Pion structure from leading neutron electroproduction

Transcription

1 Net Generation Nuclear Physics with JLab12 and EIC Florida International University February 1, 216 Pion structure from leading neutron electroproduction Wally Melnitchouk with Chueng Ji (NCSU), Josh McKinney (UNC), Nobuo Sato (JLab), Tony Thomas (Adelaide) 1

2 Large flavor asymmetry in proton sea suggests important role of chiral symmetry in high-energy reactions 2.2 Drell-Yan process Flavor asymmetry NA 51 CTEQ4M d _ / u _ d 2 = 4 2 d b d t 9Q 2 X e 2 q (q( b ) q( t )+ q( b )q( t )) q E866, PRD 64, 522 (21) for b σ pd 2σ pp 1 2 t ( 1+ d( t ) ū( t ) ) 1 d ( d ū) =.118 ±.12 2

3 e p Sullivan process in DIS ( du) C C C + Sullivan, PRD 5, 1732 (1972) C C d >ū e n Flavor asymmetry Large flavor asymmetry in proton sea suggests important role of chiral symmetry in high-energy reactions 1 5 REEVALUATION OF THE GOTI'FRI X X O c ~ Q.2 CL I Q. 1 SG )k I I I ~ I I I O.1.1 Q' = 4 GeV' Q.Q5 II I I I I I I I FIG. 1. The difference F~z F2 (ful l symbols and scale to the d (F p 2 F2 n )= 1 3 right) and J '(F~z F2)d/ (open symbols and scale to the left) at Q =4 GeV, as a function of from the present reevaluation (circles) and from Ref. [1] (triangles). The etrapolated result SG from the present vmrk and the prediction model (OPM) are also shown of the simple quark-parton uncertainty from the momentum calibration is reduced compared to that given in Table 2 of Ref. [1], while the other contributions are unchanged. NMC, PRD 5, 1 (1994) To evaluate the contributions to SG from the unmeasured regions at high and low, etrapolations of F2 Fz to = 1 and = were made using the same procedures Q as described in Ref. [1]. The contribution from the region &.8 is.1~.1. For the region &.4, the epression a, appropriate for a Regge-like behavior, was again fitted to the data in the range.4 &&.15 and etrapolated to =.235(26) =. The +..6 and (.4. and the re range (up Summing measured d ( d ū) The error tematic err (correlated) F2 F2 to with that i larger than eamination the result parton mod are unchang The eva large etrap, which ra reason a pr NMC data Bielefeld stitut Heide sity were und Techn FOM, Vrije tute for Nu ported by was suppor 3

4 e ( du) p Sullivan process in DIS C C C + C C e n Sullivan, PRD 5, 1732 (1972) Thomas, PLB 126, 97 (1983) Miller, Kumano, Strikman, Weiss,... connection with QCD? Flavor asymmetry Large flavor asymmetry in proton sea suggests important role of chiral symmetry in high-energy reactions 5 REEVALUATION OF THE GOTI'FRI X X O c ~ Q.2 CL I Q. 1 SG ( d ū)() = 2 3 )k I I I ~ I I I 1 O.1.1 Q' = 4 GeV' Q.Q5 II I I I I I I I FIG. 1. The difference F~z F2 (ful l symbols and scale to the right) and J '(F~z F2)d/ (open symbols and scale to the left) at Q =4 GeV, as a function of from the present reevaluation (circles) and from Ref. [1] (triangles). The etrapolated result SG from the present vmrk and the prediction model (OPM) are also shown. dy y f (y) q (/y) of the simple quark-parton uncertainty from the momentum calibration is reduced compared to that given in Table 2 of Ref. [1], while the other contributions are unchanged. To evaluate the contributions to SG from the unmeasured pion light-cone momentum distribution in nucleon regions at high and low, etrapolations of F2 Fz to = 1 andf = (y) were = 3g2 NN made using the same procedures as described in Ref. [1]. The 16 2 y t F NN 2 dt (t) contribution from the(tregionm 2 &.8 ) 2 is.1~.1. For the region &.4, the epression a, appropriate for a Regge-like behavior, was again fitted to the data in the range.4 &&.15 and etrapolated to Q =. The +..6 and (.4. and the re range (up Summing measured The error tematic err (correlated) F2 F2 to with that i larger than eamination the result parton mod are unchang The eva large etrap, which ra reason a pr NMC data Bielefeld stitut Heide sity were und Techn FOM, Vrije tute for Nu ported by was suppor 4

