Global Analysis of Fragmentation Functions. Global Analysis of Fragmentation Functions

Transcription

1 Global Analysis of Fragmentation Functions I. Introduction II. autaka Sudoh (E) Sep. 3, 6 Global Analysis of Fragmentation Functions III. Uncertainty Estimation IV. Numerical Results V. Summary In collaboration with M. Hirai (TITech), S. umano (E), and T.-H. Nagai (The Grad. Univ.)

2 Introduction Fragmentation Functions (FFs) are a key issue in high energy hadron production processes. FFs D(): probability to produce a hadron with momentum fraction from a parent prton Analysis of FFs with their uncertainties must be important to search for new phenomena Present Status (for light hadrons) reter: S. reter, PRD6, 54 () parton ( - ) distribution Many ansat for determination of distributions P: B.A. niehl, G. ramer, B. Potter, NPB58, 54 () (A: S. Albino, B.A. niehl, G. ramer, NPB75, 8 (5)) parton ± distribution (no parton ( - ) distribution) nd moment is problematic. (A: Flavor decomposed distribution) Independent global analysis of FFs including new data Estimate their uncertainties (It s new!!!) Page-

3 Cross Section of ee hx ± Observable: σ tot h dσ d q α, σtot = σ q s ( Q ) Ph q Eh = : scaling variable Q Q σ ξ h d d = C i ξ Q μf, R d i ξ h (,, ) Di, μf ξ Q = μ = s : CMS energy FR, Coefficient Function calculable in pqcd Fragmentation Function extracted from experiments DGLAP equation: α ( μ ) dξ s h D (, ),, j μ = Pij αs Di ξ μ ln μ i ξ ξ ( ) () αs ( μ ) () Pij (, αs ) = Pij () Δ Pij () P ij : j i splitting function Page-3

4 Ansat (for ± ) Function form (most simplest form) αu D (, μ ) = N ( ) ud, αu D (, μ ) = N ( ) udss,,, αc βc cc, (, c) = c ( ) αb βb (, ) ( ) bb, b = b g D (, μ ) = N ( ) g u g u βu βu D m N D m N α βg Constraint condition nd moment should be finite and less than nd Γ ( α β 3) nd N = M, M D( ) d Γ ( α ) Γ ( β ) D q = D q ( ) h nd α >, β >, < M = D ( ) d < i i i i D i = n D f i D i 3, μ < Q < m 4, m Q m = 5, m Q m 6, m < c c < < b b < < t t Q Page-4

5 Experimental Data: ee hx ± the number of Data: 64,.( ),.5( ) Q > s < MZ > s MZ TASSO TCP HRS TOPAZ SLD SLD [light quark] SLD [ c quark] SLD [ b quark] ALEPH OPAL DELPHI DELPHI [light quark] DELPHI [ b quark] s ( ),4,,3,34, データ数 σ tot ee h dσ d Inclusive X-section hx ± We do not include the data of charged hadron and jet production in order to reduce ambiguities of both theory and experiments. Page-5

6 Input parameters and results χ Analysis μ = n f = 4 QCD Λ =. (LO),.33 (NLO) m c α varies with a change of n s =.43, m = 4.3 b f Total χ = LO NLO 453.9[ ], [ ] Uncertainty estimation: Hessian method χ ( aˆ ) Δ = = χ χ ( aˆ δa) χ ( aˆ) Hijδaiδaj, Hij i, j ai aj Da (, ˆ) Da (, ˆ) ( ) ij a a [ ] δd =Δχ H i, j i j Δχ N=4, Δχ =5.94: ( N, s) ds=.683 [(N.s): χ distribution] Page-6

7 Optimied Distribution ( ).5 pion Q = (for u,d,s,g) Q =(.43) (for c) Q =(4.3) (for b) g [LO] u [LO] d [LO] c [LO] b [LO] LO D() pion Q = (for u,d,s,g) Q =(.43) (for c) Q =(4.3) (for b) g [NLO] u [NLO] d [NLO] c [NLO] b [NLO] D() NLO Page-7

8 Optimied Distribution ( ) D().5 pion Q = (for u,d,s,g) Q =(.43) (for c) Q =(4.3) (for b) g [NLO] [LO] u [NLO] [LO] d [NLO] [LO] c [NLO] [LO] b [NLO] [LO] Page-8

9 Comparison with reter ( ) LO results.5 pion Q = (for u,d,s,g) Q =(.43) (for c) Q =(4.3) (for b) g [LO] u [LO] d [LO] c [LO] b [LO] initial scale: Q =.6 evolved to Q = Mass threshold is different D() Our results D().5 Q = (for u,d,s,g) Q =(.4) (for c) Q =(4.5) (for b) reter g [LO] u [LO] d [LO] c [LO] b [LO] Page-9

10 Comparison with P ( ) LO results (Initial scales and mass thresholds are different.).5 pion Q = (for u,d,s,g) Q =(.43) (for c) Q =(4.3) (for b) g [LO] u [LO] d [LO] c [LO] b [LO] i ( )/ distribution!! D() Our results ± u u u ie.. D = ( D D )/ D().5 Q = (for u,d,s,g) Q =(.99) (for c) Q =(9.46) (for b) P g [NLO] u [NLO] d [NLO] c [NLO] b [NLO] Page-

11 Comparison with reter ( ) NLO results.5 pion Q = (for u,d,s,g) Q =(.43) (for c) Q =(4.3) (for b) g [NLO] u [NLO] d [NLO] c [NLO] b [NLO] initial scale: Q =.4 evolved to Q = Mass threshold is different D() Our results D().5 Q = (for u,d,s,g) Q =(.4) (for c) Q =(4.5) (for b) reter g [NLO] u [NLO] d [NLO] c [NLO] b [NLO] Page-

12 Comparison with P ( ) NLO results (Initial scales and mass thresholds are different.).5 pion Q = (for u,d,s,g) Q =(.43) (for c) Q =(4.3) (for b) g [NLO] u [NLO] d [NLO] c [NLO] b [NLO] i ( )/ distribution!! D() Our results ± u u u ie.. D = ( D D )/ D().5 Q = (for u,d,s,g) Q =(.99) (for c) Q =(9.46) (for b) P g [NLO] u [NLO] d [NLO] c [NLO] b [NLO] Page-

13 FFs with Uncertainties ( ) Page-3

14 Comparison with Data Comparison with inclusive X-section data at high energy Preliminary!! Page-4

15 (Data-Theory)/Theory Comparison with Data () Page-5

16 FFs for ± Function form: αu D (, μ ) = N ( ) u udd,, αs D (, μ ) = N ( ) s αu D (, μ ) = N ( ) αc βc cc, (, c) = c ( ) αb βb (, ) ( ) bb, b = b g D (, μ ) = N ( ) g u u s g βu βs βu D m N D m N α βg NLO results Page-6

17 Summary Global analysis of FFs was done for independent parametriation Determine function forms in LO, NLO analyses Large correlation between gluon and disfavored distributions In particular, determination of gluon distribution is difficult Uncertainties of FFs were estimated Large error bands in low region (especially for gluon) Uncertainties could be small by doing NLO analysis Outlook: It is under analysis for other hadrons(coming soon!!) Application for other processes of high energy hadron production Page-7