Indirect Studies of Electroweakly Interacting Particles at 100 TeV …seminar/pdf_2019_zenki/... · 2019-07-24 · Indirect Studies of Electroweakly Interacting Particles at 100 TeV

Indirect Studies of

Electroweakly Interacting Particles

at 100 TeV Hadron Colliders

So Chigusa

Department of Physics, University of Tokyo

July 23, Seminar @ Osaka University

SC, Yohei Ema, and Takeo MoroiPLB 789 (2019) 106 [arXiv:1810.07349]

Tomohiro Abe, SC, Yohei Ema, and Takeo Moroi(submitted to PRD) [arXiv:1904.11162]

Introduction EWIMP effect EWIMP detection EWIMP properties Conclusion

ElectroWeakly Interacting Massive Particle (EWIMP)

EWIMP : massive particle with non-zero weak charges

Good dark matter (DM) candidate · · · “WIMP miracle”

MSSM

Lightest SUSY particle

Higgsino · · · 1 TeV

e.g. “natural SUSY”H. Baer, et al. [1203.5539], etc.

Wino · · · 3 TeV

e.g. “Mini-Split”A. Arvanitaki, et al. [1210.0555], etc.

Minimal Dark Matter

Large weak SU(2)L charge

Suppressed interaction with SM

5-plet fermion · · · 10 TeV

(7-plet scalar)

M. Cirelli, et al. [hep-ph/0512090], etc.

There are many search methods : BUT Higgsino is difficult2 / 25


Indirect detection of DM

Look for EWIMP DM annihilation into SM particles in the sky

Wino Dark Matter Mass (GeV)210 310

)-1

s3v

(cm

σ

-2610

-2510

-2410

-2310

-2210 Expectation

4 years observation

SculptorSextans

Draco Ursa Minor

Combined (15 dSphs)

wino cross section

B. Bhattacherjee+ ’14

Wino (and MDM)

Already exclude mW in sub-TeV region and ∼ 2 TeV

Higgsino

Too small cross section to detect3 / 25


Direct detection of DM

Look for recoiled nuclei by collision between EWIMP DM

101 102 103 104

WIMP mass [GeV/c2]

10−49

10−48

10−47

10−46

10−45

10−44

10−43

WIM

P-nu

cleo

nσ S

I[c

m2 ] XENON100 (2016)

LUX (2017)

PandaX (2017)

XENON1T (2017)

XENON1T (1 t year, this work)

XENONnT (20 t year Projection)

Billard 2013, neutrino discovery limit

XENON1T ’18

��

��

��

��

��

��

��

��

��

��

��

J. Hisano+ ’15Wino & MDM

Region of future interest

Higgsino

Small cross section below neutrino bacground4 / 25


Production at collider

Difficulty : event recognition

disappearing track search

⇔ requires long life time, small BG

ATLAS Simulation

π+

χ01

~χ+

1~︸︷︷︸

SCT 30∼52 cm

︸︷︷︸pixel 3∼12 cm

ATLAS [1712.02118]

CMS [1804.07321]

100 200 300 400 500 600 700 [GeV]±

1χ∼m

0.01

0.020.030.04

0.1

0.20.30.4

1

2

34

10

[ns]

± 1χ∼τ

)theory

σ1 ±Observed 95% CL limit ( )expσ1 ±Expected 95% CL limit (

, EW prod. Obs.)-1ATLAS (8 TeV, 20.3 fbTheory (Phys. Lett. B721 (2013) 252)ALEPH (Phys. Lett. B533 (2002) 223)

ATLAS-1=13TeV, 36.1 fbs

> 0µ = 5, βtan production

±

1χ∼±

1χ∼,

0

1χ∼ ±

1χ∼

cτW ∼ 6 cm, mW < 460 GeV excluded

cτH ∼ 1 cm, mH < 152 GeV excluded for pure Higgsino

Higgsino mixed with gaugino : cτ ≪ O(cm)

mono-X search : recognize events with initial state radiationno bound on Higgsino @ LHC H. Baer, et al. [1401.1162]

