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GRAVITON PRODUCTION AT
HADRON COLLIDERS
Priscila de Aquino
Katholieke Universiteit Leuven (KUL) & Université Catholique de Louvain (UCL)
23rd Rencontres de BloisJune 1st, 2011
based on P. d. A, Kaoru Hagiwara, Qiang Li, Fabio Maltoni, arXiv: 1101.5499
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
OUTLINE
Introduction
Hierarchy problem
Extra dimensional models
Phenomenology of graviton emission?!?
Simulating graviton emission in a multi-jet final state
Results and conclusions
2
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
The SM agrees to a great deal with the experimental data we have today, but there are several reasons to expect new physics at TeV scale.
The Hierarchy problem:
Standard Model Radiative corrections to the Higgs mass:
If mH < 200 GeV there might be new physics at the TeV scale
INTRODUCTION
3
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
PHENOMENOLOGY!
4
New and interesting pheno at LHCNew expectations for NP{The LHC era!
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
PHENOMENOLOGY!
• Madgraph/MadEvent =
Spin-2 particles recently incorporated!
software that allow to generate amplitudes and events for any process in any model
[K. Hagiwara, J. Kanzaki, Q. Li and K. Mawatari, arXiv:0805.2554]
[J. Alwall et al, JHEP 0709:028, 2007]
4
Careful pheno analysis at colliders = Accurate simulation necessary!
New and interesting pheno at LHCNew expectations for NP{The LHC era!
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
PHENOMENOLOGY!
5
We want to explore theories with spin-2 particles, and look for the phenomenology of graviton emission...
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
PHENOMENOLOGY!
Our aim: study graviton production in a multi-jet final state at hadron colliders for generic models that contain spin-2 particles!
5
... several LHC studies in monojet final-state, but what about processes with many jets in the final state?!?
We want to explore theories with spin-2 particles, and look for the phenomenology of graviton emission...
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
MATCHING SCHEME
• Increasing √s more events with larger multiplicities
Accurate simulations need to correctly account for the presence of QCD radiation
6
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
MATCHING SCHEME
• Increasing √s more events with larger multiplicities
Accurate simulations need to correctly account for the presence of QCD radiation
ME calculations Parton Shower simulator
• parton-level description
• valid for hard/separated partons
• needed for multi-jet descriptions
• hadron-level description
• valid for collinear/soft partons
• needed for realistic studies
MadGraph Pythia / Herwig
Complementary approach Match them!
6
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
Goal: Obtain accurate predictions for non-trivial observables
HT DISTRIBUTION
HT = Scalar sum of the PT of all jets above a threshold PT0
Important distributions to be analyzed:
• PT graviton and jets• η graviton and jets
7
• HT has been proven to be larger in signal than in QCD di-jet events
• It provides a way to discriminate from SM background
HT =!
PT (jets)
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
PHENOMENOLOGY
In order to obtain accurate predictions for non-trivial observables:
• Generate inclusive sample with MG/ME + Pythia matching
• Compare multi-jet matching X mono-jet NLO
Use NLO for normalization, and matching for distributions!
Processes:
• NLO: p p G + jet + X (inclusive)• Matching: p p G + n-jets, with n=1,2,3
8
Which theories to consider ?!?:
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
BEYOND STANDARD MODEL
Attempt to explain the HP BSM theories
• ADD: model with large extra dimensions[ N. Arkani-Hamed, S. Dimopoulos, G. Dvali, 1998 ]
• RS: model with a warped extra dimension [ L. Randall, R. Sundrum, 1999 ]
• MGM: 4D model that contains a massless graviton[ G. Dvali, arxiv:0706.2050 ]
[ X. Calmet, S. D. H. Hsu, D. Reeb, arxiv:0803.1836 ]
9
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
BEYOND STANDARD MODEL
Attempt to explain the HP BSM theories
• ADD: model with large extra dimensions[ N. Arkani-Hamed, S. Dimopoulos, G. Dvali, 1998 ]
• RS: model with a warped extra dimension [ L. Randall, R. Sundrum, 1999 ]
• MGM: 4D model that contains a massless graviton[ G. Dvali, arxiv:0706.2050 ]
[ X. Calmet, S. D. H. Hsu, D. Reeb, arxiv:0803.1836 ]
9
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
RS MODEL
10
RS model = 5 dimensions, warped metric, compactified in a S1/Z2
ds2 = e!2!|y|!µ"dxµdx" + dy20 πy
! = e!!"R MPl
R
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
RS MODEL
10
RS model = 5 dimensions, warped metric, compactified in a S1/Z2
ds2 = e!2!|y|!µ"dxµdx" + dy20 πy
! = e!!"R MPl
R
• Graviton propagating on δ
• KK tower
• massive graviton
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
RS MODEL
10
RS model = 5 dimensions, warped metric, compactified in a S1/Z2
ds2 = e!2!|y|!µ"dxµdx" + dy20 πy
! = e!!"R MPl
Phenomenology on graviton emission = decayed product!