5 Connection with QCD Chiral epansion of moments of f (y) model-independent leading nonanalytic (LNA) behavior h i d ū 1 d ( d ū) = dy f (y) = 2g2 A (4 f ) 2 m2 log(m 2 /µ 2 ) + terms analytic in m 2 Thomas, WM, Steffens PRL 85, 2892 (2) can only be generated by pion cloud nonzero cloud contribution predicted by QCD! 5

6 Connection with QCD Nonanalytic behavior vital for chiral etrapolation of lattice data 3 u d 3 2 u d 2 1 u d ept. m 2 (GeV m 2 2 ) (GeV 2 ) Detmold, WM, Negele, Renner, Thomas PRL 87, 1721 (21) allows lattice QCD calculations (at unphysical m ) to be reconciled with eperiment GeV m 2 Π GeV 2 6

7 Chiral effective theory Effective low-energy theory of pions & nucleons L N = g A 2f N µ 5 µ N 1 (2f ) 2 N µ ( µ ) N g A =1.267 f = 93 MeV lowest order approimation of chiral perturbation theory Lagrangian cf. pseudoscalar (PS) Lagrangian L PS N = g NN N i 5 N + NN term Weinberg, PRL 18, 88 (1967) gives the classic Sullivan result - full PV theory more complicated! 7

8 Pion cloud corrections to electromagnetic N coupling Chiral effective theory N rainbow (c), rainbow (d), Kroll-Ruderman (e), bubble (f), tadpole (g) (a) (c) (b) (d) (e) Verte renormalization ( 1 1 1) ū(p) µ u(p) =ū(p) µ u(p) (f) (g) taking + components: = M p + ū(p) + u(p) e.g. for N rainbow contribution, N µ = ˆ p µ C. Ji, WM, Thomas, PRD 88, 765 (213) 8

9 Pion splitting functions Each diagram can be represented by splitting function f i (y) N! N (light-cone momentum distribution function) N (p) (k) N (p k) y = k+ p + Verte renormalization is 1 i 1 = k + moment of dy f i (y) f i (y) 9

10 Pion splitting functions Summary of splitting functions: where 1 1 i = dy f i (y) f (y) =f (on) (y)+f ( ) (y) f N (y) =f (on) (y)+f (o ) (y) f ( ) (y) f KR (y) =f (o ) (y) 2f ( ) (y) f tad (y) = f bub (y) = 2f (tad) (y) k p (a) (b) has on-shell (y >) and (y) contributions! 1

11 Pion splitting functions Summary of splitting functions: 1 1 i = dy f i (y) where f (y) =f (on) (y)+f ( ) (y) f N (y) =f (on) (y)+f (o ) (y) f ( ) (y) f KR (y) =f (o ) (y) 2f ( ) (y) f tad (y) = f bub (y) = 2f (tad) (y) with components f (on) (y) = g2 A M 2 (4 f ) 2 f (o ) (y) = g2 A M 2 (4 f ) 2 f ( ) (y) = g 2 A 4(4 f ) 2 f (tad) (y) = 4 g 2 A f ( ) (y) dk 2? dk 2? y(k 2? + y2 M 2 ) [k 2? + y2 M 2 +(1 y)m 2 ] 2 y k? 2 + y2 M 2 +(1 k dk? 2 2 log? + m 2 on-shell contribution equivalent to PS ( Sullivan ) µ 2 y)m 2 (y) 11

12 Pion splitting functions Summary of splitting functions: 1 1 i = dy f i (y) where f (y) =f (on) (y)+f ( ) (y) f N (y) =f (on) (y)+f (o ) (y) f ( ) (y) f KR (y) =f (o ) (y) 2f ( ) (y) f tad (y) = f bub (y) = 2f (tad) (y) with components f (on) (y) = g2 A M 2 (4 f ) 2 f (o ) (y) = g2 A M 2 (4 f ) 2 f ( ) (y) = g 2 A 4(4 f ) 2 f (tad) (y) = 4 g 2 A f ( ) (y) dk 2? dk 2? y(k 2? + y2 M 2 ) [k 2? + y2 M 2 +(1 y)m 2 ] 2 y k? 2 + y2 M 2 +(1 k dk? 2 2 log? + m 2 µ 2 y)m 2 N rainbow & KR contain new off-shell contribution (y) 12

