LSPがGravitinoになるモデルと LHCでの物理
Koichi Hamaguchi (Tokyo U.)@ LHCが切り拓く新しい素粒子物理学, Mar. 2008

Plan
Gravitino と SUSY models
Gravitino と Cosmology
Gravitino LSP と LHC での物理

Gravitino と SUSY models

Standard Model(1) solves the naturalness problem(2) leads to coupling unification(3) has dark matter candidate

1

∪

Super

1string∪Super

1stringElectroweak Symmetry と比べてみるElectroweak Symmetry と比べてみるElectroweak Symmetry と比べてみる

gauge boson massmV = g !ϕ"gauge couplingHiggs VEVgravitino massmGe = √

13MP"F #SUGRA coupling

SUSY breaking VEVGravitino
Gravitino Interaction: extremely weak111∼
suppressed by ∼(or ∼)F
MP mGeMP1"F # : model dependent
Gravitino Mass mGe = √3MP!

100TeV

106 GeV107 GeV108 GeV109 GeV 1010 GeV 1011 GeV!F "mGeeV

keV

MeV

GeV

GMSB

Gravitino が LSP になるモデル

TeV

AMSB,
̃gMSB
mMSB
gravity-MSB(mSUGRA 含む)

NLSP (Next-to-Lightest SUSY Particle)
In Gravitino LSP scenario, the NLSP decay
always include the gravitino.
Interaction∼1F∼1MP mGeNLSP (Next-to-Lightest SUSY Particle)
In Gravitino LSP scenario, the NLSP decay
always include the gravitino.
For a slepton NLSP,.....
Γ(τ̃ → G̃τ ) "m5τ̃
248πm2G̃ Mpl!

m2G̃
1− 2mτ̃

Lifetime (decay length) of NLSP staumG̃ττ̃cττ̃eV"4e.g., for mτ̃ = 100 GeV ,MeVGeVkeV
ps

nsμs

mmmkm

mssecdayGravitino と Cosmology

Gravitino と Cosmology

初期宇宙論的には寿命が１秒を超えたら “Long-lived”

どこかでDM生成

１秒より前のシナリオは色々工夫出来る
どこかでDM生成

１秒より後は余計な事しちゃダメGravitino Problems(gravitinoがLSPの場合)

Sorry, I drop references.

Gravitino Problems
stable (LSP) gravitino

unstable gravitino

mGe / GeV(NOTE: precise line positions in this figure may be out-dated.)

Sorry, I drop references.

Gravitino Problems
stable (LSP) gravitino

unstable gravitino
BBN

allowe dmGe / GeV(NOTE: precise line positions in this figure may be out-dated.)

Sorry, I drop references.

Gravitino Problems
stable (LSP) gravitino

unstable gravitino
BBN

LSP fromgravitino

allowe dmGe / GeV(NOTE: precise line positions in this figure may be out-dated.)

Sorry, I drop references.

Gravitino Problems
stable (LSP) gravitino
overclosure

unstable gravitino
BBNdewallo
mGe / GeVLSP fromgravitino

allowe d(NOTE: precise line positions in this figure may be out-dated.)

Sorry, I drop references.

Gravitino Problems
warm
stable (LSP) gravitinoDM

allowe doverclosure

unstable gravitino
BBNdewallo

16 eV

mGe / GeVLSP from
gravitinoallowe d(NOTE: precise line positions in this figure may be out-dated.)

Sorry, I drop references.

Gravitino Problems
NLSP
warmstable (LSP) gravitino
BBNDM

allowe doverclosure

unstable gravitino
BBNdewallo

16 eV

mGe / GeVLSP fromgravitino

allowe d(NOTE: precise line positions in this figure may be out-dated.)

Sorry, I drop references.

Gravitino Problems

allowe dstable (LSP) gravitino

unstable gravitino

dew
allo

16 eV

mGe / GeV

allowe d(NOTE: precise line positions in this figure may be out-dated.)

Sorry, I drop references.

Gravitino Problems
ここホントはstable (LSP) gravitino
unstable gravitino

allowe d

6TeVくらいdew
allo

16 eV

mGe / GeV

thermalleptogenesis

allowe d(NOTE: precise line positions in this figure may be out-dated.)

