Studying Gauginos in Supersymmetric Model

at Future 100 TeV pp Collider

Takeo Moroi (Tokyo)

Asai, Chigusa, Kaji, TM, Saito, Sawada, Tanaka, Terashi & Uno

arXiv:1901.10389 [hep-ph]

YUCHE 2019 @ Yonsei University (2019.02.26)

1. Introduction

SUSY particles may be quite heavy (even if they exist)

) [GeV]g~m(

1000 1200 1400 1600 1800 2000 2200

) [G

eV

]0 1χ∼

m(

500

1000

1500

2000

2500

3000

35000 lep. [1712.02332]

0

1χ∼q q→g~

3 b-jets [1711.01901]≥0

1χ∼b b→g~

2 lep. SS [1711.01901, 1706.03731]≥ 3 b-jets +≥0

1χ∼t t→g~

0 lep. + 1 lep. [1712.02332, 1708.08232]0

1χ∼Wq q→g~

2 lep. SS ≥ 7-11 jets + 1 lep. + ≥0

1χ∼WZq q→g~

[1708.02794, 1708.08232, 1706.03731]

3 lep. [1805.11381, 1706.03731]≥2 lep. OS SF + ν∼/l~

via 0

1χ∼)νν(ll/q q→g~

[SUSY-2016-30]τ 1 ≥ν∼/τ∼ via 0

1χ∼)νν/ντ/ττ(q q→g~

[1802.03158]γ 1 ≥0

1χ∼ via G

~/Z)γ(q q→g~

ATLAS Preliminary

-1=13 TeV, 36.1 fbs

All limits at 95% CL

July 2018

)0

1χ∼

)<m(g~m(

800 1000 1200 1400 1600 1800 2000 2200

[GeV]g~m

0

200

400

600

800

1000

1200

1400

1600

[G

eV

]10χ∼

m

CMS

10χ∼q q→g~,g~g~→pp July 2018

(13 TeV)-135.9 fb

Expected

Observed

)miss

T1704.07781 (H

)T21705.04650 (M

)T

α1802.02110 (

Do we have a chance to study SUSY particles at colliders?

⇒ Future circular colliders (FCCs) with ECM ∼ 100 TeV maybe an option

Today, I would like to discuss:

• FCC studies of pure gravity mediation model of SUSYbreaking based on anomaly mediation

• In particular, measurements of gaugino masses

Outline

1. Introduction

2. Model

3. Gauginos at FCCs

4. Gaugino Mass Determinations

5. Summary

2. Model

Mass spectrum of our interest

• Sfermion and Higgsino masses are of O(100) TeV

⇒ Heavy stops are good for mh ≃ 125 GeV

⇒ SUSY CP / flavor problems are relaxed

• Gaugino masses are loop suppressed, and are of O(1) TeV

⇒ Wino can be dark matter

⇒ Gauginos are primary targets of collider experiments

Such a mass spectrum is phenomenologically viable

⇒ What is the underlying theory?

Anomaly mediation + pure gravity mediation[Giudice, Luty, Murayama & Rattazzi; Randall & Sundrum; Ibe, TM & Yanagida;

Ibe & Yanagida; Arkani-Hamed et al.]

MSSM

Higgsinos

Sfermions

Gauginos

D = 6 Kahler interaction

Anomaly mediation

Giudice-MasieroSUSY breaking sector

(No singlet)

• The most general supergravity Lagrangian with Planck-suppressed interactions

• No singlet in SUSY breaking sector

• Scalar masses are of the order of the gravitino mass m3/2

Gaugino masses in the PGM model

M1 ≃g21

16π2

(11m3/2 + L

)

M2 ≃g22

16π2

(m3/2 + L

)

M3 ≃g23

16π2

(−3m3/2

)

L ≡ µ sin 2βm2

A

µ2 −m2A

lnµ2

m2A

• Wino (gaugino for SU(2)L) is likely to be the LSP

•∣∣∣∣∣∣10g

21

3g23mg̃ −

g21g22mW̃

∣∣∣∣∣∣<∼mB̃<∼

10g213g23

mg̃ +g21g22mW̃

Motivation 1: Wino LSP as dark matter

0

0.1

0.2

0.3

1 2 3Wino Mass (TeV)

Non−perturbativePertu

rbativ

e

Ω (

Win

o)

[Hisano, Matsumoto, Nagai, Saito & Senami] [Moroi, Nagai, Takimoto]

• Thermally produced Wino can be DM, if mW̃ ≃ 2.9 TeV

⇒ Can we test such a Wino at colliders?

