Measuring b-Quark Fragmentation in LHC Data: Project Report

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18 - 10 - 2016

PARTICLE PHYSICS EXPERIMENT

MEASURING b-QUARK FRAGMENTATION IN LHC DATA PROJECT REPORT

Simon Tollman with supervisors Dr Andy Buckley, Chloe Gray and Dr Chris Pollard and input from Dr Valerio Dao and Dr Gabriel Facini Summer student project

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Abstract

In this project I made a proof-of-concept measurement of b-quark fragmentation functions using data from 13 TeV proton-proton collisions recorded by the ATLAS experiment at the LHC. I used charged tracks in top-quark pair production events and identified tracks from b-hadron decays using displaced vertices. I also made the measurement on an MC event sample and there is good agreement between the two. However, the amount of momentum typically shared by the parent b-quark and its final-state b-hadron is found to be lower than was found in a similar measurement made on data collected by the DELPHI experiment and a pseudo-measurement made using "true" simulated particles.

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Introduction

When a b-quark is produced in a collision it immediately combines with quarks and gluons to form a hadron. The resulting radiation pattern - the typical behaviour of decay products in terms of variables like energy and momentum - is distinctive because of the b-quark’s large mass . As a result, the final state b-hadron retains an unusually large proportion of the b-quark’s momentum as the other constituent quarks and bosons are comparatively light. The b-quark jet is a cone with its point centred on the primary vertex, containing hadrons and other particles produced when the b-quark hadronizes. The large b-hadron mass makes b-quark jets distinguishable from jets from light quarks or gluons (CMS Collaboration, 2013).

The radiation pattern can be characterised by the b-quark momentum fragmentation function - the amount of momentum shared by the parent b-quark and its final-state b-hadron (DELPHI Collaboration, 2010). This was measured in fragmentation of bottom-quark pairs from Z decays, using data collected in electron-positron collisions by the DELPHI experiment at the Large Electron-Positron collider (LEP), CERN (DELPHI Collaboration, 2010). It has however never been measured in proton-proton collisions using its successor, the Large Hadron Collider (LHC) at CERN with a far higher beam energy, now √s = 13 TeV.

[figure 1] (DELPHI Collaboration, 2010) The left image shows the measurement of the b-quark momentum fragmentation function (in the direction of the lepton beam) made by the DELPHI experiment. The right image shows the momentum fragmentation function of the background (in the direction of the lepton beam) made up of light quark and gluon jets (DELPHI Collaboration, 2010). The right shifted peak in the left image is due to large fraction of the parent b-quark’s momentum retained by the b-hadron.

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A second measurement made with a hadron rather than a lepton collider is important, needed to better understand b-quark hadronisation, improve simulations and improve measurements made in the presence of large b backgrounds, for example Higgs boson to bottom-quark pair processes (Goncalves et al., 2015). Further it is important that theorists have access to a second measurement, made in a different experiment, for comparative study.

In this project I made a preliminary measurement of the b-quark momentum fragmentation function using data from 13 TeV proton-proton collisions recorded by the ATLAS experiment at the LHC. I used charged tracks in top-quark pair production events, using displaced vertices to identify tracks from b-hadron decays. I made the same measurement on a Monte Carlo (MC) simulation event sample and compared the results.

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Sample

[figure 2] (above) Top pair production at the LHC, Feynman diagrams (Kohn, 2012, modified 2016).

I used top pair production events as a source of b’s because top pairs are comparatively easy to produce and decay to a bottom quark and antiquark (Olive et al, 2014). Top pairs are produced at the LHC by gluon fusion or quark annihilation [figure 2], with the former process dominating (ibid.). Top pair decay channels go ttĚ„ → Wâ şb Wâ ťbĚ„ generating two bhadron jets and W’s decay to an đ?’†, đ?œ‡ or đ?œ?, and neutrino, or a hadron (ibid.)

[figure 3] (by author, 2016) Top pair đ?’†-đ?œ‡ decay, Feynman diagram.

