Properties of Proton-proton Collision and. Comparing Event Generators by Multi-jet Events

Transcription

1 Properties of Proton-proton Collision and Comparing Event Generators by Multi-jet Events Author: W. H. TANG 1 (Department of Physics, The Chinese University of Hong Kong) Supervisors: Z. L. MARSHALL 2, A. SFYRLA 3 (ATLAS, CERN) Date: 16 August 2013 Reference number: CERN-STUDENTS-Note Introduction There are many regimes to be deeply investigated in the field of high energy physics and particles physics. The Large Hadron Collider (LHC) in Geneva, Switzerland is built to study those physics. A lot of Monte Carlo event generators are constructed to simulate the Standard Model. One of purposes of the LHC is obtaining data from real experiment to test the predictions of all Monte Carlo event generators. 2 Jets 2.1 Proton-proton (pp) collision Two beams of proton moving in opposite direction in LHC collide in all detectors. One of the detectors is ATLAS (A Torodial LHC Apparatus). Two high energy, accelerated butches of protons collide in the detector. The partons, including quarks and gluons, inside two protons interact during the collision. Many particles are created, decay and form new particles, e.g. hadronization - forming colorless hadrons from isolated partons. Outgoing particles from the collision are detected by three major components of ATLAS: the inner detector or tracker, the calorimetry (including electromagnetic calorimeter and hadronic calorimeter), and the muon system. They are used to measure the momentum and energy of particles, record the tracks of particles and classify the particles. The measurement is sent to three levels triggers and data acquisition system to be shortened. After that, the data is processed by offline software and algorithm and saved. 2.2 Jet description Based on the data from proton-butch-collision (event), the recorded clusters are reconstructed to be jets by jet algorithm. Each outgoing jet from collision point (the origin) is fundamentally described by four 1 Mr. W. H. Tang s contact: sylartang@hotmail.com 2 Dr. Z. L. Marshall s contact: zmarshal@cern.ch 3 Dr. A. Sfyrla s contact: anna.sfyrla@cern.ch

2 p.2/22 parameters: four-momentum. However, due to the spherical-like properties after collision, it is more convenient that describing the jet by spherical-related coordinates: (i) polar angle around the incoming protons, which is along with the z-axis, ; (ii) rapidity, it is noted that in case of massless object, which is defined as pseudo-rapidity, the relation between rapidity and azimuthal angle is more obvious. Usually, the masses of jets are low enough so that and are near same. This strong correlation leads to the interchange of use of and ; and (iii) transverse momentum. Now, a jet is described by (Figure 1). y-axis Outgoing jet x-axis Incoming protons z-axis Central plane (x-y plane) Figure 1: Description of jet. 2.3 Jet algorithm All events to be dealt with are processed by anti- relating to the size of final jets D = 0.4: jet algorithm with fundamental parameter where is the opening angle between constituents and in space. The constituents are combined into jet until is the smallest among and, and no constituents are excluded from jets. Anti- jet algorithm tends to group high- objects together. In anti- jet algorithm, the constructed final jets are conical-like, the edge of jet is in the local minimum of energy. 2.4 Central jet selection First, the rapidity (or pseudo-rapidity ) goes from zero on plane to (positive or negative) infinity along z-axis. From the formula, the jet of large means (a large fraction of energy contributes in z-axis), the jet is near the direction of incoming

