Searching for dark sector at LHC
through “dark jet”

Beyond the BSM workshop
Mengchao Zhang
Hotel Tenbo 2018-10-03
Based on :1712.07279(Myeonghun Park, MZ)Outline
1.Introduction

2.How to tag a “Dark Jet”

3.An example at LHC

4.Conclusion and outlook

Motivation:Dark sector might becomplicated
1.The simplest WIMP model maybe not enough: null results,small scale problem(cusp-problem, 8 …)
2.We need to consider other paradigm(SIMP, asymmetricDM), or a different DM, like a composite particle originatedfrom dark sector confinement.
3.There are some popular NP models that can give you such
DM candidate, Mirror World, Dark QCD, Hidden Valley…

These models look like…
the Standard Model, g, l, q ...

Mediator

Dark sector
00X, Z ...

⇡, ⇢, p ...

00, g , q ...

⇡d , ⇢d , pd ...
SU (N )0SU (3) ⇥ SU (2) ⇥ U (1)or SU (N )0 ⇥ U (1)0or ...

Dark quark can be produced at collider through mediator particles.
Once produced, dark parton => shower => hadronization=> dark meson decay back to SM.
c⌧ ⇡ 80mm✓14◆✓

2GeVf ⇡d◆2 ✓0.1GeVmq◆2 ✓2GeVm⇡ d◆⇣mX ⌘ 4
1T eV

This kind of jet looks like….
It’s very, very model dependent.
How long is lifetime of dark meson ⇡d , ⇢d ...?
How much invisible particle inside a dark jet?
Most dark mesons are stable or stable enough.
Invisible Jet (Missing Energy)

Most dark mesons are long-lived.
Emerging Jet (Displaced Track)
JHEP 1505, 059 (2015)

A fraction of dark mesons are stable.
Semi-visible Jet (Transverse Mass)
Phys. Rev. Lett. 115, no. 17, 171804 (2015)

Most of dark mesons decay to visible particles promptly.
”QCD-like” Dark Jet (What Can You Do?)Outline
1.Introduction

2.How to tag a “Dark Jet”, when it looks like a QCD Jet

3.An example at LHC

4.Conclusion and outlook

One example of one-prong jet tagging
Quark/Gluon Jet discrimination:

JHEP 1304, 090 (2013)quark-jet and gluon-jet are di↵erent,
even both of them are QCD-jet.

Why are they different? Casimir Scaling
JHEP 1707, 091 (2017)

Gluon-Jet↵S CA

Quark-Jet↵S CFStrength of parton shower is controlled by thisfactor, so Gluon-Jet is broader than Quark-Jet,
and there are more hadrons insider Gluon-Jet.
Their di↵erence is decided by ratio CA /CF , it’s called Casimir Scaling.

So for a Dark-Jet …
Gluon-Jet↵S CA

Dark-Jet↵d Cd

We have a modified Casimir Scaling in Gluon/Dark Jet discrimination,
CA /CF should be changed to ↵S CA /↵d Cd .
So, if ↵d is very di↵erent with ↵S ...

Our dark sector setting
Our four benchmark setting. High confinement scale isrequired by short dark meson lifetime.

Running coupling ofdifferent setting.

Variable 1: two points energy
correlation function C1( )Definition:

withand Rij =q(⌘i

Leading order re-summation result:with( )

L(C1 ) = ln1+1qq( )

1

4C1 /R01

4C1 /R0( )⌘j ) 2 + ( ij)2Casimir Scaling

Variable 1: two points energy
correlation function C1( )Meson level: parton level distribution convolute with a ”shape function”.
And the mean value of shape function is proportional to ⇤.
( )Dark meson decay: push up C1 further:Cβ1 distribution at different level for point B

0.14

parton levelmeson levelparticle level
detector level

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Probability

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Cβ1

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Variable 1: two points energy
correlation function C1( )Distribution of di↵erent jets

receiver operating characteristic(ROC) curveVariable 2: Charged Track multiplicity
PerformanceVariable 3: E-ratio
Useful to some special final states, defined as:

Kaons inside dark jet Bis very importantMultiple variables analysisHow to combine the discriminant ability of different
variables? We use boosted decision tree(BDT).
BDT gives you a mapping from a set of variables toa BDT score:{var1,var2,var3,...} ! BDT score

Final discriminant performance
You can combine multiple variables to enhance the discriminant performance. Here we use boosted decision tree(BDT).