• Non-thermal production of Wino DM is also possible

Motivation 2: Heavy stops are good for mh ≃ 125 GeV

m2h ≃ m2

Z cos2 2β +3m4

t

2π2v2

log m2t̃

m2t

+A2

t

m2t̃

1− A2t

12m2t̃

[Okada, Yamaguchi & Yanagida; Ellis, Ridolfi & Zwirner; Haber & Hempfling]

[TeV] S

M10

2103

10

[G

eV

]h

m

105

110

115

120

125

130

135

= 10βtan

= 5βtan

= 4βtan

= 3βtan

= 2.5βtan

⇒ The stop masses of O(10− 1000) TeV are suggested

Motivation 3: Cosmological gravitino problemWino Mass = 500 GeV Wino Mass = 1 TeV

He4

DD

He4He (ITG)4He (ITG)4

He / D3

ΩLSP

M2 = 1.0 TeV

M1 = 1.4 TeV

M3 = 3.0 TeV

M2 = 0.5 TeV

M1 = 0.9 TeV

M3 = 2.0 TeV

[Kawasaki, Kohri, TM, Takaesu]

⇒ With m3/2>∼ 10 TeV, the reheating temperature as high as

TR>∼ 109 GeV is possible

⇒ Simple thermal leptogenesis may work[Buchmuller, Di Bari & Plumacher; Giudice, Notari, Raidal, Riotto & Strumia]

Summary of Motivations

• Higgs mass of mh ≃ 125 GeV is easily realized

• Wino can be the LSP, which is a viable candidate of DM

• Cosmological gravitino problem is easily avoided

• Gauge coupling unification is OK

• SUSY CP / flavor problems may be avoided

Hierarchy between the SUSY scale and the EW scale is sizable

⇒ It’s better than the hierarchy between Planck scale andthe EW scale

3. Gauginos at FCCs

Let us consider

• How and how well we can determine gaugino masses

• Possibility to test the scenario

Sample points for MC studies (mW̃ < mB̃ < mg̃)

Point 1 Point 2

m3/2 [TeV] 250 302L [TeV] 800 756

mB̃ [TeV] 3.7 4.1mW̃ [TeV] 2.9 2.9mg̃ [TeV] 6.0 7.0

σ(pp → g̃g̃) [fb] 7.9 2.7

Gluino decay

g̃ → q̄qB̃, q̄qW̃

q~

g~

q

q

B~ q

~

g~

q

q

W~

Assumptions:

• Br(g̃ → qq̄W̃ ) = Br(g̃ → qq̄B̃) = 0.5

• Gluino decays into all the generations universally

Bino decay

B̃ → W∓W̃±, hW̃ 0

B~

W~

B~

h

W~

W

0

In the sample point of our choice:

• B̃ → W̃±W∓ dominates

• B̃ → ff̄W̃± is negligible

Charged Wino decay: W̃± → W̃ 0π±

• ∆mW̃ ≃ 165 MeV

• cτW̃±→W̃ 0π± ≃ 5.8 cmW~

π

W~ 0

Charged Wino may be identified as short high-pT track

• W̃±-tracks can be reconstructed by inner pixel detector

• Requiring W̃±-like tracks, SM background can be reduced

Long-lived W̃± at FCC-hh: case with pp → W̃±W̃±,0j

• Inner pixel detector has several layers at LT<∼ 10− 15 cm

[Saito, Sawada, Terashi & Asai 1901.02987]

2000− 1500− 1000− 500− 0 500 1000 1500 2000

z [mm]

0

50

100

150

200

250

300

350

400

450

500

Ra

diu

s [m

m]

2−10

1−10

1

10

210

310

410

510

610

Nu

mb

er

of ch

arg

ino

de

ca

ys

-1 = 100 TeV, 30 absFCC-hh,

Alternative layout (#3)

0 1 2 3 4 5

Chargino mass [TeV]

Higgsino

Wino

-1=100 TeV, 30 abs discovery, FCC-hh, σ5

-1=14 TeV, 3 absExpected exclusion, HL-LHC (ATLAS),

-1=14 TeV, 3 abs discovery, HL-LHC (ATLAS), σ5

-1=13 TeV, 36.1 fbsObserved exclusion, ATLAS,

Disappearing Track

• FCC-hh may cover the Wino mass up to 4− 5 TeV

• Sensitivity depends on the detector layout

The events of our interest: gluino pair production

• Multi-jets

• Charged Wino track(s), identified by the pixel detector

Beam pipe (IP)

Inner pixex detector

Outer tracker

ECAL

HCAL

Charged Wino

Jet

Expectation for the pixel detector

• 4th or 5th layer at LT ∼ 10− 15 cm

• Timing information is available: δt ∼ O(10 ps)

Timing information can be converted to the Wino velocity

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

0.25

δ β

/ β

β

δt = 50psec

δt = 40psec

δt = 30psec

δt = 20psec

δt = 10psec

⇒ δβ

β∼ (a few− 10) %× β(true)

4. Gaugino Mass Determinations

Flow-chart of our MC study

MadGraph5 for gluino pair production

ROOT

PYTHIA (decay and hadronization)

Delphes (detector simulation)

Analysis Code

Cuts

Invariant masses

Hemisphere analysis...

