Jets plus missing energy from light gravitino production ...susy2013.ictp.it/lecturenotes/01_Monday/SUSY_Phenomenology/Oex… · Jets plus missing energy from light gravitino production

Jets plus missing energyfrom light gravitino production at the LHC

Bettina Oexl

Vrije Universiteit Brussel and International Solvay Institutes

JHEP 1210 (2012) 008 (arXiv:1206.7098)P.de Aquino(VUB), F.Maltoni(UCL), K.Mawatari(VUB), BO

26.8.2013, SUSY 2013

New physics particles may show up asjet(s) plus missing energy

massive gravitons

weakly interacting massive particles

neutralino

gravitino

very light: m3/2 = O(10−13 − 10−12 GeV)No-scale supergravity: Ellis, Enqvist,Nanopoulos, Phys Lett. B147 (1984) 99Extra dimensions: Gherhetta, Pomarol, Nucl.Phys B586(2000)141(hep-ph/0003129)

...

Bettina Oexl, Vrije U. Brussel 2

New physics particles may show up asjet(s) plus missing energy

massive gravitons

weakly interacting massive particles

neutralino

gravitino very light: m3/2 = O(10−13 − 10−12 GeV)No-scale supergravity: Ellis, Enqvist,Nanopoulos, Phys Lett. B147 (1984) 99Extra dimensions: Gherhetta, Pomarol, Nucl.Phys B586(2000)141(hep-ph/0003129)

...


For a light gravitino:two processes contribute to jets + /ET

When the gravitino is very light,direct production in association withgluinos (squarks) becomes considerable.At LO, we obtain monojet + /ET signal.

Figure 2. Schematic diagrams for pp → partons+G̃G̃. In the first row the leading gluino-gravitino(red) and gluino-pair (black) diagrams are sorted. The diagrams are ordered with the number of

additional QCD partons in rows, while with the total parton multiplicity in columns.

To combine the two approaches avoiding double counting, one needs an appropriate

merging procedure. Several multi-jet merging algorithms have been proposed (see also [? ]):

the CKKW-based method [? ? ], the MLM scheme [? ? ], the pseudo-shower algorithm [?

], and the shower-kT scheme [? ].

In our analysis we make use of the shower-kT scheme, which is based on event rejection,

as implemented in MadGraph [? ? ] for fixed-order ME generation and interfaced to

Pythia6.4 [? ] for PS and hadronization. In this scheme, ME multi-parton events are

generated with a minimum separation, Qcut and pTmin , between final-state partons (ij) and

between final- and initial-state partons (iB) characterized by the kT jet measure:

d2ij = min(p2Ti , p

2Tj )∆R

2ij > Q

2cut, d

2iB = p

2Ti > p

2Tmin

, (3.1)

with ∆R2ij = 2[cosh(ηi − ηj) − cos(φi − φj)], where pTi , ηi and φi are the transversemomentum, pseudorapidity and azimuth of particle i [? ]. The renormalization scale for

αs for each QCD emission vertex is set to the kT value, while the factorization scale for

the parton densities and the renormalization scale for the hard 2→2 process is given by thetransverse mass of the particles produced in the central process. The ME-level events are

then passed to Pythia and showered using the pT -ordered shower, and Pythia reports the

scale QPShardest of the hardest emission in the shower. For lower parton-multiplicity samples

an event is rejected if QPShardest > Qcut, while for the highest multiplicity sample an event

is rejected if QPShardest > QMEsoftest, the scale of the softest ME parton in the event. See more

details in [? ].

3.1 Physics parameters and observables

Throughout the present study, we consider a gluino with mass mg̃ = 800 GeV, which lies

above the exclusion limit for certain simplified SUSY models or general gauge mediation

models [? ? ], and conduct analyses for the LHC at√

s = 14 TeV. All the left- and right-

handed squarks are fixed at 3 TeV. The corresponding LO gluino-pair production cross

– 6 –

Taking into account additional jets frominitial/final state radiation,this process leads to the same finalstate as gluino (squark) pair poduction,dijet + /ET .












d2ij = min(p2Ti , p

2Tj )∆R

2ij > Q

2cut, d

2iB = p

2Ti > p

2Tmin

, (3.1)








details in [? ].







