The Radiative Return at Φ- and B-Meson Factories

Transcription

1 The Radiative Return at Φ- and B-Meson Factories J.H. KÜHN INSTITUT FÜR THEORETISCHE TEILCHENPHYSIK KARLSRUHER INSTITUT FÜR TECHNOLOGIE I II Basic Idea Monte Carlo Generators: Status & Perspectives III Charge Asymmetry and Radiative Φ-Decays IV Nucleon Form Factors at B-Factories V Pion and Kaon Form Factors at large Q 2 and τ νk K VI Experimental Results VII Conclusions (with H. Czyż, G. Rodrigo, K. Melnikov; and S. Binner, A. Grzelinska, E. Nowak, G. Rodrigo, A. Wapienik)

2 I BASIC IDEA photon radiated off the initial e + e (ISR) reduces the effective energy of the collision dσ(e + e hadrons + γ) = H(Q 2, θ γ ) dσ(e + e hadrons) measurement of R(s) over the full range of energies, from threshold up to s large luminosities of factories compensate α/π from photon radiation radiative corrections essential (NLO) advantage over energy scan (BES, CMD2, SND): systematics (e.g. normalization) only once High precision measurement of the hadronic cross-section at DAΦNE, CLEO-C, B-factories J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 2

3 DAΦNE versus B-factories: configurations in the cms - frame GeV γ GeV γ e + e π + very hard photon: clear kinematic separation between photon and hadrons π no natural kinematic separation cuts to control FSR versus ISR ( two step process: e + e γ ρ( γππ) see below ) J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 3

4 Rough estimates (999) for rates: π + π γ : E γ > MeV s [GeV ] L [fb ] #events, θ min = multi-hadron-events (R 2) s =.6 GeV Q 2 -interval [GeV ] #events, θ min = 7 [.5, 2. ] [ 2., 2.5 ] [ 2.5, 3. ] [ 3., 3.5 ] actually (2): L 3fb (KLOE) L 5fb (BABAR) J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 4

5 Lowest order dσ ( dq e + 2 e γ + had(q 2 ) ) = σ ( e + e had(q 2 ) ) { s 2 +Q 4 α πs s(s Q 2 ) ( log(s/m 2 e ) ), no angular cut s 2 +Q 4 ( ) s(s Q 2 ) log +cos θmin cos θ min s Q2 s differential luminosity: dl dq 2 ( Q 2, s ) = α πs { cos θ min } } L(at s) J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 5

6 all errors dominated by systematics Monte Carlo Generator J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 6

7 Basic Ingredients for Pion Formfactor ISR pion form factor to be tested FSR radiation from pointlike pions (probably overestimated) virtual Compton scattering additional radiation: collinear (EVA MC) (Binner, JK, Melnikov) or NLO calculation (PHOKHARA MC) J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 7

8 II MONTE CARLO GENERATORS P H O K H A R A References etc. rodrigo/phokhara J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 8

9 QED corrections at leptonic side basic building block for all hadronic final states J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 9

10 PHOKHARA 2.: A π + π, µ + µ, 4π ISR at NLO: virtual corrections to one photon events and two photon emission at tree level γ γ 2 γ 2 γ + + FSR at LO: π + π, µ + µ tagged or untagged photons modular structure J.H. Kühn The Radiative Return at Φ- and B-Meson Factories

11 PHOKHARA 3. specifically developed for π + π (plus photons) allows for simultaneous emission of photons from initial and final state, including virtual corrections (interference neglected). dominated by two step process : e + e γ ρ ( γ ππ) importance of ππγ as input for a µ J.H. Kühn The Radiative Return at Φ- and B-Meson Factories

12 ¾ ¾ µ ¾ µ µ ¾ µ ¾ µ µ e + π + µ ¾ e (a) π (b) µ (c) (d) µ (e) (f) µ J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 2

