Mass methods

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Variable/Method Reference(s)/Code Realm of Applicability Precision Good for Fails for Unknown/Future directions
MT (ancient) One definition is the Barger's M_T (Phys.Rev.D36:295,1987)[1], that you can see applied for just one missing particle in hep-ph/0812.4313[2] one missing particle
Meff hep-ph/9610544[3], hep-ph/0006276[4] Discovery of NP with massive particles. Bad, quoted to be 20%-50% on masses in references, but needs to be interpreted in a specific model. Discovery above SM contribution and estimating mass scale of particles with dominant cross section. Does not identify process, but gives some information on particle content of dominant topologies.
HT always does not identify process in any way
Edges hep-ph/9610544[5] (lots) Cascade decay chains. Gives one relationship between NP masses per pair of visible final state particles. Quoted as 4% on LSP in fast simulation pheno study of SPS1a, hep-ph/0410303 [6] Mass differences in leptonic decays. Dependence on absolute mass scale is weak. Can be fooled by false solutions. Intermediate 3-body decays? Combinatoric (other side) jets not considered. Calorimeter nonlinearity?
MT2 hep-ph/9906349[7]
MT2 kink ("stransverse" mass) arXiv:0709.0288[8] 4-body final state, 2 missing large mass differences and large pT small mass differences or no pT
MTn 4-body final state, n missing
MTgen arXiv:0708.1028[9]
M2C arXiv:0712.0943[10]
M3C arXiv:0811.2138[11]
\sqrt{s}_{min} arXiv:0812.1042[12] See also Eq.5 of arXiv:0902.4864 and Eq.53 of hep-ph/0508097 which may be the same. (thanks K.C. Kong)
Exactly-constrained Polynomials arXiv:0707.0030[13] 4 on-shell intermediate resonances, 2 missing Apply to squark-neutralino2-slepton-neutralino1 cascade where other side is squark-neutralino1.
Multi-event Polynomial intersection arXiv:0802.4290[14] 5 or more on-shell intermediate resonances, 2 missing Statistics of histograms created with n-event subsets; If mass differences are fixed and the masses are increased, what happens? (Sabine Kraml); Develop methods for asymmetric chains and < 6 intermediate resonances.
"Wedgebox" techniques arXiv:0802.0022
  • more references can be found eg in [[15]]
  • How can we define "Precision" in a manner that lets us meaningfully compare different methods? A lot of process-specific assumptions and backgrounds usually enter the application of each method.
  • In general, all methods need to be systematically tested in cases where the assumptions needed for the method are not satisfied.
  • Appropriate consideration of ISR/FSR jets is not usually considered. Requires 2->3 matrix elements where the hard scattering process includes a possible extra hard quark/gluon radiation.



  • Models to be studied

SUSY at SPS1a (Sezen), UED at SPS1a (Tommaso), U(1)_B-L (Lorenzo) for event generation

Technicolor (Sasha; see separate point below)

question 1): what should be used for ued ?? comphep feynrules and madgraph have been validated against each other, but there is contradiction w pythia... tommaso renaud and the others should try to figure out what's going on by contacting claude and benjamin and priscila ([16], arXiv:0906.2474[ might be due to different version of ued implemented; if so, should be documented

  • Signatures

3 lepton + MET

2 lepton + MET

2 lepton + 2 jets + MET

2 lepton + 4 jet (+ MET) OR 4 lepton + 2 jets + MET

4 lepton + MET

  • Methods

polynomial: Sezen, (Bob)

Webber's linear method: Renaud + Bob

MT2: Chris + Monoranjan, Michael

MT2-assisted methods: Michael

Meff + sqrt(s)_min: Jean-Raphael + Asesh

Edges: Tania, Phillip

MT: Lorenzo (S.Moretti and A.Belyaev are happy to collaborate)

  • Event samples

- Parton level, no shower, no hadronization, no detector

- Parton level, no shower, no hadronization, no detector, 1 extra hard jet

- Parton level + shower + hadronization + detector

question 1): which generator should be used for 2->3 ?? herwig cannot do this

question 2): what about delphes validation ?? sezen works on it

  • Parton level cuts (open to discussion)

- Pt: Generic Pt > 20 GeV on all objects including EtMiss

- Eta: eta cut is usually very detector dependent. Which part of the detector can be trusted for which object, excluding "crack region", ... There is also how close to beam pipe you can detect things. So to keep thing simple I would vote to have only a cut on Eta max independently of the objects.