Sorry, I drop references.

Gravitino Problems

allowe dstable (LSP) gravitino

unstable gravitino
thermalleptogenesis

dew
allo

16 eV

mGe / GeV

allowe d(NOTE: precise line positions in this figure may be out-dated.)

Sorry, I drop references.

Gravitino Problems

allowe dstable (LSP) gravitino

unstable gravitino
thermalleptogenesisdewallo

16 eV

mGe / GeV

nonthermal
leptogenesis

allowe d(NOTE: precise line positions in this figure may be out-dated.)

Sorry, I drop references.

Gravitino Problems

allowe dstable (LSP) gravitino

unstable gravitino
thermalleptogenesis

dew
allo

nonthermal
leptogenesis

allowe d Affleck Dine

baryogenesis

16 eV

mGe / GeV(NOTE: precise line positions in this figure may be out-dated.)

Sorry, I drop references.

Gravitino Problems

allowe dstable (LSP) gravitino

unstable gravitino
thermalleptogenesis

In addition, direct production of gravitinos
from inflaton ➜ exclude many inflation models nonthermaldew
allo

leptogenesis

allowe d Affleck Dine

baryogenesis

16 eV

mGe / GeV(NOTE: precise line positions in this figure may be out-dated.)

Sorry, I drop references.

Gravitino Problems

allowe dstable (LSP) gravitino

unstable gravitino
thermalleptogenesis

In addition, direct production of gravitinos
from inflaton ➜ exclude many inflation models nonthermal

dew
allo

Fig. from Endo,leptogenesis
Takahashi,Yanagida, ’07

allowe d Affleck Dine

baryogenesis

16 eV

mGe / GeV(NOTE: precise line positions in this figure may be out-dated.)

Sorry, I drop references.

Gravitino Problems

allowe dstable (LSP) gravitino

unstable gravitino
thermalleptogenesis

In addition, direct production of gravitinos
from inflaton ➜ exclude many inflation models nonthermaldew
alloFig. from Endo,leptogenesis
Takahashi,
Yanagida, ’07

allowe d Affleck Dine

baryogenesis

16 eV

mGe / GeV

実は、gravity-MSB (mSUGRA含む）は(NOTE:precise line positions in this figure may be out-dated.)
宇宙論的には非常に苦しい！

Sorry, I drop references.

gravitino と cosmology• 実は、gravity-MSB（mSUGRA 含む）は宇宙論的には非常に苦しい。

• naive な宇宙シナリオを考えると、

mG > 10 TeV (AMSB or mMSB) と,
mG < 10 eV /mG ˜ 1GeV（GMSB) が楽。

• ただし他の領域も exclude されているワケではなくinflation model を工夫して、再加熱温度も下げてbaryogenesisも低温のを選んで・・・ と１秒より前の初期宇宙シナリオを工夫（無茶）すれば何とかなります。

• 逆にLHC で LSP (gravitino or not) やNLSP の性質が分かれば、宇宙論に強い制限！

Gravitino LSP と LHC での物理と NLSP
コライダー的には寿命がcτ= O(1mm - 10m) なら(?) “Long-lived”
cτ > O(100m) なら “stable”

NLSP lifetime
Γ(τ̃ → G̃τ ) "m5τ̃
248πm2G̃ Mpl!

1−m2G̃
m2τ̃

Lifetime (decay length) of NLSP staumG̃ττ̃cττ̃eV"4e.g., for mτ̃ = 100 GeV ,MeV
GeV

keV
psnsμsmmmkm

ms

secdayNLSP lifetime
Γ(τ̃ → G̃τ ) "m5τ̃
248πm2G̃ Mpl!

1−m2G̃
m2τ̃

"4Lifetime (decay length) of NLSP staumG̃eVττ̃cττ̃
promptdecaye.g., for mτ̃ = 100 GeV ,MeVGeV

keV
psnsμsmmmkmDetector
Size

mssec

day

No In-flight decay,
but maybe accessible.

NLSP lifetime
Γ(τ̃ → G̃τ ) "m5τ̃
248πm2G̃ Mpl!