13 Contributions to a µ from π + 2 γ π Estimates δa µ (quark, γ, m q = 8 MeV) =.88 δa µ (quark, γ, m q = 66 MeV) = δa µ (π + π, γ) = 4.39 J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 3

14 6 7 8 da had (s) ds inclusive e e e e e e a had 9 6 E cut = MeV 4 E cut = 2 MeV E cut = MeV s(gev 2 ) E cut [MeV] Differential contribution to a had,γ µ from π + π γ intermediate states for different cutoff values compared with the complete contribution (virtual plus real corrections, labelled inclusive ) evaluated in sqed (FSR), as well as Integrated contribution to a had,γ µ as a function of the cutoff E cut. with the contribution from the π + π intermediate state. J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 4

15 A Large effect for Q 2 < m 2 ρ eliminated by suitable cuts on π + π configuration (suppress 2γ events ) d(ifsnlo) d(ifslo) dq 2 dq a e e ( ) Æ 8 Æ Ô s =.2 GeV Æ 8 Æ d(ifsnlo) d(isrnlo) dq 2 dq c e e ( ) p 5 p 5 : Æ 3 Æ Æ no M tr cut M tr cut Q 2 (GeV 2 ) Q 2 (GeV 2 ) 8 9 or measure photon J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 5

16 III Charge Asymmetries and Radiative Φ-Decays (H. Czyż, A. Grzelinska, JK) interference: interference odd under π + π asymmetric differential distribution: interf. = A(θ) = Nπ+ (θ) N π (θ) N π+ (θ) + N π (θ) Photon coupled to pointlike pion additional contribution on top of Φ-resonance (KLOE!) e + e ( Φ γ f,2 π + π ) interference! J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 6

17 Significant influence of scalar resonances on charge asymmetry N(θ π +>9 ) N(θ π +<9 ) N(θ π +>9 )+N(θ π +<9 ) A s = mφ 2 < θ π ± < 6 45 < θ γ < 35 e + e π + π γ f KK model f no str. α φ = π f no str. α φ = 2 no f Q2 (GeV).8.9 Interference between ISR and FSR amplitude for Φ γππ J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 7

18 F.-B. asymmetry Data 22 Monte Carlo.3.2. F.-B. asymmetry Data 26 Monte Carlo M 2 ππ [GeV2 ] M 2 ππ [GeV2 ] M 2 ππ [GeV2 ] M 2 ππ [GeV2 ] J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 8

19 IV NUCLEON FORM FACTORS (PHOKHARA 4.) Q 2 4m 2 N accessible at B-factories study e + e γ N N (with N = p or n) hadronic current: J µ = ie ū(q 2 ) ( F N (Q2 ) γ µ F N 2 (Q2 ) 4m N Q = q + q 2, q = (q q 2 )/2 [γ µ, /Q] ) v(q ), or G M = F + F 2, G E = F + Q2 4m 2 F 2 J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 9

20 Result: dσ = 2s L µνh µν dφ 2 (p + p 2 ; Q, k) dφ 2 (Q; q, q 2 ) dq2 2π, L µν H µν = (4πα)3 {( G NM Q 2 2 τ ) GNE 2 ( 32s βn 2 (s + )( (p q) 2 + (p 2 q) 2 ) Q2 ) y y 2 s 2 ( + 2 G N M 2 + )[( τ GN E 2 + ) (s 2 + Q 4 ]} ) y y 2 s(s Q 2 ) 2, where y,2 = s Q2 ( cos θ γ ), τ = Q2 2s 4m 2 N, β 2 N = 4m2 N Q 2 J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 2

21 A Separation of G M 2 and G E 2 through angular distribution: L µν H µν = (4πα)3 ( + cos 2 θ γ ) Q 2 ( cos 2 θ γ ) ( 4 G N M 2 ( + cos 2 ˆθ) + ) τ GN E 2 sin 2 ˆθ ˆθ = angle of nucleon with respect to γ-direction in hadronic rest frame ( ) valid for s/q 2, corrections and optimal frame EPJ C 35 (24) 527 Similarity to e + e N N : dσ dω = α2 β N 4Q 2 ( G N M 2 ( + cos 2 θ) + ) τ GN E 2 sin 2 θ J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 2

