Oddelek za fiziko Top quark physics Seminar Author: Tina Šfiligoj Mentor: prof. dr. Svjetlana Fajfer Ljubljana, february 2012 Abstract Top quark physics is a very active area in particle physics as it might serve as a window to physics beyond the Standard Model. In this seminar I give a brief overview of top quark physics. Historical background for the top quark discovery and theory of top quark production and decay are presented along with some basic properties of top quarks and their measurements at hadron colliders. I also discuss experimental results where deviations from the Standard Model predictions have been observed.
1. Introduction... 2 1.1 Kaon decay... 3 1.2 meson oscillations... 4 2. Top quark production and decay... 4 2.1 Top quark production at hadron colliders... 4 2.2 Top quark decay... 5 2.2.1 Secondary decays... 5 2.3 Top quark production... 6 2.3.1 Pair production... 6 2.3.2 Single production... 8 3. Top quark properties... 8 3.1 Top quark mass... 8 3.2 boson helicity in top quark decays... 10 3.3 Charge asymmetry... 11 4. Conclusion... 13 5. References... 14 1. Introduction The existence of the top quark was suggested by Kobayashi and Maskawa in 1973 in order to complete the three-generation standard model of elementary particles. The clue that there should exist elementary fermions not seen before came from the observation of CP violating kaon decays. Kobayashi and Maskawa showed that with the introduction of the third generation of fermions the CP violation could be explained. Already in 1974 the tau lepton ( third generation electron ) was discovered and soon after, in 1977, the discovery of the bottom quark, the down-type partner of the top quark followed. The new discoveries together with the quark lepton symmetry structure of the first two generations were strongly promising clues that there should be the up-type quark of the third generation to complete the symmetry. However, it was not until 1995 that CDF and D0 collaborations at the Tevatron claimed the discovery of the top quark. The reason it took experimental physicists so long to observe the top quark lies mainly in its very large mass. It is more massive than any other elementary particle and nearly four times more massive than the second-heaviest constituent of matter, the bottom quark. Its large mass makes the top quark special and opens a new area of physics top quark physics. Because of the properties of strong interaction a bare quark cannot exist it dresses itself with other quarks, antiquarks and gluons from the vacuum thus forming hadrons. This process is called hadronization and occurs in a characteristic time of strong interaction, about. Due to its large mass, the top quark has a very short lifetime, about, which is about ten times shorter than 2
the typical hadronization time. The top quark therefore decays before forming hadrons, thus providing physicists with the unique opportunity to study a bare quark. Moreover, its mass is of the same order of magnitude as electroweak symmetry breaking (EWSB). This suggests that it might play a fundamental role in the mechanism of EWSB which is not well understood yet. Research in top quark physics might serve as a window to new physics. Both copious production of top quarks (large statistics) and precision measurements could yield results incompatible with the predictions of the standard model and physicists are looking for such discrepancies. 1.1 Kaon decay CP symmetry is a product of C-symmetry and P-symmetry. C stands for charge conjugation under which a particle transforms into its antiparticle and P stands for parity transformation, or space coordinates inversion. CP symmetry states that the same physical laws should hold under the product of both transformations. Before experiments with kaon decays the CP symmetry was thought to be conserved in all processes, but it was discovered that the CP symmetry is violated in certain weak processes. Kaon is a meson carrying nonzero strangeness quantum numbers. Neutral kaon is composed of a down quark and a strange antiquark ( ) and its antipartner of. The actual physical neutral kaon states are linear combinations of and [1]: The subscripts and denote the short-/long-lived states that have different lifetimes. is a CPeven particle while is a CP-odd particle: Kaons decay into either two or three pions. Pions are mesons composed of up and down quarks and have negative parity. Since CP symmetry is a discrete symmetry its quantum numbers are multiplicative, meaning that the CP value for pions is. Thus, if CP symmetry is to be conserved must decay into two and into three pions. However, experiments show that this is not always the case as in about 1 in 500 decays symmetry. 3 decays into two pions, obviously violating CP It was later shown that this phenomenon occurs via neutral meson mixing. It is a process in which a neutral meson transforms into its own antiparticle by exchanging a boson between its valence quark and antiquark, transforming them into an up-type quark and an up-type antiquark which then exchange another boson transforming into two down-type quarks which form the original particle s antiparticle.
