(21) 1.14(33)(21) x x 10 10-6

-6 QEDQED value(one value(one-loop)-loop) = = 1.4388 1.4388 x x 10 10-6 -6 PreviousPrevious mmt mmt. .(1994) (1994) = = 1.50(11) 1.50(11) x x 10 10-6 [von[von Busch Busch et et al. al., ,Phys. Phys.LettLett. .B B 325 325, ,300 300 (1994)] (1994)] P-Ps Four Photon Decay Measurements

World Average 1.6 c2 = 0.507 ) 6 1.4 ) (x10 g

Crystal Ball QED value 1.2 )/(P-Ps -> 2 g

1.0 (P-Ps -> 4

Gammasphere

0.8 P-Ps Four Photon Branching Ratio Measurements

1990 1992 1994 1996 1998 2000 2002 Time Reversal Symmetry in O-Ps Decay

In the decay (O-Ps -> 3g), the photon momentar r all lie in a plane. Define the normal vector to the plane as (k 1´ k 2), where 1 and 2 are the highest energy photons. r r r k ´ k S ( 1 2) r k 3 r r k 1 k 2 Polarized 3S positronium 1 T r r Under (naive) Time Reversal, the photon momenta and spin all reverse. k 1´ k 2 does not reverse. r r ( ) k ´k ( 1 2) r r k 2 k 1 r r S k 3 3 S1 positronium

r r r s × k ´ k ( 1 2) is a T-odd observable. r r r s × k ´ k O-Ps is an eigenstate of C and P, so ( 1 2 ) is CPT- odd Polarized Postronium – easier than it sounds

Polarization of positrons from b+ decay is P = +v/c Calculate average polarization of e+ emitted from a source:

P(68Ge) = 91% P(22Na) = 65% 1.0 1.0 0.8 0.8

0.6 68Ge 0.6 22Na 0.4 0.4 0.2 0.2 Polarization of beta Polarization of beta 0.0 0.0 0.0 0.5 1.0 1.5 0.0 0.1 0.2 0.3 0.4 0.5 Energy of beta (K.E.) (MeV) Energy of beta (K.E.) (MeV)

Use upward betas only, average over emission direction to Ps moderator r r v v P = = 0.686× c c

Polarized e+ and unpolarized e- => polarized Ps formed (spin statistics of O-Ps, P-Ps)

P(Ps) = 2/3 P(e+) = 41% (68Ge) = 30% (22Na) Search for Time Reversal Symmetry Violation CPT Violation Data -- June/July, 2002 (analysis in progress) 68Ge CPT data: Direction of observed normal vectors for 3 photon events passing cuts: Annihilation Event Selection criteria: 1. Sum Energy = 1022 keV +/- 5 keV 2. Prompt photons 3. Vector Momentum Sum < 100 keV/c 4. Distance of decay plane to origin < 2 cm 5. Colinearity (no two detectors colinear w/ center of GS f) angle (

Live time: 6 Azimuthal 2.6 x 10 seconds Some kind of record (for masochism) 1.7 x 107 counted clean O-Ps decays

Polar angle (q) QuickTime™ and a JPEG A decompressor are needed to see this picture. Testing CPT in Ps Annhilation

Polarized Or -Ps has a T-even distribution of decay planes with s respect to . dG 3 æ 2 ö = G0 ç1 + nˆ ×sˆ ÷ dWn 16p è ø r r r Search for a cos(q) distribution of decay planes with respect to spin. s × k ´ k ( 1 2) Determine polarization from cos2 (q) distribution of decay planes Data Analysis: • Simulate GS angular response to cos2 (q), cos(q), isotropic distributions • Sort to find good annihilations • Fit angular data to simulated angular dependence • Extract polarization • Extract T -odd limit.

r r r CurrentCurrent Limits Limits on on this this T Tviolatingviolating signature: signature: C × s × k ´ k n [ ( 1 2)] C = +0.020 ± 0.023 n Factor of 10 improvement B.K.B.K. Arbic Arbic et et al al.,., Phys. Phys. Rev. Rev. A A 37 37,3189(1988).,3189(1988). with Gammasphere data set

Analysis in progress Cn = +0.014± 0.019 S.K.S.K.AndrukhovichAndrukhovich et et al al.,., Inst. Inst. and and Exp. Exp. Techniques Techniques 43 43, ,453 453 (2000). (2000). Constraining T-Odd New Physics

W. Bernreuther, U. Löw, J.P. Ma, and O. Nachtmann, Z. Phys. C 41, 143 (1988).

A CP-odd interaction would cause mixing between S and P states in Ps. Mixing parameter d: MP,nS dn = E nS - E P Scale of CP odd physics

1. rCP << 1/me (Heavy New Physics, short distance scale) If so, write an effective lagrangian L = L4e + Leeg + Lee2g + Lee3g +K • Constrained by high energy e+ e- scattering: L 4e =i ×f ×(e e)(e g5e) Optimistic (direct data applies): f <1/(1.8 TeV)2 Þ d » 10-15 Pessimistic (slipping thru cracks): f <1/(100 MeV)2 Þ d » 10-6 2 • Related to EDM of e- de mn -27 (deme ) Leeg = -i × ×(eg 5s eFmn ) Þ d »10 d µ 2 e2 , , Left-Right Symm. -- too massive

2. rCP >~ 1/me + g CP violation in mixing matrix? L µ N L gmVleptEL Wm • No CP violation in Ps to order L = x ee +ix e g e f Complicated Higgs sector: ( s p 5 ) • Constrained somewhat by (g-2)e, other atomic limits -5 Fine-tuning could evade de but have d »10 S f P e- e+ Final State T-Odd effects in Ps -> 3g W. Bernreuther, U. Löw, J.P. Ma, and O. Nachtmann, Z. Phys. C 41, 143 (1988).

e-

e+

-10 r QED effects: “light by light” scattering nˆ = 8.66(45)´10 s Gammasphere Ps CPT Data, partial analysis

15% of data set, one spin angle Cw < 0.008

3 15x10 (O - Ps ® 3g) sorted events r r r Dot product s ×(k 1 ´k 2 ) Data Monte Carlo -- allowed (energy weighting) Monte Carlo -- CPT odd

10

5 Scaled counts

0

-0.4 -0.2 0.0 0.2 0.4 cos(q) (spin -- normal angle) Conclusions

• Charge conjugation symmetry: still conserved • Improved measurement of five (!) photon decay of Ps • Agreement with QED • Anyone want to do 1st order corrections? • (Ps -> 6 g) looks impossible to detect • Time reversal symmetry/CPT: data look good so far. • Sun to rise in east tomorrow.

• Gammasphere: a really nice instrument. • Ps: an interesting little system, still useful.