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GRAVITON PRODUCTION AT HADRON COLLIDERS Priscila de Aquino Katholieke Universiteit Leuven (KUL) & Université Catholique de Louvain (UCL) 23rd Rencontres de Blois June 1st, 2011 based on P. d. A, Kaoru Hagiwara, Qiang Li, Fabio Maltoni, arXiv: 1101.5499

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Page 1: GRAVITON PRODUCTION AT HADRON COLLIDERS · account for the presence of QCD radiation ME calculations Parton Shower simulator • parton-level description • valid for hard/separated

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

Page 2: GRAVITON PRODUCTION AT HADRON COLLIDERS · account for the presence of QCD radiation ME calculations Parton Shower simulator • parton-level description • valid for hard/separated

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

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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

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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!

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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!

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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...

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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...

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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

Page 9: GRAVITON PRODUCTION AT HADRON COLLIDERS · account for the presence of QCD radiation ME calculations Parton Shower simulator • parton-level description • valid for hard/separated

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

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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)

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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 ?!?:

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

Page 24: GRAVITON PRODUCTION AT HADRON COLLIDERS · account for the presence of QCD radiation ME calculations Parton Shower simulator • parton-level description • valid for hard/separated

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

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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

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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

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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

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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!

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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

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P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders

Thank you!!

18

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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)]

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P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders

ADD @ LHC

20

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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

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P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders

RS @ LHC

21

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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

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P. de Aquino, 23rd Rencontres de Blois 01/06/11Graviton production @ hadron colliders

FULL INCLUSIVE RS @ LHC14

22

!" !# $ # "%&%$

"

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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

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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

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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

Page 37: GRAVITON PRODUCTION AT HADRON COLLIDERS · account for the presence of QCD radiation ME calculations Parton Shower simulator • parton-level description • valid for hard/separated

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