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I only used đ?’†-đ?œ‡ decay events [figure 3] as they are easiest to distinguish from background. In the case where a W decays hadronically extra quarks are added to events making it harder to identify candidate b’s, while đ?’†-đ?’† and đ?œ‡-đ?œ‡ decays can be characteristic of other processes. Top pairs decay dileptonically with a probability ~6.4%, spread evenly across each possible combination of đ?’† and đ?œ‡, đ?’†-đ?’†, đ?œ‡-đ?œ‡, đ?’†-đ?œ‡ and đ?œ‡-đ?’† (Olive, 2014). Thus ~3.2% decay đ?’†-đ?œ‡.

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SV1

Secondary vertices in b-quark fragmentation (the point at which the b-hadron decays) are identifiable due to the relatively long lifetime of the b-hadron, allowing it to travel a greater distance before decaying. As a result secondary vertices are identifiable, displaced measurably from primary vertices by a few millimetres (Lehmacher, 2008). In the project, secondary vertices in sample events were defined using the SV1 secondary vertex tagging algorithm (ATLAS Collaboration, 2016).

SV1 looks for a vertex displaced from the primary vertex using tracks’ displacement from the primary vertex. It defines a jet cone about the calorimeter jet axis, point on the primary vertex, as a function of the calorimeter jet transverse momentum (ibid.); �R = 0.239 + exp[ -1.22 - 0.0164 pTcaloJet]. Tracks falling within this cone are associated to either the primary vertex, secondary vertex, or both. The secondary vertex is then used as a proxy for the B hadron four-momentum [figure 4].

[figure 4] Jet cones with �R indicated (Bartosik, 2016, modified 2016).

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Quantities

The primary four-momenta I used were [figure 5]:

1. The calorimeter jet (“caloJet�), a measurement of the energy of the b-quark jet including neutral particles. It is measured in the hadronic calorimeter component of the ATLAS detector (ATLAS Collaboration, 2008).

2. The sum of the four-momenta of tracks associated to the secondary vertex, used as a charged proxy for the B hadron. Neutral particles are not included as they do not interact with the tracker component of the ATLAS detector (ibid.).

3. The sum of the four-momenta of the union of tracks associated to the primary vertex tight selection and those associated to the secondary vertex, used as a proxy for the bquark jet. Neutral particles are not included, as in 2. above.

I used three projections of these four-momenta in calculations[figure 6]. The transverse momentum, perpendicular the beam axis, đ?‘?T, the longitudinal momentum , parallel the jet axis, đ?‘?long, and the relative transverse momentum, perpendicular the jet axis, đ?‘?Trel. [figure 5] (top) (Universitat Hamburg, n.d., modified 2016) Tracks associated to the primary and secondary vertices within a jet cone. The secondary vertex and flightpath of the B hadron are labelled SV and B. [figure 6] (middle) (by author, 2016) Four-momenta projections đ?‘?T, đ?‘?long and đ?‘?Trel. [figure 7] (bottom) (by author, 2016) Fragmentation function definitions (ATLAS Collaboration, 2011).

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Each of these projections has an associated momentum fragmentation function, đ?‘§đ??ľ, đ?‘§đ??ľlong and đ?‘§đ??ľTrel [figure 7], the quotient of the momentum associated with the b-hadron in a given projection and the momentum of the jet (ATLAS Collaboration, 2011). 5

TAG AND PROBE

To identify candidate b quarks and hadrons, I used a "tagand-probe" method, in which a pure but unbiased sample of b-jets is obtained by making demands of a b-jet which, if satisfied, imply another is almost certainly genuine without placing explicit requirements on it. The "probe" jet with the loose requirements can then be used for unbiased measurements.

[figure 8] (Universitat Hamburg, n.d., modified 2016) Tag and probe method.

The tag selection goes: > Select events with 1! đ?‘’ and 1! đ?œ‡. > Valid jets have caloJet đ?‘?T > 30GeV && | đ?œ‚ | < 2.1. > Accept events with 2! valid, isolated jets. > Jet b-tagged if JetMV2c10 > 0.8244273. > If (b tagged) && (number of probe-SV1 associated tracks > 0), measure probe.

