probe triple partons interaction through three quarkonia ... · quarkonium production and double...
TRANSCRIPT
Introduction The frame of Calculation Numerical Result Summary
Probe triple partons interaction throughthree quarkonia associated production at
LHC
Yu-Jie Zhang
Beihang Univeisity
Hadron 2019 @ GXNU
Based on Hua-Sheng Shao, YJZ,PRL122(2019)192002/Arxiv:1902.04949
August 18, 20193 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Outline
1 IntroductionMultiparton scatteringQuarkonium productions
2 The frame of Calculation
3 Numerical ResultNumerical Result of J/ψ + J/ψ + J/ψ + XNumerical Result for Υ+ J/ψ + φ
4 Summary
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Introduction
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Multiparton scattering
SPS, DPS, and TPS
SPS, DPS, and TPS1 Single parton scattering (SPS) / Double-parton scattering
(DPS): involve one / two partons in each hadron colliding.2 Triple-parton scattering (TPS): involve three partons in
each hadron colliding. TPS are absent due to their morecomplicated final states and much fewer yields.
J/ψ
J/ψ
J/ψ
p
p
J/ψ
J/ψ
J/ψ
p
p
J/ψ
J/ψ
J/ψ
p
p
Figure: SPS/DPS/TPS triple J/ψ production at SPPC3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Multiparton scattering
MPI
MPI1 The cross sections of MPI are either strongly model
dependent or assuming no correlation between MPI.2 We assume no correlation between MPI.3 The DPS studies at the LHC and Tevatron suggest that no
correlation assumption is a rather good approximation.4 A N-parton scattering (NPS) cross-section (1708.07519)
σNPSf1···fN
=mN!
∏Ni=1 σ
SPSfi
(σeff,N)N−1 , (1)
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Multiparton scattering
NPS
NPS1 A N-parton scattering (NPS) cross-section (1708.07519)
σNPSf1···fN
=mN!
∏Ni=1 σ
SPSfi
(σeff,N)N−1 , (2)
2 The factor mN! : the indistinguishable final state symmetry.
3 σSPSfi
: the SPS cross section of producing final state fi .
4 σeff,N: the effective cross section, which should bedetermined by experiments.
5 The DPS and TPS cases correspond to N = 2 and N = 3.6 Ref. 1612.05582 derives σeff,3 = (0.82 ± 0.11)× σeff,2.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Multiparton scattering
σeff,2 and heavy quarkonium (1710.06315, 1811.07474)
σeff,2
1 σeff,2 ∼10 mb: extracted from the quarkonium data.2 σeff,2 ∼15 mb: extracted from the weak gauge boson data.3 However, it is still far from being conclusive in view of the
remaining large uncertainties.
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1. CDF 4j 1.8 TeV 325 nb-1
2. LHCb J�Ψ+C mesons H4 channelsL 7 TeV 355 pb-1
3. ATLAS W+jj 7 TeV 36 pb-1
4. CMS same sign WW Honly Σeff lower limitL 8 TeV 19.7 fb-1
5. CMS W+jj 7 TeV 5 fb-1