5 / 25


Invitation : indirect study using colliders

Today I introduce

Indirect search with ℓℓ/ℓν production @ 100TeV collider

qa

qb

�

�/ν

χ0, χ±

γ, Z,W

Features

Independent of EWIMP lifetime ⇒ Good for Higgsino

Clean events : 2 energetic leptons (+ jet)

⇒ Signal shape as a func. of lepton inv. mass is usable

to control systematic errors

to determine EWIMP mass and charges6 / 25


Table of contents

1 Introduction

2 EWIMP effects on the processes

3 EWIMP detection and statistical method

4 Determination of EWIMP properties

5 Conclusion

7 / 25


Table of contents

1 Introduction




5 Conclusion

7 / 25


Vacuum polarization effect from EWIMP

Assume all new physics except EWIMPs are decoupled

χ0, χ±

γ, Z,W γ, Z,W

finiteq

∝ i(q2gµν − qµqν)f

(q2

m2

)

f is a loop function

f(x) =

1

16π2

∫ 1

0dy y(1− y) ln(1− y(1− y)x− i0) (Fermion)

1

16π2

∫ 1

0dy (1− 2y)2 ln(1− y(1− y)x− i0) (Scalar)

EWIMP effects are parametrized by parameters C1 and C2

Leff = LSM + C1g′2Bµνf

(− ∂2

m2

)Bµν + C2g

2W aµνf

(−D2

m2

)W aµν

8 / 25


Group theoretical factors C1, C2

SU(2)L n-plet with U(1)Y charge Y contributes

C1 =κ

8nY 2, C2 =

κ

96(n3 − n),

κ =

16 (Dirac fermion)

8 (Weyl or Majorana fermion)

2 (complex scalar)

1 (real scalar)

For popular EWIMPs

Higgsino Wino 5-fermion (Y = 0) 7-scalar (Y = 0)

C1 1 0 0 0

C2 1 2 10 7/29 / 25


Neutral current (NC) / Charged current (CC)

Parton level scattering amplitude for qaqb → ℓℓ (NC) / ℓν (CC)

M =

qa

qb

�

�/ν

γ, Z,W

q︸︷︷︸MSM

+

qa

qb

�

�/ν

χ0, χ±

γ, Z,W

︸︷︷︸MEWIMP

+ · · ·

Differential cross section for fixed q2 ≡ s′

|M|2 = |MSM|2 + 2ℜ [MSMM∗EWIMP] + · · ·

dσab

d√s′

≡dσab

SM

d√s′

+dσab

EWIMP

d√s′

+ · · ·

Define the size of correction

δabσ (√s′) ≡

dσabEWIMP/d

√s′

dσabSM/d

√s′ 10 / 25


Cross section correction from EWIMPs

Plot of δabσ with m = 1 TeV EWIMPs

1000 2000 3000 4000 5000 6000 7000√s′ [GeV]

−2.0

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

δ σ[%

]

peak at√s′ = 2m

HiggsinoWino5-plet scalar

Peak structure at√s′ = 2m plays an important role

“threshold effect”

χ0, χ±

γ, Z,W γ, Z,W

11 / 25


Event generation

√s = 100TeV, L = 30 ab−1 for SM, binned by collision energy

MadGraph5 aMC@NLO : hard process @ NLO

Pythia8 : parton shower (PS), hadronization

Delphes3 : detector simulation

pp → �+�− + PS pp → �+�−(NLO) + PS pp → �+�−j + PS

Delphes

Detector

Simul.

1000 2000 3000 4000 5000Invariant mass [GeV]

102

103

104

105

106

107

108

Nevents

e + e − invariant mass distribution (30ab−1)

EWIMP effect is included by rescaling

NSM+EWIMP =

NSM∑events

[1 + δabσ (

√s′)

]12 / 25


Table of contents

1 Introduction




5 Conclusion

12 / 25


Statistical treatment (optimistic)

Consider number of events in i-th bin of collision energy

− x = {xi} : prediction for SM (Now use NSM)

− x = {xi} : experimental data (Now use NSM+EWIMP instead)

Compare signal (S) with statistical error (δB)