3 p.3/22 proton beam, there is a large chance that the corresponding constituents did not interact with other particles. This implies high validity of jets having small or. Second, there is large uncertainty in due to the high acceleration, however, the momenta in x- and y-direction are well controlled so it guarantees the conservation laws of momentum in x- and y-axis. Hence, only is considered but not. It is noted that the jets with too low lose a lot of information of collision of high energy particles so a -cutoff is usually set for data selection. Based on above, the following central jet selection is employed during data selection in this studies:, where leading is based on the arrangement of decreasing. The events with four or more central jets are used. 3 Properties of proton-proton collision A studied sample of events with center of mass energy is generated by Pythia 6 with -filter JZ4 and anti- jet algorithm with D = 0.6. The sample is processed by anti- jet algorithm with D = 0.4 before being studied to demonstrate some basic properties of pp collision and jet algorithm with central jet selection plots The transverse momenta of first four leading jets are plotted (Figure 2). The sharp peak of of first leading jet is mostly due to the cutoff of -filter (JZ4, its -range is from 500GeV to 1000GeV, details in Appendix B), which is more obvious in the logarithm plot (Figure 3). In the logarithm plot, the front cutoff is very clear but not also the back cutoff. The initial filtered data (cluster) is generated with size parameter of final jet D = 0.6 but the size parameter of final jet in writing process is set at 0.4. Hence, there may be a leakage in momentum and energy when defining jet of size D = 0.4 for a large cluster of size D between 0.4 and 0.6. This leads to the possibility of jets with energy below the lower cutoff of 500GeV. The decreasing tail implies the lower possibility of high energy (or momentum). The -plot of latter three sub-leading jets are smoother and concentrate at even lower value of Figure 2: Transverse momenta of first four leading jets. Figure 3: Transverse momentum of leading jet in logarithm scale. The sharp cutoff comes from the -filter.

4 p.4/ plots In the -plots (Figure 4), the count of first four leading jets concentrate at zero (central plane), and decease with the magnitude. This can be understood from the fact that decreasing possibility of energy and the definition of rapidity, as following. Proposing the relation between jet count and jet energy to be for the feature of decreasing, it is noted that the factor of guarantees the dimensionless property inside the exponential term. Then, in case of massless jet, the definition and (set ) imply that. With, so, which has similar shape with the plot from data. It should be pointed out that the decreasing exponential approximation only includes the effect of ratio, in simplest way and omitting other factors (e.g. jet mass). This is valid for moderate jet energies and very roughly true so this cannot explain the order of flatness. Figure 4: of first four leading jets plots The -plots are approximately horizontal lines (Figure 5). It is expected from the cylindrical symmetry about z-axis.

5 p.5/22 Figure 5: of first four leading jets plots The opening angle between two jets is defined as, in other words, it is the distance between jets in phane. Geometrically, the opening angle measures the relative position of outgoing jets. Four variables are investigated (Figure 6) : (i) between first and second leading jet; (ii) between first and third leading jet; (iii) between first and fourth leading jet; and (iv) Smallest opening angle among first four leading jets. For the -plot, there is a sharp peak at about 3 to 3.1, it is near the value of. It indicates the strong correlation of outgoing motions of first two leading jet: the jets prefer in motion of opposite direction after collision, with the conservation law of momentum. Moving from second leading jet to latter jets, the correlation in opening angle with first leading jet becomes weaker so the peak becomes flatter and the distribution is more uniform. However, there is a new accumulated peak at, it will be discussed at later section 3.6. Small peak problem. Figure 6: Opening angles among first four leading jet.

6 p.6/ Invariant mass plots The invariant mass is constructed by two jets, defined as the Lorentz-invariant sum of four-momenta of corresponding two jets. There are two variables to be studied (Figure 7) : (i) the invariant mass constructed from first and second leading jet ; and (ii) the invariant mass constructed from third and fourth leading jets. Due to the higher momentum and energy of first two leading jets, -plot concentrates at higher value than -plot. It is also noticed that there is a small peak at for that -plot. It will be discussed at the next section 3.6 Small peak problem. Figure 7: Invariant masses among first four leading jets. 3.6 Small-peak problem From the -plot, the small-peak event is defined by its invariant mass is between 100GeV and 250GeV. There are 188 small-peak events out of 79,188 central jet events (0.24%), and out of total 200,000 events (0.094%). The,, and of first and second leading jet of small-peak events are plotted. The -plots of these jets highly concentrate at ~300GeV and ~250GeV for first and second leading jets, respectively (Figure 8). Only a few events locate at the peak of normal -plot (~500GeV). Although no obviously new distribution appears on the -plot (Figure 9) and -plot (Figure 10), almost all small-peak events locate from ~0.4 to ~0.6 on the -plot (Figure 11) but not the normal value.

