RESONANCE at LARGE MOMENTUM TRANSFERS

Transcription

1 1 V. M. Braun, M. Göckeler, R. Horsley, T. Kaltenbrunner, A. Lenz, Y. Nakamura, D. Pleiter, P. E. L. Rakow, J. Rohrwild, A. Schäfer, G. Schierholz, H. Stüben, N. Warkentin, J. M. Zanotti µ ELECTROPRODUCTION µ of the N 1535µ µ RESONANCE at LARGE MOMENTUM TRANSFERS BABAR, µ µ Vladimir M. Braun 1 Universität Regensburg µ Institut für Theoretische Physik µ µ µ µ

2 Electroproduction of N 1535µ electromagnetic transition matrix element N P µj em N Pµ N P µ The helicity amplitudes A 12 Q 2 µ S 12 Q 2 µ The differential cross section G 1 q 2 µ m 2 N Vereshkov and Volchanskiy, PRD 76 (2007) qq q 2 µ i G 2 q 2 µ q 5 N Pµ m N µ µ µ Q 2 m N m N µ 2 2«em mn 5 m2 N mn 2 µ Q 2 G 1 Q 2 µ m N m N m N µg 2 Q 2 µ µ Q 2 m N m µ N µ 2 «em mn 5 m2 N mn 2 µ Q m N m N µg 1 Q 2 µ m N G 2 Q 2 µ d dq 2 en en µ «emm N MN 2 mn 2 µ 2Q 2 s mn 2 µ2 1 µ µ 2 S 12 Q 2 µ 2 A 12 Q 2 µ 2 µ µ V. M. Braun (Regensburg) Electroproduction of N 1535µ October / 11

3 QCD theory Direct lattice calculations of form factors restricted to Q 1a, currently a 006 unlikely to go beyond Q 2 3 GeV 2 black box Light-cone sum rules 008 fm GeVµ; µ µ µ need N light-cone distribution amplitudes (DAs) or at least good interpolating current µ in approaches based on duality, separation of states of different parity is very difficult: µ 0qqqN pµ f N N pµ 0qqqN pµ f N 5 N pµ In this work calculate moments of N light-cone distribution amplitudes on the lattice use them as input in LCSRs to calculate form factors µ µ µ V. M. Braun (Regensburg) Electroproduction of N 1535µ October / 11

4 µ µ µ µ µ µ µ µ µ Preliminaries Distribution Amplitides Results Conclusions QCD theory why light-cone sum rules? Q Q b ~ 1/Q x 1 b ~ 1/ Λ QCD µ Hard rescattering: Small b Average 0 x 1 µ µ Soft (Feynman): Average b Large x 1 µ µ µ pqcd hard contributions are included soft contribution is built as a sum of contributions of DAs of increasing twist: expansion parameter 2 µ QCD s 0µ twist where s 0 is interval of duality there is no double counting but separation of soft and hard is schemeand scale-dependent This technique provides one with the most direct relation between form factors µ and parton structure that is available at present, with no other parameters µ V. M. Braun (Regensburg) Electroproduction of N 1535µ October / 11

5 Lattice Calculation QCDSF/DIK configurations generated with N f 2 flavors of clover fermions m GeV volume afm Lfm , 01350, , 1029, , 01359, , 0587, , 1356, 01361, 1183, 0856, 0648, µ µ , , 0421 µ Irreducible spinor representations of H 4µ d 92 (0 derivatives) d 112 (1 derivative) d 132 (2 derivatives) µ 2µ 1i, 2µ 2i µ, 2µ 3i 2µ 4i, 2µ 5i, 2µ 6i 0µ 1µ 2µ 6i 1i 7i, 2µ 8i, 2µ 9i 1µ 2i, 1µ 3i, 1µ 2µ 4i 10i, 2µ 11i, 2µ 12i, 2µ 13i 2µ µ 14i, 2µ 15i, 2µ 16i, 2µ 17i, 2µ 18i 0µ 1i, 0µ 2i, 0µ 3i, 0µ 4i, 0µ 5i 12 0µ 1 7i, 0µ 8i, 0µ 9i 12 1µ 2 5i, 1µ 6i, 1µ 7i, 1µ 8i Kaltenbrunner, Göckeler, Schäfer, Eur.Phys.J.C55(2008)387 Göckeler et al., [QCDSF Collaboration], paper in preparation µ µ Nonperturbative renormalization of three-quark operators V. M. Braun (Regensburg) Electroproduction of N 1535µ October / 11