6. D0 Γ+3j H2 channelsL 1.96 TeV 8.7 fb-1
7. ATLAS 4j 7 TeV 37.3 pb-1
8. D0 2Γ+2j 1.96 TeV 8.7 fb-1
9. D0 J�Ψ+J�Ψ 1.96 TeV 8.1 fb-1
10. LHCb J�Ψ+J�Ψ HDifferent SPS modelsL 13 TeV 5 fb-1
syst. err. 25%
syst. err. 15%
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WÄ jj
æ æ
ZÄ jj
æ æ æ æ
W±ÄW±A B C D E F G H
A. Fit DrelpT 13 TeV 300 fb-1
B. Fit DrelpT 100 TeV 300 fb-1
C. Fit DlrelpT 13 TeV 300 fb-1
D. Fit DlrelpT 100 TeV 300 fb-1
E. Fit DΗl l 13 TeV 300 fb-1
F. Fit DΗl l 13 TeV 3000 fb-1
G. Fit DΗl l 100 TeV 300 fb-1
H. Fit DΗl l 100 TeV 3000 fb-1
HbL
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Σef
f@m
bD
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Multiparton scattering
σDPSeff , Atlas, 1811.11094
DPS and W ,Z
Experim
ent
(energ
y,
final sta
te,
year)
0 5 10 15 20 25 30
[mb]eff
σ
ATLAS
AFS (√
s = 63 GeV, 4 jets, 1986)UA2 (
√
s = 630 GeV, 4 jets, 1991)CDF (
√
s = 1.8 TeV, 4 jets, 1993)CDF (
√
s = 1.8 TeV, γ+ 3 jets, 1997)DØ (
√
s = 1.96 TeV, γ+ 3 jets, 2010)
LHCb (√
s = 7 TeV, J/ψΛ+c , 2012)
LHCb (√
s = 7 TeV, J/ψD+s , 2012)
LHCb (√
s = 7 TeV, J/ψD+, 2012)
LHCb (√
s = 7 TeV, J/ψD0, 2012)ATLAS (
√
s = 7 TeV, W+ 2 jets, 2013)CMS (
√
s = 7 TeV, W+ 2 jets, 2014)DØ (
√
s = 1.96 TeV, γ+ b/c + 2 jets, 2014)DØ (
√
s = 1.96 TeV, γ+ 3 jets, 2014)DØ (
√
s = 1.96 TeV, J/ψ + J/ψ, 2014)ATLAS (
√
s = 8 TeV, Z + J/ψ, 2015)
LHCb (√
s = 7&8 TeV, Υ(1S)D0,+, 2015)DØ (
√
s = 1.96 TeV, J/ψ +Υ, 2016)DØ (
√
s = 1.96 TeV, 2γ+ 2 jets, 2016)ATLAS (
√
s = 7 TeV, 4 jets, 2016)ATLAS (
√
s = 8 TeV, J/ψ + J/ψ, 2017)CMS (
√
s = 8 TeV, Υ+Υ, 2017)LHCb (
√
s = 13 TeV, J/ψ + J/ψ, 2017)
CMS (√
s = 8 TeV, W±W±, 2018)ATLAS (
√
s = 8 TeV, 4 leptons, 2018)
Figure: DPS3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Multiparton scattering
dphi @ D0, Shao, YJZ, 1605.03061
Br(
J/ψ
→µ
+µ
- )Br(
Υ→
µ+µ
- )×d
σ/d
|∆φ| [fb]
|∆φ(J/ψ,Υ)|
prompt J/ψ+Υ(1S,2S,3S) production at 1.96 TeV Tevatron
SPS: kT smearing ⟨kT⟩=3 GeV
COM: Set I LDMEs
σeff=2.2 mb
σeff=5 mb
σeff=15 mb
DR
EW-INTER
DRLI
EW-INTER
COMDPS
D0 Data
10-5
10-4
10-3
10-2
10-1
100
101
102
103
0 1 2 3
HELAC-Onia 2.0
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Multiparton scattering
Double parton scattering Picture (Enterria, Snigirev, 1708.07519)
DPS
PDPSpp→ab = PSPS
pp→a × PSPSpp→b
=σ(pp → a + X )
σinel(pp)× σ(pp → b + X )
σinel(pp)(3)
Then σnPSeff ∼ σinel(pp). But σinel(pp) ∼ 30 − 50 mb and
σDPSeff ∼ 10 − 15 mb.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Multiparton scattering
TPS
TPS (1612.05582, 1703.07163, 1710.1152)
TPS theoretical studies in literature are limited to openheavy-flavor productions so far. The complete study includingSPS and DPS is not available.
c
c̄
c
c̄
c
c̄x′3
x′2
x′1
x1 x2
x3
p
p
Figure: TPS of pPb → cc̄ + cc̄ + cc̄ (PRL118, 122001).
