![Page 1: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/1.jpg)
PRODUCTION AT HADRON COLLIDERS
Hee Sok Chung Argonne National Laboratory
Based on Geoffrey T. Bodwin, HSC, U-Rae Kim, Jungil Lee, PRL113, 022001 (2014)
Geoffrey T. Bodwin, HSC, U-Rae Kim, Jungil Lee, Yan-Qing Ma, Kuang-Ta Chao, in preparation
![Page 2: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/2.jpg)
OUTLINE
• Leading-power fragmentation in quarkonium production
• Cross section and polarization of
• direct
• and
• prompt
• Summary
2
![Page 3: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/3.jpg)
HEAVY QUARKONIUM
3
• Bound states of a heavy quark and a heavy antiquark : e.g. , , , , , , , ...
•
• which allow nonrelativistic description : for charmonia, for bottomonia
• Typical energy scales , Ideal for studying interplay between perturbative and nonperturbative physics
J/ ⌘c 0 �cJhc ⌥(nS) �bJ⌘b
2mb > 2mc � ⇤QCD
mJ/ ⇡ m⌘c ⇡ 2mc, m⌥(1S) ⇡ m⌘b ⇡ 2mb,
v2 ⇡ 0.3 v2 ⇡ 0.1
m > mv > mv2 ⇡ ⇤QCD
![Page 4: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/4.jpg)
S-w
ave
P-w
ave
Spin SingletSpin Triplet
J/ ⌘c 0,
�cJ hc
S-w
ave
P-w
ave
Spin SingletSpin Triplet
⌥(nS)
�bJ
⌘b
hb
Charmonia Bottomonia
HEAVY QUARKONIUM • Quark model assignments of some heavy quarkonia
![Page 5: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/5.jpg)
• The -differential cross section has been measured at hadron colliders like RHIC, Tevatron and the LHC.
• is usually identified from its leptonic decay.
• Large contributions from B hadron decays are subtracted to yield the “prompt” cross section, which includes contributions from direct production and from decays of heavier charmonia
INCLUSIVE PRODUCTION
5
![Page 6: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/6.jpg)
INCLUSIVE PRODUCTION
6
• Color-singlet model (CSM) : A pair with same spin, color and C P T is created in the hard process, which evolves in to the . The universal rate from to (color-singlet long-distance matrix element) is known from models, lattice measurements, and fits to experiments.
p p
cc̄
J/
color-singlet LDME
cc̄
cc̄
J/
J/
![Page 7: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/7.jpg)
INCLUSIVE PRODUCTION
7
• CSM is incomplete :
• A color-octet (CO) pair can evolve into a color singlet meson by emitting soft gluons.
• In the effective theory nonrelativistic QCD, CO LDMEs are suppressed by powers of .
• In many cases, color-octet channels are necessary : • For S-wave vector quarkonia ( ),
CSM severely underestimates the cross section.• For production or decay of P-wave quarkonia
( ), CS channel contains IR divergences that can be cancelled only when the CO channels are included.
cc̄
J/ , (2S),⌥(nS)
�cJ ,�bJ
![Page 8: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/8.jpg)
INCLUSIVE PRODUCTION
8
• CSM prediction vs. measurement at Tevatron
• LO CSM ( ) is inconsistent with both shape and normalization.
• Radiative corrections are larger than LO and has different shape ( ), but still not large enough 10 -3
10 -2
10 -1
1
10
5 10 15 20
BR(J/ μ+μ-) d (pp_ J/ +X)/dpT (nb/GeV)s =1.8 TeV; | | < 0.6
pT (GeV)
LO colour-singletcolour-singlet frag.
⇠ 1/p4T
⇠ 1/p8T
![Page 9: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/9.jpg)
INCLUSIVE PRODUCTION • NRQCD can be used to describe the physics of scales
smaller than the quarkonium mass.
