Summer Project 2010: Heavy Gluon Resonance

Stefan and Jack's working page!

Purpose

Many models of physics beyond the standard model predict new heavy particles that would give rise to resonances at the LHC in the invariant mass spectrum from different final state particles. Often the new particles are weakly coupled and give rise to resonances where the width is narrow with respect to its mass. In this case the mass distribution due to the new particle is normally well described by the Breit-Wigner function, which appears on top of the SM background.

Recently models which predict a heavy gluon have gained a lot of interest. These models are often related to some scenario of RS extra dimensions, where KK modes give rise to heavy versions of the SM particles. These models have been suggested as potential candidates to solve various problems with the SM, e.g. X, Y, Z.

In the case of a heavy gluon, the relatively strong gluon coupling together with its large mass results in a large resonance width and the shape of the mass distribution can become significantly different from a Breit-Wigner function. The distribution shape can in this case be altered by several different effects, which hence should be included in simulations and taken into account if necessary in the proceeding experimental searches.

In this study we address the different effects on the mass distribution of a heavy gluon and provide the functionality to simulate it within the MC generator Pythia8. The study is not related to a particular model, but strongly influenced by the RS models. For this reason we focus on the scenario with a gluon that primarily decays into top quarks and the coupling constants are chosen to cover typical values of the above models. These processes also often implies serious experimental challenges, e.g. related to the top reconstruction or various detector effects, however, in this study we limit our scope only to the mass distribution predicted by the theoretical model. This is obviously only the first step towards a distribution relevant for the experimental analysis, however, the purpose of these results is to indicate the significance of the various effects before convolving it with additional effects from the detector and reconstruction.

Document:

• ac_kkgluon_170810.tar.gz
• ac_kkgluon_200810.tar.gz (SA)
• ac_kkgluon_230810.tar.gz (JC)
• ac_kkgluon_230810_2.tar.gz (JC)
• ac_kkgluon_250810.tar.gz (SA)
• ac_kkgluon_100910.tar.gz (SA)
• ac_kkgluon_200910.tar.gz (SA)
• ac_kkgluon_121010.tar.gz (SA)

Process (Stefan)

Model Assumptions (might combine with other section)

The study focus on the shape of the invariant mass distribution of ttbar events from the kk-gluon process. Therefore the following assumptions are made in order to minimize the parameter space,

• gqR = gqL = 0.2
• gbR = gbL = 0 (?)
• gtR = gtL = 2, 3, 4
• mg = 1.5, 3, 4 TeV (?)

In most of the models with a heavy gluon the coupling to the top quark is much larger than the others and fore this reason the light quark coupling mainly determines the cross section where as the top coupling determines the width. Since the study is focus on the mass shape, the light quark coupling is kept fixed and the small contribution from bottom quarks to the total width is neglected unless explicitly states. Only vector couplings (i.e. gxR = gyL) are considered, since the effects on the mass distribution from having the different couplings to different helicity states are small. Deviations from this default scenario is addressed at the end.

Effects from a Large Width (deviations wrt a BW, without interference)

The following effects are expected to some extent when the width start to become large wrt the gluon mass.

• Shift of peak due to PDFs. (DP values in table)
• Develops a tail due to PDFs. (TF values in table) pure_data.txt
• Deviation from BW functional form (due to sHat dependence). (plot, if noticeable)

_We need a mass distribution plot here that illustrates as well as possible these effects for only one characteristic (extreme?) case_ As table X shows, a significant fraction of the total predicted cross section can be contianed in the IR tail and hence not contributing to the resonance peak.

• pure_grid.gif
• largewidth_ill.gif

Effects from Interference (deviations wrt previous scenario, i.e. |SM|^2 + |KK|^2)

• Shift of the peak. (DP values in table) dpintdata.txt
• Deformation of peak. (plot if noticeable?) posnegplot.gif posnegplot2.gif
• Constructive/destructive contributions. (A/B values)

Other Effects

• gtR = gtL, mass spectrum. (plot)
• gtR = gtL & gqR = gqL, give AFB. (plot)
• Bottom contribution to total width. (value)

???

Papers and Code

1. B. Lillie, L. Randall, L.-T. Wang, The Bulk RS KK-gluon at the LHC , JHEP 0709 074 2007.
2. K. Agashe et al., LHC Signals from Warped Extra Dimensions , Phys. Rev. D77 (2008) 015003.
3. Ben Lillie, Jing Shu, Tim M.P. Tait, Kaluza-Klein Gluons as a Diagnostic of Warped Models , Phys. Rev. D76 (2007) 115016.
4. A. Djouadi, G. Moreau, F. Richard, R. K. Singh The forward-backward asymmetry of top quark production at the Tevatron in warped extra dimensional models , arXiv:0906.0604v1 [hep-ph].

Test Code: pythia8140_gkk_110810.tgz
I took the opportunity to implement it in the latest version (v8.140), so the first thing to do would be to test it against the available (pure) kk-gluon process in the official v8.140. The new process should now contain,

• Possibility to give individual helicity couplings for the kk-gluon, i.e. wrt qR, qL, bR, bL, tR, tL (see example/main28.cc for the proper parameters).
• Should work with negative values of the couplings.
• Access to KK gluon width with, pythia->particleData.resWidth(5100021, mGluon, 1, true, false), BUT only when running KK-only! In the case of KK + SM the width reflect a value for the coherent process.
• Fixed interference bug.

-- StefanAsk - 14-Jul-2010

The gluon mass distribution

• A root macro to plot the histogrm together with a Breit-Wigner function: plotBW.C and rootlogon.C.
  (the style settings are defined in the rootlogon.C file which should be located in the same directory).