Si

δBi=

|xi − xi|√xi

≃ |xi − xi|√xi

Following test statistic tests validity of SM

q0 ≡∑i:bin

S2i

δB2i

q0 obeys a χ2 distribution within SM13 / 25


Idea of fitting based analysis

Systematic errors may modify theoretical predictiondσSM

d√s′, xi

luminosity error

beam energy error

choice of renormalization scale

choice of factorization scale

choice of PDF

etc · · ·mchar

Cross section

dσSM

dmchar

dσSM

dmcharfsys(θ,mchar)

Idea of fitting based analysis

Absorb above errors into additional parameters θ

(Similar to “side band analysis”)

14 / 25


Fitting systematic errors

− y = {yi} : prediction for SM

− y = {yi} : data with one of errors included

luminosity error (±5%)

beam energy error (±1%)

choice of renormalization scale (2Q,Q/2)

choice of factorization scale (2Q,Q/2)

choice of PDF

By introducing fitting function fsys,i(θ), fitting procedure is

yi(θ) ≡ yifsys,i(θ)

χ2 = minθ

∑i:bin

(yi − yi(θ))2

yi(θ)

χ2 checks if above systematic errors can be absorbed into θ

15 / 25


Fitting based analysis

Consider five parameters function

fsys,i(θ) = eθ1(1 + θ2pi)p(θ3+θ4 ln pi+θ5 ln

2 pi)i

pi = 2√

s′i/√s

CDF collaboration ’08

Systematic errors are fitted well (χ2/d.o.f. < 1)

Define new theoretical prediction xi(θ)

xi(θ) ≡ xi fsys,i(θ) ; xi(0) = xi

Test statistic q0 that obeys χ2 distribution within SM

q0 ∼ minθ

∑i:bin

(xi − xi(θ))2

xi(θ)

16 / 25


Detection reach

500 1000 1500 2000 2500 3000mass [GeV]

0

1

2

3

4

5

6

√ q 0Integrated luminosity 30ab−1

Higgsino (w/o fit)

Wino (w/o fit)

Higgsino (w/ fit)

Wino (w/ fit)

Higgsino Wino

5σ (w/ fit) 760 GeV 1.4 TeV

5σ (w/o fit) 1.7 TeV 2.5 TeV

It is important tounderstand

systematic errors

17 / 25


Detection reach

500 1000 1500 2000 2500 3000mass [GeV]

0

1

2

3

4

5

6


Higgsino (w/o fit)

Wino (w/o fit)

Higgsino (w/ fit)

Wino (w/ fit)

Higgsino (Controlled)

Wino (Controlled)

Higgsino Wino

5σ (w/ fit) 760 GeV 1.4 TeV

5σ (contr.) 850 GeV 1.6 TeV

5σ (w/o fit) 1.7 TeV 2.5 TeV

It is important tounderstand

systematic errors

17 / 25


Fit result of systematic errors and σ

Best fit values for ℓℓ (NC)

Sources of systematic errors θ1 θ2 θ3 θ4 θ5Luminosity: ±5% 0.07 0 0 0 0

Beam energy: ±1% negligible

Renormalization scale: 2Q,Q/2 0.6 0.9 0.4 0.08 0.006

Factorization scale: 2Q,Q/2 0.5 0.7 0.3 0.07 0.007

PDF choice 0.4 0.7 0.3 0.06 0.004

Each value: possible size of |θ| within SM due to errors

Let’s call them as “σ” · · · standard deviation of |θ|

Sources of systematic errors σ1 σ2 σ3 σ4 σ5Combined 0.9 1.3 0.5 0.1 0.01

18 / 25


Profile likelihood (controlled) method

We assume θ are distributed according to Gaussian

distributions with standard deviations σ

Definition of test statistic q0

q0 ≡ minθ

∑i:bin

(xi − xi(θ))2

xi(θ)︸︷︷︸try to fit data

+

5∑α=1

θ2ασ2α︸︷︷︸

control size of θ

q0 obeys χ2(1) within SM Wilk ’38

19 / 25


Detection reach

500 1000 1500 2000 2500 3000mass [GeV]

0

1

2

3

4

5

6


Higgsino (σ→0)

Wino (σ→0)

Higgsino (σ→∞)

Wino (σ→∞)

Higgsino (Controlled)

Wino (Controlled)

Better understanding of systematic errors will push up the

detection reach : temporally 850GeV at 5σ for Higgsino

20 / 25


Comparison with other approaches

Higgsino production at√s = 100 TeV, L = 30 ab−1

disappearing track search

(for pure Higgsino cτH ∼ 1 cm)

0 500 1000 1500

Higgsino Mass m [GeV]

0

1

2

3

4

5

6

S/B

5

95%

20% bkg.