– 6 –


For a light gravitino:two processes contribute to jets + /ET

When the gravitino is very light,direct production in association withgluinos (squarks) becomes considerable.At LO, we obtain monojet + /ET signal.












d2ij = min(p2Ti , p

2Tj )∆R

2ij > Q

2cut, d

2iB = p

2Ti > p

2Tmin

, (3.1)








details in [? ].







– 6 –

Taking into account additional jets frominitial/final state radiation,this process leads to the same finalstate as gluino (squark) pair poduction,dijet + /ET .












d2ij = min(p2Ti , p

2Tj )∆R

2ij > Q

2cut, d

2iB = p

2Ti > p

2Tmin

, (3.1)








details in [? ].







– 6 –


We obtain bound on gravitino mass

We investigate the signature of the two processesfor different gravitino masses.

1 2 3 4 5 610

10

10

Jet multiplicity

num

ber

of events

LHC 14 TeV

m = 800 GeVg~

m = 1,3,9 x 10 GeVA,B,C3/2

-13

Z + jets

A

B

C

2

3

4

!"= 10 fb-1

pTj > 50 GeV

1 2 3 4 5 610

10

10

Jet multiplicity

num

ber

of events

LHC 14 TeV

m = 800 GeVg~

m = 1,3,9 x 10 GeVA,B,C3/2

-13

Z + jets

A

B

C

2

3

4

!"= 10 fb-1

pTj > 150 GeV

Figure 8. Jet multiplicities for an integrated luminosity of 10 fb−1, with pTj > 50 GeV (left) andpTj > 150 GeV (right). The detail is the same as figure 7.

produce mono-jet events, while the g̃g̃ production is likely to give di-jet events.

As seen in figures 7 and 8, the distributions are significantly different among the three

benchmarks as well as between the signal and the background. In other words, they are

sensitive to the gravitino mass when it is light enough so that the g̃G̃ associated production

process can contribute to the signal. We note that, although we fixed the gluino mass at

800 GeV in the present study, a different gluino mass also alters the distributions, which

could allow us to explore both the gravitino and gluino masses at the LHC.

5 Summary

We have studied a jets plus missing energy signature at the LHC in a scenario where the

gravitino is the LSP and the gluino is the NLSP which promptly decays into a gluon and

a gravitino. We considered a very light gravitino of m3/2 ∼ O(10−13 GeV), where twoproduction subprocesses can yield jets+ �ET : gluino-gravitino associated production andgluino-pair production. By using the shower-kT ME+PS merging scheme implemented in

MadGraph, we have simulated the inclusive signal samples as well as the SM Z+jets

irreducible background.

Special attention has been devoted to the ME+PS merging procedure to avoid double

counting for such a signal which contains two different types of subprocesses. In addition

to checking the Qcut independence of the cross sections and the smoothness of the distri-

butions, we have generated the merged g̃G̃ and g̃g̃ signal samples separately and confirmed

that the sum of them reproduced the full inclusive results.

To show how distributions of the jets+ �ET signature can provide information on thegravitino and gluino masses, we have investigated three benchmark scenarios which exem-

plify the different final states. Due to the fact that the distributions are quite different

between the g̃G̃ and g̃g̃ production processes and due to the m−23/2 scaling of the g̃G̃ produc-tion cross section, the kinematical distributions and the jet multiplicity exhibit distinctive

features among the three cases as well as between the signal and the background. The LHC

may be able to explore the parameter space around our benchmark points and hence to

– 13 –

Simple final state observables allow to extract information aboutgravitino mass when the gravitino is light enough.


The gravitino

The two contributing sub-processes

Gluino-gravitino associated productionGluino-pair productionMatrix element / parton shower merging

Jets plus /ET signal and background

ValidationBackground reductionResults

Spin 3/2 particles at colliders

The gravitino mass is directly related to the SUSYbreaking scale

In local SUSY theories, the gravitino isthe spin 3/2 superpartner of the graviton.