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Quarkonium productions
Quarkonium productions
NLO J/ψ at LHCb, Chao/Wang/Kniehl, 1506.03981
) [GeV/c]ψ(J/T
p0 5 10 15
θλ
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
NLO NRQCD(1)NLO NRQCD(2)NLO NRQCD(3)
NLO CS
2.5 < y < 4.0
= 7 TeVsLHCb
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Quarkonium productions
CO LDMEs, 1212.2037
Butenschoen, Gong, Wang, Chao, Ma, Shao, Wang, Zhang52
Kniehl18 Wan, Zhang53 default set set 2 set 3
〈OJ/ψ(3S[1]1 )〉 1.32 GeV3 1.16 GeV3 1.16 GeV3 1.16 GeV3 1.16 GeV3
〈OJ/ψ(1S[8]0 )〉 0.0497 GeV3 0.097 GeV3 0.089 GeV3 0 0.11 GeV3
〈OJ/ψ(3S[8]1 )〉 0.0022 GeV3 −0.0046 GeV3 0.0030 GeV3 0.014 GeV3 0
〈OJ/ψ(3P[8]0 )〉 −0.0161 GeV5 −0.0214 GeV5 0.0126 GeV5 0.054 GeV5 0
〈Oψ′
(3S[1]1 )〉 0.758 GeV3
〈Oψ′
(1S[8]0 )〉 −0.0001 GeV3
〈Oψ′
(3S[8]1 )〉 0.0034 GeV3
〈Oψ′
(3P[8]0 )〉 0.0095 GeV5
〈Oχ0 (3P[1]0 )〉 0.107 GeV5
〈Oχ0 (3S[8]1 )〉 0.0022 GeV3
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Quarkonium productions
Double J/ψ, Lansberg, Shao, 1410.8822
Energy and quarkonium cuts σexp. σSPS,prompt
LOσ
SPS,prompt
NLO(⋆) σDPS,prompt χ2
LHCb√
s = 7 TeV, Pψ1,2
T< 10 GeV,
2 < yψ < 5 [34]
18 ± 5.3 pb 41+51−24
pb 46+58−27
31+11−6.3
(+24−15
) pb 0.5 − 1.2
D0
√s = 1.96 TeV, P
ψ1,2
T> 4 GeV, SPS: 70 ± 23 fb 53+57
−27fb 170+340
−110fb – –
|ηψ| < 2.0 [12] (+ µ cuts in caption) DPS: 59 ± 23 fb – – 44+16−9.1
(+7.5−5.1
) fb 0.06 − 0.5
CMS√
s = 7 TeV, Pψ1,2
T> 6.5 → 4.5 GeV
depending on |yψ1,2| ∈ [0, 2.2] (see the
caption) [35]
5.25 ± 0.52 pb 0.35+0.26−0.17
pb 1.5+2.2−0.87
pb 0.69+0.24−0.14
(+0.039−0.027
) pb 1.09 − 1.14
ATLAS√
s = 7 TeV, Pψ1,2
T> 5 GeV and |yψ1,2
| <2.1 (+ µ cuts in the caption) [48]
– 6.4+4.3−2.6
fb 36+49−20
fb 19+6.8−4.0
(+2.2−1.6
) fb N/A
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Quarkonium productions
Double J/ψ at CMS, Sun, Han, Chao, 1404.4042
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Quarkonium productions
Double J/ψ at CMS, Lansberg, Shao, Yamanaka, YJZ 1906.10049d
σ/d
M [
nb/G
eV
]
M(J/ψ+J/ψ) [GeV]
Prompt J/ψ+J/ψ production at √s=7 TeV LHC
NLO* SPS
NLO*+LI SPS
CMS
10-6
10-5
10-4
10-3
10-2
10-1
10 20 30 40 50 60 70 80
HELAC-Onia 2.0
dσ
/d∆
y [
nb]
|∆y(J/ψ,J/ψ)|
Prompt J/ψ+J/ψ production at √s=7 TeV LHC
NLO* SPS
NLO*+LI SPS
CMS
10-5
10-4
10-3
10-2
10-1
100
0 0.5 1 1.5 2 2.5 3 3.5 4
HELAC-Onia 2.0
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Quarkonium productions
Quarkonium production and double parton scattering
Many quarkonium associated production processes seemsto be dominant by Double-Parton Scattering (DPS).
1 J/ψ + W and J/ψ + Z , (ATLAS, arXiv:1401.2831,1412.6428)
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Quarkonium productions
Quarkonium production and double parton scattering
Many quarkonium associated production processes seemsto be dominant by Double-Parton Scattering (DPS).
1 J/ψ + W and J/ψ + Z , (ATLAS, arXiv:1401.2831,1412.6428)
2 J/ψ + charm and Υ+ charm (LHCb, arXiv:1205.0975,1510.05949)
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Quarkonium productions
Quarkonium production and double parton scattering
Many quarkonium associated production processes seemsto be dominant by Double-Parton Scattering (DPS).