• NRQCD factorization conjecture for production of
• Short-distance cross sections are essentially the production cross section of that can be computed using perturbative QCD
• The LDMEs are nonperturbative quantities that correspond to the rate for the to evolve into
• LDMEs have known scaling with 9
Bodwin, Braaten, and Lepage, PRD51, 1125 (1995)
Short-distance cross section LDME
QQ̄
QQ̄
![Page 10: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/10.jpg)
INCLUSIVE PRODUCTION • NRQCD factorization conjecture for production of
• Usually truncated at relative order : , , , channels for
• The short-distance cross sections have been computed to NLO in by three groups :
• It is not known how to calculate color-octet LDMEs, and are usually extracted from measurements
10
Bodwin, Braaten, and Lepage, PRD51, 1125 (1995)
Short-distance cross section LDME
Kuang-Ta Chao’s group (PKU) : Ma, Wang, Chao, Shao, Wang, ZhangBernd Kniehl’s group (Hamburg) : Butenschön, KniehlJianxiong Wang’s group (IHEP) : Gong, Wan, Wang, Zhang
![Page 11: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/11.jpg)
INCLUSIVE PRODUCTION • In order to extract CO LDMEs from measured cross
sections we need to determine the short-distance cross sections as functions of
• NLO corrections give large K-factors that rise with ; this casts doubt on the reliability of perturbation theory
11 Ma, Wang, Chao, PRL106, 042002 (2011)
![Page 12: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/12.jpg)
POLARIZATION PUZZLE
• NRQCD at LO in predicts transverse polarization at large
• Disagrees with measurement
• NLO corrections are large in the and channels
• NRQCD at NLO still predicts transverse polarization
12
(GeV/c)Tp5 10 15 20 25 30
α
-1-0.8-0.6-0.4-0.20
0.20.40.60.81
CDF DataNRQCD
-factorizationTk
(a)
CDF, PRL99, 132001 (2007)Braaten, Kniehl, and Lee, PRD62, 094005 (2000)
CMS, PLB727, 381 (2013)Butenschoen and Kniehl, PRL108, 172002 (2012)
: Transverse
: Unpolarized
: Longitudinal
![Page 13: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/13.jpg)
LP FRAGMENTATION • Large NLO corrections arise because new channels
that fall off more slowly with open up at NLO
• The leading power (LP) in ( ) is given by single-parton fragmentation
• Corrections to LP fragmentation go as 13
Collins and Soper, NPB194, 445 (1982)Nayak, Qiu, and Sterman, PRD72, 114012 (2005)
Fragmentation Functions
Parton productioncross sections
z : fraction of momentum transferred from parton k to hadron
i, j, k run over quarks, antiquarks, and gluon
d�
dp2T
[ij ! cc̄+X]
=XXX
k
ZZZ 1
0dz
d�
dp2T
[ij ! k+X]D[k ! cc̄+X] +O(m2c/p
6T )
![Page 14: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/14.jpg)
FRAGMENTATION FUNCTIONS • Fragmentation functions (FFs) for production of
can be computed using perturbative QCD
• A gluon can produce a pair in state directly : gluon FF for this channel starts at order , involves a delta function at
• A gluon can produce a in state by emitting a soft gluon : gluon FF for this channel starts at order , involves distributions singular at
• A gluon can produce a in state by emitting a gluon : gluon FF for this channel starts at order , does not involve divergence at order
14
cc̄
Collins and Soper, NPB194, 445 (1982)
cc̄
cc̄
cc̄
z = 1
z = 1
![Page 15: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/15.jpg)
FRAGMENTATION FUNCTIONS • For the and channels, gluon
polarization is transferred to the pair, and therefore the is mostly transverse.
• For the channel, the is unpolarized because it is isotropic.