Figure 1. Neutral kaon oscillations [2]. It was this process that led Kobayashi and Maskawa to suggest the existence of another generation of quarks. 1.2 meson oscillations The first prediction of the value of the top quark mass came from studies of neutral meson oscillations. Neutral meson is constituted of a antiquark and a (or ) quark and is denoted (or ). B mesons oscillate between the two states by exchanging a boson between the two constituent quarks that transform into a top and an antitop quark. Figure 2. Neutral B meson mixing [3]. The oscillation frequency is proportional to the third power of the top quark s mass. It was the first hint that the mass of the top quark should be large which was confirmed later on when it was discovered. 2. Top quark production and decay 2.1 Top quark production at hadron colliders Because of its large mass, high center-of-mass energy ( ) collisions are required to produce the top. High enough energies are reached at the Tevatron with and at the LHC currently operating at. Since the Tevatron has shut down in September 2011 the LHC remains the only collider able to produce top quarks. 4
The Tevatron is a circular collider with two detectors ( and ) positioned around the accelerator. It operated in two runs. From 1992 to 1996 Run I at provided more than of integrated luminosity for each detector, which was sufficient to discover the top quark. From 2002 to 2011 Run II at was ongoing, providing approximately of integrated luminosity for each experiment. The acquired data are still being processed. The LHC is a circular collider. Two experiments at the LHC, ATLAS and CMS are designed to study top quarks. Since 2009 the LHC is running at about of integrated luminosity. and has up to the end of 2011 provided Because of the higher center-of-mass energy the cross section for top production at the LHC is and is about 20 times larger than at the Tevatron ( ) [4]. This means about ten times more top events at the LHC than at the Tevatron given the above stated luminosities. 2.2 Top quark decay Top quark decays almost exclusively into a boson and a quark via the weak interaction. Decay width of the top quark calculated at leading order (LO) in perturbative theory is given by [5]: where is the Fermi (weak) coupling constant is the top quark mass and is the CKM matrix element; represents the probability of the top decaying into a bottom quark. At next-to-leading order (NLO) in QCD (quantum chromodynamics) the decay width is Here, terms of order, and (where is the bottom quark mass, is the boson mass and is the strong coupling constant) are neglected. At NLO the precision of the calculation is already better than the detector resolution and it is therefore sufficient to calculate the width to this level. Decay width is inversely proportional to the particle s lifetime, (here we have used the natural unit system with ). The latest results give and. 2.2.1 Secondary decays As the top quark can only be detected by measuring its decay products which alone decay or hadronize before reaching the detector it is also important to know their decay modes. 5
The boson decays either hadronically into a pair ( ) or leptonically into a pair ( ), where is a charged lepton ( or ) and is its (anti)neutrino partner. Decay of a boson into a tau lepton ( ) and is treated separately as the tau has a very short lifetime ( ) and decays before hitting the detector. Moreover it is massive enough to decay into quarks thus producing jets which further complicates the measurements. The other component of the decay products, the quark hadronizes, thereby producing jets. Identification of -jets is called tagging which stands for various methods designed to determine whether the observed jet originated from a quark. 2.3 Top quark production Figure 3. Top quark pair production and its decays [6]. Top quarks are produced either in top-antitop ( ) pairs via the strong interaction or singly via the weak interaction. At hadron colliders pair production is the predominant source of top quarks while single top production has only been claimed in 2009 by CDF and D0 collaborations at the Tevatron. As single production has smaller cross section and larger background compared to pair production it has not yet been studied in detail. However it is an important process to search for the possible effects of new physics. 2.3.1 Pair production pairs are produced via the strong interaction either by quark-antiquark annihilation (which account for approximately 85% of pair production events at the Tevatron and 15% at the LHC) or by gluon fusion (approximately 85% at the LHC and 15% at the Tevatron) []. We see that the numbers are roughly reversed for the two colliders. The difference follows from the parton density distribution functions of protons as in collisions the interacting partons are mostly valence quarks whereas in collisions these are mostly sea partons. 6
Figure 4. Feynman diagrams for top pair production at leading order for right) [7]. annihilation (left) and gluon fusion (middle, pair production cross section is determined by measuring the final state decay products. The final states can be divided roughly into four categories which are described below. Alljets channel In alljets final state both bosons decay hadronically, producing jets. Branching ratio for this channel is about 46% which provides good statistics and since all hadrons are detected the full event kinematics can be reconstructed. However, background is large in this channel coming mostly from QCD multijet events. Dilepton channel In dilepton final state both bosons decay into a charged lepton (electron or muon) and its neutrino partner. This channel is very clear with little background but has low statistics with branching ratio of about 6%. The additional problem is that