1 J/ψ + W and J/ψ + Z , (ATLAS, arXiv:1401.2831,1412.6428)
2 J/ψ + charm and Υ+ charm (LHCb, arXiv:1205.0975,1510.05949)
3 J/ψ + J/ψ (D0, arXiv:1406.2380; CMS, arXiv:1406.0484)
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Quarkonium productions
Quarkonium production and double parton scattering
Many quarkonium associated production processes seemsto be dominant by Double-Parton Scattering (DPS).
1 J/ψ + W and J/ψ + Z , (ATLAS, arXiv:1401.2831,1412.6428)
2 J/ψ + charm and Υ+ charm (LHCb, arXiv:1205.0975,1510.05949)
3 J/ψ + J/ψ (D0, arXiv:1406.2380; CMS, arXiv:1406.0484)4 Υ+ J/ψ (D0, arXiv:1511.02428)
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Quarkonium productions
Quarkonium associated production
Quarkonium associated production at hadron colliders1 σ(J/ψ + cc̄)@α4
s : Artoisenet, Lansberg, Maltoni, 0703129.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Quarkonium productions
Quarkonium associated production
Quarkonium associated production at hadron colliders1 σ(J/ψ + cc̄)@α4
s : Artoisenet, Lansberg, Maltoni, 0703129.2 σ(Υ + 3jets)@α5
s : Artoisenet, Campbell, Lansberg,Maltoni, Tramontano, 0806.3282.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Quarkonium productions
Quarkonium associated production
Quarkonium associated production at hadron colliders1 σ(J/ψ + cc̄)@α4
s : Artoisenet, Lansberg, Maltoni, 0703129.2 σ(Υ + 3jets)@α5
s : Artoisenet, Campbell, Lansberg,Maltoni, Tramontano, 0806.3282.
3 σ(Bccc + c̄ + c̄ + c̄)@α6s : Chen, Wu, 1106.0193.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Quarkonium productions
Quarkonium associated production
Quarkonium associated production at hadron colliders1 σ(J/ψ + cc̄)@α4
s : Artoisenet, Lansberg, Maltoni, 0703129.2 σ(Υ + 3jets)@α5
s : Artoisenet, Campbell, Lansberg,Maltoni, Tramontano, 0806.3282.
3 σ(Bccc + c̄ + c̄ + c̄)@α6s : Chen, Wu, 1106.0193.
4 σ(J/ψ + J/ψ + J/ψ + g)@α7s : Shao, YJZ, 1902.04949 ....
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
The frame of Calculation
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Total triple J/ψ hadroproduction cross sections
DPS and TPS cross sectionsWe will use the following concrete formula:
σDPS(pp → J/ψJ/ψJ/ψ + X )
=σSPS(pp → J/ψJ/ψ + X )σSPS(pp → J/ψ + X )
σeff,2,
σTPS(pp → J/ψJ/ψJ/ψ + X )
=16
[
σSPS(pp → J/ψ + X )]3
(σeff,3)2 (4)
to calculate DPS and TPS cross sections.
In total, there are three different SPS cross sections, i.e., thoseof one, two and three J/ψ production, to be computed.3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
SPS cross sections
Hadron and Parton level cross sections
σ(h1h2 → JJJ ) =∑
a,b
fa/h1⊗ fb/h2
⊗σ̂(ab → C + J + J + X ). (5)
Parton level cross section
d σ̂(ab→JJJ ) =∑
n1,n2,n2
σ̂(ab → cc̄[n1]cc̄[n2]cc̄[n3] + X )
〈OJ (n1)〉〈OJ (n2)〉〈OJ (n3)〉 (6)
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
One of 28774 Feynman Diagrams of SPS
J/ψ
J/ψ
J/ψ
p
p
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Feynman Diagrams of DPS
J/ψ
J/ψ
J/ψ
p
p
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Feynman Diagrams of TPS
J/ψ
J/ψ
J/ψ
p
p
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