7 p.7/22 Figure 8: Transverse momenta of first two leading jets in small-peak events. Figure 9: events. of first two leading jets in small-peak It should be reminded that the size parameter of final jet during creating events and during writing data is set to 0.6 and 0.4, respectively. Hence, the origin of the small peak is guessed to be the following: A cluster which size between 0.4 and 0.6 is created in small amount of events, however, the setting of anti- jet algorithm limit the size of final jet when writing data, the cluster is processed to split into two or more neighboring smaller jets but not one single big jet. These explain the lower -peaks at 250GeV and 300GeV, and the dr-peak mostly locating between 0.4 and 0.6. The distribution of component of sum of four-momenta of first two leading jets (Figure 12) is very similar to the normal -plot of leading jet on figure 2, this is a strong evidence. Figure 10: events. of first two leading jets in small-peak Figure 11: Opening angle between first two leading jets in small-peak event.

8 p.8/22 Figure 12: component of sum of four-momenta of first two leading jets. 4 Comparing event generators by multi-jet events 4.1 Events Inspiring by Geer s studies (1996) on different event generators and effects from the number of jets in an event, it is interested to compare data from different event generators. There are six event generators to be compared: (i) Pythia 6 with CTEQ6L1; (ii) Pythia 6 with MRST LO**; (iii) Pythia 8 with CT10; (iv) Pythia 8 with CT10 + CTEQ6L1; (v) Herwig with CTEQ6L1; and (vi) Sherpa with CT10. It should be noticed that the -filters applied on (i) to (v) are all JZ0 to JZ7 but those applied on (vi) are JZ1 to JZ3 only so the cutoff on plots (vi) appears earlier. The center of mass energy of event is set at 8TeV. All six event generators are processed by anti- jet algorithm with D = Event generators There are two main parts in a event generator. The first part is the generating programs, which take different approximations in the algorithm. Pythia 6, Pythia 8 4, Herwig and Sherpa are employed in this studies. The second part is the setting of parton distribution functions (in short, PDFs). The structure of partons inside proton undoubtedly mainly affects the result of pp collision. However, the partons (quarks and gluons) in proton are in ultra-high energy regime so the structure of proton still cannot be deduced from first principle. Moreover, the perturbation method does not work due to the strong coupling (strong interaction) between partons. Hence, the parton 4 Pythia 8, see [3] 5 Herwig++, see [4] 6 Sherpa 1.4.1, see [5]

9 p.9/22 distribution function (PDF) is introduced to characterize the content of protons, e.g. spatial wave functions and momenta of partons, and strong coupling constant between partons. In this studies, there are three employed PDFs: CTEQ6L1 7 (CTEQ6 with leading order approximation in QCD matrix elements); CT10 8 (CTEQ with next-to-leading order approximation in QCD matrix elements); and MRSTLO** (MRST with leading order approximation in QCD matrix elements and next-to-leading-order strong coupling constant). 4.3 Investigated variables spectrum of leading jet Event generator (i) without central jet selection is used to demonstrate the -spectrum (Figure 13). The smooth decreasing shape is a feature of QCD pp-collision. Moreover, the colorful regions and cutoffs show the function of -filter well. Figure 13: -spectrum of leading jet generated by Pythia 6 with the PDF of CTEQ6L1, without central jet selection. 7 CTEQ6L1, see [6] 8 CT10, see [7] 9 MRST2008, see [8]

10 p.10/ Highlighted variables In total, 13 variables are plotted 10 : of first four leading jets, sum of for an event, momentum ratios, opening angles, and invariant masses. However, in the normal plots, the plots are close to each other so it is difficult to evaluate them. Hence, a new quantity using event generator (i) for reference line is defined to distinguish the plots and well compare among them: It is found that there are four highlight variables: (Figure 14), (Figure 15), (Figure 16) and (Figure 17). These plots have most splitting in their ratio plots, it implies that the six event generators are more distinguishable in these variables. It is noted that generator (iii) and (iv) are very close to each other in all plots due to their fundamental similarity, in both generating programs and the PDF, so the ratio method does not well for them. Figure 14: Transverse momentum of leading jet. Figure 15: Transverse momentum of second leading jet. 10 All plots are appended in Appendix C.