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Results

Fragmentation functions are represented as histograms normalised such that the integral of the curve is unity. The domain is the b momentum fraction measurement and the range, the proportion of jets with this measurement. Profile histograms show the average momentum shared by a parent b-quark of a given momentum and its finalđ?‘§đ??ľ = đ?’‘TSV / đ?’‘TPVâˆŞSV

state b-hadron.

The fragmentation functions perpendicular the beam axis (đ?‘§đ??ľ) and parallel to the jet axis (đ?‘§đ??ľlong) are very similar in shape [figures 9 and 10]. Data peaks moderately at ~0.75 and MC measurements at ~0.65 in both projections before falling off more đ?‘§đ??ľlong = đ?’‘TPVâˆŞSV¡đ?’‘TSV / | đ?’‘TPVâˆŞSV |2

rapidly. These measurements show a slight leftward shift present in all measurements of MC events relative to those of data, i.e. slightly less momentum is shared between the parent b-quark and final-state b-hadron in the MC model.

[figure 9] (above) (by author, 2016) đ?‘?T fraction, đ?‘§đ??ľ, histogram. [figure 10] (below) (by author, 2016) đ?‘?long fraction, đ?‘§đ??ľlong, histogram.

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The profile plots (showing the average momentum shared by a parent b-quark of a given momentum and its final-state b-hadron) in these projections are very similar in shape too. Again MC predictions were slightly lower than what was measured in the data (as per the leftward shift in the histograms). In the MC measurements the average fragmentation function â&#x;¨đ?‘§đ??ľâ&#x;Š = 0.605 in the lowest momentum jets (i.e. 60.5% of the jet’s momentum is carried through to the b-hadron). This decreases on the domain 0 - 240 GeV to â&#x;¨đ?‘§đ??ľâ&#x;Š = 0.575, a 5% decrease. In the data measurements, plot points are more scattered, though all still fall between â&#x;¨đ?‘§đ??ľâ&#x;Š = 0.575 and â&#x;¨đ?‘§đ??ľâ&#x;Š = 0.655.

/ GeV

/ GeV

[figure 11] (left) (by author, 2016) Average đ?‘?T fraction against đ?‘?T(PV

SV1)

[figure 12] (right) (by author, 2016) Average đ?‘?long fraction against đ?‘?T(PV

profile histogram. SV1)

profile histogram.

The projection perpendicular the jet axis does not resemble the other two. The range of momentum fractions đ?‘§đ??ľTrel in this plane was much smaller and did not exceed 0.07. The probability of a given đ?‘§đ??ľTrel decays exponentially, peaking at lowest đ?‘§đ??ľTrel with 0.44 in the data and 0.515 in MC events. The MC curve is shifted slightly to left from the data curve as in the other two projections [figure 13].

The profile histogram decays with higher momentum jets from â&#x;¨đ?‘§đ??ľTrelâ&#x;Š = 0.0202 to 0.0125 [figure 14]. This difference, though smaller, is proportionally larger than those seen on the same domain in figures 11 and 12, constituting a drop of 38%. Again the data plot points are more scattered.  

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đ?‘§đ??ľlong = đ?’‘TPVâˆŞSVĂ—đ?’‘TSV / | đ?’‘TPVâˆŞSV |2

/ GeV

[figure 13] (left) (by author 2016) đ?‘?Trel fraction đ?‘§đ??ľTrel, histogram. [figure 14] (right) (by author 2016) Average đ?‘§đ??ľTrel, â&#x;¨đ?‘§đ??ľTrelâ&#x;Š,against đ?‘?T(PV

SV1),

profile.

Figure 15 is a histogram of the track multiplicity of probed secondary vertices, i.e. the number of tracks associated to the secondary vertex in a probed jet. The first bin with a population greater than zero is multiplicity = 2, and the distribution peaks sharply at multiplicity = 3. The MC distribution is slightly broader with a less sharp peak than that of the data. [figure 15] (by author, 2016) Probed secondary vertex track multiplicity, histogram.

