Graviton + jets

I. People

• Priscila de Aquino,
• Qiang Li,
• Fabio Maltoni,
• Kaoru Hagiwara
• Claude Duhr?

II. Aim

To study graviton production through multi-jet final state processes at hadron colliders taking into account the following models: ADD, RS and a massless graviton model. The goal is to compare one model to another considering they are expected to have the same signature.

(For RS graviton,we will not consider its decay)

III. Structure of the Paper

III.1) Introduction

Small motivation for this work and introduction for each model.

III.2) Description of the models

2.1 - Definition of each model

2.2 - Implementation in MG

2.3 - Choice of parameters (including exclusion limits)

III.3) Validation of the inclusive samples

3.1 - How the matching is done

(In this case, the scale is fixed by the matching, different from the NLO calculation case)

3.2 - Comparison with Qiang's NLO results

(See section V for more information)

+

III.4) Results: distributions at the Tevatron and the LHC

• Plots to be shown:
• Pt missing (graviton)
• Rapidity (MC level)
• Pt of leading jet
• Pt of 2nd jet
• Ht distribution

III.5) Conclusions

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IV. Event generation: MLM matching

IV.1) General Parameters for the matching:

a) run_card.dat:

• • ickkw=1,
  • ktscheme=1 (MLM matching with KT scheme)
  • ptj=50 GeV (minimum pt for the jets)
  • etaj=4.5 (max rapidity for the jets)
  • xqcut=45 GeV
  • LHC: Pt grav = 450 GeV (minimum pt for the graviton)
  • Tevatron: Pt grav = 120 GeV
  • Htjmin = L_MG ("Step function" for the massless_grav case) => only for the massless case

(In order to analyze Pt grav > 500 GeV for the LHC and Pt grav > 150 for the Tevatron, we will fix a lower parameter to generate the events.)

+ g>

b) pythia_card.dat:

• • QCUT=50 GeV

c) param_card.dat:

RS - I) For both Tevatron and LHC

• • M1_grav = 100 GeV (Not physical done only to see how it approaches the massless case)
  • L_RS = 3 TeV (limit given in 0909.1587 (fig. 1) and (fig. 2))

RS - II) For both Tevatron and LHC

• • M1_grav = 1 TeV
  • L_RS = 3 TeV

+ In the RS model, L_RS=M1_grav/x1/(k/M_Pl) (See Phys.Rev.Lett. 84, 2080 (2000)), x1 is the first root of the Bessel function of order 1, x1~=3.83. Thus from Fig.4 in 0710.3338, for M1_grav=1TeV, L_RS ~>2.6TeV

Massless graviton) For both Tevatron and LHC

• • L_MG = 1 TeV

ADD)

• • L_ADD = 5 TeV (LHC), 1 TeV (Tevatron)
  • NADD= 2, 4, 6
  • Lower mass limit = 0.01 GeV
  • Higher mass Limit = L_ADD

IV.2) Results and Plots

IV.2.1) Matching results (comparison with NLO/LO)

First we show each matched results via its MatchChecker report. We also show here the comparative plots in which we compare (for each ADD run) the matched result with the NLO/LO result, given the K factor of normalization.

+ a) MatchChecker reports

Model ---------------------	Parameters ---------------------	Name of the Run ---------------------	Plots ---------------------
ADD	L_ADD = 5 TeV NADD = 2	ADD_LHC_Run01	LHC Plots report
		ADD_Tevatron_Run01
	L_ADD = 5 TeV NADD = 4	ADD_LHC_Run02	LHC Plots report
		ADD_Tevatron_Run02
	L_ADD = 5 TeV NADD = 6	ADD_LHC_Run03	LHC Plots report
		ADD_Tevatron_Run03
Massless	L_MG = 1 TeV	Ml_LHC_Run01	LHC Plots report
		Ml_Tev_Run01
	L_MG = 2 TeV	Ml_LHC_Run02	LHC Plots report
	L_MG = 3 TeV	Ml_LHC_Run03
RS	L_RS = 1TeV M_grav = 1 TeV	RS_LHC_Run01	LHC Plots report
		RS_Tev_Run01
	L_RS = 1 TeV M_grav = 100 GeV	RS_LHC_Run02	LHC Plots report
		RS_Tev_Run02
	L_RS = 3 TeV M_grav = 1 TeV	RS_LHC_Run03	LHC Plots report
		RS_Tev_Run03
	L_RS = 3 TeV M_grav = 100 GeV	RS_LHC_Run04	LHC Plots report
		RS_Tev_Run04

+ b) Comparative plots: NLO/LO & matching results

DD model	LHC Comparative plot (PtGrav) for d=2​LHC Comparative plot (PtGrav) for d=4​ LHC Comparative plot (PtGrav) for d=6​LHC combined comparative plot​
Massless grav. model	LHC combined comparative plot
RS model	LHC combined comparative plot​

+ c) Jet Rates for the LHC samples

DD model	Jet rates​
Massless grav. model	Jet rates
RS model	Jet rates

PS. The number of events is normalized by the total number of events of each run.