  • Data storage

at Cern (people at Cern)

  • Deadlines (preliminary)

data generation until mid august

results mid november

  • Technicolor model

by A. Belyaev

possible signatures (partly in accordance w above):

A) 1 lepton + ETmiss

B) 1 lepton + ETmiss + jets

C) 2 leptons + ETmiss

D) 2 leptons + ETmiss + jets

E) 3 leptons + ETmiss

F) 4 leptons + ETmiss

Sasha plans to apply basically all methods on this model by himself but is happy to share data and knowledge.


Here people who generated data which is ready for analyses should shortly describe what is available, in which format, and where the data can be obtained. We will put up sth similar later on when first data analyses have been performed.

  • U(1)_B-L (Lorenzo)

At the moment, you can find 2 samples of events in my public directory at CERN:


called B-L_1k.lhe and B-L_j_1k.lhe, produced with CalcHEP.

In details, they are 1000 events from the process:

pp -> ~n,~n

with ~n = ~n1,~n2,~n3 are the heavy neutrinos further decayed;

where p = u,U,d,D,s,S,c,C,G (gluon).

The same for the extra jet

j = u,U,d,D,s,S,c,C,G,

where the kinematical cuts:

P_T > 20 GeV

|eta_j| < 3 have been applied in the generation.

Inclusive cross-sections (regardless of the final state in which the heavy neutrinos decay) are:

B-L_1k.lhe, parton level, cs = 80.32 fb

B-L_j_1k.lhe, parton level with extra jet, cs = 20.02 fb

Notice that excluding taus means to decrease the above cross-sections at least by a factor 2/3 roughly (no mixing between heavy neutrinos, so ~n3 is almost always excluded).

Finally, I introduced new LHA numbers for neutrinos and Z':

nu_h1 = 9910012

nu_h2 = 9910014

nu_h3 = 9910016

H1 = 9900025

H2 = 9900026

Zp = 9900032

I don't state the masses for the Z' and the neutrinos, so you will have something to work out and enjoy.

Production of SUSY/UED samples

This section describes how we generated signal samples. For both models, the mass spectrum is corresponding to sps1a point.

  • UED model is obtained from FeynRules with R = 1/500 and alpha_s computed at 1/R. This is not relevant for further steps and mass spectrum is overwritten to reproduce susy sps1a one. The new mass spectrum with equivalence between UED and susy particles can be seen [[17][on this link]]. Input files for madgraph are in this [[18][directory]].
  • Matrix element generation is done with Madgraph 4.4.24. Madevent was used to generate the following processes : gogo, gogoJ, gosq, gosqJ, sqsq, sqsqJ, neuneu, neuneuJ where go = gluino, sq = (anti-)squark, neu = color neutral gaugino or slepton, J = uu~dd~ss~cc~g. param_card.dat can be found on these directories for[[19][ued]] and similarly for susy.
  • SUSY/UED decays chains with possible 3-bodies decays are done with BRIDGE v1.8 [20]
  • Matching between samples with/without ISR is done using Madgraph MLM matching procedure with k_T jet algorithm and QCUT = 40 GeV. To avoid double-counting in sqsqJ and gosqJ samples, events with an intermediate gluino resonance were removed using EXCRES key. This procedure is at the moment working only when interfacing directly pythia with madgraph. In order to solve this a 3-steps procedure had to be done :
    1. get list of rejected events from matching procedure by running pythia directly on madgraph samples
    2. run pythia on BRIDGE samples in inclusive mode (keeping all events)
    3. rejects events from resulting pythia samples via the step1 list when building Delphes files from STDHEP.

To do that, a modified version of Delphes 1.8 was built. The code can be found at the following link [21]

  • Detector simulation/emulation is done with Delphes 1.8 using default detector and trigger cards.
  • Data
Process SUSY UED Background ttbar Background W+jets Background Z+jets
gogo [22] [23]
gogoJ [24] [25]
gosq [26] [27]
gosqJ [28] [29]
sqsq [30] [31]
sqsqJ [32] [33]
neuneu [34] [35]
neuneuJ [36] [37]
  • For the above mcdb links, lhe files are files dumped by madevent so before bridge, pythia and delphes. They can be used to reprocess data with more recent releases of the following steps. In order to analyze data, you should use the Delphes files.
  • If you want to study 2 to 2 hard matrix elements, with extra radiation generated only by the Pythia parton shower, you should select the samples gogo(incl)+gosq(incl)+sqsq(incl)+neuneu(incl)
  • If you want to study 2 to 2 plus 2 to 3 hard matched matrix elements including 0+1 extra jets properly described by the ME and matched with Pythia's parton shower, you should select the samples gogo(excl)+gogoJ(incl)+gosq(excl)+gosqJ(excres)+sqsq(excl)+sqsqJ(excres)+neuneu(excl)+neuneuJ(incl)

