# 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. Not early data study (requires high luminosity) 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? 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[15]
multiple new variables ("improved" edges) arXiv:0906.2417[16]
• more references can be found eg in [[17]]
• 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.

## Contents

### Outcome

• 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 ([18], arXiv:0906.2474[19]) 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

• Selection cuts / Object definition (open to discussion)

We are currently using Delphes standard cuts for object definition; these here are ADDITIONAL cuts which should/ might be employed on the analysis level (but also might mimick actual detector behaviour in that sense); open to discussion but we should agree on some of these soon.

- MET > 100 GeV (careful; delphes definition includes muons as met; needs to be corrected in analyses)

- Jets: Pt > 50 GeV and |Eta| < 3 (!! new value) (what is delphes default ??)

- Lepton (electron or muon): Pt > 10 GeV and |Eta| < 2.5 + isolated (IsoIPt < 6 GeV + ?IsoIFalg? )

- open to discussion: value of isopt (delphes default: 2; higher values problematic ??)

- must have exact number of isolated lepton for the given signature.

- all objects in final analyses are defined at reconstruction level (NOT open to discussion)

- should we introduce additional "chain specific" selection cuts (as eg in [20]) ?? (Tania)

- decays involving taus: taken w a grain of salt. Should include mtautau working group results [[21]] at a later stage.

• Delphes definitions (check the manual [22])

- electron (or muon): match of PID, existence of the track (|eta|<2.5) and PT > 10 GeV (in particular, no fakes);

- MET: opposite of the (vectorial, just x- and y- axis) sum of the calorimetric deposits. In particular no muons in MET, as it is the (opposite of the) sum of the particles that are measured with calorimetry).

also:

- bool IsolFlag // stores the result of the tracking isolation test

- float IsolPt // sum of all track pt in isolation cone (GeV/c)

meaning that if your lepton pass successfully the isolation test, the IsolFlag is set to TRUE (=1). Otherwise, IsolFlag = FALSE (=0). The isolation test consist in checking that there is no track with pt> 2 GeV/c in a given cone (dR=0.5) around the considered lepton. In addition, IsolPT contains the sum of the pt of all tracks (no cut on their pt) around the considered lepton, in a cone of 0.5

• Data storage

at Cern (people at Cern)

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.

## Data Samples

### U(1)B − L (Lorenzo Basso)

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

/afs/cern.ch/user/b/basso/public/

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.

### SUSY/UED

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 [[23][on this link]]. Input files for madgraph are in this [[24][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[[25][ued]] and similarly for susy.
• SUSY/UED decays chains with possible 3-bodies decays are done with BRIDGE v1.8 [26]
• 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 [27]

• Detector simulation/emulation is done with Delphes 1.8 using default detector and trigger cards.
• Data
Process SUSY UED
gogo [28] [29]
gogoJ [30] [31]
gosq [32] [33]
gosqJ [34] [35]
sqsq [36] [37]
sqsqJ [38] [39]
neuneu [40] [41]
neuneuJ [42] [43]

• 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)
• PYTHIA cross sections in pb (please use these values ONLY when reweighting your data)
Process SUSY UED
gogo_incl 4.52945324
gogo_excl 1.6438189
gogoJ_incl 3.82788336
gogoJ_excl 1.61233539
gosq_incl 19.955731
gosq_excl 8.81417937
gosqJ_incl 14.6035886
gosqJ_excres 12.9400783
sqsq_incl 6.56187537
sqsq_excl 3.12992379
sqsqJ_incl 7.57441121
sqsqJ_excres 4.69966331
neuneu_incl 1.97293405
neuneu_excl 1.34835017
neuneuJ_incl 3.53726506
neuneuJ_excl 3.53726506

### Backgrounds

(Tommaso Lari)

ttbar+jets W+jets Z+jets
[44] [45]

Other possible backgrounds include diboson, and single top. These are not generally as important as the above, but should be kept in mind in case your analysis would be sensitive to these.

