Hadronic Parity Violation

Transcription

1 Hadronic Parity Violation Barry R. Holstein UMass May 9, 007 INT Talk

2 Analogy TV Detective Show 10 Min. Problem: (Body!) 35 Min. Clues (including red herrings) 5 Min. Solution (Culprit brought to justice) INT Talk 1

3 Hadronic Parity Violation 10 Years Problem: No contact between theory and experiment 35 Years Clues DDH plus better experiments 5Years Solution Better theory plus definitive experiments INT Talk

4 Problem: Parity violating effects in strong and electromagnetic hadronic interactions. Examples: First experiment PV in pp by Tanner (1957) 180 Hf (8 ) 180 Hf + γ A γ = (1.66 ± 0.18) 10 PRC4, 1906 (1971) n La A z =(9.55 ± 0.35) 10 PRC44, 187 (1991) INT Talk 3

5 Theoretical Clues Seminal paper: Parity Nonconservation in Nuclei, F. Curtis Michel PR133B, 39 (1964) Great Progress in Particle/Nuclear Physics Standard Model BUT remain great unsolved problems at low energy: i) ΔI = 1 Rule ii) CP Violation iii) Hypernuclear Weak Decay iv) Hadronic Parity Violation AlldealwithJ hadron μ J μ hadron INT Talk 4

6 Theoretical Picture H w = G F J μj μ with J μ = J hadron μ + J lepton μ Then i) J lepton μ J μ lepton μ e + ν e + ν μ ii) J lepton μ J μ hadron n p + e + ν e iii) J hadron μ J μ hadron hadronic PV Canonical size: H w /H str G F m π 10 7 Isolate via PV effects in strong and/or EM processes INT Talk 5

7 Standard Model Picture H w = G F (J c J c + 1 J n J n ) with J c μ =ūγ μ (1 + γ 5 )(cos θ c d +sinθ c s) J n μ =ūγ μ (1 + γ 5 )u dγ μ (1 + γ 5 )d sγ μ (1 + γ 5 )s 4sin θ w J em μ Then leads to H w (ΔS =0)carries ΔI =0, 1, 1980: DDH Approach Meson exchange gives good picture of PC NN interaction, with INT Talk 6

8 ( H st = ig πnn Nγ 5 τ πn+g ρ N γ μ + i μ V M σ μνk ν) τ ρ μ N ( +g ω N γ μ + i μ S M σ μνk ν) ω μ N so use for PV NN Then need PV weak couplings: H wk = h π N(τ π)3 N + N ( ) h 0 ρτ ρ μ + h 1 ρρ μ 3 + h ρ 6 (3τ 3ρ μ 3 τ ρμ ) γ μ γ 5 N INT Talk 7

9 + N(h 0 ωω μ +h 1 ωτ 3 ω μ )γ μ γ 5 N h 1 ρ N(τ ρ μ ) 3 σ μν k ν M γ 5N Gives two-body PV NN potential V PNC = i f ( ) πg πnn τ1 τ 3 [ ] p1 p (σ 1 +σ ) M,f π(r) ( ) g ρ (h 0 ρτ 1 τ + h 1 τ1 + τ ρ + h (3τ1 3 τ 3 ) τ 1 τ ) ρ 3 6 { } p1 p ((σ 1 σ ) M,f ρ(r) [ ] p1 p +i(1 + χ V )σ 1 σ M,f ρ(r) ) ( ) ) g ω (h 0 ω + h 1 τ1 + τ ω 3 { } p1 p ((σ 1 σ ) M,f ω(r) [ ] p1 p +i(1 + χ S )σ 1 σ M,f ω(r) ) INT Talk 8

10 ( ) { } (g ω h 1 ω g ρ h 1 τ1 τ p1 p ρ) (σ 1 +σ ) 3 M,f ρ(r) ( ) [ ] τ1 τ g ρ h 1 p1 p ρ i (σ 1 + σ ) M,f ρ(r) where 3 f V (r) =exp( m V r)/4πr Problem is to calculate seven weak couplings INT Talk 9

11 Historical Approaches Theoretical 1964: Michel Factorization <ρ + n H c wk p >= G cos θ c <ρ + n V μ +A μ p > G cos θ c <ρ + V μ + 0 >< n A μ p > 1968: Tadic, Fischbach, McKeller SU(3) Sum Rule <π + n Hwk p c >= 3 tan θ c( <π p H wk Λ 0 > <π Λ 0 H wk Ξ >) 1980: DDH Quark Model plus Symmetry INT Talk 10

12 Represent states by N > b qsb q s b q s 0 > M > b qsd q s 0 > and H wk G ψoψ ψo ψ Then structure of weak matrix element is <MN H wk N>= G < 0 (b qs b q s b q s )(b qs d q s ) ψoψ ψo ψ(b qsb q s b q s ) 0 > R INT Talk 11