J/ψ + J/ψ + J/ψ + X
SPS cross sections with pT (J/ψ) > 2GeV
σSPS Order 14 TeV 100 TeV
J/ψ +X α3s 72± 1 µb 300 ± 8 µb
J/ψJ/ψ +X α4s 67± 2 nb 343 ± 13 nb
J/ψJ/ψJ/ψ +X α7s 1± 0.6 pb 4.2± 3.2 pb
σ(J/ψJ/ψJ/ψ +X) Order 14 TeV CMS @ 14 TeV 100 TeV
TPS α9s 620 ± 20 pb 45± 1.5 pb 45000 ± 1500 pb
DPS α7s 480 ± 20 pb 35± 1.5 nb 10000 ± 1000 pb
SPS α7s 1± 0.6 pb 0.07± 0.04 pb 4.2± 3.2 pb
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
J/ψ + J/ψ + J/ψ + X
Triple J/ψ production at 100 TeV SPPC
σ(M
(3J/ψ
)>M
min
)×B
r3 [
fb]
Mmin [GeV]
Prompt 3-J/ψ production at √s=100 TeV
σeff,2=10 mb,σeff,3=10 mb
6 fb-1
300 fb-1
3 ab-1
10 ab-1
100 events
SPS
DPS
TPS
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
0 10 20 30 40 50 60 70 80 90 100
HELAC-Onia 2.0
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
J/ψ + J/ψ + J/ψ + X
Triple J/ψ production at 100 TeV SPPC
σ(P
T>
PT
,min
)×B
r3 [
fb]
PT,min [GeV]
Prompt 3-J/ψ production at √s=100 TeV
σeff,2=10 mb,σeff,3=10 mb
kT smearing ⟨kT⟩=3 GeV
|yJ/ψ|<2.4
300 fb-1
3 ab-1
10 ab-1
100 events
SPS
DPS
TPS
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
0 1 2 3 4 5 6 7 8 9 10
HELAC-Onia 2.0
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
J/ψ + J/ψ + J/ψ + X
Triple J/ψ production at 75 TeV SPPC
σ(M
(3J/ψ
)>M
min
)×B
r3 [
fb]
Mmin [GeV]
Prompt 3-J/ψ production at √s=75 TeV
σeff,2=10 mb,σeff,3=10 mb
6 fb-1
300 fb-1
3 ab-1
10 ab-1
100 events
SPS
DPS
TPS
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
0 10 20 30 40 50 60 70 80 90 100
HELAC-Onia 2.0
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
J/ψ + J/ψ + J/ψ + X
Triple J/ψ production at 75 TeV SPPC
σ(P
T>
PT
,min
)×B
r3 [
fb]
PT,min [GeV]
Prompt 3-J/ψ production at √s=75 TeV
σeff,2=10 mb,σeff,3=10 mb
kT smearing ⟨kT⟩=3 GeV
|yJ/ψ|<2.4
300 fb-1
3 ab-1
10 ab-1
100 events
SPS
DPS
TPS
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
0 1 2 3 4 5 6 7 8 9 10
HELAC-Onia 2.0
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
J/ψ + J/ψ + J/ψ + X
J/ψJ/ψJ/ψ + X at CMS/Atlas
Search TPS at CMS/Atlas
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
J/ψ + J/ψ + J/ψ + X
J/ψJ/ψJ/ψ + X at CMS/Atlas
Search TPS at CMS/Atlas1 Integrated luminosity of CMS/Atlas is about 160 fb−1 at√
s = 13 TeV.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
J/ψ + J/ψ + J/ψ + X
J/ψJ/ψJ/ψ + X at CMS/Atlas
Search TPS at CMS/Atlas1 Integrated luminosity of CMS/Atlas is about 160 fb−1 at√
s = 13 TeV.2 Br [J/ψ → µ+µ−] = 0.059.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
J/ψ + J/ψ + J/ψ + X
J/ψJ/ψJ/ψ + X at CMS/Atlas
Search TPS at CMS/Atlas1 Integrated luminosity of CMS/Atlas is about 160 fb−1 at√
s = 13 TeV.2 Br [J/ψ → µ+µ−] = 0.059.3 Number of events for 3J/ψ(µ+µ−) with pT (J/ψ) > 2 GeV
is about 2700 ± 72 , which is 1500 ± 50 from TPS and1200 ± 50 from DPS.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
J/ψ + J/ψ + J/ψ + X
J/ψJ/ψJ/ψ + X at CMS/Atlas
Search TPS at CMS/Atlas1 Integrated luminosity of CMS/Atlas is about 160 fb−1 at√
s = 13 TeV.2 Br [J/ψ → µ+µ−] = 0.059.3 Number of events for 3J/ψ(µ+µ−) with pT (J/ψ) > 2 GeV
is about 2700 ± 72 , which is 1500 ± 50 from TPS and1200 ± 50 from DPS.
