J PC =1 - - states spectroscopy, study of their decays Calculation of hadronic contributions into a µ and α QED (m Z )

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1 Study of e + e - a n n i h i l a ti on a t l ow e n e r g i e s Vladimir D ru z h in in Budker I n s t i t ut e o f N uc l ea r P h y s i c s ( N o v o s i b i rs k R us s i a ) S N D - Ba Ba r L ep t o n -P h o t o n A ug us t 0 0 7

2 e + e - a n n i h i l a t i o n i n t o h a d r o n s J PC =1 - - states spectroscopy study of their decays Calculation of hadronic contributions into a µ and α QED (m Z ) Dominant uncertainty from lowest order hadronic piece. Cannot be calculated from QCD ( first principles ) but: we can use experiment () h a d γ had µ γ γ From dispersion relations

3 A & # $ B / - *+ 6? >: ; ;=< : / ) ( l. o a µ had R(s) i s d e f i n e d a s: central value R(s) = σ (0) (e + e γ * hadrons) σ (0) (e + e µ + µ ) uncertainty ) s ( R ) s ( K ds.). ( s µ m α $ % = o l a π 3 had µ π m 4 a µ [exp] - a µ [SM] = (7.5 ± 8.4) standard deviations ) α = α 3 ε s Z ( R ds Re Z M (0) ) π Z M ( ) ( 3 had i M s s π m 4

4 Current/Future activities in R e + e - c.m. energy R

5 # ISR method Mass spectrum of h ad ron i c sy stem f i n th e e e f γ reacti on i s rel ated to cross secti on of e e f reacti on at E = m. m s = 1 σ ( e e f γ ) m + E γ = W ( s x ) σ ( e e f )( m ) x = dm s s + d 5 %$

6 % & #% % 4 3 % : 7 Measurement of R in Novosibirsk & $# /. * ) ( & + % # & # 5 % F ED <>C B= =? : = : <>? <<>= ; 9: π 4π 3 π 6 6 φ ω ρ 6

7 Measurement of R in Novosibirsk σ nb π + π - π + π - π o Cross section (nb) KK π + π - π + π - π + π - π o π o π o γ+ηγ ωπ + π - +ηπ + π s -- GeV e + e - c.m. energy & %$ % $ $ # 7

8 8 Pion f or m f a c t or S N D CMD-

9 Comparison of CMD- and S N D 9

10 Pion f or m f a c t or ( K L O E ) 10

11 ; New KLOE measurement. )* - )*+ )* ( $%& # KLOE 00 KLOE 001 σ (nb) preliminary µµ ππ M ππ (GeV ) KLOE 00 SA KLOE 00 LA 5 43 /10 σ (nb) preliminary : f 0 γ for LA ϕ M 11 ππ (GeV )

12 KLOE: e + e - ωπ B( φ ωπ ) = (5.63 ± 0.70) ± 1. (SND) 0 Γ( ω π γ) Γ( ω 3π) = ± ± (PDG) 1

13 BaBar R m e as u re m e n t p ro g ram u s i n g I S R 13

14 %$ # &. & / 7 : 4 14 *+- ) ( %.10 / 3 π + π π π 0 π π + π π + π 3π + 3π π + π π 0 π π + π η π + π π 0 π 0 π + π π 0 ΛΛ ΛΣ 0 Σ 0 Σ π π ; π+π π0π0 π+π 3π0 4 π + π

15 15 BaBar I S R : π + π π 0 π 0 BaBar preliminary α µ # + (*) $% & & - ) & %

16 BaBar I S R : π + π π 0 π 0 BaBar preliminary Intermediate states: ωπ 0 a 1 (160)π ρ + ρ ρ 0 f 0 (980) 16

17 BaBar I S R : π + π π 0 π 0 non ωπ ωπ ρ + ρ - 17

18 BaBar I S R : π + π π + π π 0 ρ3π Internal structure: ηπ + π = ηρ 0 ωππ ρx = ρ ± 3π + ρ 0 3π X = π( ) o r a ( ) ηρ 0 ωππ 18

19 BaBar I S R : ωπ + π π ω ω ωf 0 (980) 1.35 ± ± ± ± BaBar3π

20 BaBar I S R : π + π π + π η η / (958)ρ 0 1 (185)ρ0 Internal structure: ηπ + π π + π = ηρ(1450) η / (958)ππ = η / (958)ρ 0 f 1 (185)ππ = f 1 (185)ρ 0 ρ (150)? m=.15±0.04±0.05 GeV Γ=0.35±0.04±0.05 GeV 0