When SUSY breaks spontaneously, thegravitino becomes massive by absorbing thegoldstino (super-Higgs mechanism).

3/2

1/2

-3/2

-1/2

(spin)

(goldstino)

I(

m3/2 ∼ M2SUSYMPl



Interactions of the helicity 3/2 componentsare suppressed by the Planck scale.

Interactions of the helicity 1/2 componentsare suppressed by the SUSY breaking scale.

3/2

1/2

-3/2

-1/2

(spin)

(goldstino)

If the SUSY breaking scale is low, the gravitino interactions(goldstino interactions) can be important at colliders.

The gravitino mass is m3/2 ∼ M2SUSYMPl

.


Experimental bound on gravitino masswith modified parton shower parameters and translate into a 5% to 10% uncertainty on the signal yieldsin the SR3 region, depending on the squark and gluino masses. Systematic uncertainties due to PDFsresult in uncertainties on the signal yields that vary between 5% and 60% for squark and gluino massesincreasing from 50 GeV and 2.6 TeV. Finally, variations of the renormalization and factorization scalesby factors of two and one-half introduce a 15% to 35% uncertainty on the signal yields with increasingsquark and gluino masses.

[GeV]g~/q~m0 500 1000 1500 2000 2500 3000 3500

[pb]

! " A

"

#

-310

-210

-110

1q~=m_g~95% CL SR3, m_

Expected limit

Observed limit

exp# 1±

exp# 2±

=2.0e-05 [eV]G~m

=4.0e-05 [eV]G~m

=6.0e-05 [eV]G~m

=8.0e-05 [eV]G~m

=1.0e-04 [eV]G~m

=2.0e-04 [eV]G~m

=3.0e-04 [eV]G~m

=4.0e-04 [eV]G~m

=5.0e-04 [eV]G~m

=8.0e-04 [eV]G~m

-1 Ldt=10.5 fb$ = 8 TeVs

ATLAS Preliminary

Figure 10: Cross section times acceptance times efficiency for the gravitino+squark/gluino productionas a function of the squark/gluino mass in the case of degenerate squark and gluinos. Different values forthe gravitino mass are considered and the predictions are compared with model-independent limits.

Figure 10 presents, for the case of degenerate squark and gluinos, the σ × A × " as a function ofthe squark/gluino mass for different gravitino masses. For comparison, the model-independent 95% CLlimits are shown. Expected and observed 95% CL limits on the gravitino-squark/gluino mass plane arepresented in Figure 11, and are computed using the same procedure as in the case of the ADD andWIMPsmodels. Gravitino masses below 1·10−4 eV (4·10−5 eV) are excluded at 95%CL for squark/gluino massesof 500 GeV (1.7 TeV). These results significantly improve previous results at LEP and the Tevatron andconstitute the best bounds on the gravitino mass to date. For very high squark/gluino masses the NWAemployed is violated since the partial width for the gluino and squark to decay into a gravitino and aparton becomes more than 25% of its mass and other decay channels should be considered. Finally, limitson the gravitino mass are also computed in the case of non-degenerate squarks and gluinos. Scenarioswith mg̃ = 4 ·mq̃, mg̃ = 2 ·mq̃, mg̃ = 1/2 ·mq̃, and mg̃ = 1/4 ·mq̃ are explored in Figure 12, where 95% CLlimits on the gravitino mass are presented as a function of the squark mass. In this case, 95% CL lowerbounds on the gravitino mass in the range between 3 · 10−4 eV and 3 · 10−5 eV are set depending on thesquark and gluino masses.

7 Summary and conclusions

In summary, we report results on the search for new phenomena in events with an energetic jet and largemissing transverse momentum in proton-proton collisions at

√s = 8 TeV at the LHC, based on ATLAS

data corresponding to an integrated luminosity of 10.5 fb−1. The measurements are in agreement with theSM predictions for the background. The results are translated into model-independent 95% confidencelevel upper limits on σ×A× ". The results are also presented in terms of new limits on the production of

18

Search for new phenomenain monojet plus missingtransverse momentum

(ATLAS-CONF-2012-147)

For degenerate gluino/squark masses (mg̃ = 500 GeV):mG̃ > 1 · 10−13 GeV.