15
cc̄cc̄
cc̄
![Page 16: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/16.jpg)
LP FRAGMENTATION • LP fragmentation explains the large, -dependent
K-factors that appear in fixed-order calculations
• channel is already at LP at LO : NLO correction is small
• and channels do not receive an LP contribution until NLO : NLO corrections are large
16
![Page 17: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/17.jpg)
• LP fragmentation reproduces the fixed-order calculation at NLO accuracy at large The difference is suppressed by
• The slow convergence in channel is because the fragmentation contribution is small (no function or plus distribution from IR divergence)
LP FRAGMENTATION
17
![Page 18: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/18.jpg)
LP+NLO • We combine the LP fragmentation contributions with
fixed-order NLO calculations to include corrections of relative order
• We take in order to suppress possible non-factorizing contributions
18
LP fragmentation resummed leading logs
LP fragmentation to NLO accuracy
fixed-order calculation to NLO
corrections of relative order
![Page 19: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/19.jpg)
LP+NLO • Alternatively, one can consider the LP fragmentation
to supplement the fixed-order NLO calculation
19
LP fragmentation resummed leading logs
LP fragmentation to NLO accuracy
fixed-order calculation to NLO
Additional fragmentation contributions
![Page 20: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/20.jpg)
channel and channels
LP CONTRIBUTIONS THAT WE COMPUTE
• We resum the leading logarithms in to all orders in
• Corrections to LP contributions give “normal” K-factors ( )
20
LO NLO NNLO
NLO NNLO
NNLO
Fragmentation functions
Pa
rto
n p
rod
uct
ion
cro
ss s
ecti
on
s
Gribov and Lipatov, Yad. Fiz. 15, 781 (1972) / Lipatov, Yad. Fiz. 20, 181 (1974)Dokshitzer, Zh. Eksp. Teor. Fiz. 73, 1216 (1977) / Altarelli and Parisi, NPB126, 298 (1977)
- NLO NNLO
- NNLO
-
Fragmentation functions
Not yet available Leading logarithms onlyAvailable
. 2
![Page 21: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/21.jpg)
RESUMMATION OF LEADING LOGARITHMS• The leading logarithms can be resummed to all orders
by solving the LO DGLAP equation
• This equation is diagonalized in Mellin space; the inverse transform can then be carried out numerically
• Because the FFs are singular at the endpoint, the inversion is divergent at ; special attention is needed for contribution at
21
z = 1
z ⇡ 1
d
d logµ2f
✓DS
Dg
◆=
↵s(µf )
2⇡
✓Pqq 2nfPgq
Pqg Pgg
◆⌦✓DS
Dg
◆
DS =P
q(Dq +Dq̄)
![Page 22: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/22.jpg)
RESUMMATION OF LEADING LOGARITHMS• We split the integral :
• is chosen so that near
22
z
N �̂(z) ⇡ �̂(1)zN
Z 1
0dz �̂(z)D(z) =
Z 1�✏
0dz �̂(z)D(z) +
Z 1
1�✏dz �̂(z)D(z)
⇡Z 1�✏
0dz �̂(z)D(z) + �̂(z = 1)
Z 1
1�✏dz zND(z)
z ⇡ 1Z 1
1�✏dz zND(z) =
Z 1
0dz zND(z)�
Z 1�✏
0dz zND(z)
Well defined in Mellin space (Mellin transform of D(z))
Well behaved numerically
![Page 23: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/23.jpg)
LP+NLO • The additional fragmentation contributions have
important effects on the shapes in the channel
• Large corrections to the shape of the channel because the LO and NLO contributions cancel at about
23
![Page 24: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/24.jpg)
PRODUCTION • We obtain good fits to
the cross section measurements by CDF and CMS
• was used in the fit
• 25% theoretical uncertainty from varying fragmentation, factorization and renormalization scales
24
CDF, PRD71, 032001 (2005)CMS, JHEP02, 011 (2012)Bodwin, HSC, Kim, Lee, PRL113, 022001 (2014)
![Page 25: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/25.jpg)
PRODUCTION • The data falls off faster
than and channels
• The fit constrains the and channels to cancel
• channel dominates the cross section
• This possibility was first suggested by Chao et al.
25
Chao, Ma, Shao, Wang, Zhang, PRL108, 242004 (2012)
hOJ/ (1S[8]0 )i = 0.099± 0.022 GeV3
hOJ/ (3S[8]1 )i = 0.011± 0.010 GeV3
hOJ/ (3P [8]0 )i = 0.011± 0.010 GeV5
![Page 26: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/26.jpg)
POLARIZATION • Because of dominance,
is almost unpolarized
• FIRST PREDICTION OF UNPOLARIZED IN NRQCD
• This is in good agreement with CMS data and much improved agreement with CDF Run II data
• Caveat : feeddown ignored26
CMS, PLB727, 381 (2013)CDF, PRL 85, 2886 (2000), PRL99, 132001 (2007)
Bodwin, HSC, Kim, Lee, PRL113, 022001 (2014)
![Page 27: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/27.jpg)
PROMPT PRODUCTION • can also be
produced from decays of and
• LDMEs from fit to CMS and CDF cross section data
• LDMEs from fit to ATLAS cross section data