Place to write down stuff done (Jack)

rel_int_limit_mg1.gif

Week 5 of 9

1) Definition of 'standard' parameter space:

• light quark coupling = 0.2.
• bottom coupling = 1, unless forced to use 0.
• top coupling = 2, 3, 4.
• gluon mass = 1, 3, 4 TeV.

2) Interference plots

• int_rel.gif
• int_comparison.gif
  • Black: SM + KK + int
  • Red: SM + KK
  • Blue: KK
  • Green: SM

3) Shape parametrisation

• Delta Peak (DP): The difference between the observed resonance peak and the gluon mass
  • 
• Tail Fraction (TF): The fraction of the distribution contained in the 'tail':
  • 
• Peak Fraction (PF): The fraction of the distribution contained within two widths of the peak:
  • 
• Calculation of shape parameters for standard parameter space: fullparspc_1e6_200_params.txt
  • PF seems to be not very useful, TF is better.

4) Interference parametrisation

Week 4 of 9

1) Theoretical sigma

• Wrote a macro for calculating the theoretical cross section: CSPlotScript.cxx.
• Plot with standard parameters (mg3, q0.2, b1, t3): CStheory.gif.
• From a few quick tests, it seems the widths I calculate from this are on the order of 2 or 3% less than those given by pythia. I guess that can only come from errors in my calculation of the strong coupling (e.g. using only the first term). But the next term actually reduces the coupling strength by around 5%ish (I think). Anyway, not too important - just need to bear in mind that these plots should be considered rough rather than precise.
• Observation - Interference seems to cut very strongly into the cross section below the resonance.

2) Comparison between old and new pythia versions

• Resonance plots using old and new pythia versions with 4 parameter sets: oldnewpythiacomparison.gif
  (They seem close enough, except for the obvious higher peaks in the new version due to the smaller total width, especially when bottoms are considered)
• Integrated cross sections from old and new pythia: OldNewPythCS.txt (Same story)

3) Comparison of peak-finding methods

• I upgraded the BW fitting macro (JplotBW.C) in two ways:
  1. The mass and with can now be passed to the function (using the FixParameter() method to pass fixed parameters).
  2. Instead of fitting in a small range around the gluon mass, it fits in a small range around the resonance peak. It does this using the getPeak() function which returns the location of the largest bin within the resonance region (which it finds by scanning from the right and finding a local maximum). I can think of more efficient ways to implement, but not worth the time.
• I included this in a new macro which runs through a batch of histograms (a root file and associated txt file) and estimates the location of the resonance peak for each histogram using two methods:
  1. BW fit (where the range over which the curve is fitted should be optimised for best results)
  2. Centre of mass calculation - finds the highest bin in the resonance, then takes the bins within +/- 5 bins (so 11 bins total) and calculates the centre of mass (peak = sum(energy * bin height)/energy range).
• I found the BW gave best results when the range was +/- 0.2*width.
• Tabulated results of test: peaktestdata.txt
  • There are 4 parameter sets used, and for each parameter set I did the test using 1e5, 1e6, 5e6 and 1e7 events in 300 bins. I also did another histogram for each parameter set at 1e6 in 200 bins (indicated by the 200b in the histogram name). It can be assumed that the results with 1e7 events are the most accurate. However this number of events takes too long to generate for normal use, so best performance at 1e6 should be pursued.
  • It is clear that the BW method is most robust when the number of events is low, while the COM method is very sensitive to this.
  • Some specific comparisons:
    • mg4_q02_b0_t4_1e6 - Here BW is slightly better, because the highest bin is not at the centre of the resonance
    • mg3_q02_b1_t4_1e6_200b_t - Although I called this COMfailure3.gif, they're actually both OK. I think BW is a little better, and COM gives a delta peak about 7% smaller.
    • mg4_q02_b0_t4_1e6_200b_t - Here the two methods give delta peak values which differ by around 10%. It is difficult to see by eye which is better here, but according to the results of the 1e7 test with the same parameters, the BW is closer.
  • For the histograms I have tested, when COM and BW differ the BW always seems to give the better result. We thought that BW would be worse for the broader peaks, but actually COM suffers here too because when you have a broad peak there is greater scope for the highest bin to be displaced from the 'real' peak. I think for large numbers of events COM wins, which is something to keep in mind later. I can think of ways to improve COM (e.g. suppose the COM method gives a resonance peak which is displaced some way from the centre of the maximum bin - then we can say, ok call the bin next to the maximum bin the new centre and re-evaluate the COM about the new bin), but not sure if it is worth it right now. Perhaps the BW method will suffer when we include FSR, so this is something to re-evaluate later. But for the time being, I think it is best to use the BW with a range of +/- 0.2*width.

-- JackCollins - 23-Jul-2010

Weeks 1-3

• Learnt to use some basic root functionality & how to interface with pythia.
• Initial rudimentary resonance characterisation.
• Changed main_gkk to read settings from txt files to remove necessity for constant recompilation (now takes the name of the txt file as an argument. Required changes to root analysis files too).
• Made root macro to run main_gkk.exe many times on a batch of txt files. So the different settings files to be used are called, e.g., settings1.txt, settings2.txt etc., then there is another txt file batch.txt which is simply a list of the settings file names. "batch.txt" is then passed as an argument to the macro which runs in root. (It seems unnecessary to use root for this, but I don't know of another way).
• main_gkk.exe now produces both a root file and an associated txt file (filename.root & filename.txt). The txt file is a list of the histogram names in the associated root file, along with the gluon mass used, and the width and cross section data. This allows root macros for histogram analysis (e.g. peak finding) to be automated by running off these txt files.

• Effect of varying mass: mass.gif
• Effect of varying top coupling: top.gif

-- JackCollins - 23-Jul-2010