Theoretical aspects and status of MC generators for radiative return analysis

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1 Theoretical aspects and status of MC generators for radiative return analysis H. CZYŻ, IF, UŚ, Katowice GLASGOW 2007 Motivation - what is the radiative return What do we have on the market Tests - comparisons, which were performed Plans 1

2 What do we like to measure and why: WHAT : σ(e + e hadrons) WHY: a had,lo µ = α2 3π 2 4m 2 π ds s K(s) R(s) R(s) = σ(e+ e hadrons) σ point UŚ, Katowice MC generators for radiative return Glasgow

3 THE RADIATIVE RETURN METHOD dσ(e + e hadrons + γ(isr)) = H(Q 2, θ γ ) dσ(e + e hadrons)(s = Q 2 ) 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,...) High precision measurement of the hadronic cross-section at meson-factories UŚ, Katowice MC generators for radiative return Glasgow

4 From EVA to PHOKHARA and... EVA: e + e π + π γ tagged photon (θ γ > θ cut ) ISR at LO + Structure Function FSR: point-like pions [Binner et al.] e + e 4π + γ ISR at LO + Structure Function [Czyż, Kühn,2000] H.C., A. Grzelińska, J. H. Kühn, E. Nowak-Kubat, G. Rodrigo, A. Wapienik PHOKHARA 6.0: π + π, µ + µ, 4π, NN, 3π, KK, Λ( ) Λ( ) ISR at NLO: virtual corrections to one photon events and two photon emission at tree level γ γ 2 γ 2 γ + FSR at NLO:π + π, µ + µ,k + K tagged or untagged photons Modular structure + UŚ, Katowice MC generators for radiative return Glasgow

5 From EVA to... e + e 4π + γ ISR at LO + Structure Function [Czyż, Kühn] e + e hadrons + γ upgraded by BaBar - not public (?) PHOTOS [Barberio et al.] for FSR EVA: e + e π + π γ tagged photon (θ γ > θ cut ) ISR at LO + Structure Function FSR: point-like pions [Binner et al.] e + e π + π + γ FSR studies [Pancheri,Shekhovtsova,Venanzoni] UŚ, Katowice MC generators for radiative return Glasgow

6 KKMC S. Jadach, B. F. L. Ward and Z. W as YFS exponentation high accuracy only for muon pairs can we hope for: upgrades??? UŚ, Katowice MC generators for radiative return Glasgow

7 S.Jadach: KKMC- Pisa 2003 UŚ, Katowice MC generators for radiative return Glasgow

8 Dubna - Novosibirsk papers 2003 A. B. Arbuzov, E. Bartos (Bratislava), V. V. Bytev, E. A. Kuraev, Z. K. Silagadze muon and pion pairs analytic formulae based on RG - SF Comparisons with PHOKHARA planned first results in February 2008?? UŚ, Katowice MC generators for radiative return Glasgow

9 S.Jadach: KKMC UŚ, Katowice MC generators for radiative return Glasgow

10 É ¾ (GeV) ¾ PHOKHARA vs. KKMC cnd. ¼ ¼½¾ KKMC/Ber-1 KKMC(al)/Ber-1 KKMC(al2)/Ber-1 ¼ ¼½ ¼ ¼¼ ¼ ¼¼ ¼ ¼¼ ¼ ¼¼¾ ¼ ¼ ¼¼¾ ¼ ¼¼ ½ ¼ ¼ ¼ ¼ ¾ ¼ UŚ, Katowice MC generators for radiative return Glasgow

11 PHOKHARA generation tests H. Czyż, A. Grzelińska, J.H. Kühn and G. Rodrigo EPJ C27 (2003) dσ PHOKHARA /dσ analytic GeV virtual + soft two hard photons Q 2 (GeV 2 ) UŚ, Katowice MC generators for radiative return Glasgow

12 PHOKHARA generation tests G. Rodrigo, H. Czyż, J.H. Kühn and M. Szopa, Eur.Phys.J.C24 (2002)71. (σ MC -σ Gauss )/σ Gauss x x Q 2 (GeV 2 ) cos θ γ UŚ, Katowice MC generators for radiative return Glasgow

13 KKMC vs. PHOKHARA - ISR virt. corr. C. Glosser, S. Jadach, B. F. L. Ward and S. A. Yost Phys. Lett. B 605 (2005) 123; Phys. Rev. D 73 (2006) a precison not direct tests UŚ, Katowice MC generators for radiative return Glasgow