The gravitino






The setup

The gravitino is the LSP with m3/2 ∼ O(10−13 − 10−12) GeV.

The gluino is the NLSPand promptly decays into a gluon and a gravitino: g̃ → gG̃ .

We assume R-parity conservationand all other superparticles to be heavy.


Gluino-gravitino associated productionstrongly dependent on gravitino mass












d2ij = min(p2Ti , p

2Tj )∆R

2ij > Q

2cut, d

2iB = p

2Ti > p

2Tmin

, (3.1)








details in [? ].







– 6 –

500 1000 1500 2000gluino mass [GeV]

0.001

0.01

0.1

1

10

100

1000

cros

s se

ctio

n [p

b]

σ(pp → g̃ G̃ ) ∼ 1(MPlm3/2)2

m3/2 = 1 · 10−13GeVm3/2 = 3 · 10−13GeVm3/2 = 9 · 10−13GeV

Associated production becomes relevant for very light gravitinos.y


Gluino-pair production is independentof gravitino mass












d2ij = min(p2Ti , p

2Tj )∆R

2ij > Q

2cut, d

2iB = p

2Ti > p

2Tmin

, (3.1)








details in [? ].







– 6 –

500 1000 1500 2000gluino mass [GeV]

0.001

0.01

0.1

1

10

100

1000

cros

s se

ctio

n [p

b]

1

(MPlm3/2)2

m3/2 = 1 · 10−13GeVm3/2 = 3 · 10−13GeVm3/2 = 9 · 10−13GeV

Depending on the masses we expect dijet or monojet signal (LO).g














d2ij = min(p2Ti , p

2Tj )∆R

2ij > Q

2cut, d

2iB = p

2Ti > p

2Tmin

, (3.1)








details in [? ].







– 6 –

500 1000 1500 2000gluino mass [GeV]

0.001

0.01

0.1

1

10

100

1000

cros

s se

ctio

n [p

b]

1

(MPlm3/2)2

m3/2 = 1 · 10−13GeVm3/2 = 3 · 10−13GeVm3/2 = 9 · 10−13GeV















d2ij = min(p2Ti , p

2Tj )∆R

2ij > Q

2cut, d

2iB = p

2Ti > p

2Tmin

, (3.1)








details in [? ].







– 6 –

500 1000 1500 2000gluino mass [GeV]

0.001

0.01

0.1

1

10

100

1000

cros

s se

ctio

n [p

b]

mg̃ = 800 GeV1

(MPlm3/2)2

m3/2 = 1 · 10−13GeVm3/2 = 3 · 10−13GeVm3/2 = 9 · 10−13GeV



Matrix element / parton shower merging

For production processes with large partonic center-of-mass energy,initial and final state radiation becomes important.We generate pp → G̃ G̃ + 1, 2, 3 partons:

Hard partonsare well described by afixed order matrix elementapproach.

Soft/collinear partonsare well described by aparton shower.

The two approaches are merged usingthe shower-kT scheme.J.Alwall, S.deVisscher, F.Maltoni, JHEP 0902(2009)017

1-parton 2-partons 3-partons

p

p

g

g

~

G~

G~


Shower-kT -scheme

Based on event rejection:

Matrix element multi-parton events are generated (MadGraph)with a minimum separation between final state partons

d2ij = min(p2Ti, p2Tj ) ∆R

2ij > Q

2cut

and between final and initial state partons

d2iB = p2Ti> p2Tmin .

In our analysis, we use Qcut = 100 GeV and pT ,min = 50 GeV.

Events are then showered using the pT -ordered shower (Pythia).


Shower-kT -scheme

Pythia reports the scale QPShardest of the hardest emission in theshower.

For lower parton-multiplicity samples an event is rejected ifQPShardest > Qcut.