I have developed a filter to reduce the size of the delphes files. Because of the structure of the delphes program I had to apply the filter at the truth level; I have chosen the following filter:

• count the number of electron or muons with pt > 5 GeV and eta<3.2
• compute the missing energy from the neutrino momenta
• if nlep < 2, require ptmiss > 80*GeV
• if nlep == 2, require ptmiss > 40*GeV
• if nlep > 2 accept the event

## 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://svn.cern.ch/reps/brunelie/LesHouches09/MassAndSpin/DelphesAna
source setup.sh
make all
./bin/delphesana myfiles.list [cross-section(pb)] [luminotity(fb-1)]
or if you want to merge files from different processes :
python python/run_delphesana.py


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/run_delphesana.py. 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: libdelphesana.so: cannot open shared object file: No such file or directory I had to create a soft link to the library: ln -s lib/libdelphesana.so 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 [46] 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 setup.sh AFTER downloading the MT2 library [47]; 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 [48]:

- 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.

LHE format to NTUPLEs

At pg 5 of [49] 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: a.belyaev@soton.ac.uk

## Results

### 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)
Same 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
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.

• MT2-kink study
MT2 kink method for same sign stau1 events

First attempt of MT2 kink method on same sign stau1 events (generator level) : make a scan of the edge of the MT2 distribution as function of the neutralino test mass; the kink is expected at the correct neutralino mass ...

MT2 kink method for same sign stau1 events, Pt(X) distribution
MT2 kink method for same sign stau1 events

Check of the influence of Pt(X) cut on the kink for p p -> X + stau1 + stau1 -> X + tau + neutralino + tau + neutralino. The difference is shown with and without a Pt(X) < 80 GeV cut. In the limit of Pt(X) -> 0 one expects the kink to disappear, which to some extend can indeed be seen here.

### Edge study, first results, SUSY

(Tania)

• wanted upper edges: mll : 81 GeV, m_qll : 456 GeV, m_lqmax: 399 GeV, m_lqmin: 321 GeV (where q=d, values for u slightly lower)
• 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, analysis level, neu2 induced
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, all events after osof background subtraction (cut on Z invariant mass and Compton peak); 268 entries
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 [50] 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 148 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). The secondlast plot shows results after osof background subtraction (note the "wrong" labelling, contains in fact 268 events); we see that w this simple subtraction procedure, we could subtract most of the background. Main background source were events where at least one muon comes from a tau decay; muon background with no tau parents is flat (apart from the Compton peak).

• Background from neu2-> stau tau -> tau tau neu1

About 1/3 of the total dimuon background comes from cases where we actually have the chain neu2->stau tau -> neu1 tau tau, and the taus then decay (directly or indirectly) into muons (ie the taus are not reidentified as taujets)!!! Although we can subtract these events easily using the osof subtraction, it clearly means that (s)taus need to be treated w more care (needs further investigation). In total, about 2/3 of the dimuon background events have staus somewhere in the production/ decay chain. First hints for the 'inverse triangle' shape can eg be found in [[51]]. Look also at other results from the Helmholtz mtautau working group (link above under object definition).

• importance of jet identification

To scare you (and motivate you to give more input), here is what happens from generator to analysis level is your selection criterium is "hardest jet" only; i have plotted mlq,max. I ALWAYS only included samples from the correct decay chain, and I demand 2 os muons on both generator and analysis level, as well as a neu2 on the generator level. Shifts in mlqmax of anything larger than about 4-5 GeV will probably completely ruin the analysis here. We do need a smart(er) jet idenification criterium

mlqmax invariant mass, generator level, neu2 induced
mlqmax invariant mass, analysis level, neu2 induced
absolute difference between mlqmax invariant mass, generator and analysis level, neu2 induced only
mlqmax invariant mass, analysis level, neu2 induced, 'proper' jet choice
mlqmax invariant mass, analysis level, neu2 induced, random (= uncorrelated) jet choice

### Further edge studies

(Philipp, sqsg+gosq+gogo+neuneu samples)

• mll while looking at events with neu2 and smuR only:
mll, generator level, neu2+smur events
mll, analysis level, neu2+smur events

