fragmentation contributions to production and the...
TRANSCRIPT
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Fragmentation contributions to production and
the polarizationat the Tevatron and the LHC
U-Rae Kim (Korea University)!in collaboration with!
Geoffery T. Bodwin, Hee Sok Chung (Argonne National Laboratory), Jungil Lee (Korea University),
Kuang-Ta Chao (Peking University), Yan-Qin Ma (University of Maryland)
Phys. Rev. Lett. 113, 022001 (2014)13th LHC Physics Monthly Meeting, Nov. 29th 2014 !
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Outline• Nonrelativistic QCD factorization
• J/PP polarization puzzle
• Our approach to the puzzle
• Calculation details
• Result and Conclusion
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Nonrelativistic QCD
factorization
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Nonrelativistic QCD (NRQCD) factorization
4
• According to NRQCD factorization conjecture, a heavy quarkonium H production cross section can be factorized into
short-distance coefficient (SDC, perturbative, als)
long-distance matrix element (LDME, nonperturbative, v)
• 3s18, 3pJ8, 1s08, and3s11 channels contribute to J/psi production through order v^4
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J/PP polarization
puzzle
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Prompt d/d (d’) production and NRQCD6
• Color-singlet (CS) model failed to explain the d (ddd) surplus • The introduction of the color-octet (CO) mechanism from
NRQCD has resolved the surplus problem. [Braaten, Fleming, PRL74, 3327 (1994)] • Here, LDMEs are determined by fitting with the experimental data • One can predict other independent physical quantities
by making use of these determined LDMEs because LDME is global Polarization
10-3
10-2
10-1
1
10
5 10 15 20
BR(J/sAµ+µ-) dm(pp_AJ/s+X)/dpT (nb/GeV)
3s =1.8 TeV; |d| < 0.6
pT (GeV)
totalcolour-octet 1S0 + 3PJcolour-octet 3S1LO colour-singletcolour-singlet frag.
10-4
10-3
10-2
10-1
1
5 10 15 20
BR(s(2S)Aµ+µ-) dm(pp_As(2S)+X)/dpT (nb/GeV)
3s =1.8 TeV; |d| < 0.6
pT (GeV)
totalcolour-octet 1S0 + 3PJcolour-octet 3S1LO colour-singletcolour-singlet frag.
Kraemer, Prog. Part. Nucl. 47, 141(2001)
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Prompt d/d (d’) polarization7
• In 2000, the theoretical prediction to the polarization of the prompt J/PP and P’ has been published:
• The dominance of the CO spin-triplet S-wave channel predicts the transverse polarization at large pt.
• But, the experiment disproved this theoretical prediction.
Braaten, Lee, Kneihl, PRD62,094005
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QCD NLO correction8
• Full NLO QCD corrections to the J/PP production
-1-0.8-0.6-0.4-0.2
00.20.40.60.8
1
5 10 15 20 25 30pT [GeV]
λ θ(p
T)
CDF data: Run I / II/
CS, LOCS, NLOCS+CO, LOCS+CO, NLO
Helicity frame
|y| < 0.6√s± = 1.96 TeVpp± → J/ψ + X
pT [GeV]
dσ/d
p T(pp± →
J/ψ+X
) × B
(J/ψ→μμ
) [n
b/Ge
V]
√s± = 1.96 TeV|y| < 0.6
CDF dataCS, LOCS, NLOCS+CO, LOCS+CO, NLO
10-4
10-3
10-2
10-1
1
10
10 2
4 6 8 10 12 14 16 18 20
[Kneihl, Buthenchoen] PRL106, 022003 (2011) PRL108, 172002 (2012)
5 10 15 20 25 30
1
0.8
0.6
0.4
0.2
0
!0.2
!0.4
!0.6
!0.8
!1
pT !GeV"
Λ Θ
NLO 3PJ!8"NLO 3S1!8"NLO 1S0!8"NLO 3S1!1"
CDF Run !
CDF Run "
NLO Total
J#Ψ polarizationhelicity frame
5 10 15 20 25 3010!4
10!3
10!2
10!1
1
10
102
pT !GeV"dΣ#dp T#
Br!J#Ψ%
Μ'Μ!"!nb#
GeV"
CMS DataCDF DataTotal LHCTotal Tevatronfeed!downM0
M1
3S1$1%
[Chao, Ma, Shao, Wang]PRL106, 042002 (2011)PRL108, 242002 (2012)
[Gong, Wan, Wang, Zhang] PRL110, 042002 (2013)
• All groups have failed to predict the polarization—> we need to consider the NNLO corrections
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Our approach to the puzzle
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/ 29Leading-power (LP) factorization and NRQCD
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• Accoriding to LP factorization, leading power terms in 1/pt2 for quarkonium HH production can be factorized into
where,: single parton ii production cross section: single parton fragmentation function, nonperturbative
: light-cone momentum of parent parton ii
: light-cone momentum of parent parton ii: factorization scale
• If we apply LP factorization to NRQCD factorization, we get
perturbative• Dominant at large pt, relatively easy to evaluate
/ 29Dokshitzer–Gribov–Lipatov–Altarelli–Parisi
(DGLAP) equation• Leading-log (LL) terms can be summed over all
orders in alp by solving DGLAP equation.