For the highest multiplicity sample an event is rejected if QPShardestis bigger than the scale of the softest ME parton in the event.


The gravitino






We obtain distinguishable distributions for differentgravitino masses

pp → jets + /ET : We verified that the sum of the two contributingsubprocesses reproduces the full inclusive result.

0 500 1000 1500 20000.001

0.01

0.1

1

Full Sampleg Gg g

~~~~

HT (GeV)

dσ/d

HT

(pb/

GeV

) LHC 14 TeVA

B

C

m = 800 GeVm = 1,3,9 x 10 GeVA,B,C3/2

~g-13

HT =∑

j pjTm3/2 ∼

(MSUSY)2

Mpl(1)

m3/2 = 1 · 10−13GeV (2)m3/2 = 3 · 10−13GeV (3)m3/2 = 9 · 10−13GeV (4)

.pp → g̃G̃ → gG̃G̃ (5)

.pp → g̃g̃ → ggG̃G̃. (6)

1

mg̃ = 800 GeV

Associated production scales with 1m2

G̃

and has a peak aroundmg̃2

(energy of the gluon coming from the gluino decay in gluino rest frame).




0 500 1000 1500 20000.001

0.01

0.1

1

Full Sampleg Gg g

~~~~

HT (GeV)

dσ/d

HT

(pb/

GeV

) LHC 14 TeVA

B

C

m = 800 GeVm = 1,3,9 x 10 GeVA,B,C3/2

~g-13

HT =∑

j pjTm3/2 ∼

(MSUSY)2

Mpl(1)

m3/2 = 1 · 10−13GeV (2)m3/2 = 3 · 10−13GeV (3)m3/2 = 9 · 10−13GeV (4)

.pp → g̃G̃ → gG̃G̃ (5)

.pp → g̃g̃ → ggG̃G̃. (6)

1

mg̃ = 800 GeV

Associated production scales with 1m2

G̃

and has a peak aroundmg̃2

(energy of the gluon coming from the gluino decay in gluino rest frame).