13 Pion splitting functions Summary of splitting functions: 1 1 i = dy f i (y) where f (y) =f (on) (y)+f ( ) (y) f N (y) =f (on) (y)+f (o ) (y) f ( ) (y) f KR (y) =f (o ) (y) 2f ( ) (y) f tad (y) = f bub (y) = 2f (tad) (y) with components KR needed for gauge invariance (1 1 )+(1 KR 1 ) =(1 N 1 ) f (on) (y) = g2 A M 2 (4 f ) 2 dk 2? y(k 2? + y2 M 2 ) [k 2? + y2 M 2 +(1 y)m 2 ] 2 f (o ) (y) = g2 A M 2 (4 f ) 2 dk? 2 y k? 2 + y2 M 2 +(1 f ( ) g 2 A k (y) = 4(4 f ) 2 dk? 2 2 log? + m 2 µ 2 f (tad) (y) = y 4 f ( ) (y) singular = contribution only in PV theory g 2 A y)m 2 (y) 13

14 Pion splitting functions Summary of splitting functions: 1 1 i = dy f i (y) where f (y) =f (on) (y)+f ( ) (y) f N (y) =f (on) (y)+f (o ) (y) f ( ) (y) f KR (y) =f (o ) (y) 2f ( ) (y) f tad (y) = f bub (y) = 2f (tad) (y) with components tadpole & bubble equal & opposite (1 tad 1 )= (1 bub 1 ) f (on) (y) = g2 A M 2 (4 f ) 2 f (o ) (y) = g2 A M 2 (4 f ) 2 f ( ) (y) = g 2 A 4(4 f ) 2 f (tad) (y) = 4 g 2 A f ( ) (y) dk 2? dk 2? y(k 2? + y2 M 2 ) [k 2? + y2 M 2 +(1 y)m 2 ] 2 y k? 2 + y2 M 2 +(1 k dk? 2 2 log? + m 2 µ 2 y)m 2 (y) 14

15 UV regularization For point-like nucleons and pions, integrals divergent Finite size of nucleon provides natural scale to regularize integrals, but does not prescribe form of regularization freedom in choosing regularization prescription (long-distance physics independent of choice!) F = ( 2 k?) 2 2 m 2 F = 2 t F =ep (t m 2 )/ 2 k? cutoff monopole in t k 2 = k2? + y2 M 2 eponential in t 1 y F =ep (M 2 F = apple 1 (t m 2 ) 2 (t 2 ) 2 s)/ 2 1/2 eponential in s = k2? + m2 y Pauli-Villars + k2? + M 2 1 y F = y (t) ep (t m 2 )/ 2 Regge 15

16 UV regularization Detailed shape of splitting function depends on regularization, but common general features e.g. on-shell function f (on) N (y) f (on) (y) (b) y y t mon t ep s ep PV Regge If bare nucleon has symmetric sea, then only pion coupling diagrams contribute (a) Bishari (scaled) k? cut sharp cutoffs d ū =[f + + f bub ] q 16

17 Pion cloud corrections to electromagnetic N coupling Flavor asymmetry N rainbow (c), rainbow (d), Kroll-Ruderman (e), bubble (f), tadpole (g) (a) (c) (b) (d) (e) Verte renormalization ( 1 1 1) ū(p) µ u(p) =ū(p) µ u(p) (f) (g) taking + components: = M p + ū(p) + u(p) e.g. for N rainbow contribution, N µ = ˆ p µ contribute to d ū 17

18 E866. d ū Flavor asymmetry data can be fitted with range of regulators.6 (a) N (b) ( d ū) t mon t ep s ep PV Regge Bishari (.5) k? cut E average pion multiplicity hni N = with eception of k? cutoff and Bishari models, all others give reasonable fits, large- asymmetry to be probed by FNAL SeaQuest ept. 1 dy f (on) N (y)

19 E866. d ū Flavor asymmetry data can be fitted with range of regulators Is pion cloud the only eplanation for the asymmetry? are there other data that can discriminate between different mechanisms? semi-inclusive production of leading neutrons (LN) at HERA! 19

20 Leading neutron production at HERA EUS & H1 collaborations measured spectra of neutrons produced at very forward angles, n <.8 mrad EUS L 1 y can data be described within same framework as E866 flavor asymmetry? simultaneous fit never previously been performed! 2