13 with R a complicated radial integral i.e., a Wigner-Eckart theorem <MN H wk N> known geometrical factor R Find three basic structures Here first is factorization, diagrams but two additional Represent in terms of Reasonable Range and Best Value INT Talk 1

14 DDH DDH Coupling Reasonable Range Best Value h π h 0 ρ h 1 ρ h ρ h 0 ω h 1 ω 5-3 all times sum rule value INT Talk 13

15 Experimental Can use nucleus as amplifier first order perturbation theory ψ J + > φ J + > + φ J >< φ J H wk φ J + > E + E = φ J + > +ɛ φ J > ψ J > φ J > + φ J + >< φ J + H wk φ J > E E + = φ J > ɛ φ J + > Then enhancement if ΔE << typical spacing. Examples are INT Talk 14

16 INT Talk 15

17 Typical results: Circular polarization in 18 F E1 decay of MeV excited state P γ (1081) = ( 7 ± 0) 10 4 Caltech/Seattle (3 ± 6) 10 4 Florence ( 10 ± 18) 10 4 Mainz ( ± 6) 10 4 Queens ( 4 ± 30) 10 4 Florence Asymmetry in decay of polarized KeV excited state of 19 F A γ = { ( 8.5 ±.6) 10 5 Seattle ( 6.8 ± 1.8) 10 5 Mainz Circular Polarization in 1 Ne E1 decay of Mev excited state P γ = { (4 ± 4) 10 4 Seattle/Chalk River (3 ± 16) 10 4 Chalk River/Seattle INT Talk 16

18 AlsoresultsonNNsystemswhicharenotenhanced: pp: PSI A tot z (45.0 MeV)= (1.57 ± 0.3) 10 7 pp: Bonn A z (13.6 MeV)= (0.93 ± 0.0 ± 0.05) 10 7 pα: PSIA z (46.0 MeV)= (3.3 ± 0.9) 10 7 INT Talk 17

19 Summary of present results in nuclei: Excited Measured Experiment Theory Reaction State Quantity ( 10 5 ) ( 10 5 ) 13 C(p,α) 14 N J=0 +,T=1 [A z(35 ) 0.9 ± MeV -Az(155 )] J=0,T= MeV 19 F(p,α) 0 Ne J=1 +,T=1 A z(90 ) 150 ± MeV Az 660 ± 40 J=1,T=0 Ax 100 ± MeV 18 F J=0,T=0 P γ 70 ± ± MeV 40 ± ± ± 58 7 ± 57 mean 1 ± F J= 1,T + 1 Aγ 8.5 ± ± MeV 6.8 ±.1 mean 7.4 ± Ne J= 1,T = 1 Pγ 80 ± MeV INT Talk 18

20 Graphical Summary INT Talk 19

21 Recent Additions A: Anapole Moment Background usual analysis of magnetic field away from currents involves multipole expansion dipole, quadrupole, octupole, etc. If parity violated a new possibility: toroidal current a B j Leads to local field! Another view: Consider matrix element of Vμ em with parity violation: INT Talk 0

22 <f Vμ em i >=ū(p f )[F 1 (q )γ μ F (q ) iσ μνq ν M +F 3 (q 3 1 ) 4M (γ μγ 5 q q μ qγ 5 )+F 4 (q ) iσ μνq ν γ 5 M ]u(p i) Here F 1 (q ),F (q ) usual charge, magnetic form factors. F 4 (q ) violates both P,T and is electric dipole moment. F 3 (q ) violates only T and is anapole moment note q dependence local! Since involves axial current spin dependent find via spin-dependent PV effect. Performed by Wieman et al. in 6S-7S 133 Cs transitions. Effective interaction is H eff w = G F (κ Z + κ a ) α e J nuc ρ(r) INT Talk 1

23 Here κ Z =0.013 is direct Z-exchange term and κ a =0.11 ± is anapole moment In terms of DDH h π 0.1(h 0 ρ +0.6h 0 ω)=(0.99 ± 0.16) (h h 0 ) F 19 F 133 Cs pp 0 05 Tl p f h h 1 INT Talk

24 B: SAMPLE Experiment Looks for PV electron scattering in backward direction interference of photon and Z-exchange e ; e ; 0 Z (a) (b) Asymmetry given by A = G F q α [ #G γ E GZ E +#Gγ M GZ M + #(1 4sin θ w )G γ M GZ A #G γ E +#Gγ M ] Results: INT Talk 3

25 INT Talk 4

26 INT Talk 5

27 TRIUMF E497 pp scattering at 1 MeV special energy S-P vanishes sensitive to P-D mixing A L =(0.84 ± 0.9 ± 0.7) 10 7 INT Talk 6