4 We can introduce cut of phase space to distinguish SPS,DPS, and TPS contributions.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
J/ψ + J/ψ + J/ψ + X
Triple J/ψ production at LHC
σ(M
(3J/ψ
)>M
min
)×B
r3 [
fb]
Mmin [GeV]
Prompt 3-J/ψ production at √s=13 TeV LHC
σeff,2=10 mb,σeff,3=10 mb
6 fb-1
23 fb-1
300 fb-1
3 ab-1
100 events
SPS
DPS
TPS
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
0 10 20 30 40 50 60 70 80 90 100
HELAC-Onia 2.0
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
J/ψ + J/ψ + J/ψ + X
Triple J/ψ production at LHC
σ(|
∆y|>
|∆y| m
in)×
Br3
[fb
]
|∆y|min
Prompt 3-J/ψ production at √s=13 TeV LHC
σeff,2=10 mb,σeff,3=10 mb
kT smearing ⟨kT⟩=3 GeV
6 fb-1
23 fb-1
300 fb-1
3 ab-1
100 events
SPS
DPS
TPS
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
0 0.5 1 1.5 2 2.5 3 3.5
HELAC-Onia 2.0
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
J/ψ + J/ψ + J/ψ + X
Triple J/ψ production at LHC
σ(P
T>
PT
,min
)×B
r3 [
fb]
PT,min [GeV]
Prompt 3-J/ψ production at √s=13 TeV LHC
σeff,2=10 mb,σeff,3=10 mb
kT smearing ⟨kT⟩=3 GeV
|yJ/ψ|<2.4
150 fb-1
300 fb-1
3 ab-1
100 events
SPS
DPS
TPS
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
0 1 2 3 4 5 6 7 8 9 10
HELAC-Onia 2.0
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Numerical Result for Υ+ J/ψ + φ
Υ, J/ψ, φ at LHCb
1 σ(Υ) ∼ 0.20 µb (1804.09214), σ(J/ψ) ∼ 15 µb(1509.00771), and σ(φ) ∼ 3 mb (1107.3935).
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Numerical Result for Υ+ J/ψ + φ
Υ, J/ψ, φ at LHCb
1 σ(Υ) ∼ 0.20 µb (1804.09214), σ(J/ψ) ∼ 15 µb(1509.00771), and σ(φ) ∼ 3 mb (1107.3935).
2 We have gotten σSPS [Υ + J/ψ] ∼ 10 pb in 1605.03061.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Numerical Result for Υ+ J/ψ + φ
Υ, J/ψ, φ at LHCb
1 σ(Υ) ∼ 0.20 µb (1804.09214), σ(J/ψ) ∼ 15 µb(1509.00771), and σ(φ) ∼ 3 mb (1107.3935).
2 We have gotten σSPS [Υ + J/ψ] ∼ 10 pb in 1605.03061.3 SPS Υ+ J/ψ + φ: O(α9
s), very small.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Numerical Result for Υ+ J/ψ + φ
Υ, J/ψ, φ at LHCb
1 σ(Υ) ∼ 0.20 µb (1804.09214), σ(J/ψ) ∼ 15 µb(1509.00771), and σ(φ) ∼ 3 mb (1107.3935).
2 We have gotten σSPS [Υ + J/ψ] ∼ 10 pb in 1605.03061.3 SPS Υ+ J/ψ + φ: O(α9
s), very small.
4 DPS Υ+ J/ψ + φ: about 3 × σSPS[Υ + J/ψ] σ[φ]σDPS
eff∼ 10 pb
for pT (φ) > 2 GeV and σDPSeff ∼ 10 mb.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Numerical Result for Υ+ J/ψ + φ
Υ, J/ψ, φ at LHCb
1 σ(Υ) ∼ 0.20 µb (1804.09214), σ(J/ψ) ∼ 15 µb(1509.00771), and σ(φ) ∼ 3 mb (1107.3935).
2 We have gotten σSPS [Υ + J/ψ] ∼ 10 pb in 1605.03061.3 SPS Υ+ J/ψ + φ: O(α9
s), very small.
4 DPS Υ+ J/ψ + φ: about 3 × σSPS[Υ + J/ψ] σ[φ]σDPS
eff∼ 10 pb
for pT (φ) > 2 GeV and σDPSeff ∼ 10 mb.