• mll while looking at all opposite-sign muon events in analysis level. Subtracting the (reverse) triangle shaped background yields the familiar triangle shape for mll:
mll, analysis level, opposite-sign muon pairs
mll, analysis level, opposite-sign muon pairs, background

• mqll while looking at events with neu2 and smuR only. On generator level we're using the final state quark in the decay chain, on analysis level we choose the jet that produces the mqll value that's closest to the generator level one. We see nice agreement:
mqll, generator level, neu2+smur events, proper quark
mqll, analysis level, neu2+smur events, proper jet

• When compared with the 'proper jet' plot above, the 'hardest jet' plot illustrates that correctly identifying the jet is the key problem and just simply choosing the hardest jet by itself isn't satisfactory:
mqll, analysis level, neu2+smur events, hardest jet

• One way to sort out the incorrectly identified jets is to compute mqll with random jets and compare it with the hardest jet case. The 'diff' plot illustrates that this is only viable with more statistics as the fluctuations are of the order of the signal. Note that the 'random jet' events haven't been normalized here. Ideally one would normalize them so that the tail (>500 GeV here) matches the tail in the 'hardest jet' case. That way the tail would disappear in the subtraction. This again requires a rough understanding of the masses.
mqll, analysis level, neu2+smur events, random hard jet
mqll, analysis level, neu2+smur events, difference between hardest and random jet

### (Simple) Transverse Mass study, Next results, SUSY & UED

(Lorenzo)

• ALL 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 Reconstructed level OS electrons in SUSY and UED from all channels. No other requirements in the chain.

SUSY OS Electrons Transverse mass, Rec. level
UED OS Electrons Transverse mass, Rec. level

Again, the 4 leptons at generator level, asking for 2 neutralino2:

SUSY 4l Transverse mass (asking for 2 neutralino2), generator level
UED 4l Transverse mass (asking for 2 neutralino2), generator level

Just for comparison, I put the Generator level 2 OS Taus, which is the sample with higher statistics. What you see is a smooth curve, which does NOT resemble what this variable looks like when applied to a suitable environment (it should look like a asymmetric peak with a sharp edge at the endpoint).

SUSY OS Tau Tau Transverse mass, generator level

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

### Meff study, SUSY

(J-R)

• gogo_incl sample

Mass effective defined as: Sum Pt of the 4 objects + MET. No preselection cuts + object at 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
2 jets + 2 leptons signature
4 leptons signature

One would normally identify the correlation between M_eff and M_SUSY by simulating many different mass point for M_SUSY. For the scope of what we want to do, we can probably assume that we know this correlation number C: M_SUSY = C * M_eff with it uncertainty. We could use the uncertainty given by the reference papers. M_SUSY = Min(M_gluino, M_squark).

### Polynomials with 4-tau events, SUSY

(Bob McElrath)

• excl samples (analysis level)
• 4 tau's defined as any combination of mu, e, or tau jet.
• 2 or more jets with p_T > 50 GeV (only p_T > 50 jets are considered)
• All possible combinations of jets and tau's are considered.
• I Monte Carloed over pair choice to get 10*(# events) in the histogram. (Our paper computed all N*(N-1) possible pairs -- more time consuming)
• Because this method needs pairs of events, and our framework currently processes one file at a time, these plots consist of pairs taken from each signal sample separately. (e.g. gogo pairs, sqsq pairs, etc, so no pairs with one event from the gogo sample and another from the sqsq sample) This needs to be fixed...
• Slepton/Neutralino mass peaks are broader than in our paper, while the squark is narrower. This is likely due to the extra missing energy in the tau decays.