1−m2G̃
m2τ̃

"4Lifetime (decay length) of NLSP staumG̃

eVe.g., for mτ̃ = 100 GeV ,MeVGeVkeV

NLSPの寿命を測る事が重要なターゲット

ττ̃

ps

ns

μs

ms

F == SUSY breakingmmm scalekmcττ̃sec√day

3 mGe MP を測る事(= gravitino mass mGを測る事)
eDetector
promptNo In-flight decay,
Sizedecay
but maybe accessible.

GravitinoandNLSP atthe LHC!
G

τ! NLSPχ!0 NLSP 2γ + ET,miss!
G!
G
NLSP

NLSP

“kink” incharged track
non-pointing
photoncharged track

the same asχ!0 LSP signal....

Gravitino
andNLSP at
the LHC!
G

τ! NLSPχ!0 NLSP 2γ + ET,miss!
G!
G
NLSP

NLSP

“kink” incharged track

charged track

寿命測れる

non-pointing
photonthe same asχ!0 LSP signal....

Gravitino
andNLSP at
the LHC!
G!
G!
G
NLSP

NLSP

次のトークで？

τ! NLSP
χ!0 NLSP 2γ + ET,miss“kink” incharged track

charged track寿命測れるnon-pointing
photonthe same asχ!0 LSP signal....

Gravitino
and
NLSP atthe LHC!
G!
G!
GNLSP

NLSP

次のトークで？

τ! NLSPχ!0 NLSP 2γ + ET,miss“kink” incharged track

charged track

寿命測れる

non-pointing
photon
寿命測れる

the same asχ!0 LSP signal....

Gravitino
and
NLSP atthe LHC!
G!
G!
GNLSP

NLSP

次のトークで？

τ! NLSP“kink” incharged track

charged track

Kawagoe, Kobayashi, Nojiri, Ochi, ’03
寿命測れるχ
!0 NLSP 2γ + ET,missnon-pointing
photon
寿命測れる

the same as
χ!0 LSP signal....

Gravitino
and
NLSP atthe LHC!
G!
G!
GNLSP

NLSP

次のトークで？

τ! NLSPχ!0 NLSP 2γ + ET,miss“kink” incharged track

charged track

寿命測れる

non-pointing
photon
寿命測れる

the same asχ!0 LSP signal....

Gravitino
and
NLSP atthe LHC!
G!
G!
G
NLSP

NLSP

次のトークで？

τ! NLSP“kink” incharged track
寿命測れる？!

χ!0 NLSP 2γ + ET,misscharged track

寿命測れる

non-pointing
photon
寿命測れる

the same asχ!0 LSP signal....

Gravitino
andNLSP at
the LHC!
G!
G!
GNLSPNLSP

次のトークで？
白井さんのτ! NLSP

トークで寿命測れる？!

χ!0 NLSP 2γ + ET,miss“kink” incharged track

charged track

寿命測れる

non-pointing
photon
寿命測れる

the same asχ!0 LSP signal....

Gravitino
andNLSP at
the LHC!
G!
G!
GNLSP

NLSP

次のトークで？
白井さんのτ! NLSP

トークで寿命測れる？!

χ!0 NLSP 2γ + ET,miss“kink” incharged track

charged track
寿命測れる？

寿命測れる

non-pointing
photon
寿命測れる

the same asχ!0 LSP signal....

Gravitino
andNLSP at
the LHC!
G!
G!
GNLSP

NLSP

次のトークで？
白井さんのτ! NLSPトークで寿命測れる？!

χ!0 NLSP 2γ + ET,miss“kink” incharged track

charged track

寿命測れる+ SUGRA test?!

non-pointing
photon
寿命測れる

寿命測れる？

the same asχ!0 LSP signal....

Gravitino
andNLSP at
the LHC!
G!
G!
GNLSP

NLSP

次のトークで？
白井さんのτ! NLSP

トークで寿命測れる？!

χ!0 NLSP 2γ + ET,miss“kink” incharged track

charged track

寿命測れる+ SUGRA test?!

non-pointing
photon
寿命測れる

寿命測れる？

the same asχ!0 LSP signal....

Long-lived staus @ LHC
We will see long-lived charged particle (like muon).