0 500 1000 1500 20000.001

0.01

0.1

1

Full Sampleg Gg g

~~~~

HT (GeV)

dσ/d

HT

(pb/

GeV

) LHC 14 TeVA

B

C

m = 800 GeVm = 1,3,9 x 10 GeVA,B,C3/2

~g-13

HT =∑

j pjTm3/2 ∼

(MSUSY)2

Mpl(1)

m3/2 = 1 · 10−13GeV (2)m3/2 = 3 · 10−13GeV (3)m3/2 = 9 · 10−13GeV (4)

.pp → g̃G̃ → gG̃G̃ (5)

.pp → g̃g̃ → ggG̃G̃. (6)

1

mg̃ = 800 GeV

Gluino-pair production is independent of m3/2 and has a peakaround mg̃ due to the two gluino decays.


Correlation between p1st jetT and /ET

Scatter plots of the pp → jets + /ET signal differ for the three cases(minimal cut: /ET > 200 GeV ).

m 32=110-13 GeV

A

0 500 1000 15000

500

1000

1500

PT1 st jetHGeVL

ET

mis

sHG

eVL

m 32=310-13 GeV

B

0 500 1000 15000

500

1000

1500

PT1 st jetHGeVL

ET

mis

sHG

eVL

m 32=910-13 GeV

C

0 500 1000 15000

500

1000

1500

PT1 st jetHGeVL

ET

mis

sHG

eVL

Associated production

is dominant.We find strongcorrelation /ET ∼ p1st jetTin high pT region.

Intermediate

case.

Gluino pair production is

dominant.No such a strongcorrelation is observed.


Correlation between p1st jetT and /ET


m 32=110-13 GeV

A

0 500 1000 15000

500

1000

1500

PT1 st jetHGeVL

ET

mis

sHG

eVL

m 32=310-13 GeV

B

0 500 1000 15000

500

1000

1500

PT1 st jetHGeVL

ET

mis

sHG

eVL

m 32=910-13 GeV

C

0 500 1000 15000

500

1000

1500

PT1 st jetHGeVL

ET

mis

sHG

eVL

Associated production

is dominant.We find strongcorrelation /ET ∼ p1st jetTin high pT region.

Intermediate

case.

Gluino pair production is

dominant.No such a strongcorrelation is observed.


Background can be reduced efficiently


m 32=110-13 GeV

A

0 500 1000 15000

500

1000

1500

PT1 st jetHGeVL

ET

mis

sHG

eVL

Z + jets

B m 32 = 310-13 GeV

0 500 1000 15000

500

1000

1500

PT1 st jetHGeVL

ET

mis

sHG

eVL

m 32=910-13 GeV

C

0 500 1000 15000

500

1000

1500

PT1 st jetHGeVL

ET

mis

sHG

eVL

The dominating background is pp → Z (→ νν̄)+ jets.

We apply the cut p1st jetT > 500 GeV or /ET > 500 GeV.




m 32=110-13 GeV

A

0 500 1000 15000

500

1000

1500

PT1 st jetHGeVL

ET

mis

sHG

eVL

Z + jets

B m 32 = 310-13 GeV

0 500 1000 15000

500

1000

1500

PT1 st jetHGeVL

ET

mis

sHG

eVL

m 32=910-13 GeV

C

0 500 1000 15000

500

1000

1500

PT1 st jetHGeVL

ET

mis

sHG

eVL

The dominating background is pp → Z (→ νν̄)+ jets.

We apply the cut p1st jetT > 500 GeV or /ET > 500 GeV.




m 32=110-13 GeV

A

0 500 1000 15000

500

1000

1500

PT1 st jetHGeVL

ET

mis

sHG

eVL

Z + jets

B m 32 = 310-13 GeV

0 500 1000 15000

500

1000

1500

PT1 st jetHGeVL

ET

mis

sHG

eVL

m 32=910-13 GeV

C

0 500 1000 15000

500

1000

1500

PT1 st jetHGeVL

ET

mis

sHG

eVL

σ (pb) A B C bkg/ET > 200 GeV 7.50 1.53 0.90 19.4

+ p1st jetT > 500 GeV or /ET > 500 GeV 3.81 0.85 0.55 0.81


Results: pT distribution

pT of leading jet

0 500 1000 15000.001

0.01

0.1

1

PT1st jet (GeV)

dσ/d

P T1s

t je

t (p

b/G

eV)

LHC 14 TeV

m = 800 GeVg~m = 1,3,9 x 10 GeVA,B,C3/2

-13A

Z + jets

BC

pT of second jet

0 500 1000 15000.001

0.01

10

1

PT2nd jet (GeV)

dσ/d

P T2n

d je

t (p

b/G

eV)

LHC 14 TeV

m = 800 GeVg~

A

B

C

Z + jets m = 1,3,9 x 10 GeVA,B,C3/2

-13

Similar distributions because firsthard jet comes from gluino decayin both subprocesses.Signal dominates background inlow pT region for all three cases.

Two gluino decays lead to twohard gluon jets.Second jet in associatedproduction comes from QCDradiation and tends to be soft.