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A(3 variables)A(8 variables)B(3 variables)
B(8 variables)C(3 variables)C(8 variables)D(3 variables)D(8 variables)

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Gluon Jet AcceptanceExclude 99% Gluon-Jet,
reserve >30% Dark-Jet.

1Dark Jet Acceptance

Dark Jet Acceptance( )Combination of C1 , track Multi, and E-ratio is good enough.

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A(3 variables)A(8 variables)B(3 variables)
B(8 variables)C(3 variables)C(8 variables)D(3 variables)D(8 variables)

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Quark Jet AcceptanceExclude 99% Quark-Jet,
reserve >50% Dark-Jet.

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Uncertainty estimation
You can only use Pythia8 to do Dark QCD simulation.
So we rescale the renormalization scale in parton shower process toestimate the theoretical uncertainty.
1.0(0.5µ2 ! 2.0µ2 )Dark JetBAcceptance

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Dark sector setting A
is used here, which has alarge running coupling.

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Gluon Jet AAcceptanceOur result looks quite robust.

Outline
1.Introduction

2.How to tag a “Dark Jet”

3.An example at LHC

4.Conclusion and outlook

10Qd

1g
1

Xd 1800 2000
400 600 800 1000 1200 1400 1600gq̄mXd [GeV]

Qd1q
CMS
reportuse
displacedvertexto1400 600 800 1000 1200 X
1400d 1600 1800 2000
searchforg mediatorparticles.
q̄
mXd [GeV]

Expected limit
Expected limit ± 1σObserved limit

103

Qdqc τπd [mm]g m = 5 GeVπd† -1
Xfb
16.1
d (13 TeV)

95% C.L. upper limit on cross section [fb]c τπd [mm]q
CMS Preliminary

95% C.L. upper li

CMS report: based on
displacedvertex10q

CMS Preliminary

Xd† 16.1 fb-1 (13 TeV)mπd = 10 GeV
Expected limit
Expected limit ± 1σObserved limit

103
Qd

95% C.L. upper limit on cross section [fb]95% C.L. upper liby assuming that all the Yukawa couplings are negligible except for the coupling to the dow
1010quark.

3
3
1010
Figure 1: Feynman diagrams for pair production of mediator particles, with mediator decay t

a quark and a dark quark in the BSSW model
via (left) gluon fusion and (right) quark-antiquar
102
102annihilation.
102

102

The decay length of the lightest dark meson (dark pion) is given by Eq. 1 [6]:If dark meson decay promptly,
10 this✓its ◆✓
◆2 ✓
◆2 ✓
◆⇣
methodloseeffect.
mXd ⌘412 GeV
100 MeV
2 GeV
1010ct ⇡ 80 mm

k4

f pd
1mdownm pd

1 TeV10,1(1where1k is the NCd ⇥ 3 matrix of Yukawa couplings between
the mediator particle, the quark
1600 800 1000 1200 1400 1600 1800 2000
400 600 800 1000 1200 1400 1600 1800 2000
and the400darkquarks, f pd is the dark pion decay constant,
mdown is the mass of the down quarkmXd pion,[GeV]
mXd [GeV]
mpd is the mass of the dark
and mXd is the mass of the mediator particle.

vertices in detector. By counting the number of displaced vertices, one can obtain robust limiton the mass of mediator particle X[35, 83]. If the decay length of a dark meson is shorter
than 1mm, analyses with displaced vertices will lose sensitivity. In this section we will show
how tagging dark jet with jet-substructures can be used to enhance a search sensitivity for
promptly decaying dark mesons.
We consider dark sector setting A in Tab.2 as an example for the LHC study. Our analysis
is based on the search for pair-produced resonances in four-jet final states on ATLAS [84].
Here we briefly describe a cut flow used in ATLAS report [84]:Tagging the QCD-like “Dark jet”