Wino velocity smearing

Wino info.

Requirements on signal events:

• Two W̃±-tracks with LT > 10 cm and |η| < 1.5

• p(miss)T > 1 TeV

p(miss)T : Missing pT evaluated only from jets

We assume:

• Charged Wino can be identified if LT > 10 cm

• Velocity resolution of W̃± is 6 %

• There is no error in the charged Wino direction

Wino track can also be used to eliminate SM backgrounds

⇒ Fake track rate ∼ O(10−5) per track

⇒ SM backgrounds are negligible

Measurement 1: Wino mass

• Wino velocity may be determined with timing information

• Momenta of Winos can be estimated using MET infor-mation (if two Wino tracks are observed)

⇔ Momentum is assumed to be carried away by jets andWinos

We determine Wino momenta by solving:

c1n⃗W̃1,T+ c2n⃗W̃2,T

= −p⃗miss ≡ −∑i:jets

p⃗i,T

p⃗W̃1= c1n⃗W̃1

p⃗W̃2= c2n⃗W̃2

Wino mass in terms of observables:

m(rec)

W̃=

1

βW̃±γW̃±|p⃗W̃±| ≡

√1− β2

W̃±

βW̃±|p⃗W̃±|

We use the events with:

• W̃± with LT > 10 cm and β(obs) < 0.8 for reconstruction

• 2nd W̃± track for background reduction

• No isolated lepton

Reconstructed Wino mass

histmwno1

Entries 250

Mean 2952

Std Dev 920.8

Mwno(Gauss) 54.8± 2911

σ 54.8± 695.8

A 2.2± 23.2

C 0.2527± 0.7339

0 2000 4000 6000

Wino Mass (GeV)

0

5

10

15

20

25

30-1#

/ 2

00

Ge

V / 1

0 a

bhistmwno1

Entries 250

Mean 2952

Std Dev 920.8

Mwno(Gauss) 54.8± 2911

σ 54.8± 695.8

A 2.2± 23.2

C 0.2527± 0.7339

Sample Point 1 histmwno1

Entries 103

Mean 3104

Std Dev 1056

Mwno(Gauss) 101.9± 3119

σ 105.3± 752.6

A 1.259± 7.987

C 0.2033± 0.4189

0 2000 4000 6000

Wino Mass (GeV)

0

2

4

6

8

10

-1#

/ 2

00

Ge

V / 1

0 a

b

histmwno1

Entries 103

Mean 3104

Std Dev 1056

Mwno(Gauss) 101.9± 3119

σ 105.3± 752.6

A 1.259± 7.987

C 0.2033± 0.4189

Sample Point 2

• True value: 2900 GeV

• Fit: Gaussian + constant

Reconstructed Wino mass: pp → W̃+W̃−j

• True Wino mass: 2900 GeV

• βW̃± < 0.8

• p(miss)T > 1 TeV

0 2000 4000 6000

Wino Mass (GeV)

0

1

2

3

4

5

-1#

/ 2

00

Ge

V / 3

0 a

b

Wino Mass (10cm & 10cm)

histmwno1

Entries 32

Mean 2769

Std Dev 658.1

Mwno(Gauss) 113.8± 2775

σ 80.5± 643.8

A 0.859± 3.966

C 02− 2.787e±10 − 6.106e

Wino Mass (10cm & 10cm)

⇒ δm(obs)

W̃≃ 130 GeV (with L = 30 ab−1)

Measurement 2: Bino mass

B~

W~

W : fat jet

: short high p trackT

• Wino momentum is known (if LT is long enough)

• W -jet may be identified as a fat jet

⇒ We use jets with mj ∼ mW

Reconstructed Bino mass (assuming mW̃ is known)

m(rec)

B̃=

√(mW̃uW̃± + pW )2 with uW̃± = (γW̃±, βW̃±γW̃±n⃗W̃±)

Jet mass distribution (for Point 1)

40 60 80 100 120 140 160 180 200Jet Mass (GeV)

0

2000

4000

6000

8000

10000

-1#

/ 2 G

eV /

10 a

b

We require:

