The Radiative Return and Form Factors at Large Q 2 J.H. K UHN, - PowerPoint PPT Presentation

The Radiative Return and Form Factors at Large Q 2 J.H. K¨ UHN, TTP, KARLSRUHE I Basic Idea II Monte Carlo Generators: Status & Perspectives III Nucleon Form Factors at B-Factories Pion and Kaon Form Factors at large Q 2 IV and τ → νK − K 0 V Conclusions 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 The Radiative Return and Form Factors at Large Q 2 J.H. K¨ uhn, TAU 04 2

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 ] The Radiative Return and Form Factors at Large Q 2 J.H. K¨ uhn, TAU 04 3

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 s 2 + Q 4 − s − Q 2 πs � 1+cos θ min � s ( s − Q 2 ) log cos θ min 1 − cos θ min s � � dL = α ⇒ differential luminosity: Q 2 , s � � · · · L (at s ) πs dQ 2 e.g. θ min = 30 ◦ ; √ s = 10 . 58 GeV ; Q = 1 GeV ; ∆ Q = 0 . 1 GeV ∆ Q 2 = 7 . 6 · 10 − 6 L (at s ) dL Q 2 , s � � dQ 2 100 fb − 1 at 10.58 GeV ⇒ 0.76 pb − 1 per scan point at 1 GeV The Radiative Return and Form Factors at Large Q 2 J.H. K¨ uhn, TAU 04 4

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) or NLO calculation (PHOKHARA MC) The Radiative Return and Form Factors at Large Q 2 J.H. K¨ uhn, TAU 04 5

II MONTE CARLO GENERATORS P H OTONS FROM KARLSRUHE H ADRONICALLY R ADIATED References etc. → http://cern.ch/german.rodrigo/phokhara The Radiative Return and Form Factors at Large Q 2 J.H. K¨ uhn, TAU 04 6

A PHOKHARA 2.0: π + π − , µ + µ − , 4 π ❶ LL at a fixed order + • ISR at NLO: virtual corrections subleading terms (1 % ) to one photon events and two photon emission at tree level ❷ Full angular dependence γ γ γ 2 2 γ + + ❸ Momentum conservation • FSR at LO: π + π − , µ + µ − ❹ Tagged or untagged • tagged or untagged photons photon • modular structure The Radiative Return and Form Factors at Large Q 2 J.H. K¨ uhn, TAU 04 7

� 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 The Radiative Return and Form Factors at Large Q 2 J.H. K¨ uhn, TAU 04 8

★ ★ ✏ ★ ✕ ✏ ✩ ✘ ✏ ✙ ✩ ✏ ✩ ✕ ✚ ✎ ✓ ✒ ✌ ✒ ✏ ✍ ✑ ✏ ✏ ★ ✏ ✏ ✏ ★ ✏ ✏ ✓ ✏ ★ ✒ ✏ ✓ ★ ✏ ✗ ✛ ✜ ✏ ✁ ✁ � ✥ � ✧ ✁ ★ � ✁ ★ ★ ★ ★ ★ ★ ✩ ★ ✦ ✥ ✢ ☛ ✌ ✣ ★ ✛ ☞ ✣ ☞ ✠ ✟ � ☛ ✡ ✠ ✜ ✟ ✤ ✤ ✞ ✏ 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 ) ⇒ Talk by D. Leone or measure photon The Radiative Return and Form Factors at Large Q 2 J.H. K¨ uhn, TAU 04 9

Experimental Perspectives BABAR, BELLE higher Q 2 available ⇒ measurement of R( Q 2 ) from threshold up to at least 5 GeV. Examples: ππ ◮ 4 π ± ◮ ◮ K K ππ ◮ K K K K The Radiative Return and Form Factors at Large Q 2 J.H. K¨ uhn, TAU 04 10

PHOKHARA 4.0 • µ + µ − γ with FSR at NLO • vacuum polarisation can be switched on • nucleon pair production included The Radiative Return and Form Factors at Large Q 2 J.H. K¨ uhn, TAU 04 11

To be done: • three mesons: 3 π ( → ρπ ), KKπ • KKππ , 4 K • narrow resonances parameters of J/ψ , ψ ′ : Γ f Γ tot ; f = µ + µ − , π + π − , 3 π , 4 π , 4 K , ... observable: Γ e σ f σ f σ µ + µ − ( off resonance ) ? compare : = σ µ + µ − ( on resonance ) f = µ + µ − , π + π − , 4 π , . . . virtual photon only (I=1) f = 3 π , K ¯ K , K ¯ Kπ , . . . 3 gluon intermediate state (I=0) The Radiative Return and Form Factors at Large Q 2 J.H. K¨ uhn, TAU 04 12

