The Radiative Return at Φ - and B -Meson Factories KARLSRUHE–KATOWICE–VALENCIA J. H. K¨ uhn I Basic Idea II Monte Carlo Generators: Status & Perspectives III Charge Asymmetry and Radiative Φ -Decays ( ⇒ H. Czy˙ z) IV Nucleon Form Factor at B-Factories V Conclusions (with H. Czy˙ z, A. Grzelinska, E. Nowak, G. Rodrigo) 1
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 DA Φ NE, CLEO-C, B-factories J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 2
DA Φ NE versus B-factories: configurations in the cms - frame 10 GeV 1 GeV γ γ + − e e + π − π very hard photon: clear kine- no natural kinematic separation ➪ cuts to control FSR versus matic separation between pho- ton and hadrons ISR ( two step process: e + e − → γ ρ ( → γππ ) ⇒ see below ) J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 3
Rough estimates for rates: π + π − γ : E γ > 100 MeV √ s [ GeV ] L [ fb − 1 ] # events, θ min = 7 ◦ � 16 · 10 6 1.02 1.35 3.5 · 10 6 10.6 100 multi-hadron-events (R ≡ 2 ) √ s = 10 . 6 GeV Q 2 -interval [ GeV ] # events, θ min = 7 ◦ 9.9 · 10 5 [ 1 . 5 , 2 . 0 ] 7.9 · 10 5 [ 2 . 0 , 2 . 5 ] 6.6 · 10 5 [ 2 . 5 , 3 . 0 ] 5.8 · 10 5 [ 3 . 0 , 3 . 5 ] J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 4
Lowest order e + e − → γ + had( Q 2 ) e + e − → had( Q 2 ) dσ � � � � = σ dQ 2 s 2 + Q 4 log( s/m 2 � � � � e ) − 1 , no angular cut s ( s − Q 2 ) × α πs s 2 + Q 4 − s − Q 2 � 1+cos θ min � s ( s − Q 2 ) log cos θ min s 1 − cos θ min � � dL = α ⇒ differential luminosity: Q 2 , s � � · · · L (at s ) πs dQ 2 J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 5
Basic Ingredients for Pion Formfactor ◮ ISR pion form factor ➪ to be tested ◮ FSR radiation from point- like pions (probably overestimated) ◮ additional radiation: collinear (EVA MC) (Binner, JK, Melnikov) or NLO calculation (PHOKHARA MC) J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 6
II MONTE CARLO GENERATORS P H OTONS FROM KARLSRUHE H ADRONICALLY R ADIATED References etc. → http://cern.ch/german.rodrigo/phokhara J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 7
A http://cern.ch/german.rodrigo/phokhara J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 8
A J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 9
A J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 10
A PHOKHARA 2.0: π + π − , µ + µ − , 4 π • ISR at NLO: virtual corrections to one photon events and two photon emission at tree level γ γ γ 2 2 γ + + • FSR at LO: π + π − , µ + µ − • tagged or untagged photons • modular structure J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 11
QED CORRECTIONS AT LEPTONIC SIDE = ⇒ BASIC BUILDING BLOCK FOR ALL HADRONIC FINAL STATES J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 12
� PHOKHARA 3.0 ◮ 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. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 13
★ ★ ✏ ★ ✕ ✏ ✩ ✘ ✏ ✙ ✩ ✏ ✩ ✕ ✚ ✎ ✓ ✒ ✌ ✒ ✏ ✍ ✑ ✏ ✏ ★ ✏ ✏ ✏ ★ ✏ ✏ ✓ ✏ ★ ✒ ✏ ✓ ★ ✏ ✗ ✛ ✜ ✏ ✁ ✁ � ✥ � ✧ ✁ ★ � ✁ ★ ★ ★ ★ ★ ★ ✩ ★ ✦ ✥ ✢ ☛ ✌ ✣ ★ ✛ ☞ ✣ ☞ ✠ ✟ � ☛ ✡ ✠ ✜ ✟ ✤ ✤ ✞ ✏ A Large effect for Q 2 < m 2 ρ eliminated by suitable cuts on π + π − configuration (suppress 2 γ events ) e e ( ) e e ( ) 1 1 0 14 0 05 a c : 15 ( ISRNLO ) p p ( IFSLO ) 0 04 0 12 dQ 2 dQ 2 ✔✖✕ 50 130 s = 1.02 GeV 0 03 d 0 ✂✝✆ 180 0 1 d no M tr cut ( IFSNLO ) ( IFSNLO ) ✂☎✄ 0 180 0 02 dQ 2 0 08 dQ 2 0 01 d 0 06 d 0 0 04 0 01 M tr cut 0 02 0 02 0 0 03 0 02 0 04 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 1 Q 2 ( GeV 2 ) Q 2 ( GeV 2 ) or measure photon J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 14