τ̃Fig. from ATLAS webpage

τ̃Fig. from CMS webpage

Spectacular events!
Many SUSY informations can be obtained!

But,..... we cannot see the stau decay (and gravitino)

stopper-detector

Maybe... stoppers next to main detectors.

Hamaguchi, Nojiri, De Roeck’06

stopper-detector

CMS

8
6
4
20-2-4-6-8-12-1015m-8-6-4-2

0

2

4

6

8

10

120-2-4-6-8-105g/cm3(total weight 8kt)

15m

3.5m

10864215m

3.5m➔ maybe possible to install stopper-detectors.

test of SUGRAプランクスケールが LHC で測れる ?!

Planck scale measurement
W.Buchmüller, K.Hamaguchi, M.Ratz, T.Yanagida ’04

Planck scale measurement
W.Buchmüller, K.Hamaguchi, M.Ratz, T.Yanagida ’04

stopper-detector

We assume two stoppers next to CMS.

Hamaguchi, Nojiri, De Roeck’06

stopper-detector

CMS

8
6
4
20-2-4-6-8-12-1015m-8-6-4-2

02

4

6

8

10

120-2-4-6-8-105g/cm3(total weight 8kt)

15m

3.5m

108
64
215m

3.5m

➔ maybe possible to install stopper-detectors.

stopper-detector

We assume two stoppers next to CMS.

Hamaguchi, Nojiri, De Roeck’06-8-6-4-2024

68

10120-2-4-6-8-10

12.0x[m]

15m

10.0

3.5m

15m

15m
-6 -4 -2

10
8
6
4
2

y-position[m]

CMS

8
6
4
20-2-4-6-8-12-105g/cm3(total weight 8kt)

stopper-detector

02

3.5m
4

6

6

6

4

4

2

200-2-2-4-4-6-6-6 -4 -2 0 2 4z-positon[m]610 12x[m]➔ maybe possible to install stopper-detectors.

stopper-detector

We assume two stoppers next to CMS.

Hamaguchi, Nojiri, De Roeck’06

CMS(a)
160-6-4-202468

10123.5m

80

10.0602∆ ln L

100815m

12.0x[m]120

64-6 -4 -2

40

3.5m

024660

65

70

75

2200

602015m

4060

Ejet [GeV]

80

100

0120

650

55

480

Eτ [GeV](c)2090

95 100400.5-2-485

21Pτ-80-2-4-6-8-10108642Low Stat.
Best Fit15m

140(b)
10y-position[m]number of events / bin

86420-2-4-6-8-12-105g/cm3(total weight 8kt)

stopper-detector-2-40-6-6-0.5-6 -4 -2 0 2 4-1 z-positon[m]610 12x[m]➔ maybe possible to install stopper-detectors.
50

55

60

65

70

75

80

Eτ [GeV]8590

95 100stopper-detector

We assume two stoppers next to CMS.

Hamaguchi, Nojiri, De Roeck’06

CMS

(a)
160-6-4-202

46810123.5m

80

10.0602∆ ln L

100815m

12.0x[m]12064-6 -4 -2403.5m

0246606570752200602015m

4060

Ejet [GeV]

80

100

0120

65055

480

Eτ [GeV](c)209095 100

400.5-2-485

21Pτ-80-2-4-6-8-10

108642Low Stat.
Best Fit

15m

140(b)
10

y-position[m]number of events / bin864
20-2-4-6-8-12-105g/cm3(total weight 8kt)

stopper-detector-2-40-6-6-0.5-6 -4 -2 0 2 4-1 z-positon[m]610 12x[m]➔ maybe possible to install stopper-detectors.
5055

60

65707580

Eτ [GeV]8590

95 100Gravitino
andNLSP at
the LHC!
G!
G!
GNLSP

NLSP

次のトークで？
白井くんのτ! NLSP

トークで

F determination

χ!0 NLSP 2γ + ET,miss“kink” incharged track

charged track

F determination+ SUGRA test?!

non-pointing
photonF determination

F determination

the same asχ!0 LSP signal....

