Jets plus missing energy from light gravitino production...
Transcript of Jets plus missing energy from light gravitino production...
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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
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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)
...
Bettina Oexl, Vrije U. Brussel 3
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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 .
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 –
Bettina Oexl, Vrije U. Brussel 4
-
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 .
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 –
Bettina Oexl, Vrije U. Brussel 5
-
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.
Bettina Oexl, Vrije U. Brussel 6
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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
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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
Bettina Oexl, Vrije U. Brussel 8
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The gravitino mass is directly related to the SUSYbreaking scale
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
.
Bettina Oexl, Vrije U. Brussel 9
-
The gravitino mass is directly related to the SUSYbreaking scale
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
.
Bettina Oexl, Vrije U. Brussel 10
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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.
Bettina Oexl, Vrije U. Brussel 11
-
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 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.
Bettina Oexl, Vrije U. Brussel 13
-
Gluino-gravitino associated productionstrongly dependent on gravitino mass
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 –
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
Bettina Oexl, Vrije U. Brussel 14
-
Gluino-pair production is independentof gravitino mass
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 –
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
Bettina Oexl, Vrije U. Brussel 15
-
Gluino-pair production is independentof gravitino mass
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 –
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
Bettina Oexl, Vrije U. Brussel 16
-
Gluino-pair production is independentof gravitino mass
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 –
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
Depending on the masses we expect dijet or monojet signal (LO).g
Bettina Oexl, Vrije U. Brussel 17
-
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~
Bettina Oexl, Vrije U. Brussel 18
-
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~
Bettina Oexl, Vrije U. Brussel 19
-
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).
Bettina Oexl, Vrije U. Brussel 20
-
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).
Bettina Oexl, Vrije U. Brussel 21
-
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.
Bettina Oexl, Vrije U. Brussel 22
-
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
-
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).
Bettina Oexl, Vrije U. Brussel 24
-
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).
Bettina Oexl, Vrije U. Brussel 25
-
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
Gluino-pair production is independent of m3/2 and has a peakaround mg̃ due to the two gluino decays.
Bettina Oexl, Vrije U. Brussel 26
-
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.
Bettina Oexl, Vrije U. Brussel 27
-
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.
Bettina Oexl, Vrije U. Brussel 28
-
Background can be reduced efficiently
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
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.
Bettina Oexl, Vrije U. Brussel 29
-
Background can be reduced efficiently
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
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.
Bettina Oexl, Vrije U. Brussel 30
-
Background can be reduced efficiently
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
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
Bettina Oexl, Vrije U. Brussel 31
-
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.
Bettina Oexl, Vrije U. Brussel 32
-
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.
Bettina Oexl, Vrije U. Brussel 33
-
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.
Bettina Oexl, Vrije U. Brussel 34
-
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.
Bettina Oexl, Vrije U. Brussel 35
-
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
-
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
Bettina Oexl, Vrije U. Brussel 37
-
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
Bettina Oexl, Vrije U. Brussel 38
-
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.
Bettina Oexl, Vrije U. Brussel 39
-
Bettina Oexl, Vrije U. Brussel 40
-
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
limittheory"Observed -1Expected limit
exp" 1±exp" 2±
NWA limitHeavy superparticle limit
-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
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_!=1/4 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
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
Bettina Oexl, Vrije U. Brussel 42
-
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.
Bettina Oexl, Vrije U. Brussel 43
-
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.
Bettina Oexl, Vrije U. Brussel 44
-
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
Bettina Oexl, Vrije U. Brussel 46
BodyAppendix