28 Wavefunction effects Miller J. Miller Phys. Rev. C (003) points out i) correlations in pion exchange ii) use of proper strong interaction couplings re: Bonn potential yields changes in obtained couplings and possible consistency: INT Talk 7

29 Now What? INT Talk 8

30 A Vision Note low energy NN PV characterized by five amplitudes: i) d t (k) 3 S 1 1 P 1 mixing: ΔI =0 ii) c t (k) 3 S 1 3 P 1 mixing: ΔI =1 iii) d 0,1, s (k) 1 S 0 3 P 0 mixing: ΔI =0, 1, Unitarity requires d s,t (k) = d s,t (k) exp i(δ S (k)+δ P (k)) Danilov suggests d i (k) λ i m i (k) INT Talk 9

31 so lim c t(k),d t (k),d 0,1, s (k) =ρ t a t,λ t a t,λ 0,1, s k 0 a s Need five independent experiments use nuclei with A 4. Interpret using Desplanques and Missimer i) pp scattering pp(13.6mev) A L = 0.48Mλ pp s pp(45mev) A L = 0.8Mλ pp s ii) pα scattering pα(46mev ) A L = M[0.48(λ pp s +1 λpn s )+1.07(1 λ t+ρ t )] INT Talk 30

32 iii) Radiative Capture np dγ a) Circular Polarization : P γ = M(0.63λ t 0.16λ np s ) b) Photon asymmetry : A γ = 0.11Mρ t iv) Neutron spin rotation in He dφ nα dz =[0.85(λ nn s 1 λpn ) 1.89(ρ t 1 λ t)]m N rad/m s Status of experiments a) pp(13.6 MeV) performed at Bonn b) pp(45 MeV) performed at PSI c) pα(46 MeV) performed at PSI d) P γ (np) Athens, Duke,??? e) A γ (np) done at Lansce; scheduled and moved t f) φ nα scheduled at NIST; move to SNS? INT Talk 31

33 i) Precision Experiments What s needed? a) Bowman et al. LANSCE, SNS b) Snow et al. NIST, SNS c) HIγS, Shanghai? ii) State of the art NN theory: Carlson, Wiringa, Schiavilla, etc. i) Apply to p 4 He and n 4 He ii) Apply to pd and nd iii) Others... iii) Use Effective field theory ideas BH, Ramsey-Musolf, van Kolck, etc. Effective potential is Λ 3 χ ( ) τ1 + τ {[C 1 +(C + C 4 ) 3 INT Talk 3

34 + C 3 τ 1 τ + I ab C 5 τ a 1 τ b ] ( σ 1 σ ) { i,f m (r)} ( ) τ1 + τ +[ C 1 +( C + C 4 ) + C 3 τ 1 τ + I ab C 5 τ a 1 τ b ] i ( σ 1 σ ) [ i,f m (r)] ( ) τ1 τ +(C C 4 ) ( σ 1 + σ ) { i,f m (r)} +C 6 iɛ ab3 τ1 a τ b ( σ 1 + σ ) [ i,f } m (r)] (1) 3 3 with I = and f m ( r) is function that INT Talk 33

35 i) strongly peaked, with width 1/m about r =0 ii) approaches δ (3) ( r) in zero-width (m ) limit. e.g., f m (r) = m 4πr exp ( mr) Check counting in pionless theory in point approximation p-wavefunction vanishes: λ t (C 1 C 3 ) ( C 1 3 C 3 ) λ 0 s (C 1 + C 3 )+( C 1 + C 3 ) λ 1 s (C + C 4 )+( C + C 4 ) 8 λ s 3 (C 5 + C 5 ) ρ t (C C 4 )+C 6 Using finite size corrections find corrections, e.g. M N ρ t = Λ 3[B ( 1 C 1 C 4+C 6 )+B 3 ( 1 C 1 C 4 C 6 )] INT Talk 34

36 with B = and B 3 = Connect with DDH via C DDH 1 = 1 Λ 3 ωg ω h 0 ω C DDH = 1 Λ 3 ωg ω h 1 ω C DDH 3 = 1 Λ 3 ρg ρ h 0 ρ C DDH 4 = 1 Λ 3 ρg ρ h 1 ρ C5 DDH = 1 4 Λ 3 ρg ρ h ρ 6 C6 DDH = 1 Λ 3 ρg ρ h 1 ρ and C i DDH /Ci DDH =1+χ ω i =1, INT Talk 35

37 C i DDH /Ci DDH =1+χ ρ i =3, 4, 5 Result is understanding of PVNN by?? INT Talk 36

38 Predicting the Future After reliable set of couplings obtained a) Confirm via other experiments in A<4 systems b) Use these to analyze previous results in heavier nuclei c) Confront measured numbers with fundamental theory via lattice and/or other methods d) Reliably predict effects in other experiments INT Talk 37