• W̃± with LT > 10 cm and β(obs) < 0.9 for reconstruction

• Jet with 70 GeV < mj < 90 GeV

Reconstructed Bino mass (using true Wino mass)

histmbno1

Entries 581

Mean 4232

Std Dev 706.3

Mbno(Gauss) 9.3± 3628

σ 10.80± 70.38

A 2.90± 19.26

C 0.217± 3.917

3000 4000 5000 6000

Bino Mass (GeV)

0

5

10

15

20

25

30

-1#

/ 3

0 G

eV

/ 1

0 a

bhistmbno1

Entries 581

Mean 4232

Std Dev 706.3

Mbno(Gauss) 9.3± 3628

σ 10.80± 70.38

A 2.90± 19.26

C 0.217± 3.917

Sample Point 1 histmbno1

Entries 264

Mean 4353

Std Dev 701.9

Mbno(Gauss) 11.3± 4060

σ 10.80± 62.51

A 2.08± 10.51

C 0.137± 1.621

3000 4000 5000 6000

Bino Mass (GeV)

0

2

4

6

8

10

12

-1#

/ 3

0 G

eV

/ 1

0 a

b

histmbno1

Entries 264

Mean 4353

Std Dev 701.9

Mbno(Gauss) 11.3± 4060

σ 10.80± 62.51

A 2.08± 10.51

C 0.137± 1.621

Sample Point 2

• True value: 3660 GeV (Pt.1) / 4060 GeV (Pt.2)

• Fit: Gaussian + constant

Measurement 3: Gluino mass (with hemisphere analysis)

pp

j

j j

j

j

jj

W~

W~

Hemisphere 1

Hemisphere 2

Reconstructed gluino mass

m(rec)g̃ =

√P 2Hemisphere with PHemisphere ≡ PW̃± +

∑j∈H

pj

Hemisphere analysis with two observed Wino tracks

• Two charged Winos are assigned to different hemispheres:

W̃±A ∈ HA (A = 1, 2)

• For each high pT jet:ji ∈ H1: if d(pH1

, pji) < d(pH2, pji)

ji ∈ H2: if d(pH2, pji) < d(pH1

, pji)

Momentum of A-th hemisphere HA

pHA= pW̃±

A+

∑ji∈HA

pji

Distance function[See De Roeck (Editor), CMS Physics TDR]

d(pH , pj) =(EH − |pH | cos θHj)EH

(EH + Ej)2

We study the invariant mass of hemispheres containing W̃±

• Two long enough W̃± tracks

• No isolated lepton

• We use jets with |η| < 2

Hemisphere analysis with two charged Winos

• Momenta of Winos are determined using missing momen-tum information

• Each hemisphere contains one W̃± (and jets)

• Invariant mass of the hemisphere is regarded as (recon-structed) gluino mass

Reconstructed gluino mass (with true Wino mass):

histmgno1

Entries 756

Mean 6242

Std Dev 1782

Mgno(Gauss) 54.7± 5932

σ 49.3± 1224

A 2.17± 42.24

C 0.277± 1.687

5000 10000

Gluino Mass (GeV)

0

10

20

30

40

50

60

-1#

/ 2

00

Ge

V / 1

0 a

bhistmgno1

Entries 756

Mean 6242

Std Dev 1782

Mgno(Gauss) 54.7± 5932

σ 49.3± 1224

A 2.17± 42.24

C 0.277± 1.687

Sample Point 1 histmgno1

Entries 348

Mean 6883

Std Dev 1918

Mgno(Gauss) 100.0± 6631

σ 85.7± 1511

A 1.15± 15.54

C 0.2231± 0.7323

5000 10000

Gluino Mass (GeV)

0

5

10

15

20

25

-1#

/ 2

00

Ge

V / 1

0 a

b

histmgno1

Entries 348

Mean 6883

Std Dev 1918

Mgno(Gauss) 100.0± 6631

σ 85.7± 1511

A 1.15± 15.54

C 0.2231± 0.7323

Sample Point 2

• True value: 6000 GeV (Pt.1) / 7000 GeV (Pt.2)

• Fit: Gaussian + constant

5. Summary

Gaugino mass determinations may be possible

Sample Point 1 (with L = 10 ab−1):

δmB̃ δmW̃ δmg̃

δm(stat)

X̃8GeV 61GeV 59GeV

Due to δmW̃ 61GeV − 61GeV

Total 62GeV 61GeV 85GeV

⇒ Test of the model∣∣∣∣∣∣10g21

3g23mg̃ −

g21g22mW̃

∣∣∣∣∣∣<∼mB̃<∼

10g213g23

mg̃ +g21g22mW̃

Information about the mechanism of SUSY breaking

Sample Point 1

Sample Point 1

⇒ Determination of m3/2, |L|, · · ·⇒ Impact on cosmology

FCC-hh can have significant impact on BSM studies

• Discovery

• Measurements