Analysis of Delphes files

in order to do quick analysis for testing, I (Renaud) have written my own small program simply based on MakeClass. You can find it there if you wish :

svn co svn+ssh://
make all
./bin/delphesana myfiles.list [cross-section(pb)] [luminotity(fb-1)]
or if you want to merge files from different processes :
python python/

To run your own analysis, edit the file src/delphesana.cpp to book, compute, and fill the histograms you're interested. Recompile with make and re-run with python python/ This will generate an output .root file for each input channel. It will then sum the channels and create sum.root.

Note (J-R): When I first tried, I got error: ./bin/delphesana.exe: error while loading shared libraries: cannot open shared object file: No such file or directory I had to create a soft link to the library: ln -s lib/ to make it work.

More on Delphes files analysis

some guideline through the use of delphesana:

  • in general, the data.root files give you some standard information about the decay chains which have been generated. You can find more info at the Delphes user manual [38] or, alternatively, in the .h files in the include subdirectory of delphesana
  • (for some machines, you have to comment out the infile.good() quest in delphesana.cpp)
  • running it for MT2: comment out the respective lines in AFTER downloading the MT2 library [39]; also comment out the respective lines in delphesana.cpp (you need to recompile of course). This will then result in an ONSCREEN output of MT2 (there is NO histogram automatically generated; this you have to add yourself)
  • general variables: you need to modify delphesana.cpp in src/. There are samples histograms in output.root like eg hEtago (eta of gluino); these are all defined and booked in delphesana.cpp. (Comments about different ways of treating the files are welcome).
  • Update for dumping of decay chains (thanks to Renaud): modify the files in src/Utils.cpp, then
svn up
svn co interface/SPDCWebber.h
svn co src/SPDCWebber.cpp
  • status tag in the gen.particle branch [40]:

- status = 1 : an existing entry, which has not decayed or fragmented. This is the main class of entries, which represents the `final state' given by the generator.

- status = 2 : an entry which has decayed or fragmented and is therefore not appearing in the final state, but is retained for event history information

- status = 3 : a documentation line, defined separately from the event history.

  • More comments welcome

LHE format to NTUPLEs

At pg 5 of [41] there is the description of how to convert from .lhe files to ntuples.

The script is called nt_maker: if you want it, or you want more information about it, I suggest to ask to Sasha Belyaev. Mail:

MT2 study on SUSY SPS1A Sample

(Michael Tytgat)

Some very first plots of an MT2 study on the SUSY SPS1A sample. Here, the "gogo_incl" and "gosq_incl" were taken. The analysis looks for events of the type pp-> X + stau1 stau1-> X + tau tau chi_1^0 chi_1^0. Plots are normalized to 1fb-1. Mass of the stau1 here is 134.491GeV. MT2 is computed using the exact neutralino mass (96.69GeV).

Generator level

Number of leptons vs. sleptons (all)
Number of leptons vs. sleptons (all)
Same sign stau1 events
Same sign stau1 events
Opposite sign stau1 events
Opposite sign stau1 events

The upper edge of these MT2 spectra shown above should give a lower limit of the stau1 mass, which seems to work :-)

Reconstructed events

Same sign 2 tau jet events
Same sign 2 tau jet events
Opposite sign 2 tau jet events
Opposite sign 2 tau jet events

Things are a bit more problematic here, lack of statistics to begin with ... No special selection on the tau jets yet.

Edge study, first results, SUSY


  • sqsq sample

Studies starting with m_mumu for opposite sign muons. First plot is generator level, muons are forced to come from neu2-> smuR mu -> mu mu neu1; second plot is analysis level with the same preselected muons (ie neu2 required in the decay chain). Third plot is including ALL opposite sign muon pairs: selected were events with ossf leptons of 2nd generation only. I did a precut on the invariant mass to exclude Z-> mu mu events. Expected upper edge: 81.39 GeV. This can well be determined from the mass edge, looking at generator level (= a cross check madgraph got things ok) and analysis level where the neu2 was inforced only (ie "correct" muons are not too much changed by delphes); however, including all events w 2 os mus, we get a lot of background mainly stemming from hadronic decay to mus, where the hadrons come from the shower. There might be ways around that though; this is not a dedicated study for that channel. Also lacking: statistics (y axis is arbitrary here, ie i set weight = 1).