Simple observables provide informationon gravitino and gluino mass

Jet multiplicity distribution

1 2 3 4 5 610

10

10

Jet multiplicity

num

ber

of e

vent

s

LHC 14 TeV

m = 800 GeVg~

m = 1,3,9 x 10 GeVA,B,C3/2-13

Z + jets

A

B

C

2

3

4

ℒ = 10 fb-1

pTj > 150 GeV

m3/2 ∼(MSUSY)

2

Mpl(1)

m3/2 = 1 · 10−13GeV (2)m3/2 = 3 · 10−13GeV (3)m3/2 = 9 · 10−13GeV (4)

.pp → g̃G̃ → gG̃G̃ (5)

.pp → g̃g̃ → ggG̃G̃. (6)

1

When we count onlyhard jets, we recoverLO expectations.

The distributions are sensitive to the gravitino masswhen it is light enough.

Once gluino pair production dominates,no information about gravitino mass can be extracted.


The gravitino






Spin 3/2 particles might give interesting signatures

When E � mG̃ , the gravitino can be replaced by thespin 1/2 goldstino (goldstino equivalence theorem).

When E ∼ mG̃ , the theorem does not apply andwe have to use full spin 3/2 formalism.

Other spin 3/2 particles than thegravitino are proposed:excited tops (compositeness models).

t

t∗

t̄

W.J.Stirling, E.VryonidouJHEP 1201 (2012) 055


Spin 3/2 particles can be simulated!

We implemented and validated the support for interactionsof spin 3/2 particles.

‘Simulating spin-3/2 particles at colliders’

N.D. Christensen, P. de Aquino, N. Deutschmann, C. Duhr, B. Fuks,C. Garcia-Cely, O. Mattelaer, K. Mawatari, BO, Y. Takaesu

arXiv:1308.1668 [hep-ph]

A full chain of tools is availableto study spin 3/2 particles:

FeynRules http://feynrules.irmp.ucl.ac.be/,MadGraph https://launchpad.net/madgraph5,CalcHep http://theory.sinp.msu.ru/ pukhov/calchep.html.

[ GeV ] tt

M0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

]-1

[ p

b G

eVtt

/ dM

σd

-610

-510

-410

-310

-210

-110

1

= 300 GeVt*M

= 500 GeVt*M

= 800 GeVt*M

Standard Model

at the LHC (14 TeV)t t →p p


Summary

We studied a jets +/ET signature at the LHC in a scenario wherethe gravitino is very light and the gluino is the NLSPwhich promptly decays into a gluon and a gravitino.

The LHC may be able to explore the parameter space around ourbenchmark points and henceprovide information on the gluino as well as the gravitino mass,yielding information on the SUSY breaking scale.

Spin 3/2 particles can be simulated at colliders.


Goldstino gravitino equivalence theorem

Replace the spin-3/2 gravitino field by the spin-1/2 goldstino fieldas ψµ ∼

√2/3 ∂µψ/m3/2.

The effective interaction Lagrangian in non-derivative form is

Lint =±im2

φiL/R√

3MPlm3/2

[ψ̄PL/R f

i (φiL/R)∗ − f̄ iPR/Lψ φiL/R

]− mλ

4√

6MPlm3/2ψ̄[γµ, γν ]λaF aµν .

The gluino decay width is given by Γ(g̃ → gG̃ ) = m5g̃

48πM2Plm

23/2

.

For mg̃ = 800GeV and m3/2 = 3 · 10−13GeV the width is 4.1GeV.Bettina Oexl, Vrije U. Brussel 41

ATLAS limits on light gravitinos

[GeV]q~m0 200 400 600 800 1000 1200

[eV]

G~m

-610

-510

-410

-310

q~ m_!=2 g~95% CL SR3, m_Observed limit

limittheory"Observed -1Expected limit

exp" 1±exp" 2±

NWA limitHeavy superparticle limit

-1 Ldt=10.5 fb# = 8 TeVs

ATLAS Preliminary

[GeV]q~m0 500 1000 1500 2000 2500

[eV]

G~m

-610

-510

-410

-310

q~ m_!=1/2 g~95% CL SR3, m_Observed limit


exp" 1±exp" 2±


-1 Ldt=10.5 fb# = 8 TeVs

ATLAS Preliminary

[GeV]q~m0 100 200 300 400 500 600

[eV]

G~m

-610

-510

-410

-310

q~ m_!=4 g~95% CL SR3, m_Observed limit


exp" 1±exp" 2±


-1 Ldt=10.5 fb# = 8 TeVs

ATLAS Preliminary

[GeV]q~m0 500 1000 1500 2000 2500

[eV]