14 PHOKHARA tests matrix elements tests generation tests KKMC comparison +... UŚ, Katowice MC generators for radiative return Glasgow

15 PHOKHARA generation tests G. Rodrigo, H. Czyż, J.H. Kühn and M. Szopa, Eur.Phys.J.C24 (2002)71. (σ(10-4 )-σ(10-3 ))/σ(10-3 ) (σ(10-5 )-σ(10-4 ))/σ(10-4 ) Q 2 (GeV 2 ) UŚ, Katowice MC generators for radiative return Glasgow

16 PHOKHARA: ISR tests summary technical precision: few 10 4 physical precision: 0.5% plans: accuracy 0.2% UŚ, Katowice MC generators for radiative return Glasgow

17 LA Bhabha luminosity: G. Balossini, C. M. Carloni Calame, G. Montagna, O. Nicrosini and F. Piccinini, Nucl. Phys. B 758 (2006) 227 accuracy: 0.1% Comparisons with BHWIDE and MCGPJ: agreement within 0.1% BHWIDE: S. Jadach, W. Placzek and B. F. L. Ward, Phys. Lett. B 390 (1997) 298 MCGPJ: A. B. Arbuzov, G. V. Fedotovich, F. V. Ignatov, E. A. Kuraev and A. L. Sibidanov, Eur. Phys. J. C 46 (2006) 689 UŚ, Katowice MC generators for radiative return Glasgow

18 FSR in PHOKHARA e + π + e π e + π + e π UŚ, Katowice MC generators for radiative return Glasgow

19 FSR at KLOE, additional contributions: e + e φ (f 0 (980) f0 + f 0 (600) σ )γ ππγ e + p 1 γ φp f 0Q π + q 1 π q 2 e p 2 γ k π + q 1 e + p 1 γ φp K K f 0 Q K π q 2 e p 2 γ k UŚ, Katowice MC generators for radiative return Glasgow

20 DAΦNE versus B-factories: configurations in the cms - frame 10 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 UŚ, Katowice MC generators for radiative return Glasgow

21 LO FSR DAΦNE versus B-factories: GeV GeV FSR/ISR no cuts FSR/ISR Æ 140 Æ 15 Æ or 165 Æ Q 2 (GeV 2 ) Q 2 (GeV 2 ) UŚ, Katowice MC generators for radiative return Glasgow

22 NLO FSR DAΦNE versus B-factories: 0.12 e + e π + π γ(γ) 0.06 e + e π + π γ(γ) dσ(ifsnlo) / dσ(isrnlo) 1 dq 2 dq θ γ <15, θ γ > < θ π +,π <140 s =1.02GeV dσ(ifsnlo) / dσ(isrnlo) 1 dq 2 dq < θ γ < < θ π +,π <150 s =10.52GeV Q 2 (GeV 2 ) Q 2 (GeV 2 ) UŚ, Katowice MC generators for radiative return Glasgow

23 Controlling NLO FSR dσ(ifsnlo(f0)) / dσ(ifsnlo(nof0)) -1 dq 2 dq s =mφ e + e π + π γ(γ) M tr cut f0kkmodel f0 nostr. α φ = π f0 nostr. α φ = 2 50 < θ π ± <130 θ( p π + + p π ) <15 or > Q 2 (GeV 2 ) d (IFSNLO) d (ISRNLO) 1 dq 2 dq e e ( ) M trk 0 85GeVforQ 2 m 2 Ô s 10 52GeV 0 0 Æ 180 Æ Æ 180 Æ Q 2 (GeV 2 ) b 1 6 UŚ, Katowice MC generators for radiative return Glasgow

24 Test of FSR model interference: interference odd under π + π asymmetric differential distribution: interf. = 0 A(θ) = Nπ+ (θ) N π (θ) N π+ (θ) + N π (θ) UŚ, Katowice MC generators for radiative return Glasgow

25 Charge asymmetries F-B asymmetry defined for π + A FB (Q 2 ) = N(θ π + >90 ) N(θ π +<90 ) N(θ π +>90 )+N(θ π +<90 ) ( Q 2 ) charge asymmetry A C (θ π ) = N(π+ ) N(π ) N(π + )+N(π ) (θ π) UŚ, Katowice MC generators for radiative return Glasgow

