Fragmentation contributions to production and the...

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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

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• 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]