the two final state neutrinos make it difficult to reconstruct the event as their presence is only indicated by missing energy. Lepton + jets channel The golden channel is the lepton + jets channel in which one boson decays hadronically and the other leptonically. It has a fairly large statistics with branching ratio about 34% and its decay products consist of at least four jets, one charged lepton and large missing transverse energy coming from only one neutrino. Thus the full event reconstruction is possible and background is smaller compared to the alljets state. Tau channels Branching ratio for at least one of the bosons decaying into a tau lepton (tau + leptons or tau + jets channels) is about 14% but is very problematic for analysis since the detectors are not designed to measure the tau. CDF (up to ) D0 (, PLB 704, 403, (2011)) Atlas (up to ) CMS ( ) Table 1. Combined measured cross sections for pair production [4]. 7
2.3.2 Single production Top quarks are produced singly via the weak interaction in three distinguishable channels: the - channel ( ) in which a light quark and a light antiquark annihilate into a virtual boson which decays into a top quark and a bottom antiquark, the -channel ( ) in which a light quark exchanges a virtual boson with a quark and the -channel. Figure 5. Feynman diagrams for single top production at leading order. The first diagram is s-channel, the second diagram is t-channel and the last two are Wt-channel [4]. The -channel is the dominant process both at the LHC and the Tevatron. While the -channel is the subdominant process and the -channel is negligible at the Tevatron, at the LHC the situation is reversed. This again follows from parton density distribution functions. Measuring single top quarks is difficult, partly because of the small production rate but the main reason lies in large background as it is very difficult to distinguish between single top events and + jets events. Single top quark production allows physicists to directly measure the element of the CKM matrix. This is important since the elements of the CKM matrix are free parameters of the standard model. Requiring the matrix to be unitary the element should be close to unity. High precision measurements give [7]. However direct measurements of the that are performed with single top production do not require unitarity of the matrix to determine the value. Direct measurement results give. Any deviations from the predicted value could signal the presence of new physics. It is also important to measure the three modes of single production separately as each channel could be affected by the possible new processes differently. 3. Top quark properties In this section we briefly describe the basic properties of the top quark that are being measured at the hadron colliders along with short illustrations of how the measurements are done. 3.1 Top quark mass Top quark mass is a free parameter of the standard model and therefore it is important to measure it precisely. Additionally, together with the boson mass it sets constraints on the SM Higgs mass. There are mainly three methods for directly determining top quark mass which I will briefly describe. There are also indirect ways to measure top quark mass but in contrast with direct measurements they are strongly dependent on the SM assumptions. Measurements of top mass are complicated and are performed separately in each decay channel and then combined. The results show that the value is consistent with the SM and masses obtained by different methods and in different channels 8
are also consistent with each other. The precise measured value of top quark mass changes in time; the most up-to-date value is [4] The simplest method for determining the top mass is the template method where mass dependent MC templates are constructed and fitted to the data. The most precise method is the matrix element method where per-event signal probabilities and background probabilities are calculated using LO matrix elements and using full event kinematics. Top mass is then determined by maximizing the likelihood constructed of a product of per-event probabilities. The third method is an ideogram method which is similar to the matrix element method but uses kinematic fitting (knowledge of the physical processes involved in the decay used to improve the measurements) instead of matrix elements to calculate per-event probabilities. The main source of systematic uncertainty in mass measurements arises from the jet energy scale (JES). Jet energy can be calibrated in lepton + jets and alljets events by constraining the invariant mass of the jets to the known mass of the boson. This, however, cannot be done in dilepton events but recently CDF succeeded in measuring the top quark mass in dilepton and lepton + jets channel simultaneously, using the lepton + jets calibration also in the dilepton channel. As the main source of top quarks is pair production the mass is determined using both top and antitop data, assuming them to be of equal mass which is a requirement of CPT invariance theorem. On the other hand, measuring top and antitop mass separately serves as a test of the theorem. CDF and D0 collaborations performed such measurements, obtaining the result which is consistent with the SM predictions [7]. 9
Figure 6. Top quark mass measurements by all four experiments at the Tevatron and the LHC. Mass is measured separately in different channels [7]. 3.2 boson helicity in top quark decays boson is a massive spin-one particle and can have three spin projections ( ). Projections and stand for positive (right-handed) and negative (left-handed) helicity, respectively, and projection is the longitudinal polarization of the boson. By measuring boson helicity in top quark decays the SM can be tested at the electroweak scale as in the SM weak bosons only couple to left-handed fermions. This requirement sets strong constraints on the helicity of the quark. As is illustrated in Fig. 7, negative helicity bosons are forbidden in top quark decays. Any deviations from these predictions could signal the presence of new physics. 10
