1. Fragmentation measurements in Belle and Babar and impact on RHIC
Resummation, Evolution and Factorization 2015, DESY
11/02/2015
Ralf Seidl (RIKEN)

2. What are fragmentation functions?
How do quasi-free partons fragment into confined hadrons？
Does spin play a role？Flavor dependence?
What about transverse momentum (and its Evolution)？
What experiments measure：
Normalized hadron momentum in CMS：　e+e-h(z) X ; z = 2Eh/ √s　
Hadron pairs’ azimuthal distributions：　e+e-h1 h2 X ; <cos(f1+f2)> ; Collins FF、Interference（IFF）
Cross sections or multiplicities differential in z: ep->hX, pp->hX
Additional benefits of the FF measurements：
Pol FFs necessary input to transverse spin SIDIS und pp measurements to extract Transversity distributions function
Flavor separation of all Parton distribution functions (PDFs) via FFs (including unpolarized PDFs)
Baseline for any Heavy Ion measurement
Access to exotics?
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3. Unpolarized fragmentation functions
Ph１
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4. Unpolarized fragmentation
Phys.Rev.Lett. 111 (2013) ,
Leitgab, RS, et al (Belle)
Single-hadron cross sections at leading order in as related to fragmentation functions
Only at higher orders access to gluon FFs
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5. B factory data used in global FF fits
Phys.Rev. D91 (2015) 1,
Good description of B-factory data
Together with other new data substantial improvement in uncertainties
Shift in central valuesrelevant for RHIC gluon polarization measurements
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6. New addition: single protons
arXiv:
Default Pythia and current Belle in good agreement with pions and kaons
Protons not well described by any tune
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7. Di-hadrons
Single inclusive hadron multiplicities (e+e-hX) sum over all available flavors and quarks and antiquarks:
Especially distinction between favored (ie up+) and disfavored (u̅ p+) fragmentation would be important
Idea: Use di-hadron fragmentation, preferably from opposite hemispheres and access favored and disfavored combinations:
Also: unpol baseline for interference fragmentation
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8. Setup Generally look at 4 x 4 hadron combinations ( p, K, +,-)
quark
antiquark
Ph１
Ph２
Generally look at 4 x 4 hadron combinations ( p, K, +,-)
Keep separate until end: only 6 independent yields
3 hemisphere combinations:
same hemisphere (thrust >0.8)
opposite hemisphere ( thrust >0.8 )
any combination ( no thrust selection)
16 x 16 z1 z2 binning between
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9. Correction chain Correction Method Systematics PID mis-id
PID matrices (5x5 for cos qlab and plab )
MC sampling of inverted matric element uncertainties
Momentum smearing
MC based smearing matrices (256x256), SVD unfold
SVD unfolding vs analytically inverted matrix, reorganized binning, MC statistics
Non-qqbar BG removal
eeuu, eess, eecc, tau MC subtraction
Variation of size, MC statistics
Acceptance I (cut efficiency)
In barrel reconstucted vs udsc generated in barrel
MC statistics
Acceptance II
udsc Gen MC barrel to 4p
Weak decay removal (optional)
udsc check evt record for weak decays
Compare to other Pythia settings
Acceptance III
Extrapolation to |cosq|1 in (Fit to MC)
Fit uncertainties
ISR
Keep event fraction with E> Ecms
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10. Full results for pion pairs
arXiv:
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11. Ratios to opposite charge pion pairs
arXiv:
p+p+ comparable to p+p- at low z, decreasing towards high z:
Favored and disfavored fragmentation similar at low z
Disfavored much smaller at high z
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12. Results for diagonal z1 z2 bins
Low z dominates integral:
Well defined, all tunes agree
High z not well measured, especially at Belle energies:
large spread in tunes
Default Pythia settings and current Belle setting with good agreement
arXiv:
Diagonal z1,z2 bins
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13. Hemisphere composition
Same hemisphere contribution drops rapidly
Consistent with LO assumption of
Same hemisphere: single quark  di-hadron FF: (z1+z2 <1)
Opposite hemisphere: single quarksingle hadron FF
Diagonal z1,z2 bins
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Systematic uncertainties not displayed
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14. Transverse momentum dependence
Aka un-integrated PDFs and FFs
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15. KT Dependence of FFs
Gain also sensitivity into transverse momentum generated in fragmentation
Two ways to obtain transverse momentum dependence
Traditional 2-hadron FF
use transverse momentum between two hadrons (in opposite hemispheres)
Usual convolution of two transverse momenta
Single-hadron FF wrt to Thrust or jet axis
No convolution
Need correction for qq̅ axis
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16. MC example of kT sensitivities using thrust method
MC simulation
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17. MC sample for various hadrons
MC simulation
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18. MC examples vs kT2 MC simulation