Experimental Perspectives ⇒ TALK BY STEFAN M¨ KLOE = ULLER ◮ ππ pion form factor BABAR, BELLE higher Q 2 available ⇒ measurement of R( Q 2 ) from threshold up to at least 5 GeV. Examples: 3 π ◮ 4 π ± ◮ ◮ K K ππ ◮ K K K K ◮ J/ Ψ J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 15
A 1500 300 events/(2.5 MeV/c 2 ) events/(25 MeV/c 2 ) 1000 200 500 100 0 0 0.8 0.9 1.0 1.2 1.4 1.6 1.8 M 3 π (GeV/c 2 ) M 3 π (GeV/c 2 ) The background-subtracted 3 π mass spectrum for masses between 0.70 and 1.05 MeV/ c 2 (plot on the left) and for masses from 1.05 to 1.80 MeV/ c 2 (plot on the right). BaBar J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 16
A 8 Cross section (nb) 6 4 2 0 1.5 2 2.5 3 M 3 π (GeV/c 2 ) The e + e − → π + π − π 0 cross section measured by BaBar (filled circles), by SND (open circles), and DM2 (open triangles). BaBar J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 17
A BaBar J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 18
✢ ★ ✦ ✧ ★ ✥ ★ ✦ ✩ ✥ ✪ ✫ ✬ ✭ ✮ ✯ ✰ ✤ ✤ ✲ ✗ ✚ ✗ ✗ ✜ ✗ ✗ ✾ ✗ ✺ ✣ ✗ ✗ ✗ ✿ ✽ ✿ ✱ ✳ ✗ ✺ ✺ ✻✺ ✺ ✺ ✿ ✼ ✺ ✿ ✻ ✽ ✺ ✺ ✿ ✾ ✺ ✺ ✺ ✻ ✴ ✻✼ ✵ ✶ ✷ ✸ ✹✺ ✺ ✺ ✺ ✺ ✺ ✻✽ ✺ ✺ ✻ ✾ ✺ ✗ ✗ ✻✺ ✍ ✆ ✝ ✞ ✟ ✿ ☞ ✌ ✎ ✂ ✏ ✑ ✒ ✓ ✔ ✕ ✖✗✘ ☎ ☎ ✖✗ ✺ ✻ ❀ ✺ ✻ ✾ ✽ ✼ ✿ ✁ ✻ � ✁ � ✂ ✄ ☎ ✗ ✗ ✖ ✗ ✗ ✖ ✚ ✗ ✗ ✖ ✜ ✗ ✜ ✖ ✢ ✗ ✗ ✖✣ ✗ ✗ ✘ ✗ ✗ ✘ ✙ ✘ ✗ ✙ ✗ ✗ ✚ ✗ ✗ ✚ ✗ ✗ ✛ ✘ ✗ ✛ ✿ BaBar 19 The Radiative Return at Φ - and B -Meson Factories DM1 ND SND 02 BABAR A ND DM1 CMD2 98 SND 02 CMD2 95 SND 03 CMD2 04 ✠☛✡ uhn J.H. K¨
✰ ✱ ✸ ✹ ✷ ✴ ✳ ✶ ✹✼ ✲ ✹ ✹ ✯ ✮ ✭ ✬ ✫ ✪ ★ ✩ ★ ✳ ✴ ✥ ✶ ✷ ✹ ✹ ✴ ✹ ✹✻ ✹ ✴ ✹ ✹ ✺ ✹ ✴ ✹ ✷ ✴ ✹ ✶ ✴ ✹ ✧ ✦ ✴ ✍ ✹ ✒✓ ✟ ✞✑ ✆ ✏ ✎ ✹ ✌ ✕ ✸ ✹ ✴ ✝ ✆ ✹ ✹ ✳ ✹ ✔ ✔ ✥ � ✍ ✤ ✔ ✣ ✝ ✢ ✄ ✜ ✄ ✍ ✖ ✚ ✝ ✴ ✘ ✖ ✘ ✕ ✘ ✗ ✹ BaBar 20 1.5 M( π + π - ) (GeV/c 2 ) The Radiative Return at Φ - and B -Meson Factories 1 0.5 200 100 0 events/(25 MeV/c 2 ) A ✳✵✴ GeV GeV ✞✠✟ ✡☞☛ ✳✵✴ ✞✠✟ ✙✛✚ �✂✁☎✄ uhn J.H. K¨
PHOKHARA 4.0 • µ + µ − γ with FSR at NLO • vacuum polarisation can be switched on • nucleon pair production included J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 21
III Charge Asymmetries and Radiative Φ -Decays (H. Czy˙ z, A. Grzelinska, JK, hep-ph/0412239) = ⇒ talk by Henryk Czy˙ z J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 22
IV NUCLEON FORM FACTORS (with Czy˙ z, Nowak, Rodrigo, hep-ph/0403062) Q 2 � 4 m 2 N accessible at B-factories ⇒ study e + e − → γ N ¯ N (with N = p or n ) hadronic current: � 1 ( Q 2 ) γ µ − F N 2 ( Q 2 ) � F N J µ = − ie · ¯ u ( q 2 ) [ γ µ , / Q ] v ( q 1 ) , 4 m N Q = q 1 + q 2 , q = ( q 1 − q 2 ) / 2 or G E = F 1 + Q 2 G M = F 1 + F 2 , 4 m 2 F 2 J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 23
A Separation of | G M | 2 and | G E | 2 through angular distribution: (1 + cos 2 θ γ ) L µν H µν = (4 πα ) 3 (1 − cos 2 θ γ ) Q 2 θ ) + 1 � � M | 2 (1 + cos 2 ˆ E | 2 sin 2 ˆ | G N τ | G N × 4 θ ˆ θ = angle of nucleon with respect to γ -direction in hadronic rest frame � � valid for s/Q 2 ≪ 1 , corrections and “optimal frame” → hep-ph/0403062 Similarity to e + e − → N ¯ N : d Ω = α 2 β N dσ M | 2 (1 + cos 2 θ ) + 1 � � E | 2 sin 2 θ | G N τ | G N 4 Q 2 J.H. K¨ uhn The Radiative Return at Φ - and B -Meson Factories 24
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