### Webbers method, first results

(Tania)

First parton level results from Webbers method, where I looked for osof pairs from the neu2s in the decay chain. In the sqsq sample, there are 3 interesting events on parton level; one of them however, has a neu4->neu2 decay, so it is in a sense a "background". In principle, the method is made for a 8 parameter scan (= all unknown masses), I however reduced it by assuming the mass difference to be know up to 1 GeV (quite optimistic), and equally assuming symmetric decay chains. Below are scans for these three particles and the corresponding xisq. Note the double dip structure comes from the fact that, by accident, a wrong leg assignment leads to a good xi2 value in one of the samples; this can be seen from the second plot below. In general, it has to be said that at this level of the analysis, ie using a small number of events at parton level, the method is very sensitive to wrong solutions, which can become extremely large due to the inverse matrix used in the process of xi2 determination. Therefore, wrongly determined xi2 minima, eg from wrong leg assignments, combined with a wrong mass hypothesis, could in principle dominate over rightly assigned minima... mb things get better when full parameter scans are applied and more events combined, as originally proposed (Example in numbers: correct minimum for scan: xisq = 7000 for the accuracy used in the scan. For another event, wrong assignments in combinations with wrong hypotheses lead to xi2 in the ballpark of 10^7 to 10^8, where the minimum is not necessarily from the correct mass hypothesis.) In our sample, mass hypothesis is correctly determind to be mn= 96 GeV (totl xi2=3.3 10^8); second minimum has xi2 about 1 order of magnitude higher).

mneu scan with relative differences fixed, Webbers method, 3 events from sqsq (1 wrong). Parton level
mneu scan with relative differences fixed, Webbers method,event 1334 from sqsq. Parton level

A second simple scan is the determination of the neu1 mass, where all other masses have been fixed. Using the same events as above, the lowest xi does indeed correspond to the correct mass hypothesis where mneu1 = 96 GeV; statements about errors for this mass determination method at this stage are however far from trivial, and a more sophisticated scan algorithm as well as a higher number of events is needed in order to give reliable answers for the mass determination here.

mneu scan, all masses but neu1 fixed, Webbers method, 3 events from sqsq (1 wrong). Parton level

First attempts to use this method on the gogo samples (parton level only !!) for the fixed mass differences seems hopeless. A main reason is that the method, when summing over all events, assume that we test a unique true relation for the masses, ie there is one chain occuring over and over again, and we find the correct hypothesis using xi2 minimization... however, in the gogo samples we have different initial state squarks for the decay chains, and mostly different flavours of the squarks within one event as well. So (wrongly) assuming symmetric decay chains, even with varying quark masses, leads to completely wrong results (lowest xi2 here for mneu1=0 GeV !! scan as above). A way out would be to remove the squark mass in the game (ie vary it, but do not try to determine it...). Mb refined searches work better. Equally, in our case, most gluinos decay into b-squarks; in the original paper, 3rd generation squarks were excluded and a unique squark mass was assumed. Could try to pin down the nature of the squarks by the b-jet tagging then though... Fixed masses and only scanning the neu1 mass is slightly better (124 GeV as a result), but there is a peak in xisq exaclty at the correct value... see figure below. Gogo induced samples could of course in principle be cut using a n-jet veto. Things look slightly better when the squark mass is varied but not part of the mass hypothesis; in this case, the results are 104 GeV (96 GeV) from the gogo sample for fixed masses (fixed mass differences). Below is the plot for fixed masses.

mneu scan, all masses but neu1 fixed, Webbers method, 5 events from gogo (1 wrong), most with b-squarks in the initial state. Value from scan : 124 GeV; true value: 97 GeV. Parton level

mneu scan, all masses but neu1 fixed, Webbers method, 5 events from gogo (1 wrong), most with b-squarks in the initial state. Value from scan : 104 GeV; true value: 97 GeV. Parton level. In this case, msq is not part of mass hypothesis

## Writeup

• The (preliminary) writeup for the project can be found at this link [[52]]. Note the official deadline is the 18.12.2009 (!!) so the sooner we write things up the better... people whould notify however if they do major updates on it.
• Sections which are done but not on svn (Tania; no submission possible wo cern account):

introduction, appendix (mass spectrum), appendix (delphes pre cuts and object definitions)

• If you want to use SVN, here are some useful instructions:

The magic formula to get the files is:

svn co svn+ssh://svn.cern.ch/reps/brunelie/LesHouches09/MassAndSpin/Proceedings

Once you have made the changes you want you can commit them by doing