It was proposed that some probes may have low multiplicities due to incorrectly associated tracks and that the most accurate measurements may come from higher multiplicity probes. I made further plots for each projection showing probed secondary vertices with track multiplicity ≼ 3, and ≼ 4. đ?‘§đ??ľ will be discussed in this report [figure 16, 17, 18, 19] (equivalent plots for the other two projections can be found in the project plot pack). 

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[figure 16] (upper upper) (by author, 2016) Overlay of đ?‘§đ??ľ measured in MC events for various multiplicities. [figure 17] (upper) (by author, 2016) Overlay of đ?‘§đ??ľ measured in data for various multiplicities. [figure 18] (lower) (by author, 2016) đ?‘§đ??ľ of probes of track multiplicity ≼ 3. đ?‘§đ??ľ = đ?’‘TSV / đ?’‘TPVâˆŞSV

[figure 19] (lower lower) (by author, 2016) đ?‘§đ??ľ of probes of track multiplicity ≼ 4. (See figure 9. for đ?‘§đ??ľ of probes of track multiplicity ≼ 2).

In both MC and data samples, increasing the minimum allowable track multiplicity decreased the width of đ?‘§đ??ľ distributions and sharpened the peaks. đ?‘§đ??ľ = đ?’‘TSV / đ?’‘TPVâˆŞSV

As before, the MC curves are shifted slightly to the left relative to the data, however for multiplicities ≼ 3 and ≼ 4, data and MC peaks now align at ~0.75, with the b-hadron sharing about three quarters of the parent b-quark’s transverse momentum.

đ?‘§đ??ľ = đ?’‘TSV / đ?’‘TPVâˆŞSV

đ?‘§đ??ľ = đ?’‘TSV / đ?’‘TPVâˆŞSV

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0.5

��

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Data

0.45

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tigate how much the b-hadron deviates from the path of the b-quark when the quark hadronises

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I used 2D histograms normalised to unity to inves-

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[figure 20, 21]. They show the correspondence between angular separation, ��, of the b-hadron to the b-quark and the b-quark jet’s momentum per-

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pendicular to the beam.

/ GeV

��

0.5 0.45

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MC

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I found that the b-hadron typically does not deviate

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from the path of the b-quark very much. This was

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expected due to the large mass of the b quark (sec-

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tion 1) and is evident in figures 20 and 21 which

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show the strong correspondence between b-quark transverse momenta in the range 20 - 50 GeV and

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â&#x;¨đ?›Ľđ?‘…â&#x;Š

In both the data and MC simulation measurements

�� values between 0 (no deviation) and 0.04. (a

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deviation of ~2.3 degrees). The correspondence is

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stronger in the data sample than the MC sample.

0.04 0.03 0.02 0.01 0 0

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Figure 22 shows the đ?›Ľđ?‘… against đ?‘?T(PV

SV1)

profile histogram, the average angular separation of the b

quark and hadron for a given b-quark transverse momentum. The MC measurement decreases with increases in momentum, falling 38% between 0 and 240 GeV from 0.065 to 0.04. Though the plot points are more scattered, the data showed the same decay falling 48% from 0.07 to 0.036.

[figure 20] (top) (by author, 2016) 2D histogram of đ?›Ľđ?‘… against đ?‘?T(PV

SV1)

[figure 21] (middle) (by author, 2016) 2D histogram of đ?›Ľđ?‘… against đ?‘?T(PV [figure 22] (bottom) (by author, 2016) đ?›Ľđ?‘… against đ?‘?T(PV

SV1)

in data. SV1)

in MC events.

profile histogram. 

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Conclusion

Across the board, the similarity between MC predictions and data plots was encouraging. However in both the DELPHI đ?‘§đ??ľ measurement [figure 1] and a pseudo-measurement of similar quantities using "true" simulated particles [figure 20, 21] there are inconsistencies with the project plots that will need to be investigated further and suggest possible mismodelling.

[figure 20] (left) Pseudo-measurement đ?‘§đ??ľ, histogram. [figure 21] (right) Pseudo-measurement â&#x;¨đ?‘§đ??ľâ&#x;Š against đ?‘?T(PV

SV1),

profile histogram.