Fit exponential to smaller transverse momenta for Gaussian kT dependence
MC simulation
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19. MC Gaussian widths MC simulation REF2015, Nov 2, 2015
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20. MC Gaussian widths MC simulation REF2015, Nov 2, 2015
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21. Spin dependent fragmentation
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22. Collins fragmentation function
J. Collins, Nucl. Phys. B396, (1993) 161 q
Spin of quark correlates with hadron transverse momentum
translates into azimuthal anisotropy of final state hadrons
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23. 2-hadron inclusive transverse momentum dependent cross section:
Collins fragmentation in e+e- : Angles and Cross section cos(f1+f2) method
e+e- CMS frame:
D.Boer: Nucl.Phys. B806 (2009) 23-6
j2-p e- Q j1 j2 j1 e+
2-hadron inclusive transverse momentum dependent cross section:
Net (anti-)alignment of
transverse quark spins
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24. Belle Collins asymmetries
Red points : cos(f1 + f2) moment of Unlike sign pion pairs over like sign pion pair ratio : AUL
Green points : cos(f1 + f2) moment of Unlike sign pion pairs over any charged pion pair ratio : AUC
Collins fragmentation is large effect
Consistent with SIDIS indication of sign change between favored and disfavored Collins FF
RS et al (Belle), PRL96:
PRD 78:032011, Erratum D86:039905
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25. BABAR Collins results Recently also Collins results from BABAR
Phys.Rev. D90 (2014) 5,
Recently also Collins results from BABAR
Consistent with Belle results
Also results from BESIII (arxiv )
initially consistent with Belle,
now consistent with evolution predictions ( )
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26. Explicit transverse momentum dependence
First explicit transverse momentum dependent extraction for Collins asymmetries (relative to thrust axis* or second hadron)
Global Transversity and Collins fit (arXiv: )able to reproduce the dependence
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27. Collins evolution fit Kang, Prokudin, Sun and Yuan, arXiv:1505.05589
First Transversity extraction taking TMD evolution into account
Data from Belle, Babar, HERMES and COMPASS
Still many assumptions on transverse momentum dependence necessary
Only moderate scale dependence in final results but large effect on e+e- asymmetries
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28. Next steps for Collins RHIC, JLAB and EIC
Extracted Collins fragmentation functions key to access transversity
Central rapidity RHIC results nonzero, covering moderate x
Future forward results will extend to higher x at reasonable scale
EIC based transversity/tensor charge measurements likely limited by FF precision and kT extraction
Recent theoretical improvements towards hadron in jet measurements at RHIC (Phys.Rev. D92 (2015) 5, )
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29. Kaon related Collins Preliminary results from Belle
Preliminary results from Belle
Recently submitted results from BABAR
Interpretation slightly more complex due to Inflation of FF functions:
u,d p: 2
u,d,s p,K: 6+
Quite important for EIC and strange transversity
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30. Interference fragmentation
Again azimuthal anisotropy of distribution of hadron pairs wrt transverse quark spin
Collinear treatment of interference fragmentation  evolution known (Cecciopieri et al: Phys.Lett. B650 (2007) 81-89)
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31. Interference Fragmentation（IFF) in e+e-
e+e- (p+p-)jet1(p+p-)jet2X
Theoretical guidance by papers of Boer,Jakob,Radici[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996)]
Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)]
j2-p
p-j1
Model predictions by:
Jaffe et al. [PRL 80,(1998)]
Radici et al. [PRD 65,(2002)]
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32. Belle IFF asymmetries: (z1x m1) Binning
PRL107:072004(2011)
2 d distributions of one hemisphere
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33. First transversity extraction from HERMES, COMPASS and Belle IFF data
Using Belle IFF and HERMES or COMPASS to extract transversity compared to Collins FF based global analysis:
recent IFF analysis and Collins Transversity comparable
CollinsFF evolution weak?
But many assumptions at this point
STAR and PHENIX Preliminary data not yet used
Courtoy, Bacchetta, Radici:
Phys.Rev.Lett. 107 (2011) and arXiv:
HERMES: JHEP 0806 (2008)
COMPASS: Phys.Lett. B713 (2012)
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34. Summary and outlook e+e- as clean access to fragmentation functions
Wealth of B-factory data to extract not only z dependence but also transverse momentum dependence of cross sections (+azimuthal dependence for spin)
Many precise unpolarized hadron cross sections/multiplicities published and used in global fits
extension to transverse momentum dependence ongoing using various reference axae
Spin dependent fragmentation (Collins and Interference) available, including Kaon combinations and transvserse momentum dependence
Major input for various RHIC and SIDIS measurements not only for spin but also for CNM
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