IV.2.2) Study on the shape of the curves (Pt grav) related to the mass of the graviton

Particularly for the RS model, we can see that the slope of the curve changes with the mass of the graviton (for example, compare RS with L_{RS}{{{ 3TeV/M_{grav} }}} 1 TeV against L_{RS}{{{ 3TeV/M_grav }}} 100 GeV). That is related to the fact we are plotting the pt of the graviton. The harder is the emission, the more inclined the curve will be.

For the RS model is easy to see, because we can control the graviton mass (considering it is an input in this case). For the ADD it is a bit harder because the graviton should be an integration of the KK states. However, we know that the mass density depends on the number of extra dimensions. Therefore, we should have a different slope for each curve given its number of extra dimensions (d=2,4,6).

The problem is that the difference of the slopes will not be large enough that it could be recognized from the pt of the graviton plot. Nevertheless, for the ADD model in MG, the graviton decays into 2 fake particles: x1 and x2. Hence, if we plot the invariant mass of x1 and x2 for each d=2,4,6 (Plot​), we could infeer the difference of the slope through the difference of mass density, showing the same physical behavior for both theories.

IV.3) Plan

IV.3.1) What we already have

IV.3.2) What is being taken care of

IV.3.3) What is missing

IV.3) To be discussed on our next meeting

1) How to present the comparison of matching results with NLO/LO ones? (how to show that the difference on the k factors comes from the different techniques of computing the graviton emission?)

Qiang: I think the comparison can be seen as just another validation way, in the sense that the MLM matched curve should lie inside the uncertainty band of the NLO one, after appropriate adaptation of normalization. And then further the MLM matching can give us more information such as 2nd/3rd jet distribution and jet rates, which the NLO calculation to G+J can not present

2) Confirmation of the plots we both should have: pt graviton, pt leading jet, pt 2nd jet, Ht distribution, rapidity

3) For the RS and massless model, the cuts for searching at the LHC and Tevatron are the same as for the ADD model, it is fine, right?

4) Since ADD model is only an effective model, the results we get are valid only as long as the scales involved in the hard scattering process do not exceed the fundamental scale, we need to quantify the sensitivity of our prediction to the unknown UV completion of the theory. Should we do this?

5) Does matching can give reliable results for total cross section or not? Or just for shape/distribution?
It seems the total cross section after matching is definitely not the same as G+0jet's, or G+njet's. So what is the meaning of the matched total cross section?

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V. Qiang's NLO results

For reference, the cuts in 0911.5095 (NLO QCD corrections to G+monojet) are the following:

• LHC: PTmiss>500GeV; $|\eta_j|<4.5$
• Tevatron: PTmiss>120GeV; harder jet : Ptj>150GeV with $|\eta_j|<1$; softer jet with PT>60GeV, $|\eta_j|<3.6$ is vetoed.
• mur=muf= Pt graviton
• 5 quark flavors considered
• MSTW2008LO/NLO for LO/NLO results *(Will be changed to CTEQ6L1/6M for comparison)*

A question on comparing matched results with the NLO ones:

In the NLO work, indeed different jet algorithm from the one chosen in MG/ME is used, see the jet definition on page 5 of 0911.5095:

• For the LHC, "the jets are defined by the K_T algorithm with D=0.6, and are required to satisfy $|\eta_j|<4.5$ and $PTj>50GeV$
• For the Tevatron,"jets are defined by the K_T algorithm with D=0.7, and are required to satisfy $|\eta_j|<3.6 and PTj>20GeV$
• Here D is just the jet cone separation Drjj, so should we set Drjj cut futher to the matched results, in order to compare with the NLO ones?

In the matching procedure, the separation between jets is defined by the xqcut and pythia's QCUT parameters. We have to set Drjj to zero in the run_card.dat.

VI. References