The Radiative Return at Φ- and B-Meson Factories

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1 The Radiative Return at Φ- and B-Meson Factories KARLSRUHE KATOWICE VALENCIA J. H. Kühn I II III IV V Basic Idea Monte Carlo Generators: Status & Perspectives Charge Asymmetry and Radiative Φ-Decays ( H. Czyż) Nucleon Form Factor at B-Factories Conclusions (with H. Czyż, A. Grzelinska, E. Nowak, G. Rodrigo) 1

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 1 GeV γ 1 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 for rates: π + π γ : E γ > 1MeV s [GeV ] L [fb 1 ] #events, θ min = multi-hadron-events (R 2) s = 1. GeV Q 2 -interval [GeV ] #events, θ min = 7 [ 1.5, 2. ] [ 2., 2.5 ] [ 2.5, 3. ]. 1 5 [ 3., 3.5 ] 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 ) differential luminosity: ( log(s/m 2 e ) 1 ), no angular cut s 2 +Q 4 ( ) s(s Q 2 ) log 1+cos θmin 1 cos θ min s Q2 s 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 Basic Ingredients for Pion Formfactor ISR pion form factor to be tested FSR radiation from pointlike pions (probably overestimated) 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 II MONTE CARLO GENERATORS P H OTONS FROM KARLSRUHE H ADRONICALLY R ADIATED References etc. J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 7

8 A J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 8

9 A J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 9

10 A J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 1

11 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

12 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 12

13 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 13

14 "! $ $ $ $ A Large effect for Q 2 < m 2 ρ eliminated by suitable cuts on π + π configuration (suppress 2γ events ) 1 (IFSLO) dq 2 d (IFSNLO) dq 2 d a e e s = 1.2 GeV 18 ( ) 18 1 (ISRNLO) dq 2 d (IFSNLO) dq 2 d # 5 # 4 # 3 # 2 # 1 # 1 # 2 c e e no M tr cut M tr cut ( p ) 5 p : # Q 2 (GeV 2 ) # 4 # 3 # 4 # 5 Q 2 (GeV 2 ) # # 7 # 8 # 9 1 or measure photon J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 14

15 Experimental Perspectives KLOE ππ pion form factor = TALK BY STEFAN MÜLLER BABAR, BELLE higher Q 2 available measurement of R(Q 2 ) from threshold up to at least 5 GeV. Examples: 3π 4π ± K K ππ K K K K J/Ψ J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 15

16 events/(2.5 MeV/c 2 ) 15 1 A events/(25 MeV/c 2 ) M 3π (GeV/c 2 ) M 3π (GeV/c 2 ) The background-subtracted 3π mass spectrum for masses between.7 and 1.5 MeV/c 2 (plot on the left) and for masses from 1.5 to 1.8 MeV/c 2 (plot on the right). BaBar J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 1

17 Cross section (nb) 8 4 A M 3π (GeV/c 2 ) The e + e π + π π cross section measured by BaBar (filled circles), by SND (open circles), and DM2 (open triangles). BaBar J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 17

18 A BaBar J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 18

19 # /. -, : 558: : 55 ) A $ #! #!" DM1 ND SND 2 BABAR :8: 9 DM1 CMD2 98 ND SND 2 CMD2 95 SND 3 CMD2 4 : : ; : 5 + * '( % & BaBar J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 19

20 -, + * ) ( ' & % # $ # "!. A / GeV 2 GeV 44 4 / / / 1 events/(25 MeV/c 2 ) / / / 2. / 3./ 5 4 / 1 4 / 2 4 / M(π + π - ) (GeV/c 2 ) BaBar J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 2

21 PHOKHARA 4. µ + µ γ with FSR at NLO vacuum polarisation can be switched on nucleon pair production included J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 21

22 III Charge Asymmetries and Radiative Φ-Decays (H. Czyż, A. Grzelinska, JK, hep-ph/412239) = talk by Henryk Czyż J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 22

23 IV NUCLEON FORM FACTORS (with Czyż, Nowak, Rodrigo, hep-ph/432) 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 1 (Q2 ) γ µ F N 2 (Q2 ) 4m N Q = q 1 + q 2, q = (q 1 q 2 )/2 [γ µ, /Q] ) v(q 1 ), or G M = F 1 + F 2, G E = F 1 + Q2 4m 2 F 2 J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 23

24 A Separation of G M 2 and G E 2 through angular distribution: L µν H µν = (4πα)3 (1 + cos 2 θ γ ) Q 2 (1 cos 2 θ γ ) ( ) 4 G N M 2 (1 + cos 2 1 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 1, corrections and optimal frame hep-ph/432 ) Similarity to e + e N N : dσ dω = α2 β N 4Q 2 ( G N M 2 (1 + cos 2 θ) + 1 ) τ GN E 2 sin 2 θ J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 24

25 4 5 1 /. -, + * ) ( ' & 7 % % $ "! A At least one photon satisfies: ) (GeV $ # e + e p p γ implementation in PHOKHARA (large rates 4 evt/1mev around 4GeV 2 ) J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 25

26 "! , + ( * ) ( 9 2 &%$ Angular distributions of nucleon #! (nb) 854 / ' hadronic rest frame (two choices for GM/GE) J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 2

27 similar results for neutron pair production NLO corrections from ISR included (corrections 1 2%) no FSR 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 27

28 V Conclusions continuous development of PHOKHARA radiative corrections (completed for ISR) 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 central issue: hadronic form factors! J.H. Kühn The Radiative Return at Φ- and B-Meson Factories 28