[ H. Davoudiasl, J. L. Hewett, T. G. Rizzo, Phys. Rev. D63, 075004 (2001) ]
Figure 17: Drell-Yan production of a (a) 700 GeV KK graviton at the Tevatron with k/MP l =1, 0.7, 0.5, 0.3, 0.2, and 0.1, respectively, from top to bottom; (b) 1500 GeV KK gravitonand its subsequent tower states at the LHC. From top to bottom, the curves are for k/MP l =1, 0.5, 0.1, 0.05, and 0.01, respectively.
44
R
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
RS: FULL INCLUSIVE SAMPLE• Aim: analyze jet and graviton distributions and compare the shape of matched
results with the ones given by NLO calculation!
11
• RS model,
Λ = 3 TeV, and
MG = 100 GeV
• Full inclusive sample;
• LO: pp > G, Matched: up to 2-jets
To warm up:
HT distribution
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
RS: FULL INCLUSIVE SAMPLE• Aim: analyze jet and graviton distributions and compare the shape of matched
results with the ones given by NLO calculation!
11
• RS model,
Λ = 3 TeV, and
MG = 100 GeV
• Full inclusive sample;
• LO: pp > G, Matched: up to 2-jets
200 400 600 800 1000 1200 14001
1x101
1x102
1x103
NLO resultsLO resultsMatched results
RS @ LHC14
d!/dHT
(fb/G
eV)
HT (GeV)
To warm up:
HT distribution
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
RS: FULL INCLUSIVE SAMPLE• Aim: analyze jet and graviton distributions and compare the shape of matched
results with the ones given by NLO calculation!
11
• RS model,
Λ = 3 TeV, and
MG = 100 GeV
• Full inclusive sample;
• LO: pp > G, Matched: up to 2-jets
200 400 600 800 1000 1200 14001
1x101
1x102
1x103
NLO resultsLO resultsMatched results
RS @ LHC14
d!/dHT
(fb/G
eV)
HT (GeV)
Results
1. Large NLO/LO K-factor
2. Matching normalized to NLO
3. Excellent shape agreement (NLO x Match)
4. Clearly LO results is not enough
k-factor Norm. factor
1.65 1.73
To warm up:
HT distribution
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
RS: SEMI-INCLUSIVE SAMPLE
Processes:
• LO: p p G + jet• Matching: p p G + n-jets, with n=1,2,3
12
Cuts:
PTmiss PT1st jet η Qmatch
LHC > 500 GeV > 50 GeV < 4.5 > 50 GeVTevatron > 120 GeV > 20 GeV < 4.5 > 30 GeV
Semi-inclusive graviton production @ LHC
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
600 800 1000 1200 1400 1600 1800 20000
1x10-1
1
1x101
1x102
RS Mg = 1 TeVRS Mg = 100 GeVMatched results
PT[graviton] (GeV)
d!/dP T
[gra
vito
n] (
fb/G
eV)
RS @ LHC14
RS: SEMI-INCLUSIVE SAMPLE
13
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
600 800 1000 1200 1400 1600 1800 20000
1x10-1
1
1x101
1x102
RS Mg = 1 TeVRS Mg = 100 GeVMatched results
PT[graviton] (GeV)
d!/dP T
[gra
vito
n] (
fb/G
eV)
RS @ LHC14
RS: SEMI-INCLUSIVE SAMPLE
13
600 800 1000 1200 1400 1600 1800 2000
1x10-1
1
1x101
1x102
NLO results Mg = 1 TeVNLO results Mg = 100 GeVMatched results
d!/dHT
(fb/G
eV)
HT (GeV)
RS @ LHC14
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
600 800 1000 1200 1400 1600 1800 20000
1x10-1
1
1x101
1x102
RS Mg = 1 TeVRS Mg = 100 GeVMatched results
PT[graviton] (GeV)
d!/dP T
[gra
vito
n] (
fb/G
eV)
RS @ LHC14
RS: SEMI-INCLUSIVE SAMPLE
13
600 800 1000 1200 1400 1600 1800 2000
1x10-1
1
1x101
1x102
NLO results Mg = 1 TeVNLO results Mg = 100 GeVMatched results
d!/dHT
(fb/G
eV)
HT (GeV)
RS @ LHC14
Results• Matching normalized with NLO (Norm. factors = 1.99, 1.81)
• Excellent shape agreement PT miss• Harder distribution for high HT values
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
BEYOND STANDARD MODEL
Attempt to explain the HP BSM theories
• ADD: model with large extra dimensions[ N. Arkani-Hamed, S. Dimopoulos, G. Dvali, 1998 ]
• RS: model with a warped extra dimension [ L. Randall, R. Sundrum, 1999 ]
• MGM: 4D model that contains a massless graviton[ G. Dvali, arxiv:0706.2050 ]
[ X. Calmet, S. D. H. Hsu, D. Reeb, arxiv:0803.1836 ]
14
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
ADD MODEL
ADD model D = 4 + δ dimensions, flat metric, spatial and compact
M2Pl = M !+2
" V!