500% bkg.

14 TeV, 3 ab 1

27 TeV, 15 ab 1

100 TeV, 30 ab 1

indirect study

Probe mH < 850GeV (1.7TeV)

at 5σ (95% C.L.) level

mono-jet search

(for any cτH)

0 500 1000 1500 2000

Higgsino Mass m [GeV]

0

1

2

3

4

5

6

S/B

5

95%

1% syst.

2% syst.

14 TeV, 3 ab 1

27 TeV, 15 ab 1

100 TeV, 30 ab 1

T. Han+ ’18

Our method provides

− comparable reach for pure Higgsino

− better for short lifetime Higgsino

21 / 25


Which bin contributes a lot?

Plot contribution to q0 from each bin

1000 2000 3000 4000 5000 6000 7000√s ′ [GeV]

0

1

2

3

4

5

6

7

contr

ibuti

on t

o q

0

absorbed into θ

peak still contributes

1TeV Higgsino (stat.)

1TeV Higgsino

1000 2000 3000 4000 5000 6000 7000√s′ [GeV]

−2.0

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

δ σ[%

]

peak at√s′ = 2m


Peak structure at√s′ ∼ 2m is not absorbed into θ.

It is very important for detection.

22 / 25


Table of contents

1 Introduction




5 Conclusion

22 / 25


Peak structure revisited

Leff = LSM + C1g′2Bµνf

(− ∂2

m2

)Bµν + C2g

2W aµνf

(−D2

m2

)W aµν

1000 2000 3000 4000 5000 6000 7000√s′ [GeV]

−1.5

−1.0

−0.5

0.0

0.5

1.0δ σ

[%]

peak height⇔ C1, C2

peak position⇔ m

peak at√s′ = 2m

ℓℓ (NC) depends on C1, C2

ℓν (CC) depends only on C2

We can extract m,C1, C2

23 / 25


Determination of (m,C1, C2) for 1.1TeV Higgsino

2 0 2 4 6 8 10 12C1

1

0

1

2

3

4

C2

30

3Maj

2Maj

20 21/2 21

m= 1. 1TeV

NC

CC

Combined

Solid (Dotted) : 2σ (1σ)

nY : SU(2)L n-plet

with U(1)Y charge Y

− Only doublet is allowed

− m ∼ 1.1TeV±100GeV

2 0 2 4 6 8 10 12C1

900

1000

1100

1200

1300

1400

1500

m [

GeV

]

21

C2 = 1

NC

CC

Combined

1 0 1 2 3 4C2

900

1000

1100

1200

1300

1400

1500

m [

GeV

]

C1 = 1

NC

CC

Combined

24 / 25


Conclusion

I have introduced a way for probing EWIMPs with Precise

measurement at 100 TeV colliders

I also introduced fitting based analysis, where systematic errors

are absorbed into the fit function

All the errors we have considered are fitted well

Strong discovery potential for short lifetime Higgsino

850 GeV (1.7 TeV) at 5σ (95% C.L.)

The signal shape of the EWIMP effect can also be used to

determine the EWIMP properties (mass, charge)

Peak at√s′ = 2m is important for all the analysis

25 / 25

Backup slides

25 / 25

Higgsino phenomenology

Chargino neutralino mass difference H. Fukuda, et al. [1703.09675]