26 F-B asymmetry H. C., A. Grzelińska, J.H. Kühn, Phys. Lett. B 611 (2005) 116 KLOE: Phys.Lett.B634: ,2006 N(θ π +>90 ) N(θ π +<90 ) N(θ π +>90 )+N(θ π +<90 ) s =mφ 50 < θ π ± < < θ γ <130 e + e π + π γ f0kkmodel f0 nostr. α φ = π f0 nostr. α φ = 2 nof Q2 (GeV) UŚ, Katowice MC generators for radiative return Glasgow

27 Λ formfactors e + e Λ(q 2, S 2 ) Λ(q 1, S 1 ) e + e Λ(q 2, S 2 ) Λ(q 1, S 1 )γ ISR J µ = ie ū(q 2, S 2 ) ( F1 Λ(Q2 )γ µ F 2 Λ ) (Q2 ) 4m [γ Λ µ, Q/] v(q 1, S 1 ) UŚ, Katowice MC generators for radiative return Glasgow

28 The polarized cross section dσ(e + e ΛΛ) = 1 2s L0 µν Hµν dφ 2 (p 1 + p 2 ; q 1, q 2 ) L 0 µν Hµν = 4π 2 α { G 2 M 2 ( 1 + cos 2 θ Λ) + 1 τ G E 2 sin 2 θ Λ ( + Im(G M G E )/ τ sin(2θ Λ ) S y ) Λ + Sȳ Λ Re(G M G E )/ τ sin(2θ Λ ) (S z Λ Sx Λ + Sz Λ Sx Λ + ( 1τ G E 2 + G M 2) sin 2 θ Λ Sx Λ Sx Λ ) + ( 1τ G E 2 G M 2) sin 2 θ Λ Sȳ Λ Sy Λ } ( 1τ G E 2 sin 2 θ Λ G M 2 ( 1 + cos 2 θ Λ) ) S z Λ Sz Λ UŚ, Katowice MC generators for radiative return Glasgow

29 The subsequent two body decays of Λs The measurement of the subsequent two body decays: Λ π p and Λ π + p allow for a spin analysis of the decaying Λs. The decay distribution: R Λ = 1 α Λ S Λ n π The spin vector is replaced by: S Λ α Λ n π and S Λ α Λ n π + UŚ, Katowice MC generators for radiative return Glasgow

30 e + e Λ( π + p)λ( π p) using the narrow width approximation dσ ( e + e Λ( π + p)λ( π p) ) = dσ ( e + e ΛΛ ) (S α Λ, Λ Λn π ) d Φ 2 (q 1 ; p π +, p p )d Φ 2 (q 2 ; p π, p p ) Br( Λ π + p)br(λ π p) n π +(n π ) = (0, n π +) ((0, n π )) in the Λ (Λ) rest frame UŚ, Katowice MC generators for radiative return Glasgow

31 The cross section with ISR photon emision { G M 2 ( 1 + cos 2 ) θ Λ + τ 1 G E 2 sin 2 θ Λ α Im(G M G E ) ( Λ τ sin(2θ Λ ) n y π n y ) π + L ij H ij (4πα)3 4Q 2 y 1 y 2 ( 1 + cos 2 θ γ ) +α 2 Re(G M G E ) ( ) Λ τ sin(2θ Λ ) n z π n x π + + n z π + n x π α 2 Λ ( 1τ G E 2 + G M 2) sin 2 θ Λ nx π + n x π ( α 2 1τ Λ G E 2 G M 2) sin 2 θ Λ ny π + n y π ( +α 2 1τ Λ G E 2 sin 2 θ Λ G M 2 ( 1 + cos 2 ) ) } θ Λ n z π + n z π θ Λ - Q rest frame with the z-axis opposite to the photon direction UŚ, Katowice MC generators for radiative return Glasgow

32 Asymmetry A ± y = dσ(a± >0) dσ(a ± <0) dσ(a ± >0)+dσ(a ± <0) a +( ) = sin(2θ Λ ) ny π + (π ) UŚ, Katowice MC generators for radiative return Glasgow

33 Asymmetry e + e Λ( π p) Λ( π + p)γ 30 < θ π,p,π +, p <150 A + y s=10.52gev no cuts φ = π Q2 (GeV) UŚ, Katowice MC generators for radiative return Glasgow

34 Summary and plans PHOKHARA: ISR accuracy 0.5% need for ISR accuracy 0.2% carefull study of FSR necessary tools for these studies are ready need for more codes comparisons the radiative return a tool in hadronic physics UŚ, Katowice MC generators for radiative return Glasgow

35 Summary and plans soon J/ψ and ψ(2s) in PHOKHARA 4π channels reanalysis UŚ, Katowice MC generators for radiative return Glasgow