22 ¾ ÒÎ ¾ µ É ¼ ¾ Æ Æ ÔÔ Ô ¼¾Î ¼ Æ ÔÔ ¼ Æ A ¼ ¼ Æ Æ ¼ At least one photon satisfies: ¼ Æ ÔÔ ¼ Æ ¼ Î ¼ É ¾ (GeV ¾ ) ¼ e + e p p γ implementation in PHOKHARA J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 22

23 Ó Õ µ (nb) ¼ 4.5 Î ¾ É ¾ 5 Î ¾ Å ¼ Æ ÔÔ ¼ Æ Ó Õ Ô Ó µ (nb) 4.5 Î ¾ É ¾ 5 Î ¾ Å ¼ Æ ÔÔ ¼ Æ Ô Angular distributions of nucleon ÔÔ ÔÔ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¾ Æ Æ Ô ¼¾Î ¼ ¼ ¼ ¾ Æ Æ Ô ¼¾Î ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ lab frame hadronic rest frame Ó (two choices for G M /G E ) J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 23

24 Comments similar results for neutron pair or ΛΛ production NLO corrections from ISR included (corrections 2%) no FSR ΛΛ can be studied with analysis of Λ-polarization thousands of events around 4 5 GeV 2 several events up to 7 8 GeV 2 J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 24

25 Results (from BABAR) PRD 73, 25 (26) Proton form factor BABAR FENICE DM2 DM BES PS7 E835 E76 G E /G M BABAR PS7.5 Proton form factor M pp (GeV/c 2 ) BABAR BES CLEO E835 E M pp (GeV/c 2 ) M pp (GeV/c 2 ) J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 25

26 Recent improvements model amplitudes Improved formfactors for π + π 2π, 2π + 2π, π + π (high Q 2 region) K + K, K K narrow resonances (J/ψ, ψ ) (direct vs. indirect amplitudes) J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 26

27 V MESON FORM FACTORS at LARGE Q 2 Khodjamirian, JK, EPJ C 39 (24) 4 Czyz, Grzelinska, JK, PRD 8, 944 (2) radiative return will explore large Q 2 convenient representation for F π : generalized VDM with ρ, ρ,... combined with Veneziano-type tower of resonances (Dominguez) m 2 n F π (s) = c n m 2 n s, c n = n= π( 2 m 2 n = m2 ρ ( + 2n), β = free parameter cn = ( ) n Γ(β /2), + n)γ(n + )Γ(β n) J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 27

28 finite widths parameters of ρ, ρ, ρ fitted to data Modifications: Breit-Wigner for ρ, ρ, ρ with Q 2 -dependent widths reasonable agreement between model and fit Parameter model(fit) PDG value model m ρ ± ±.34 input Γ ρ 47. ±. 49.4±. input m ω 782.4± ±.2 - Γ ω 8.33± ±.8 - m ρ 49± 465±25 34 Γ ρ 429±27 4±6 256 m ρ2 87 ±25 72 ±2 73 Γ ρ2 357±46 25± 33 m ρ Γ ρ m ρ4 model Γ ρ4 model m ρ5 model Γ ρ5 model - 49 Parameter model(fit) PDG value model β 2.48±.3 - input c π ω (8.7±.5) Arg(c π ω ).6± F 2.59±. - - Arg(F 2 ) -2.2± F 3.48± Arg(F 3 ) -2.± F 4.4± Arg(F 4 ) -2.9± F 5.43± Arg(F 5 ).9± χ 2 /d.o.f. 27/ J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 28