15
• Field propagating on δ KK tower:
• massive graviton
• couples to SM particles:
Phenomenology on graviton emission = missing energy!
[ T. Han, J. D. Lykken, R. J. Zhang, Phys. Rev. D 59, 105006 (1999)][G. F. Giudice, R. Rattazzi, J. D. Wells, Nucl. Phys. B 544, 3 (1999)]
Lint = ! 1!
!
n
G(n)µ! T
µ!SM
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
ADD: SEMI-INCLUSIVE SAMPLE
600 800 1000 1200 1400 1600 1800 20000
1x10-2
1x10-1
1 NLO results !=2NLO results !=4NLO results !=6Matched resultsSM background
PT[miss] (GeV)
d!/d
P T[m
iss]
(fb
/GeV
)
ADD @ LHC14
16
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
ADD: SEMI-INCLUSIVE SAMPLE
600 800 1000 1200 1400 1600 1800 20000
1x10-2
1x10-1
1 NLO results !=2NLO results !=4NLO results !=6Matched resultsSM background
PT[miss] (GeV)
d!/d
P T[m
iss]
(fb
/GeV
)
ADD @ LHC14
16
600 800 1000 1200 1400 1600 1800 20001x10-3
1x10-2
1x10-1
1
NLO results ! = 2NLO results ! = 4NLO results ! = 6Matched results
d!/dHT
(fb/G
eV)
HT (GeV)
ADD @ LHC14
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
ADD: SEMI-INCLUSIVE SAMPLE
600 800 1000 1200 1400 1600 1800 20000
1x10-2
1x10-1
1 NLO results !=2NLO results !=4NLO results !=6Matched resultsSM background
PT[miss] (GeV)
d!/d
P T[m
iss]
(fb
/GeV
)
ADD @ LHC14
16
600 800 1000 1200 1400 1600 1800 20001x10-3
1x10-2
1x10-1
1
NLO results ! = 2NLO results ! = 4NLO results ! = 6Matched results
d!/dHT
(fb/G
eV)
HT (GeV)
ADD @ LHC14
Results• Matching normalized with NLO:
• Norm. factors = 2.05, 2.34, 2.49
• Excellent shape agreement PT miss• Harder distribution for high HT values• Irreducible background has different shape!
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
Simulations with spin-2 particles in MG/ME: ready for phenomenology!
Phenomenology of p p G + n-jets
Detailed comparison between NLO and MLM-matching:
✓done for ADD, RS and MGM
✓Good agreement for graviton/missing PT, 1st and 2nd jet PT, graviton and jet pseudo-rapidities
✓Harder distributions for large matched HT (matching is computed up to 3 extra partons)
Upshot: matched samples (normalized to NLO) give a theoretically accurate and experimental friendly way to simulate events at the LHC
More information on: [ P. d. A, Kaoru Hagiwara, Qiang Li, Fabio Maltoni, arXiv: 1101.5499]
SUMMARY SPIN-2 PRODUCTION
17
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
Thank you!!
18
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
ADD KK SUMMATION
• In the ADD model the individual KK resonances have masses equal to m=n/R.
• The mass gap between neighboring modes ∆m is small for δ not too large. Quantitatively one finds ∆m≈ 20 keV, 7 MeV and 0.1 GeV for MS = 1 TeV and δ =4, 6 and 8.
• The discrete mass spectrum can be approximated by a continuum with a density of states dN = ρ(m)dm, where
19
!(m) =2"!/2
!(#/2)M
2Pl
M2+!S
m!!1
[ T. Han, J. D. Lykken, R. J. Zhang, Phys. Rev. D 59, 105006 (1999)][G. F. Giudice, R. Rattazzi, J. D. Wells, Nucl. Phys. B 544, 3 (1999)]
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
ADD @ LHC
20
!" !# $ # "
%
%$
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&'()*+,-./,)01#
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!"" #"" $""" $%"" $&"" $!"" $#"" %"""
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()*+,-./01.+23%
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!"#$%&'()&*'+,)-.