G~m

-610

-510

-410

-310

q~ m_!=1/4 g~95% CL SR3, m_Observed limit


exp" 1±exp" 2±


-1 Ldt=10.5 fb# = 8 TeVs

ATLAS Preliminary

Figure 12: Observed (solid line) and expected (dashed line) 95% CL lower limits on the gravitino mass asa function of the squark mass for non-degenerate squark/gluino masses and different squark/gluino massconfigurations. The dotted line indicates the impact on the observed limit of the ±1σ LO theoreticaluncertainty. The shaded bands around the expected limit indicate the expected ±1σ and ±2σ rangesof limits in the absence of a signal. The dashed-dotted line defines the validity of the narrow-widthapproximation (see body of the text). The solid red line denotes the current limit from LEP [27] on thegravitino mass assuming very heavy squarks/gluino.

[6] CDF Collaboration, T. Aaltonen et al., Search for large extra dimensions in final states containingone photon or jet and large missing transverse energy produced in pp̄ collisions at

√s = 1.96 TeV,

Phys.Rev.Lett. 101 (2008) 181602, arXiv:0807.3132 [hep-ex].

[7] CDF Collaboration, T. Aaltonen et al., A Search for dark matter in events with one jet and missingtransverse energy in pp̄ collisions at

√s = 1.96 TeV, Phys.Rev.Lett. 108 (2012) 211804,

arXiv:1203.0742 [hep-ex].

[8] CMS Collaboration, Search for New Physics with a Mono-Jet and Missing Transverse Energy inpp Collisions at

√s = 7 TeV, Phys.Rev.Lett. 107 (2011) 201804, arXiv:1106.4775 [hep-ex].

[9] CMS Collaboration, Search for dark matter and large extra dimensions in monojet events in ppcollisions at

√s = 7 TeV, JHEP 1209 (2012) 094, arXiv:1206.5663 [hep-ex].

[10] CMS Collaboration, Search for Dark Matter and Large Extra Dimensions in pp CollisionsYielding a Photon and Missing Transverse Energy, Phys.Rev.Lett. 108 (2012) 261803,arXiv:1204.0821 [hep-ex].

20


Jet multiplicity distribution dependson minimal pT of all jets

PTj > 50 GeV

1 2 3 4 5 610

10

10

Jet multiplicity

num

ber

of e

vent

s

LHC 14 TeV

m = 800 GeVg~

m = 1,3,9 x 10 GeVA,B,C3/2-13

Z + jets

A

B

C

2

3

4

ℒ = 10 fb-1

pTj > 50 GeV

PTj > 150 GeV

1 2 3 4 5 610

10

10

Jet multiplicity

num

ber

of e

vent

s

LHC 14 TeV

m = 800 GeVg~

m = 1,3,9 x 10 GeVA,B,C3/2-13

Z + jets

A

B

C

2

3

4

ℒ = 10 fb-1

pTj > 150 GeV

Lighter gravitino leads to a peak at lower jet multiplicities than heaviergravitino.

When counting only very hard jets, we recover leading order expectations:associated production tends to produce mono-jet events,gluino-pair production gives di-jet events.


Missing transverse energy

0 500 1000 15000.001

0.01

0.1

1

ETmiss (GeV)

dσ/d

E Tm

iss

(pb/

GeV

)

LHC 14 TeV

m = 800 GeVg~m = 1,3,9 x 10 GeVA,B,C3/2

-13

Z + jets

A

B

C

Lighter gravitino results in higher /ET events,because a gravitino is directly produced in association with agluino and hence can have a higher pT than the ones resultingfrom gluino decays.


Light gravitinos at linear colliders

Associated production of light gravitinosin e+e− and e−γ collisions

K. Mawatari, BO, Y. TakaesuEur.Phys.J. C71 (2011) 1783

e+e− → χ̃01G̃ → γG̃ G̃ and e−γ → ẽG̃ → e−G̃ G̃Bettina Oexl, Vrije U. Brussel 45

Higgs mechanism

SU(2) x U(1) gauge symmetryspontaneously broken

mW ∼ v

�µ0 (p) =1

mW

|~p|

E sin θ cosφE sin θ sinφE cos θ

Super-Higgs mechanism

Supersymmetry spontaneouslybroken

m3/2 ∼√F


BodyAppendix

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