Graviton + jets
I. People
 Priscila de Aquino,
 Qiang Li,
 Fabio Maltoni,
 Kaoru Hagiwara
 Claude Duhr?
II. Aim
To study graviton production through multijet 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
  
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
+ 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?
  
V. Qiang's NLO results
For reference, the cuts in 0911.5095 (NLO QCD corrections to G+monojet) are the following:
 LHC: PTmiss>500GeV;
 Tevatron: PTmiss>120GeV; harder jet : Ptj>150GeV with ; softer jet with PT>60GeV, 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 and
 For the Tevatron,"jets are defined by the K_T algorithm with D=0.7, and are required to satisfy
 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
Attachments
 ADD_LHC_Run01_Report.pdf (154.7 KB)  added by trac 5 years ago.
 ADD_LHC_Run02_Report.pdf (155.3 KB)  added by trac 5 years ago.
 ADD_LHC_Run03_Report.pdf (155.6 KB)  added by trac 5 years ago.
 Ml_LHC_Run01_Report.pdf (438.4 KB)  added by trac 5 years ago.
 Ml_LHC_Run02_Report.pdf (396.6 KB)  added by trac 5 years ago.
 RS_LHC_Run01_Report.pdf (354.9 KB)  added by trac 5 years ago.
 RS_LHC_Run02_Report.pdf (434.4 KB)  added by trac 5 years ago.
 RS_LHC_Run03_Report.pdf (147.2 KB)  added by trac 5 years ago.
 RS_LHC_Run04_Report.pdf (144.0 KB)  added by trac 5 years ago.
 Results_LHC_d2.pdf (73.9 KB)  added by trac 5 years ago.
 Results_LHC_d4.pdf (73.5 KB)  added by trac 5 years ago.
 Results_LHC_d6.pdf (74.4 KB)  added by trac 5 years ago.
 Results_LHC_ADD.pdf (74.5 KB)  added by trac 5 years ago.
 Results_LHC_RS.pdf (106.9 KB)  added by trac 5 years ago.
 JetRates_ADD.pdf (47.9 KB)  added by trac 5 years ago.
 ADD_InvMassGrav.pdf (70.6 KB)  added by trac 5 years ago.