21 Leading neutron production at HERA Measured LN differential cross section (integrated over p? ) e.g. r/ L r = d LN d inc (a) d 3 LN d dq 2 dy = y F LN(3) 2 (, Q 2,y) Q 2 = 6 GeV 2 EUS 2f (on) N (y) F 2 (/y, Q 2 ) F LN(3) (b) H1 Q 2 = 24 GeV 2 for = y quality of fit depends on range of y echange fitted y cut EUS H1 21

22 Leading neutron production at HERA At large y non-pionic mechanisms contribute (e.g. heavier mesons, absorption) (1/σ inc ) dσ p n / dz EUS 27 H1 29 π a ~ 1 2 q T <.4 GeV 2 Q 2 > 2 GeV 2 ρ+a K abs light-cone R 2 lc =.2 GeV-2 γ p n X 1 < Q 2 < 1 GeV 2 γ p n X Q 2 <.2 GeV z (= 1-y) z (= 1-y) Kopeliovich et al., PRD 85, (212) D Alesio, Pirner, EPJA 7, 19 (2) To reduce model dependence, fit the value of up to which data can be described in terms of y cut echange 22

23 Leading neutron production at HERA Fit requires higher momentum pions with increasing y cut (a).6 (GeV) y cut hni N.4.2 (b) t mon t ep s ep PV Regge Bishari k? cut E y cut values from fit to E866 data only larger values of y cut more in conflict with E866 data 23

24 Leading neutron production at HERA Combined fit to HERA LN and E866 Drell-Yan data 2 dof (a) t mon t ep s ep PV Regge Bishari k? cut EUS + H y cut (b) EUS + H1 + E y cut McKenney, N. Sato, WM, C. Ji PRD (216), arxiv:

25 Leading neutron production at HERA Combined fit to HERA LN and E866 Drell-Yan data 2 dof (a) t mon t ep s ep PV Regge Bishari k? cut EUS + H y cut # pts = (b) EUS + H1 + E y cut McKenney, N. Sato, WM, C. Ji PRD (216), arxiv: best fits for largest number of points afforded by t-dependent eponential (and t monopole) regulators 25

26 Leading neutron production at HERA Fit to EUS LN spectra for y cut =.3 (t-dependent eponential) F LN(3) 2 ( 2 i ) Q 2 = 7 GeV Q 2 = 15 GeV 2 Q 2 = 3 GeV F LN(3) 2 ( 2 i ) F LN(3) Q 2 = 48 GeV 2 =.32 Q 2 = 6 GeV y Q 2 = 1 GeV 2 =.32 Q 2 = 12 GeV y Q 2 = 24 GeV y =.6 y =.15 y =.21 y =.27 HERA+E866 fit EUS, NPB 637, 3 (22) NPB 776, 1 (27) 26

27 Leading neutron production at HERA Fit to H1 LN spectra for y cut =.3 (t-dependent eponential) F LN(3) 2 ( 2 i ) Q 2 =7.3 GeV 2 Q 2 = 11 GeV 2 Q 2 = 16 GeV F LN(3) 2 ( 2 i ) Q 2 = 24 GeV 2 Q 2 = 37 GeV 2 Q 2 = 55 GeV F LN(3) 2 ( 2 i ) Q 2 = 82 GeV 2 y =.95 y =.185 y =.275 HERA+E866 fit H1, EPJC 68, 381 (21) 2 dof =1.27 for 22 (187+15) points 27

28 Etracted pion structure function.6 y cut t mon t ep s ep PV Regge Bishari HERA+E866 fit GRS SMRS.4 F 2.2 Q 2 = 1 GeV (a) y cut = (b) = /y (c) F 2 = N a (1 ) b, a = a + a 1 log(log Q 2 ) McKenney, N. Sato, WM, C. Ji PRD (216), arxiv: stable values of F2 at from combined fit shape similar to GRS fit to N Drell-Yan data (for &.2), but smaller magnitude 28

29 Predictions at TDIS kinematics F LP(3) (a) HERA y =.1 JLab t ep (y cut =.3) t ep (y cut =.2) t mon (y cut =.2) y = (b) y =.2 HERA HERA + E866 fit SMRS GRS sea N DY total McKenney, N. Sato, WM, C. Ji PRD (216), arxiv: JLab TDIS eperiment can fill gap in coverage between HERA and N Drell-Yan kinematics 29

30 Outlook Combined analysis can be etended by including also N Drell-Yan data constrain large- region ( &.2) Generalize parametrization by fitting individual pion valence and sea quark PDFs, rather than F 2 Ultimate goal will be to use all data sensitive to pion structure (including TDIS, EIC?) to constrain pion PDFs over full range