∆m+ = ∆mrad +∆mtree

∆mrad ≃ 1

2α2mZs

2W

(1− 3mZ

2πmχ±

)≃ 355MeV,

∆mtree ≃v2

8|µ|[|X|∆X + sin 2β ℜ(Y )] ∼ 1GeV

∣∣∣∣ µ

Mi

∣∣∣∣ ,with X,Y = µ∗(g21/M1 ± g22/M2), ∆X =

√1− sin2 θX sin2 2β

cτ ≃ 0.7 cm

[(∆m+

340MeV

)3√

1− m2π

∆m2+

]−1

26 / 25

Future prospects for Higgsino at indirect detection

B. Bhattacherjee, et al. [1405.4914] R. Krall, et al. [1705.04843]

Wino Dark Matter Mass (GeV)310

)-1

s3v

(cm

σ

-2610

-2510

-2410

-2310

-2210Combined

Fermi-LAT (15 yrs)+ GAMMA-400 (10 yrs)

) = 0.1All J

10 (logδ

100 200 500 1000 20001

510

50100

5001000

mχ [GeV]

<σv>

[10-26cm

3 /s]

Continuum Gamma Rays: χ0χ0→WW+ZZ

Winos

Higgsinos

HESS GC

Fermi Dwarfs

27 / 25

Studies of indirect search at collider

Applicable to Higgsino independent of life time

qa

qb

�

�/ν

χ0, χ±

γ, Z,W

1

2

3

4

5

6

7

8

9

10

200 400 600 800 1000 1200

n

Mass [GeV]

“Higgsino”Wino

5plet MDM

obsereved 36 fb−1

expeceted 3 ab−1

δmW (1σ) ILC250 (0.2%sys.)

S. Matsumoto, et al.

Previous analysis:

D. S. M. Alves, et al. [1410.6810] @ LHC, 100 TeV

C. Gross, et al. [1602.03877] @ LHC

M. Farina, et al. [1609.08157] @ LHC

K. Harigaya, et al. [1504.03402] @ lepton collider

S. Matsumoto, et al. [1711.05449] @ HL-LHC

Up to HL-LHC era

Only a part of allowed region probed

mW < 300 GeV ≪ 3 TeV

mH < 150 GeV ≪ 1 TeV

28 / 25

From parton-level to proton cross section

Proton cross section at√s = 100 TeV can be obtained using

dLab

dmℓℓ≡ 1

s

∫ 1

0dx1dx2 fa(x1)fb(x2)δ(

m2ℓℓ

s− x1x2)

fa(x) : parton distribution function (PDF) for a

dσ

dmℓℓ=

∑a,b

dLab

dmℓℓ

dσab

dmℓℓ

29 / 25

CC process and transverse mass

For ℓν (CC), neutrino is missing

We can use pT,miss and transverse mass mT instead:

m2T ≡ 2pT,ℓ pT,miss(1− cosϕT,ℓ,miss)

(mT ≃√s′ if pℓ,z, pν,z are small)

beam axis

transverse plane

pT,miss

pT,l

ΦT,l,miss

0.0 0.5 1.0 1.5 2.0Ratio mT/m`ν

0

500

1000

1500

2000

2500

3000

3500

4000

4500

# o

f events

peak atmT =m`ν

mT >m`ν :detector effect

mT distribution in unit of m`ν

30 / 25

δσ as function of mT

ℓν (CC) events are binned by mT

1000 2000 3000 4000 5000 6000 7000√s′ [GeV]

−2.0

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

δ σ[%

]

peak at√s′ = 2m


1000 2000 3000 4000 5000 6000 7000mT [GeV]

−2.0

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

∆N/N

[%]

peak structure remains


Peak structure exists as a function of mT

31 / 25

Event generation in detail

EWIMP effect can be included with δabσ (mℓℓ)

Number of events xi in i-th bin mminℓℓ < mℓℓ < mmax

ℓℓ

For SM, xi =∑

mminℓℓ <mobs

ℓℓ <mmaxℓℓ

1

For SM + EWIMP, xi =∑

mminℓℓ <mobs

ℓℓ <mmaxℓℓ

[1 + δabσ (mtrue

ℓℓ )]