21 BaBar I S R : K + K - π + π π 0 K + K - π + π η π + π π 0 π + π η ω ϕη 1

22 BaBar I S R : K + K - π 0 K S K - π + π + K K ϕ(1680) π + π 0 $%& # π 0 K K ($ * ) +

23 =? E D? E D > : ; : BaBar I S R : K + K - π 0 K S K - π + D F G MLI A@?NJ I F G MLI A@?KJ? E E K ± K D FHG I FHG & % $ # π * + *+ ) ( 0 K and 0 K ± K K α α 67 α α ± -/ : : : 9 < ( : 3

24 & ) BaBar I S R : ϕη ϕπ 0 ϕπ 0 $#ϕπ0 ϕη % ϕ ω 1 0 * - #Γ 1 0 /.- +* () 4

25 # # % - # * # 3 7 Fit to e + e - ϕη K * K ϕ ± ± Γ Γ ϕη & )+* ( & & ϕη $# ± Γ ± % # % 0. /. & ϕ 6?> ;$< =9 89: 6?> ; 8 < ; = Γ 5

26 BaBar m e as u re m e n t s u m m ary To calculate R in the energy range 1- G ev π + π π + π 3π 0 π + π 4π 0 K K K K m us t b e m eas ured. K K ππ K the p roces s es K π π0 6

27 BaBar I S R : Bary o n F o rm f ac t o rs e + e BB (s=1/) cross section depends on two form factors electric G E and magnetic G M. σ ( e 4πα β 3m + B e BB ) = GM + G E From the measurement of cross section we extract effective form factor GM + GE / τ F = = τ 1+ 1 / τ The ratio of form factors G E /G M can be obtained from the analysis of the baryon angular distribution. The terms corresponding G M and G E have angular dependence close to 1+cos θ and sin θ respectively. Nonzero relative phase between form factors leads to polarization of outgoing baryons. For ΛΛ final state Λ decay can be used to measure polarization. m 4m B m m 7

28 Cross section and Λ f orm f actor Cross section (pb) BABAR DM Form factor M Λ (GeV/c ) M Λ (GeV/c ) 8

29 $ & $ / &. $. + ) ) $. 3. $ > Angular distribution Λ ± ± $ 1 % - *( %0 / % ( & % #$ /$ 7 # % $ $ #/ *( ( /$ &. / % / $. 3 = = < 9;: 8 % #$ $. & /$@? & &. 1 % 7$ & 8 % 7BA # % $

30 > $ N ( C ( ) ( # ) < 9 0 = C > : 9 9 E G ( > F L I : 9 Λ polarization ) D % Λ $ ) % Λ # PO > Λ ( * ) > > > ± 0.64 = ) cos (1 d Λ α ς p θ f ς Λ + α A = N ξ p θ d cos ) ( $&% θ πς ) * ) ) ; : 6 5 4/ /10 / / /3. Λ % A B ( D ) > * /10 ς φ / 0 GH GKJ GH 4 / 0 ϕ. 9 M 5 / 0 E 30

31 Octet baryon form factors Form factor p Λ Σ 0 ΛΣ Q (GeV) 31

32 Test of V C h y p oth esi s W: I =1 & VA CVC: I =1 & V γ: I =01 & V τ ν τ W hadrons e + e γ hadrons Hadronic physics factorizes in Spectral Functions. Isospin symmetry connects I=1 e + e cross section to vectorτ spectral functions: branching fractions mass spectrum kinematic factor (PS) 3

33 Comparison of e + e - and τ d at a τ ππ 0 ν 33

34 Comparison of e + e - 4π c ross sec t ions w it h τ 4πν τ spec t ral fu nc t ions 34

35 Conclusion Significant progress is reached in measurement of exclusive e + e - channels in mass range below 3 GeV Most important results expected during next year: final - π + π (KLOE) π + π π 0 (BABARCMD-) new - π + π (BaBar) Obtained data allow to determine parameters of excited ρ ω ϕ-states. Simultaneous fit of all channels? There are significant discrepancies between tau and e+edata for π 4π final states. New data from Babar and Belle on tau decays are expected 35

36 36 Γ Γ 3(π π ) (π π )π π π π π π

37 37 Belle analysis of τ ππ 0 ν