11 p.11/22 Figure 16: Sum of transverse momentum of an event. Figure 17: Ratio of an event. 4.4 Implications Due to the fundamental similarities between, and, figures 14 to 16 show similar features. First, there is a global trend that Herwig++ has a lower total cross section (i.e. normalization) than Pythia. Sherpa seems to agree with Herwig++ more than with Pythia, at least be closer at low- region. It is worth to investigate that why only Pythia 6 with CTQ6L1 has a different total cross section than others. Second, for the shape of distribution, Herwig++ has lower cross section with Pythia at lowregion, and near same at high- region. It should be noted that two Pythia 8 have near same cross section and differ a near constant factor from Pythia 6 with CTEQ6L1. However, Pythia 6 with MRSTLO** gets closer with Pythia 8 low- region but gets closer with Pythia 6 with CTEQ6L1 at high- region. The effect of PDFs to Pythia appears its significance here. Moreover, comparing Pythia 8 with CT10 and Sherpa with CT10, the effect of generating program appears. On the other hand, on figure 17, the difference between Pythia and Herwig++ is turned on, become more obviously in region from 0 to Herwig++ has a slower rise and Pythia 6 with MRSTLO** has a fast rise. All things are quite stable until reaching to 0.4. Last but not least, once a data generated from real pp collision experiment is got, it can be plotted on the hightlighted variables plots. The feature of most splitting ratio plot of those four variables allows a more clear data fitting and comparing to test the validity and stability of generating program and PDFs, in more efficient way. In a certain energy range, the most fitted generator with data tell us the most suitable description of proton structure, including the coupling effect, distribution and motion of inside partons.

12 p.12/22 5 Conclusions Basic properties of pp collision are understood by studying a sample event. The small-peak problem (section 3.6) concludes the important effect of jet algorithm but not fundamental physics. Event generators analysis from four highlighted variables (,, and ) points out the significant inter-generator difference (and also the PDFs) that affect the jet kinematic. That can be a choice in the underlying model (e.g. angular-ordered showers in Herwig++ v.s. -ordered showers in Pythia) or a treatment of showers, but from the check of variations in PDFs, it seems that is not simply due to the PDFs or to the way of calculation of strong coupling. It is worth to investigate more deeply. 6 Acknowledgments I am grateful to my supervisors Zachary Louis Marshall, Anna Sfyrla and Christopher Young for many helps on solving programming problems and understanding the physics behind the work. This work was supported by the Department of Physics, The Chinese University of Hong Kong, the ATLAS of CERN, and the Summer School of CERN. 7 References [1] Z. L. Marshall, Ph. D. thesis (California Institute of Technology 2010). [2] S. Geer and T. Asakawa, Phys. Rev. D 53, (1996). [3] PYTHIA, [4] M. Bahr, S. Gieseke and M. A. Gigg, Eur. Phys. J. C 58, (2008). [5] Sherpa Hepforge, Manual, [6] J. Pumplin, D. R. Stump, J. Huston, JHEP 0207 (2002) 012. [7] H. L. Lai, M. Guzzi and J. Huston, Phys. Rev. D 82 (2010) [8] A. D. Martin, W. J. Stirling and R. S. Thorne, Eur. Phys. J. C 63, (2009).

13 p.13/22 Appendixes A. Cross-section (upper) and filter efficiency (lower) of event generators Cross-section [nb] filter efficiency Event generators (i) (ii) (iii) (iv) (v) (vi) JZ0 JZ1 JZ2 JZ3 JZ4 JZ5 JZ6 JZ7 B. Setting of -filters Filters -range [GeV] JZ JZ JZ JZ JZ JZ JZ JZ7 >2000 C. All investigated variables plots in section Originally, three central jet selections are employed: ; ; and, to investigated all 13 variables: of first four leading jets, sum of for an event, momentum ratios, opening angles

14 p.14/22, and invariant masses. A trend of convergence from selection to, due to tighter restriction, is observed so only selection is employed in above main articles (Section 2.4). 1. Transverse momentum of first leading jet

15 p.15/22 2. Transverse momentum of second leading jet 3. Transverse momentum of third leading jet

16 p.16/22 4. Transverse momentum of fourth leading jet

17 p.17/22 5. Sum of for an event 6. Momentum ratio

18 p.18/22 7. Momentum ratio

19 p.19/22 8. Opening angle between first and second leading jet 9. Opening angle between first and third leading jet

20 p.20/ Opening angle between first and fourth leading jet

21 p.21/ Smallest opening angle between 4 leading jet 12. Invariant mass constructed by first and second leading jet

22 p.22/ Invariant mass constructed by third and fourth leading jet