5 TPS Υ+ J/ψ + φ: about σ[Υ]σ[J/ψ]σ[φ](σTPS
eff )2 ∼ 100 pb for
σTPSeff ∼ 10 mb.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Search for TPS in Υ+ J/ψ + φ at LHCb
Estimate the number of events1 Br [Υ(J/ψ) → µ+µ−] = 0.024(0.06) and
Br [φ→ K+K−] = 0.5.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Search for TPS in Υ+ J/ψ + φ at LHCb
Estimate the number of events1 Br [Υ(J/ψ) → µ+µ−] = 0.024(0.06) and
Br [φ→ K+K−] = 0.5.2 Integrated luminosity of LHCb is about 6 fb−1 at√
s = 13 TeV.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Search for TPS in Υ+ J/ψ + φ at LHCb
Estimate the number of events1 Br [Υ(J/ψ) → µ+µ−] = 0.024(0.06) and
Br [φ→ K+K−] = 0.5.2 Integrated luminosity of LHCb is about 6 fb−1 at√
s = 13 TeV.3 Number of events for Υ(µ+µ−) + J/ψ(µ+µ−) + φ(K+K−)
with pT (φ) > 2 GeV is about 440.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Search for TPS in Υ+ J/ψ + φ at LHCb
Estimate the number of events1 Br [Υ(J/ψ) → µ+µ−] = 0.024(0.06) and
Br [φ→ K+K−] = 0.5.2 Integrated luminosity of LHCb is about 6 fb−1 at√
s = 13 TeV.3 Number of events for Υ(µ+µ−) + J/ψ(µ+µ−) + φ(K+K−)
with pT (φ) > 2 GeV is about 440.4 We can introduce cut to suppress SPS and DPS
contributions.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Numerical Result for Υ+ J/ψ + φ
Υ+ J/ψ + φ at Atlas/CMS
1 σ(Υ) ∼ 0.6 µb (1211.7255), σ(J/ψ) ∼ 50 µb (1104.3038),and σ(φ) ∼ 6 mb (1402.6162).
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Numerical Result for Υ+ J/ψ + φ
Υ+ J/ψ + φ at Atlas/CMS
1 σ(Υ) ∼ 0.6 µb (1211.7255), σ(J/ψ) ∼ 50 µb (1104.3038),and σ(φ) ∼ 6 mb (1402.6162).
2 We have gotten σSPS [Υ + J/ψ] ∼ 100 pb in 1605.03061.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Numerical Result for Υ+ J/ψ + φ
Υ+ J/ψ + φ at Atlas/CMS
1 σ(Υ) ∼ 0.6 µb (1211.7255), σ(J/ψ) ∼ 50 µb (1104.3038),and σ(φ) ∼ 6 mb (1402.6162).
2 We have gotten σSPS [Υ + J/ψ] ∼ 100 pb in 1605.03061.3 SPS Υ+ J/ψ + φ: O(α9
s), very small.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Numerical Result for Υ+ J/ψ + φ
Υ+ J/ψ + φ at Atlas/CMS
1 σ(Υ) ∼ 0.6 µb (1211.7255), σ(J/ψ) ∼ 50 µb (1104.3038),and σ(φ) ∼ 6 mb (1402.6162).
2 We have gotten σSPS [Υ + J/ψ] ∼ 100 pb in 1605.03061.3 SPS Υ+ J/ψ + φ: O(α9
s), very small.
4 DPS Υ+ J/ψ + φ: about 3 × σSPS[Υ + J/ψ] σ[φ]σDPS
eff∼ 60 pb
for pT (φ) > 2 GeV and σDPSeff ∼ 10 mb.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Numerical Result for Υ+ J/ψ + φ
Υ+ J/ψ + φ at Atlas/CMS
1 σ(Υ) ∼ 0.6 µb (1211.7255), σ(J/ψ) ∼ 50 µb (1104.3038),and σ(φ) ∼ 6 mb (1402.6162).
2 We have gotten σSPS [Υ + J/ψ] ∼ 100 pb in 1605.03061.3 SPS Υ+ J/ψ + φ: O(α9
s), very small.
4 DPS Υ+ J/ψ + φ: about 3 × σSPS[Υ + J/ψ] σ[φ]σDPS
eff∼ 60 pb
for pT (φ) > 2 GeV and σDPSeff ∼ 10 mb.