• 30% theoretical uncertainty from scale variation
27
PRELIMINARY
PRELIMINARY
CDF, PRD80, 031103 (2009)CMS, JHEP02, 011 (2012)CMS-PAS-BPH-14-001
ATLAS, JHEP1407, 154 (2014)
![Page 28: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/28.jpg)
POLARIZATION • We predict that the
is slightly transverse at the Tevatron
• We predict that the is slightly transverse at the LHC Agrees with CMS data within errors
28
PRELIMINARY
PRELIMINARY
CDF, PRL85, 2886 (2000)CDF, PRL99, 132001 (2007)
CMS, PLB727, 381 (2013)
![Page 29: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/29.jpg)
PRODUCTION • and channels
contribute at leading order in
• We obtain good fits to ATLAS data
• The matrix element obtained from fit agrees with the potential model calculation
29
PRELIMINARY
→Suggests that NRQCD factorization works
ATLAS, JHEP1407, 154 (2014)
Potential model
Eichten and Quigg, PRD 52, 1726 (1995)
Our fit
![Page 30: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/30.jpg)
POLARIZATION OF FROM DECAY
• We predict that the from decay is slightly transverse at LHC
• We assume transition in (higher-order transitions have little effect)
30
PRELIMINARY
Faccioli, Lourenco, Seixas, and Wohri, PRD83, 096001 (2011)
![Page 31: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/31.jpg)
PROMPT PRODUCTION • After including
feeddown contributions, we again obtain good fits
• Again, was used in the fit
31
PRELIMINARY
PRELIMINARY
Fractions of direct and feeddown contributions
CDF, PRD71, 032001 (2005)CMS, JHEP02, 011 (2012)CMS-PAS-BPH-14-001
![Page 32: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/32.jpg)
PROMPT PRODUCTION
32
PRELIMINARY
• The direct cross section falls off faster than and channels
• The fit constrains the and channels to cancel
• channel dominates the direct cross section
![Page 33: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/33.jpg)
PROMPT POLARIZATION • Direct and
from feeddown is slightly transverse
• PROMPT HAS SMALL POLARIZATION
• This is in reasonably good agreement with CMS data
33
PRELIMINARY
PRELIMINARY
CMS, PLB727, 381 (2013)
CDF, PRL85, 2886 (2000), PRL99, 132001 (2007)
![Page 34: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/34.jpg)
SUMMARY• We present new LP fragmentation contributions that
have a significant effect on calculations of production in hadron colliders
• When we include LP fragmentation contributions, we predict the to have near-zero polarization at high at hadron colliders
• This is the first prediction of small polarization at high in NRQCD
• Work on higher-order corrections, as well as other quarkonium states is in progress
34
![Page 35: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/35.jpg)
BACKUP
![Page 36: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/36.jpg)
GLUON FRAGMENTATION INTO • Lowest-order diagrams of a gluon producing CO
36
![Page 37: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/37.jpg)
GLUON FRAGMENTATION INTO • Computation of fragmentation functions involve
Eikonal lines, and their interaction with gluons
37
![Page 38: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/38.jpg)
PREDICTIONS AT NLO
• Used cross section measurements at HERA and Tevatron to fix LDMEs, predicts transverse polarization at large
• H1 and ZEUS data are at small • Does not include feeddown
38
Butenschoen and Kniehl, Mod.Phys.Lett.A28, 1350027 (2013)
Bernd Kniehl’s group
![Page 39: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/39.jpg)
PREDICTIONS AT NLO
• Used CDF and LHCb cross section data to fit LDMEs
• Includes feeddown
• Prediction still more transverse than measurement
39
Jianxiong Wang’s group
Gong, Wan, Wang, Zhang, PRL110, 042002 (2013)
![Page 40: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/40.jpg)
PREDICTIONS AT NLO
40Shao, Han, Ma, Meng, Zhang, Chao, hep-ph/1411.3300 (2014)
Kuang-Ta Chao’s group
• Used CDF, ATLAS, CMS, LHCb cross section data to fit LDMEs
• Included feeddown
• Assumed positivity of all LDMEs, although LDME has strong factorization scale dependence
• Prediction still more transverse than data
![Page 41: PRODUCTION AT HADRON COLLIDERS - T-2t2.lanl.gov/seminars/slides/20150304_Chung.pdfMar 04, 2015 · to CMS and CDF cross section data • LDMEs from fit to ATLAS cross section data](https://reader035.vdocuments.net/reader035/viewer/2022081411/60a540d5248a8c1ad23d2d81/html5/thumbnails/41.jpg)
PREDICTIONS AT NLO
41
• Used CDF, ATLAS, CMS, LHCb cross section data to fit LDMEs
• Included feeddown
• Assumed positivity of all LDMEs, although LDME has strong factorization scale dependence
• Prediction still more transverse than data
Shao, Han, Ma, Meng, Zhang, Chao, hep-ph/1411.3300 (2014)
Kuang-Ta Chao’s group