Figure 7. Angular momentum conservation in top quark decays [8]. The three fractions of boson helicity are denoted, and, where. From the chirality of weak couplings a large fraction is expected, while is highly suppressed by a factor of and at LO. Because of the large top quark mass most bosons are expected to be longitudinally polarized with the fraction given by [4]: The SM predictions at NNLO QCD for the three fractions are, and. The most current measured values come from the CDF collaboration and are: and [9]. The central value of lies outside the SM region and it is of special interest for future measurements as it is an ideal area to search for new physics. 3.3 Charge asymmetry At NLO in perturbative QCD theory a small positive charge asymmetry in events produced via annihilation is predicted arising from interference between tree (LO) and box (NLO) diagrams as the latter are antisymmetric under the particle-antiparticle exchange. Top quarks are predicted to be emitted preferably in the direction of the incoming quarks. 11
Figure 8. Charge asymmetry graphically represented [8]. At the Tevatron where pairs are produced mostly in interaction between valence proton or antiproton quarks charge asymmetry translates into forward-backward symmetry which is conceptionally easy to measure. A common variable with which the asymmetry is measured is the particle s rapidity [7]: Here, is the velocity of the particle and is the speed of light. One possible measure for the asymmetry is the observable where is the difference between top and antitop rapidities and ( ) is the number of events with the positive (negative) rapidity difference. At the LHC the situation is somewhat different as the antiquarks come from the sea, thus carrying on average less momentum than valence quarks, resulting in produced top quarks appearing more central than antiquarks. The measure for the asymmetry is thus central asymmetry which is defined with absolute top and antitop rapidities where. However, at the LHC the asymmetry is small due to the fact that most pairs are produced via gluon fusion. 12
Figure 9. Top-antitop production at the Tevatron. The ratio is displayed for the total cross section and its invariant mass distribution for. The inclusive asymmetry in the parton frame is shown for the lepton + jets channel,, besides its bin for high invariant mass, as well as for the dilepton channel,. The asymmetry in the laboratory frame is denoted by, and is the charged lepton asymmetry. Numbers correspond to the central measured values [10]. Fig. 11 shows that the experiments measure the values of asymmetry observables consistently shifted from the SM predicted values. It is not yet clear whether the deviations arise from some systematic uncertainties or from the effects of new physics but further research in this area is certainly of particular interest at this moment as it is the only deviation from the SM predictions observed so far. 4. Conclusion In this seminar we have presented a short review of top quark physics. Main historic background for top s discovery was given including a brief overview of the physical processed that led to it. Theory of top quark production and decay was described. Basic top quark properties and their measurements along with possible signals for new physics were presented in the last section. We have seen that the top quark is a unique elementary constituent of matter and as such offers new possibilities for research. Top quark physics has been a hot topic in hadron collider physics, especially so in recent years since single top production was discovered as it is an area of particle physics where possible effects of new physics are most likely to be observed. Moreover, in top-antitop charge asymmetry measurements the only deviation from the SM predictions so far was observed, making top quark studies of particular interest for the future years to come. 13
5. References 1. Halzen, F. & Martin, A. D. Quarks and Leptons: An Introductory Course in Modern Particle Physics. (Wiley: 1984). 2. Kaon - Basic Theory. at <http://hep.uchicago.edu/kek/theory.html> (retrieved on February 18, 2012) 3. Directly determined limits on the Bs meson mixing frequency. at <http://wwwd0.fnal.gov/run2physics/www/results/final/b/b06a/b06a.html> (retrieved on February 18, 2012) 4. Deliot, F. Top Quark Physics At Hadron Colliders. arxiv:1111.6274 (2011). at <http://arxiv.org/abs/1111.6274> 5. Ellis, R. K., Stirling, W. J. & Webber, B. R. QCD and Collider Physics. (Cambridge University Press: 2003). 6. Ünalan, Z. G. A measurement of the top quark s charge. (2008). at <http://adsabs.harvard.edu/abs/2008phdt...10u> (retrieved on February 12, 2012) 7. Stelzer, B., for the CDF & D0 Collaborations. Review of Top Quark Measurements. arxiv:1004.5368 (2010). at <http://arxiv.org/abs/1004.5368> 8. Kuehn, J. H. Theory of Top Quark Production and Decay. arxiv:hep-ph/9707321 (1997). at <http://arxiv.org/abs/hep-ph/9707321> 9. Peters, Y., for the CDF & D0 Collaborations. Top quark Physics at the Tevatron. arxiv:1201.1397 (2012). at <http://arxiv.org/abs/1201.1397> 10. Westhoff, S. Top-Quark Asymmetry -- A New Physics Overview. arxiv:1108.3341 (2011). at <http://arxiv.org/abs/1108.3341> 11. Kadeer, A. & Korner, J. G. Radiative corrections to top quark decays. arxiv:0906.3474 (2009). at <http://arxiv.org/abs/0906.3474> 12. Spanò, F., for the ATLAS & C. M. S. collaborations. Top Quark Production at the LHC. arxiv:1112.3906 (2011). at <http://arxiv.org/abs/1112.3906> 14