With respect to đ?‘§đ??ľ, the DELPHI measurement and the pseudo-measurement exhibit exponential growth. This feature was observed in the project only when taking [probe] secondary vertices of multiplicity ≼ 4 exclusively, into account. Further, the DELPHI curve peaks at đ?‘§đ??ľ = 0.85 and the pseudo-measurement at đ?‘§đ??ľ = 0.9, higher than observed in the project. As a consequence of the sharper, higher value peak , the DELPHI and pseudo-measurement curves fall off more steeply towards đ?‘§đ??ľ = 1 than in project plots.

The pseudo-measurement profile histogram [figure 21] exhibits similar decay as was found in the project. Here however the fall is one of 12.5%. Also, all â&#x;¨đ?‘§đ??ľâ&#x;Š in the pseudo-measurement are greater than those obtained in the project by ~0.2 (a consequence of the comparatively right-shifted peak in figure 20).

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Moving forward, data must be unfolded so a rigorous comparison can be made to the pseudo-measurement and experimental and theoretical uncertainties need consideration, particularly possible bias introduced during secondary vertex finding. Development of the fragmentation function should also be considered.

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References

ATLAS Collaboration, 2011, “Measurement of the jet fragmentation function and transverse profile in proton-proton collisions at a centre-of-mass energy of 7 TeV with the ATLAS detector ”, CERN-PHEP-2011-148, arXiv:1109.5816v2. ATLAS Collaboration, 2016, “Performance of b-Jet Identification in the ATLAS Experiment”, CERN-PHEP-2015-216, arXiv:1512. ATLAS Collaboration, 2008, “The ATLAS Experiment at the CERN Large Hadron Collider”, JINST, 3 S08003. CMS Collaboration, 2013, “Identification of b-quark jets with the CMS experiment”, CERN-PH-EP/ 2012-262, arXiv:1211.4462v2. DELPHI Collaboration, 2010, “A study of the b-quark fragmentation function with the DELPHI detector at LEP I and an averaged distribution obtained at the Z Pole”, CERN-PH-EP/2010-057, arXiv:1102.4748v1. Goncalves D, Krauss F, Linten R. 2015, “Distinguishing b-quark and gluon jets with a tagged b-hadron”, IPPP/15/75, DCPT/15/150, MCNET-15-36, Durham University, arXiv:1512.05265v1. Lehmacher M (on behalf of the ATLAS collaboration), 2008, “b-Tagging Algorithms and their Performance at ATLAS”, 34th International Conference on High Energy Physics, Philadelphia, 2008, arXiv:0809.4896. Olive K. A. et al, 2014, “Particle Physics Booklet”, Particle Data Group, Chin. Phys. C, 38, 090001 (2014).

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Image References

[figure 1] DELPHI Collaboration, 2010, “A study of the b-quark fragmentation function with the DELPHI detector at LEP I and an averaged distribution obtained at the Z Pole”, CERN-PH-EP, 057, arXiv: 1102.4748v1. [figure 2] Kohn F, 2012, “Top pair production”, in Measurement of the charge asymmetry in top quark pair production in pp collision data at √s = 7 TeV using the ATLAS detector, PhD dissertation, Georg-AugustUniversitat Gottingen, arXiv:1204.0952v1, p7. [figure 3] By author, 2016, for project. [figure 4] Bartosik N, 2016, “b-jet tagging”, <http://bartosik.pp.ua/hep_sketches/btagging>, viewed 02-08-2016. [figure 5] Universitat Hamburg, n.d., “Two b-jets with secondary decay vertices”, <https://www.emmynoethercms.uni-hamburg.de/en/research.html>, viewed 02-08-2016, modified. [figure 6, 7] By author, 2016, for project. [figure 8] Universitat Hamburg, n.d., “Two b-jets with secondary decay vertices”, <https://www.emmynoethercms.uni-hamburg.de/en/research.html>, viewed 02-08-2016, modified. [figure 9 - 22] By author, 2016, for project. [figure 23, 24] Dr Andy Buckley, 2016, University of Glasgow School of Physics, PPE group.

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