mumu invariant mass, generator level, neu2 induced
mumu invariant mass, generator level, neu2 induced
mumu invariant mass, analysis level, neu2 induced
mumu invariant mass, analysis level, neu2 induced
mumu invariant mass, analysis level, all events (cut on Z invariant mass)
mumu invariant mass, analysis level, all events (cut on Z invariant mass)
mumu invariant mass, analysis level,non neu2-induced events (="background") only (cut on Z invariant mass)
mumu invariant mass, analysis level,non neu2-induced events (="background") only (cut on Z invariant mass)
ee invariant mass, analysis level, all events (cut on Z invariant mass)
ee invariant mass, analysis level, all events (cut on Z invariant mass)

(i do have additional files for the edge regions only i did not want to put here)

Electron results are similar; the complete combination of all e+e- (single pair !!) events is a bit messier as some of the "visible" particles coming out of madgraph/ bridge/ pythia seem to escape (often 4 e events are seen as 2 e events on the analysis level). For both ee and mumu events, the expected triangular shape [42] is clearly lost; this can also be seen from event numbers (296 of 557 events are from neu2 in the muon case, and 358 out of 687 in the electron case. did not check what the main contribution is from other sources).

Actually bookkeeping of ossf dimuon events is quite messy: there are 350 on the generator level (roughly 300 coming from the signal), then there are 1441 (!!) on the visible level (ie before the delphes run, after shower/ hadronization/ decay), and then between visible (= outcome of generator) and analysis level, 1015 of these are lost and 426 are gained (eg cases where there are 3 muons on the visible level and 1 escapes the detector). however, the background (dimuon pairs in analysis coming from signal) has _fortunately_ no peak in the edge region. most from hadronic or tau decays (or combinations). is there a way to suppress these (i guess that's a known problem) ??

(Simple) Transverse Mass study, first results, SUSY & UED


  • gogo samples

I took the Barger definition of the Transverse Mass I quoted in the table. No special requirements for the plots, just to have at least 2 taus. As known, the simple Transverse Mass doesn;t work when you have more than one missing particle, so these plots should be looked at as a disprove of the variable for SUSY/UED. Here there are Generator vs Reconstructed level OS and SS taus, in SUSY and UED from gluino-gluino production. No other requirements in the chain.


SUSY OS Tau Tau Transverse mass, generator level
SUSY OS Tau Tau Transverse mass, generator level
SUSY SS Tau Tau Transverse mass, generator level
SUSY SS Tau Tau Transverse mass, generator level
SUSY OS Tau Tau Transverse mass, reconstructed level
SUSY OS Tau Tau Transverse mass, reconstructed level
SUSY SS Tau Tau Transverse mass, reconstructed level
SUSY SS Tau Tau Transverse mass, reconstructed level


UED OS Tau Tau Transverse mass, generator level
UED OS Tau Tau Transverse mass, generator level
UED SS Tau Tau Transverse mass, generator level
UED SS Tau Tau Transverse mass, generator level
UED OS Tau Tau Transverse mass, reconstructed level
UED OS Tau Tau Transverse mass, reconstructed level
UED SS Tau Tau Transverse mass, reconstructed level
UED SS Tau Tau Transverse mass, reconstructed level

At the generator level I also plot the Transverse mass for 4 (whatever) leptons

SUSY 4l Transverse mass, generator level
SUSY 4l Transverse mass, generator level
UED 4l Transverse mass, generator level
UED 4l Transverse mass, generator level

...none of them very significant (...but it is for this reason they invented MT2! ;))

Meff study, first results, SUSY


  • gogo_incl sample

Mass effective defined as: Sum Pt of the 4 objects + MET. No preselection cuts + object an the analysis level (no truth). In the reference papers, they studied only 4 jets + MET claiming that they have less background from neutrino. I did however plot the 2 jets + 2 leptons and 4 leptons signature as well. It is possible to identify the peak of the distribution although resolution is quite bad.

4 jets signature
4 jets signature

The next step would normally be to identify correlation between M_eff and M_SUZY by simulating many different mass point for M_SUZY. For the scope of what we want to do, we can probably assume that we know this correlation number C: M_SUZY = C * M_eff with it uncertainty. We could use the uncertainty given by the reference papers.

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