• LO DGLAP evolution equation is given by
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where,: splitting function
: active quark flavor
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Our approach to the puzzle12
• At large ptr, the gluon fragmentation process that is leading power in 1ㅅ/pt expansion is dominant.(1/tttttptt)
• With LP factorization, we evaluate the NNLO or higher-order corrections including the all-orders leading-log (LL) resummation that are not considered in NLO result.
• We ignored the CS contributions to the J/PP production
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Calculation details
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Parton subprocess14
• The parton subprocesses that are LO in alp is proportional to alp.
• The parton subprocesses that are NLO in alpis proportional to alp.
Aversa, Chiappetta, Greco, Guillet, Nucl. Phys. B327, 105 (1989)
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XXXx Gluon fragmentation function15
Braaten, Yuan, Phys. Rev. D 50, 3176 (1994) Braaten, Lee, Nucl. Phys. B586, 427 (2000) Ma, Qiu, Zhang, Phys. Rev. D 89, 094029 (2014)
LO NLO
where,
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XXX, XXX Gluon fragmentation function16
Braaten, Yuan, Phys. Rev. D 50, 3176 (1994) Braaten, Chen, Phys. Rev. D55, 2693 (1997) Bodwin, Kim, Lee, JHEP1211(2012)020
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XXX quark fragmentation function17
Ma, Phys. Rev. D 53, 1185 (1996)
• Other quark fragmentation functions are proportional to alp which we exclude.
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LP J/PP production process18
• Order alp diagrams:
• Order alp diagrams:
• Because the previous NLO result also contains LP contributions through order alp, we should eliminate these corrections to avoid the double counting.
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LP J/PP production process19
• Order alp diagrams:
NNLO parton subprocess
We cannot evaluate the following process now
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LP J/PP production process20
• Order alp diagrams:
Results Order
NLO
Our result higher
(LL resum)
[NEW]NNLO
+higher(LL)LP corrections
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Result
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J\PP production cross section and LDMEs
• Our result fits well both the CMS data and the CDF data
• We determine CO LDMEs by fitting with Exp.
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Large cancellation between 3S, and 3P,23
10 12 14 16 18 2010�4
0.001
0.01
0.1
1
LHC
Tevatron3S1, is dominant
3S1, is dominant
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J\PP Polarization • we predict the polarization parameter la
at the Tevatron and the LHC:
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• The CDF data is quite well explained
• The CMS data is perfectly explained
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PromptJ\PP production25
• Prompt J/psi production includes the production from decays of psi(2s) and chicj
• We determined psi(2s) LDME by fitting with CMS and CDF cross section data CDF, PRD80, 031103 (2009) CMS, JHEP02, 011 (2012) CMS-PAS-BPH-14-001
• We determined chicj LDME by fitting with ATLAS cross section data ATLAS, JHEP1407, 154 (2014)
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psi(2S) and chicj production and polarization
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PRELIMINARY
PRELIMINARY
PRELIMINARY
PRELIMINARY
CDF, PRL85, 2886 (2000)CDF, PRL99, 132001 (2007)
CMS, PLB727, 381 (2013)
cross section psi(2s) pol. chic1, chi pol.
• Our result fits psi(2S) and chic cross section data • Our result well predicts psi(2s) polarization at the CMS
but fails at the CDF • chi , ch2 and psi(2s) are slightly transverse at large pt
Hee Sok Chung’s talk at 10th International Workshop on Heavy Quarkonium
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PRELIMINARY
PromptJ\PP production cross section27
PRELIMINARY
Fractions of direct and feeddown contributions
• Our result fits well both the CMS data and the CDF data
Hee Sok Chung’s talk at 10th International Workshop on Heavy Quarkonium
• At large p_, the feed down contribution is not negligible• The cancellation between 3s18 and 3pj8 still occurs
3S1, is dominant
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PromptJ\PP polarization28
Hee Sok Chung’s talk at 10th International Workshop on Heavy Quarkonium
• Feed down contributions are slightly transverse —> Prompt J/psi becomes slightly transverse
• The prediction agrees with the CMS data,but fails to explain the CDF data
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Conclusion29
• We evaluated the higher-order corrections by making use of LP factorization formula and DGLAP.
• Our results well predicted the prompt J/PP polarization at the CMS (world-first successful prediction)
• Dominant channel is not 3sd1 but 1ds0
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Backups
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LDMEs
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LDMEs
Kniehl Chao Wang
Our result for direct production
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Polarization parameter
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How to solve DGLAP equation
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Fitting NRQCD LDMEs
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NRQCD LDMEs
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Charmonium spectroscopy
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Another attempt48
• Relativistic corrections to CS fragmentation contribution
At large pt, one can roughly estimate the relative size of the contribution by making use of the following approximation:
By making use of the Kneihl’s result, we got k==5.2.
- Higher-order relativistic correction (~v4) to CS gluon fragmentation function for J/PP production was considered: [Bodwin, Kim, Lee JHEP11(2012)020]