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Fragmentation contributions to production at the Tevatron and the LHC

Fragmentation contributions to production at the Tevatron and the LHC. Jungil Lee (KU ) in collaboration with Geoffery T. Bodwin , Hee Sok Chung (ANL), U-Rae Kim (KU) Phys . Rev. Lett . 113, 022001 (2014) [arXiv:1403.3612[ hep-ph ]].

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Fragmentation contributions to production at the Tevatron and the LHC

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  1. Fragmentation contributions to production at the Tevatron and the LHC Jungil Lee (KU) in collaboration with Geoffery T. Bodwin, HeeSok Chung (ANL), U-Rae Kim (KU) Phys. Rev. Lett. 113, 022001 (2014) [arXiv:1403.3612[hep-ph]]. 12th LHC Physics Monthly Meeting, KIAS, 2014. 7. 25

  2. Contents • Hadron production and NRQCD factorization • polarization puzzle • Leading-power factorization • Resolution of thepuzzle • Conclusion

  3. Hadron production and NRQCD factorization

  4. Hadron Production at High Energies Parton emission from a proton (LD) Hadronization (LD) perturbative parton process (SD) Systematic analysis is allowed once perturbativeand nonperturbative factors are factorized as a product of short-distance (SD)and long-distance (LD) factors.

  5. PDF Factorization PDF parton process PDF • Nonperturbative parton distribution function (PDF)and factorize at high energiesPDFs are determined from HERA data.

  6. NRQCD Factorization Bodwin, Braaten, Lepage, PRD (1995) • For a heavy quarkonium process, factorization was proved in inclusive decay and conjectured in production:Nonperturbative NRQCD matrix elements (MEs) are determined from experimental data.

  7. polarization puzzle

  8. Leading NRQCD MEs in expansion SD LDME, global quantum number Color singlet: : determined from Color octet: for bound states Double Expansion

  9. LONRQCD explains at the Tevatron • Because dominates at large [Braaten and Fleming, PRL (1995)], one can determine from large data and then determine and from lower data. • Transverse polarization is predicted at large • As an independent test, one can test this with polarization data. Transverse Polarization Leading Power in

  10. 14-year old puzzle of polarization at the Tevatron Transverse, NLO LO Wang et al. GeV,prompt BKL Longitudinal, PRD, 2000 PRL, 2013 • NRQCD predication predicts transverse polarization at • large that confronted CDF data. • Further prediction with higher-order QCD correction still • fails to explain the large data. • The dominance of[Braaten, Fleming, PRL(1995)] • or NRQCD factorization may FAIL.

  11. dominance at large [Braaten, Fleming, PRL(1995)] may be wrong Bodwin, Kim, Lee, JHEP (2012) • By computing the color-singlet contribution to the • NNLO QCD correction to the fragmentation function for • , we have found a clue to have • a large cancellation between and . • dominates at large that replaces • previous belief since 1995. • is required to be computed to NNLO in for leading power (LP) contribution.

  12. Leading-power factorization

  13. NRQCD factorization • NRQCD factorization formula for quarkoniumH production via collision of particles A and B are given by : short-distance coefficient :NRQCD LDME related to production of hadron from state. : NRQCD factorization scale.

  14. Leading-power factorization • LP factorization formula at leading power in for quarkoniumH production is given by : single parton production cross section : single parton fragmentation function : light-cone momentum of parent parton : light-cone momentum of daughter hadron : Factorization scale

  15. LP factorization in quarkonium production • One can apply LP factorization formula to the short-distance coefficient of NRQCD: • Therefore, • By making use of the above formula, we evaluated the distribution of the

  16. LO parton processes • The cross section for LO partonprocess is proportional to .

  17. NLO parton process • The cross section for NLO partonprocess is proportional to .

  18. LO gluon fragmentation function (FF) • This FF is of order .

  19. NLO Gluon fragmentation function • This FF is of order .

  20. LO and NLO Gluon fragmentation function • This FF is known: LO: Braaten, Yuan, Phys. Rev., D50, 3176 (1994) NLO: Braaten, Lee, Nucl. Phys., B586, 427 (2000) Ma, Qiu, Zhang, arXiv:1311.7078 where

  21. LO , Gluon fragmentation function • This FF is of order.

  22. LO , Gluon fragmentation function • This FF is known:Braaten, Chen, Phys. Rev., D55, 2693 (1997) Bodwin, Kim, Lee, JHEP 1211, 020 (2012) Braaten, Yuan, Phys. Rev., D50, 3176 (1994) • There are no singular distributions in FF.

  23. LO quark fragmentation function • To consider mixing in DGLAP equation, we also need to evaluate the light-quark FF. • This FF is of order

  24. LO quark fragmentation function • This FF is known: Ma,Phys. Rev. D 53, 1185 (1996)

  25. LO , quark fragmentation function • This process is proportional to . • We ignored these FFs.

  26. LP production processes • According to the LP factorization, • Order diagrams: LO parton process LO

  27. LP production processes NEW • Order diagrams: NLO LO parton process LO quark LO , NLO parton process LO

  28. Leading-power production processes • Order diagrams: ALL NEW NLO NLO parton process LO , LO quark

  29. Resolution of the puzzle

  30. Input parameters • We took the NLO parton process fromAversa, Chiappetta, Greco, Guillet, Nucl. Phys., B327, 105-143 (1989) • CTEQ6M was chosen for PDF. • GeV. • , , , and renormalization scale . • We set the number of active flavors . • We used two-loop with the number of active flavors and MeV: • For LHC, TeV, rapidity cut • For Tevatron, TeV, rapidity cut • Feed-down effects ignored.

  31. Fitting CO LDMEs • We decided CO LDMEs by least fitting where here, at ,The results of CMS and CDF Here, we took 10 GeV data only. Theoretical prediction. , , and are unknown. : Total variance including systematic, statistical and theoretical errors

  32. differential cross section • /d.o.f=0.085 • CO LDMEs are determined as

  33. dominates at large dominates at large [OLD] (1995~) dominates at large [NEW] Cho, Leibovich (1995) • Due to the large cancellation between and , dominates in production at large .

  34. polarization puzzle RESOLVED! At the Tevatron, GeV data fit well. At the LHC, GeV data fit perfectly.

  35. Conclusion

  36. Conclusion • Replaced the (1995~) with that dominates production at large . • Resolved 14-year-old polarization puzzle by computing NNLO LP contribution. • Our results for direct must be extended to the prompt case that contains feeddowns from higher resonances like and . • Bottomonium like and can also be studied.

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