Fragmentation contribu-tions 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]]. 12th LHC Physics Monthly Meeting, KIAS, 2014. 7.

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1

Contents• Hadron production and

NRQCD factorization

• polarization puzzle

• Leading-power factorization

• Resolution of the puzzle

• Conclusion2

Hadron production and

NRQCD factoriza-tion

3

Hadron Production at High Energies

4

perturbativeparton process (SD)

Hadronization (LD)Parton emission from a proton (LD)

Systematic analysis is allowed once perturbative and nonperturbative factors are factorized as a product of short-distance (SD) and long-distance (LD) factors.

𝐻𝑝

𝑝

PDF Factorization

5

parton process

PDF

𝐻𝑝

𝑝• Nonperturbative parton distribution function (PDF)

and factorize at high energies

PDFs are determined from HERA data.

𝜎 [𝑝𝑝→𝐻+𝑋 ]= 𝒇 𝒊 /𝒑⊗ 𝒇 𝒋 /𝒑⊗�̂� [𝒊𝒋→𝑯+𝑿 ]

PDF

𝑗

𝑖

NRQCD Factorization

6

𝐻𝑝

𝑝

𝑖

• 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.

Bodwin, Braaten, Lepage, PRD (1995)

�̂� [𝑖𝑗→𝑸𝑸𝒏+ 𝑋 ] ⟨ 𝓞𝒏𝑯 ⟩

𝑗

𝑸𝑸𝒏

polarization

puzzle

7

Leading NRQCD MEs in expansion

8

≃2

⊗⟨ 𝒫 [𝑄𝑄 (𝑛)→ 𝐽 /𝜓 ]⟩

2𝐽 /𝜓 𝑐𝑐

�̂�(𝑯 ) ≃∑𝒏�̂� [𝑸𝑸 (𝒏 )] ⊗ ⟨ 𝓞𝒏

𝑱 /𝝍 ⟩SD LDME, global

𝑐𝑐𝑣2≃0.25

quantum numberColor singlet: : determined from Color octet: for bound states

Double Expansion

LO NRQCD explains at the Tevatron

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𝑺𝟏[𝟏]

❑𝟑 𝑺𝟏

[𝟖]❑𝟑 𝑷 𝑱

[𝟖]❑𝟑 + 𝑺𝟎

[𝟖]❑𝟏

𝒅𝝈𝒅𝒑𝑻

𝟐 ∝𝜶𝑺

𝟑

𝒑𝑻𝟖

𝜶 𝒔𝟑𝒗𝟒

𝒑𝑻𝟒

𝜶 𝒔𝟑𝒗𝟒

𝒑𝑻𝟖 ,

𝜶 𝒔𝟑𝒗𝟑

𝒑𝑻𝟖

𝑺𝟏[𝟏]

❑𝟑 𝑺𝟏

[𝟖]❑𝟑

𝑷 𝑱[𝟖]

❑𝟑 + 𝑺𝟎

[𝟖]❑𝟏

• 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.

TransversePolarization

LeadingPower in

14-year old puzzle of polarization at the Tevatron

10

Longitudinal,

Transverse,

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.

NLO𝜆𝜃 Wang et al.

BKL

GeV,prompt

LO

dominance at large [Braaten, Fleming, PRL(1995)] may be wrong

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• 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.

Bodwin, Kim, Lee, JHEP (2012)

𝑺❑𝟑

𝟏[𝟖 ] 𝑷❑

𝟑𝑱

[𝟖 ] 𝑺❑𝟑

𝟏[𝟏 ]

12

Leading-power factor-

ization

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NRQCD factorization• NRQCD factorization formula for quarkonium H

production via collision of particles A and B are given by

: short-distance coeffi-cient:NRQCD LDME related to production of

hadron from state.: NRQCD factorization scale.

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Leading-power factoriza-tion

• LP factorization formula at leading power in for quarkonium H 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

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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

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LO parton processes

• The cross section for LO parton process is proportional to .

⋯

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NLO parton process

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

⋯

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LO gluon fragmentation function (FF)

• This FF is of order .

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NLO Gluon fragmentation func-tion

• This FF is of order .

⋯

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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

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LO , Gluon fragmentation func-tion

• This FF is of order .

⋯

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LO , Gluon fragmentation func-tion

• 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.

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LO quark fragmentation function

• This FF is of order

• To consider mixing in DGLAP equation, we also need to evaluate the light-quark FF.

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LO quark fragmentation function• This FF is known:

Ma, Phys. Rev. D 53, 1185 (1996)

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LO , quark fragmentation function

• This process is proportional to .• We ignored these FFs.

⋯

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LP production processes

• According to the LP factorization,

⊗

LOLO parton process

• Order diagrams:

⋯

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LP production processes• Order diagrams:

⊗

NLO

LO ,

NLO parton process LO

LO parton process

⊗⋯

⋯

⋯

⋯

LO quark

NEW

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Leading-power production processes• Order diagrams:

NLO

LO ,NLO parton process

⊗⋯

⋯

⋯

LO quark

ALL NEW

Resolution of the puzzle

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Input parameters• We took the NLO parton process from

Aversa, 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.

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Fitting CO LDMEs• We decided CO LDMEs by least fitting where

𝜒2≡∑𝑖

(𝑂𝑖−𝐸 𝑖 )2

𝜎 𝑖2

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

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differential cross section

• /d.o.f=0.085• CO LDMEs are determined as

dominates at large

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dominates at large [NEW]

dominates at large [OLD](1995~)

𝑺𝟏[𝟖]

❑𝟑

• Due to the large cancellation between and , dominates in production at large .

Cho, Leibovich (1995)

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

At the LHC, GeV data fit perfectly.

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Conclusion

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Conclusion• Replaced the (1995~) with that domi-

nates production at large .• Resolved 14-year-old polarization puz-

zle by computing NNLO LP contribution.• Our results for direct must be extended

to the prompt case that contains feed-downs from higher resonances like and .

• Bottomonium like and can also be stud-ied.