6 Moments of Distribution Amplitudes Asympt. N N 1535µ f N 10 3 GeV (63)(86) 4.544(117)(223) GeV (65)(136) 37.55(101)(768) GeV (128)(268) 191.9(44)(391) µ µ ³ ³ (37)(139) (33)(155) 3 µ ³ ³ (11)(52) (20)(32) 3 ³ ³ (32)(106) (41)(136) 3 ³ ³ (64)(212) (89)(307) 7 ³ ³ (32)(106) (45)(224) 7 µ ³ ³ (113)(382) (160)(584) 7 µ ³ ³ (89)(319) (132)(497) 21 ³ ³ (41)(152) (56)(131) 21 ³ ³ (67)(219) (101)(304) 21 Table: Comparison of the lattice results as obtained from QCDSF/DIK configurations at µ 540 for the nucleon (N) and N 1535µ at 2 MS 1 GeV2. The first error is statistical, the second error represents the uncertainty due to the chiral extrapolation and renormalization. The systematic error should be considered with caution. µ N. Warkentin for the QCDSF collaboration, LATTICE-2008 µ V. M. Braun (Regensburg) Electroproduction of N 1535µ October / 11

7 µ Preliminaries Distribution Amplitides Results Conclusions Leading Twist Distribution Amplitudes of the Nucleon and N 1535µ µ µ µ (a) µ µ µ µ µ µ µ µ Figure: Barycentric plot of the distribution amplitudes for nucleon (left) and N 1535µ (right) at MS 1GeV using the central values of the lattice results. The lines of constant x 1, x 2 and µ x 3 are parallel to the sides of the triangle labelled by x 2, x 3 and x 1, respectively. (b) µ µ V. M. Braun (Regensburg) Electroproduction of N 1535µ October / 11

8 Results: N N 1535µ A 1/2 (Q 2 ) 0,15 0,1 0,05 preliminary µ JLab Hall C 2007 data µ CLAS data [1] Compilation from [2] Compilation from [2] Compliation from [2] Compilation from [2] µ µ Lattice Uncertainties(min) Lattice Uncertainties (max) µ 0 µ Q 2 µ µ [1] H. Denizli et al., Phys. Rev. C 76 (2007) [2] P. Stoler, Phys. Rept. 226 (1993) 103 µ µ µ µ µ V. M. Braun (Regensburg) Electroproduction of N 1535µ October / 11

9 Preliminaries Distribution Amplitides Results Conclusions Comparison: Electromagnetic Formfactors µ µ µ µ µ proton ub µ p G M /( µ p G D) µ 0.25 µ 0.25 µ Q 2 µ µ neutron µ n G M /( µng D) p p µpg E /G M µ µ µ Q n G E µ µ µ µ 0.25 µ 0.75 µ Q 2 µ Q Braun, Lenz, Wittmann; PRD73:094019,2006 µ µ V. M. Braun (Regensburg) Electroproduction of N 1535µ October / 11

10 µ µ Preliminaries Distribution Amplitides Results Conclusions Comparison: N N 1535µ vs. N 1232µ µ µ µ A 1/2 (Q 2 ) 0,15 0,1 0,05 preliminary µ JLab Hall C 2007 data CLAS data [1] Compilation from [2] Compilation from [2] Compliation from [2] Compilation from [2] Lattice Uncertainties(min) Lattice Uncertainties (max) Q 2 µ µ kinematic mass corrections m 2 R Q2? or macroscopic structure of the resonances? Ash G M /3G dipole µ µ µ µ µ Q 2 2, GeV Braun, Lenz, Peters, Radyushkin; PRD73:034020,2006 : J. Rohrwild; PRD75:074025,2007 µ µ µ V. M. Braun (Regensburg) Electroproduction of N 1535µ October / 11

11 Outlook Combination of lattice QCD and light-cone sum rules offers one a powerful method to study transition region to perturbative QCD All results preliminary Lattice results will improve significantly within 2-5 years NLO light-cone sum rules necessary, a large project Resummation of m 2 R Q2 corrections open problem µ µ µ µ µ Request: please present experimental results for form factors, not (not only) helicity amplitudes µ µ µ V. M. Braun (Regensburg) Electroproduction of N 1535µ October / 11