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!"#$%&'()*+',-)./
!""#$#%&'()
&!0&!"#$%&'()*+',120-)./
Figure 4. NLO/k!-MLM matching comparison for the ADD model at the LHC (!
s = 14 TeV) with! = 5 TeV. The NLO results are given by the red, green and purple bands for ! = 2, 4, 6, respectively.The matched results are given by the black curves with the same parameters as for the NLO ones. Thedominant Z " ""̄ background is also shown as a reference by the blue curve. The k!-MLM matchedcurves are normalized by the NLO results, and the normalization factors can be found in Table 4.
– 15 –
Norm. factor = 2.05, 2.34, 2.49
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
RS @ LHC
21
!" !# $ # "%
%$
%$$
%$$$
%$$$$ &'()*+,-./,)01)2)%$$)3+4
&'()*+,-./,)01)2)%)5+4
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!"
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!"#$%&'$(%)/0.*'+,
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!"" # "" $ "" %"" & """& '& "(!
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) *+ ,-. /012/,3 4 ,5 ,& "",6. 7
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3 9 2: ;. < ,-. /012/
!"
!"#$%&'()%*+',-
$!.$!"
!"#$%&'()%*/0.+',-
!"#$#%&'()
Figure 8. NLO/k!-MLM matching comparison for the RS model at the LHC with ! = 3 TeV. TheNLO results are given by the red and green bands for m1 = 1 TeV and 100 GeV respectively. Thematched results are given by the black curves with the same parameters as for the NLO ones. Thek!-MLM matched curves are normalized by the NLO results, and the normalization factors can be foundin Table 4.
– 19 –
Norm. factor = 1.99, 1.81
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
FULL INCLUSIVE RS @ LHC14
22
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#$%&'()&*'+,-".)/0
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Figure 10. NLO/k!-MLM matching comparison for the RS Model at the LHC with m1 = 100 GeV and! = 3 TeV. Di"erent cuts from the ones specified above are used to show the interesting case with large!-factors.
5.3 Large !-factors
In multi-jet final states, observables exist that can be subject to large NLO QCD corrections
at TeV scales [54]. Examples include HT or the PT of the leading jet. Such observables are
sensitive to the opening of new channels with new kinematic topologies at NLO, which are
enhanced by parton distribution e"ects or by special kinematic configurations (leading to large
logs). One is then lead to the impression that higher order corrections can be dominant and
the perturbative series is not well-behaved. In fact, one can easily show that this is not the case
for more inclusive quantities and this behaviour is due to the choice of the specific observable.
In any case, the e"ects in some specific region of the phase space can be large and need to be
accounted for. One method was introduced Ref. [54]. Here we show that multi-parton samples
with k!-MLM matching provide a reliable description also of these kind of e"ects. In Fig. 10
we collect some representative plots which show it. For simplicity, we consider the RS model at
the LHC with ! = 3 TeV and m1 = 100 GeV, with jet cuts |"j | < 4.5 and P jT > 50 GeV, and
graviton cut PGT > 50 GeV. Comparing the LO and NLO curves, one can see the appearance
of very large !-factors, especially at large PGT , leading jet PT and HT . The matched samples
– 21 –
Norm. factor = 1.73
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
PSEUDO-RAPIDITY RESULTS
Results
• MLM normalized with NLO• Excellent agreement (shape)
23
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
PSEUDO-RAPIDITY RESULTS
Results
• MLM normalized with NLO• Excellent agreement (shape)
-3 -2 -1 0 1 2 3
1
10
100
NLO results ! = 2NLO results ! = 4NLO results ! = 6Matched results
ADD @ LHC14
d!/d"[G
ravi
ton]
(fb/G
eV)
"[Graviton] (GeV)
ADD
23
P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders
PSEUDO-RAPIDITY RESULTS
Results
• MLM normalized with NLO• Excellent agreement (shape)
-3 -2 -1 0 1 2 3
1
10
100
NLO results ! = 2NLO results ! = 4NLO results ! = 6Matched results
ADD @ LHC14
d!/d"[G
ravi
ton]
(fb/G
eV)
"[Graviton] (GeV)
ADD
-3 -2 -1 0 1 2 3
100
1000
10000 NLO results Mg = 100 GeVNLO results Mg = 1 TeVMatched results
d!/d"[G
ravi
ton]
(fb/G
eV)
"[Graviton] (GeV)
RS @ LHC14
RS
23