Gravitino
andNLSP at
the LHC!
G!
G!
GNLSP

NLSP!
.
.
.
.
.
dnfilliw
白井くんの“kink” inC
charged track
H
トークでLchargedtracke
F determination
τ! NLSPhttah
F determination
F determination+ SUGRA test?!
weess’t
non-pointingeL
次のトークで？

χ!0 NLSP 2γ + ET,missphoton

F determination

the same asχ
!0 LSP signal....

質問！
中には detector 内で止まって、遅れて崩壊するやつも居るはずです。（beta < 0.4 くらい。遅すぎる？）

τ̃

τ

τ̃

G̃

何とかしてこいつら identify 出来ないでしょうか？
(cf. Dimopoulos達の “stopping gluino” (at ATLAS) hep-ph/0506242)

Backup Slides

Long-lived staus @ LHC
How thick the stopping material should be?

typically!± , χ!0 → τ!
g!, q! → χ(number of events)/bin/5fb-1

2000

1500

1000

500

0

Review of Particle Physics

02468!"

Fig. from Hamaguchi, Kuno, Nakaya, Nojiri ’04

Long-lived staus @ LHC
How thick the stopping material should be?

typicallyfor 100 GeVstau!± , χ!0 → τ!
g!, q! → χ

5m Fe(number of events)/bin/5fb-1

2000

1500

1000

500

0

Review of Particle Physics

02468!"

Fig. from Hamaguchi, Kuno, Nakaya, Nojiri ’04

Long-lived staus @ LHC
How thick the stopping material should be?

typicallyfor 100 GeV
stau!± , χ!0 → τ!
g!, q! → χ

5m Fe(number of events)/bin/5fb-1

2000

1500

1000

500

0

Review of Particle Physics

02468!"

Fig. from Hamaguchi, Kuno, Nakaya, Nojiri ’04

Long-lived staus @ LHC
How thick the stopping material should be?

typicallyfor 100 GeV
stau!± , χ!0 → τ!
g!, q! → χ

5m Fe(number of events)/bin/5fb-1

2000

1500

1000

500

0

Review of Particle Physics

02468!"

Fig. from Hamaguchi, Kuno, Nakaya, Nojiri ’04

If thick enough, part of produced staus may be stopped.

Long-lived staus @ LHC

Ideas:
Place an additional stopper-detector next tothe main detector. [ Hamaguchi, Kuno, Nakaya, Nojiri, ’04 ]Place a water tank as stopper, and then drain
the water to a reservoir. [ Feng, Smith, ’04 ]Use the stau stopped in the surrounding rock.

[ De Roeck, Ellis, Gianotti, Moortgat, Olive, Pape’05 ]Long-lived staus @ LHC

Ideas:

Only this type
can identify the timing and position ofthe stopping stau precisely.

Place an additional stopper-detector next tothe main detector. [ Hamaguchi, Kuno, Nakaya, Nojiri, ’04 ]Place a water tank as stopper, and then drain
the water to a reservoir. [ Feng, Smith, ’04 ]Use the stau stopped in the surrounding rock.

[ De Roeck, Ellis, Gianotti, Moortgat, Olive, Pape’05 ]stopper = detector??
Hamaguchi, Kuno, Nakaya, Nojiri, ’04

stopper = detector??
High segmentation is crucial to reducethe background...

τ!

τ!

τ!

High segmentation

τ!

τ!

τ!

Low segmentation

stopper = detector??
High segmentation is crucial to reducethe background...

τ!

τ!

τ!

τ!

τ!

τ!

cf.
atm. neutrino CC event < 1 event/kton/year ➔ OK.
charged particle at the surface of detector < 1/cm2/sec (?)==> For SOUDAN II type detector, this corresponds to< 10% dead time of drift tube ➔ OK.

back

BBN bound:(1) gravitino LSP + neutralino NLSP
Fig. from Feng, Su, Takatama, ’04

Very severe!

mGe < O(0.01 − 1)GeV

back

BBN bound:(3) gravitino LSP + sneutrino NLSP
Fig. from Kanzaki, Kawasaki, Kohri, Moroi,’06

BBN bound:(2) gravitino LSP + stau NLSP
Fig. from Kawasaki, Kohri, Moroi, hep-ph/0703122

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