Our analysis ins based on ATLAS report: search for pair-produced
resonances in 4-jets final state• Events are required to have at least 4 jets with pT > 120GeV and |⌘| < 2.4.
P• These 4 jets are paired by minimizing Rmin = i=1,2 | Ri 1|, with Ri the angulardistance between two jets in a pair.
• Define mavg as the average of the invariant masses of these two jets pair as mavg =12 (m1 + m2 ) with m1 and m2 are the invariant masses of two resonances. Discard eventswith large angular separation according to a resonant mass:
Rmin >

0.002 ⇥ (mavg /GeV

Rmin > +0.0013 ⇥ (mavg /GeV225) + 0.72

if mavg < 225GeV225) + 0.72

if mavg > 225GeV• Boosting the system of these two resonances (two jets pairs) to their centre-of-massframe. cos ✓⇤ is defined as the cosine of the angle between one of the resonance and thebeam-line in the centre-of-mass frame. The mass asymmetry A is defined as:
A=|m1 m2 |,m1 + m2(4.2)

Events are cut by requiring A < 0.05 and | cos ✓⇤ | < 0.3. This cut defines the inclusive
signal region (SR) selection.

This report
only use pT , ⌘,– 21 –of jets.

Let’s do something more.

Tagging the QCD-like “Dark jet”
BDT scoreBDT
ofscorehardest jet
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SIG

BKG

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fraction of eventshcol2
X pair
Entries
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Mean−0.3741
BKG
Std QCD
Dev 0.2918

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fraction of events

BDT score of2ndBDT
scorehardest jet
SIG

hcol2
Xpair
Entries
12000
Mean−0.3787
BKG
Std QCD
Dev 0.2738

BKG

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BDT score BDTof 3rdscore hardest jet

BDT score ofBDT4thscorehardest jet

Entries
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Mean−0.39
QCD BKG
Std Dev 0.2463

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BKG

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hcol2
EntriesX pair
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Mean−0.3884
BKG
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Std QCD
Dev

SIG

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fraction of events

fraction of events

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Score

hcol2
Xpair
SIG

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BDT score > 0.4 ==> Tagged as “Dark Jet”

Tagging the QCD-like “Dark jet”

BKG
MX = 500GeV MX = 700GeV MX = 900GeV
73% gluon jets.
Aftertraining
we obtain
have BDT scoresfor jets in t
Inclusiveselection
154,750360 a map to 82
22Require 1 dark jet
5,133
163
55
16.
Require 2 dark jets
162
49
16
6
Significance
2.38
0.78
0.29
Table 3. The number of signal events and background events after applying cut. Luminosity 36.7 fb 1
is chosen for the LHC. The background event number after inclusive selection have been normalized
10000
to the data observed in ATLAS report.

[fb]

and 73% gluon jets. After training we obtain a map to have BDT scores for jets in the final
1000
state.

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100[fb]1000

section of X pair at 13TeV LHC
Xprod.
pair crossXsection
95% CLfrom ATLAS report recast
Dark
jet limit
tagging
95% CLrecast
limit from Dark jet tagging
ATLAS

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M [GeV]section of XX
pair at 13TeV LHC
Xprod.
pair crossXsection
95% CLfrom ATLAS report recast
Dark
jet limit
tagging

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Conclusion and outlook
Jet is not only (⌘, , pT ) , by looking inside a jet you can get more. Jetsubstructure have been used in boosted object tagging and quark/gluon jetdiscrimination.
In this work, we indicate that if a dark sector can produce jet-like signal
at collider, then it is possible to show the property of dark sector by jetsubstructure directly.
Combination with cosmology will be more interesting:

Asymmetric Dark Matter: ⌦DM /⌦B ⇡ 5

Confinement in Dark sector may trigger SFOPT, thus:
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Phys. Rev. Lett. 115, no. 18, 181101 (2015)

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Thanks for your attention

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