29 A F π (s) 2 e + e π + π CMD2 24 CMD2 27 SND KLOE CMD2 26 model F π (s) 2 e + e π + π CMD2 27 DM2 989 J/ψ CLEO-c BaBar model s (GeV) s (GeV) data point at 3. GeV (J/Ψ ππ) leads to strong constraints J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 29

30 isospin symmetry: Ae + e K + K, K K F K + = +F (I=) + F (I=) F K = F (I=) + F (I=) resonances: ( ) F K +(s) = + c K 2 ρ BW ρ(s) + c K ρ BW ρ (s) + c K ρ BW ρ (s) ( + c K 6 ω BW ω(s) + c K ω BW ω (s) + c K ω BW ω (s)) ( ) c φ BW φ (s) + c φ BW φ (s), + 3 ( ) F K (s) = c K 2 ρ BW ρ(s) + c K ρ BW ρ (s) + c K ρ BW ρ (s) ( ) + c K 6 ω BW ω(s) + c K ω BW ω (s) + c K ω BW ω (s) ( ) η φ c φ BW φ (s) + c φ BW φ (s) + 3 J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 3

31 quark model: γ ρ K + γ ω K + 2 f ρ g ρkk K 3 2 f ω g ωkk K constraint: f ρ = f ω, g ρkk = g ωkk c ρ = c ω fit performed with (solid curves) or without (dashed curves) this constraint J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 3

32 F K +(s) 2 SND 27 SND 2 CMD unconstr. constr. A F K (s) 2 SND 26 CMD-2 24 SND 2 unconstr. constr s (GeV) s (GeV).4.5 F K +(s) 2 e + e K + K SND 27 ND 99 DM2 988 J/ψ Cleo-c unconstr. constr. F K (s) 2 e + e K K SND 26 CMD-2 23 DM 98 unconstr. constr s (GeV) s (GeV) J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 32

33 Aτ K K ν Predictions based on isospin symmetry and I = part of form factor: ( ) dbr(τ K K ν τ ) BR(τ µ ν µ ν τ ) d = Q 2 V ud 2 ) ) 2 ( ) 3/2 ( + ( 2Q2 Q2 4m2 K Q 2 2m 2 τ m 2 τ Q 2 F K K (Q2 ) 2 and F K K = F K + + F K m 2 τ BR(τ K K ν τ ) =.35.9% to be compared with BR(τ K K ν τ ) =.58 ±.6%. J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 33

34 AQ 2 distribution: will provide further constraints! CLEO uncon. 3.5 con Q 2 (GeV).6.8 (data from CLEO) J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 34

35 KLOE pion form factor, asymmetry BABAR, BELLE higher Q 2 available VI Experimental Results measurement of R(Q 2 ) from threshold up to at least 5 GeV. Examples: ππ 4π ±, π + π 2π 6π K K ππ K K K K pp, ΛΛ,... J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 35

36 ( F π 2 C,S - F π 2 K ) / F π 2 K CMD-2 SND Pion Form Factor M 2 ππ (GeV2 ) F ¼ M ¼¼ GeV ( ) KLOE SND CMD [GeV/c ] J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 36 data/qed Cross section [nb] (a) (b) (c) BABAR m µµ s [GeV]

37 4π σ(e + e - 2π + 2π - ) (nb) OLYA ND CMD CMD2 SND M3N DM GG2 DM2 BaBar OLYA ND SND CMD2 BABAR M3N GG2 DM E C.M. (MeV) E beam, MeV σ(3(π + π - )) (nb) 2.5 σ(2(π + π - π )) (nb) 5 6π E c.m. (GeV) E c.m. (GeV)

38 VII Conclusions continuous development of PHOKHARA radiative corrections more channels cooperation between theory and experiment crucial charge asymmetry as analysis tool nucleon form factors: G E and G M can be measured for a wide range of Q 2 pion form factor: structures at large Q 2 kaon form factors: K + K & K K K K prediction for τ νk K numerous experimental results during past 5 years J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 38