III 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 The Radiative Return and Form Factors at Large Q 2 J.H. K¨ uhn, TAU 04 13

Result: 2 s L µν H µν d Φ 2 ( p 1 + p 2 ; Q, k ) d Φ 2 ( Q ; q 1 , q 2 ) dQ 2 dσ = 1 2 π , L µν H µν = (4 πα ) 3 M | 2 − 1 �� � | G N τ | G N E | 2 Q 2 � 1 �� ( p 1 · q ) 2 + ( p 2 · q ) 2 32 s + 1 � × β 2 s 2 N ( s − Q 2 ) y 1 y 2 ��� 1 � ( s 2 + Q 4 ) M | 2 + 1 + 1 � �� | G N τ | G N E | 2 + 2 s ( s − Q 2 ) − 2 , y 1 y 2 where N = 1 − 4 m 2 y 1 , 2 = s − Q 2 Q 2 β 2 N (1 ∓ cos θ γ ) , τ = , 4 m 2 Q 2 2 s N The Radiative Return and Form Factors at Large Q 2 J.H. K¨ uhn, TAU 04 14

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 � � ⇒ additional rotation by θ D = 1 2 s γ c γ ≈ 1 s γ c γ 2 arctan γ ( β 2 + c 2 γ − s 2 γ /γ 2 ) γ 1 + c 2 γ � � with s γ = sin θ γ , β = ( s − Q 2 ) / ( s + Q 2 ) , γ = ( s + Q 2 ) / 2 sQ 2 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 The Radiative Return and Form Factors at Large Q 2 J.H. K¨ uhn, TAU 04 15

✤ ✤ ✣ ✤ ✥ ✤ ✣ ✥ ✢ ✜ ✤ ✗ ✛ ✖ ✘ ✗ ✚ ✗ ✙ ✤ ✤ ✗ ✣ ✣ ★ ✧ ✤ ✣ ✧ ✦ ✤ ✦ ✦ ✤ ✤ ✣ ✤ ✥ ✤ ✣ ✧ ✖ ✘ ✖ ✞ ☞ ✡ ✠ ✟ ☎ ✆ ✝ ✍ ☎ ✆ ☎ ✄ ✂ ✁ � ✌ ☛ ✎ ☛ ✕ ✔ ✓ ✍ ✌ ✎ ✠ ✒ A Implementation on basis of model for form factor: ✎✑✏ ✎✑✏ ✎✑✏ ✎✑✏ ✦✑✣ ✢✑✣ (GeV ) (GeV ) The Radiative Return and Form Factors at Large Q 2 J.H. K¨ uhn, TAU 04 16

✵ ✥ ✴ ✷ ✸ ❍ ✪ ✦ ✫ ✫ ✬ ✭ ✴ ✬ ✜ ✥ ✶ ✥ ✫ ✜✳ ✫ ✬ ❏ ✲ ✮ ✬ ✢ ■ ✫ ✥ ✫ ✬ ✜✢ ✬ ✜ ✥ ● ✪ ❁ ✾ ✽ ✿ ❀ ❁ ❋ ❊ ✼ ❂ ❃ ❂ ❄ ❅ ❆ ❇ ✽ ✻ ✹ ✲ ✢ ✫ ✬ ✭ ✮ ✰ ✮ ★ ✬ ✜ ✥ ✢ ✫ ★ ✺ ✢ ✳ ❉ ✻ � ✁ ☎ ✆ ✞ ▼ ✟ ✞ ✠ ✟ ✡ ☛ ☞ ✌ ☞ ✜✢ ✝ ✜✢ ❖ ◗ ✻ ✜✢ P ✻ ✜✢ ✻ ✆ ✜✢ ◆ ✻ � ✁ ✂✄ ☎ ✍ ✎ ✥✦ ✞ ✑ ✘ ✕ ✝ ✘ ✕ ✘ ✘ ✕ ✗ ✘ ✙ ✚ ✛ ✵ ✕ ✂ ▲ ✞ ✏ ✻ ✑ ✒ ✝ ✓ ✔ ✗ ✜✢ ✑ ✸ ✝ ✥ ✞ ❑ ❈ A ✂✖✕ FENICE(98) FENICE(94) ✂✖✕ ✧✩★ FENICE(93) ✜✢✤✣ DM2(90) ✂✖✕ DM2(83) DM1(79) ADONE(73) ✂✖✕ ✭✯✮✱✰ A : B : ✭✯✴ (nb) At least one photon satisfies: A B ✧✩★ (GeV ) (GeV ) e + e − → p ¯ e + e − → p ¯ p p γ implementation in PHOKHARA The Radiative Return and Form Factors at Large Q 2 J.H. K¨ uhn, TAU 04 17