Each event in SM data set has {mobsℓℓ ,mtrue

ℓℓ , a, b}

mobsℓℓ : observed mℓℓ from Delphes3 output

mtrueℓℓ : true mℓℓ from MadGraph5 aMC@NLO output

a, b : initial partons from MadGraph5 aMC@NLO output

∗ Detector effect causes mobsℓℓ = mtrue

ℓℓ

32 / 25

Statistical treatment in our analysis

xi(µ) ≡∑events

[1 + µ δabσ (mchar)

]; xi(θ, µ) ≡ xi(µ)fi(θ)

Definition of q0 in fitting based analysis Wilk ’38

q0 = −2 lnL(x; ˆθ, µ = 0)

L(x; θ, µ)∼ χ2(1)

L(x;θ, µ) ≡∏i

exp

[−(xi − xi(θ, µ))

2

2xi(θ, µ)

]∏α

exp

[− θ2α2σ2

α

]− ˆθ maximizes numerator L(x; ˆθ, µ = 0)

− {θ, µ} maximizes denominator L(x; θ, µ)

Within our analysis, x = xi(µ = 1) and

{θ, µ} = {0, 1} with L(x; θ, µ) = 1

33 / 25

Disappearing track search of Wino

0 1000 2000 3000 4000 5000 6000 7000

Wino Mass m [GeV]

0

1

2

3

4

5

6S

/B

5

95%

20% bkg.

500% bkg.

14 TeV, 3 ab 1

27 TeV, 15 ab 1

100 TeV, 30 ab 1

34 / 25

Other sources of systematic errors

Smooth correction seems to be well absorbed into θ : Then,

estimation error in detector effect

may also be absorbed : our method can be applied!!

higher order loop effect within SM

background process

in principle possible to take account of (future task)

Yet remaining sources:

pile-up effect

underlying event

negligible thanks to clean signal with two energetic leptons35 / 25

Comparison of several statistical treatments

500 1000 1500 2000 2500 3000mass [GeV]

0

1

2

3

4

5

6

√ q 0

Higgsino (Gaussian)

Higgsino (Top-hat)

Higgsino (6 params)

Wino (Gaussian)

Wino (Top-hat)

Wino (6 params)

36 / 25

Statistical treatment for properties determination

Consider SM+EWIMP and focus on (m,C1, C2) dependence

xi(m,C1, C2) ≡∑events

[1 + δabσ (m,C1, C2;

√s′)

]Assume x for 1.1TeV Higgsino as example:

xi = xi(m = 1.1TeV, C1 = 1, C2 = 1)Although still 3.5σ hint we try...

q(m,C1, C2) ≡ minθ

[∑i:bin

(xi − xi(θ,m,C1, C2))2

xi(θ,m,C1, C2)+

5∑α=1

θ2ασ2α

]

q tests validity of model (m,C1, C2)

37 / 25

Statistical treatment for spin determination

Next, compare with scalar EWIMP effect

xi(m,C1, C2) ≡∑events

[1 + δ(scalar)σ (m,C1, C2;

√s′)

]

1000 2000 3000 4000 5000 6000 7000√s′ [GeV]

−1.5

−1.0

−0.5

0.0

0.5

1.0

δ σ[%

]

shape of peak⇔ EWIMP spin

peak at√s′ = 2m

Higgsino5-plet scalar

Again assume 1.1TeV Higgsino as example:38 / 25

Determination of spin

2 0 2 4 6 8 10 12C1

750

800

850

900

950

1000

1050

1100

1150

1200

m [

GeV

]

C2 = 1. 2

NC

CC

Combined

0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0C2

750

800

850

900

950

1000

1050

1100

1150

1200

m [

GeV

]

C1 = 0

NC

CC

Combined

2 0 2 4 6 8 10 12C1

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

C2

1. 1TeV Higgsino & 920GeV scalar

NC

CC

Combined

Solid (Dotted) : 2σ (1σ)

− Best fit:

(m,C1, C2) = (920GeV, 0, 1.2)

− Bosonic EWIMP possibility

is still remaining39 / 25

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Indirect Studies of Electroweakly Interacting Particles at 100 TeV …seminar/pdf_2019_zenki/... · 2019-07-24 · Indirect Studies of Electroweakly Interacting Particles at 100 TeV