5 TPS Υ+ J/ψ + φ: about σ[Υ]σ[J/ψ]σ[φ](σTPS
eff )2 ∼ 2 nb for
σTPSeff ∼ 10 mb.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Search for TPS in Υ+ J/ψ + φ at Atlas/CMS
Estimate the number of events1 Br [Υ(J/ψ) → µ+µ−] = 0.024(0.06) and
Br [φ→ K+K−] = 0.5.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Search for TPS in Υ+ J/ψ + φ at Atlas/CMS
Estimate the number of events1 Br [Υ(J/ψ) → µ+µ−] = 0.024(0.06) and
Br [φ→ K+K−] = 0.5.2 Integrated luminosity of Atlas/CMS is about 160 fb−1 at√
s = 13 TeV.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Search for TPS in Υ+ J/ψ + φ at Atlas/CMS
Estimate the number of events1 Br [Υ(J/ψ) → µ+µ−] = 0.024(0.06) and
Br [φ→ K+K−] = 0.5.2 Integrated luminosity of Atlas/CMS is about 160 fb−1 at√
s = 13 TeV.3 Number of events for Υ(µ+µ−) + J/ψ(µ+µ−) + φ(K+K−)
is about 2 × 105.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Numerical Result for Υ + J/ψ + φ
Search for TPS in Υ+ J/ψ + φ at Atlas/CMS
Estimate the number of events1 Br [Υ(J/ψ) → µ+µ−] = 0.024(0.06) and
Br [φ→ K+K−] = 0.5.2 Integrated luminosity of Atlas/CMS is about 160 fb−1 at√
s = 13 TeV.3 Number of events for Υ(µ+µ−) + J/ψ(µ+µ−) + φ(K+K−)
is about 2 × 105.4 We can introduce cut to suppress SPS and DPS
contributions.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Summary
We have performed the first analysis of simultaneousproduction of J/ψ + J/ψ + J/ψ and Υ+ J/ψ + φ fromSPS/DPS/TPS contributions at LHC.
Our work shows that it is in fact most probably dominated byTPS and DPS contributions.
Finally, we show that J/ψ + J/ψ + J/ψ and Υ+ J/ψ + φproduction at LHC may be studied by experimenters.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
Multi parton scattering
The inclusive cross section to produce n hard particles inhadronic colliders is a convolution of generalized n-partondistribution functions (PDF) and elementary partonic crosssections summed over all involved partons,
σNPShh′→a1...an
=(m
n!
)
∑
i1,..,in,i ′1,..,i′
n
∫
Γi1...inh (x1, .., xn;b1, ..,bn;Q2
1 , ..,Q2n)
× σ̂i1i ′1a1
(x1, x′1,Q
21) · · · σ̂
in i ′nan (xn, x ′
n,Q2n) (7)
× Γi ′1...i
′
nh′ (x ′
1, . . . , x′n;b1 − b, . . . ,bn − b;Q2
1 , . . . ,Q2n)
× dx1 . . . dxn dx ′1, . . . ,dx ′
n d2b1, . . . ,d2bn d2b.
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
The n-parton distribution function (1708.07519)
It encodes all the 3D structure information of the hadron.1 Assumption 1: the n-PDF are factored in terms of
longitudinal and transverse components,
Γi1...inh = Di1...in
h (x1, .., xn;Q21 , ..,Q
2n)f (b1)...f (bn) (8)
2 We can get hadron-hadron overlap functionT (b) =
∫
f (b1)f (b1 − b)d2b1, where 1 =∫
T (b)d2b.3 Assumption 2: the longitudinal components reduce to the
product of independent single PDF
Di1...inh (x1, .., xn;Q2
1 , ..,Q2n) = Di1
h (x1;Q21) · · ·Din
h (xn;Q2n) (9)
3 Quarkonium at LHC
Introduction The frame of Calculation Numerical Result Summary
The cross sections and σnPSeff (Enterria, Snigirev, 1708.07519)
The cross sections of n-particle associated production
Then we can get
σnPShh′→a1...an
=(m
n!
) σSPShh′→a1
· · · σSPShh′→an
(
σnPSeff
)n−1 , (10)
σnPSeff
(
1
σnPSeff
)n−1
=
∫
d2b T n(b) (11)
3 Quarkonium at LHC