

 29 Apr 1996

Physics of Top Quark at the Tevatron

C.-P. Yuan Department of Physics and Astronomy

Michigan State University East Lansing, MI 48824, USA

Abstract. We discuss the physics of the top quark at the Fermilab Tevatron. By the year 2000, many properties of the top quark can be measured at the Tevatron.

1 Discovery of the Top Quark

The discovery of the top quark is one of the most important achievements at the Fermilab Tevatron which is currently the only collider that produces the top quark on its mass-shell. The mass of the top quark has been measured to be mt = 176\Sigma 8 (stat:)\Sigma 10(sys:) GeV by the CDF group and mt = 199+19\Gamma 21 (stat:)\Sigma 22(sys:) GeV by the DO/ group, through the detection of t_t events. The standard t_t event selection is based on the expected Standard Model (SM) decay chain t_t ! (W +b)(W \Gamma _b) and the subsequent decays of the W 's into fermion pairs. At least one W is tagged in the mode W ! ` + * by requiring an isolated high pT (transverse momentum) lepton (` = e or _) and large 6ET (missing transverse energy). In the "dilepton" analysis the leptonic decay of the other W is identified with a loose lepton selection; this mode has small backgrounds, but also a small branching ratio of just 4=81 ' 5%. In the case of the "lepton + jets" mode, the second W decays to quark pairs, giving larger branching ratio of 24=81 ' 30%. The final state of (`*b)(jj_b) is separated from the primary background, W + jets, by requiring a large multiplicity of high pT jets and also evidence of a b-jet, using either secondary vertex (silicon detector) or soft lepton (b ! c`*X) identification. For more detailed discussions on the event selection and the detector configuration which determines the acceptance and the detection efficiency of the events, we refer the readers to Ref. [1].

Assuming the SM decay mode of the top quark, the cross section oet_t for the QCD production processes q _q; gg ! t_t was measured to be 7:6+2:4\Gamma 2:0 pb by CDF and 6:4 \Sigma 2:2 pb by DO/ . For comparison, the SM result for mt = 175 GeV at ps = 1:8 TeV is oet_t = 5:52+0:07\Gamma 0:45 pb quoted from Ref. [2] in which the effects of multiple soft-gluon emissions have been properly resummed. Since the measurement of the cross section obtained from the "counting" experiments (counting the observed total tt event numbers in various decay modes) and the

measurement of the mass of the top quark (obtained from reconstructing the invariant mass of the top quark) are not strongly correlated, one can combine these results to find the best fitted values for mt and oett [3].

It is important to remember that these experiments have optimized their search for the process pp ! ttX ! bW +bW \Gamma X, so they actually report the product of the top quark production cross section oett and the branching ratio squared b2, where b = BR(t ! bW ). Furthermore, the reported production cross sections are a function of the assumed top mass value used in the analysis. In Ref. [4], we updated the above fit by including the measured values from CDF and DO/ for mt and oett \Theta b2. Finding the minimum value of O/2 yields mt = 168:6+3:0\Gamma 3:0 GeV, oett = 7:09+:68\Gamma :62 pb and b = 1:00+:00\Gamma :13.1 At the 95% confidence level (C.L.) 2, b = :74. This number, then, gives us an upper limit on BR(t ! X), where X 6= bW . From the results of the fit described above, we conclude that BR(t ! X) for X 6= bW has to be less than , 25%. This result agrees with a measurement of b = :87+:18\Gamma :32 by CDF based on single- and double-b-tagged events [5].

Obviously, measuring mt and oet_t is not all the Tevatron can/will do. In this paper, we will also discuss the single-top production cross section, some features of the t-b-W vertex, decay branching ratios, partial decay width and lifetime of the top quark, and some non-SM decay modes and exotic production mechanisms.

2 Is the Top Quark just another heavy quark?

Because the top quark is heavy and its mass is of the order of the electroweak symmetry breaking (EWSB) scale v = (p2GF )

\Gamma 1=2 = 246 GeV, its

study might provide clues to the generation of the fermion masses which could be closely related to the EWSB. Furthermore, effects of new physics originating from the EWSB would be more apparent in the top quark sector than any other light sector of the electroweak theory. Hence, the top quark system not only serves as a stage for testing the SM but also provides a window to new physics beyond the SM.

A few examples are discussed in Ref. [6] to illustrate that different models of EWSB mechanism will induce different interactions among the top quark and the W - and Z-bosons. These interactions may strongly modify the production and/or the decay of the top quark. In some models (e.g., the TopColor model [7]) observable flavor-changing neutral current (FCNC) processes (e.g., t ! cZ; cg; cfl : : :) can be mediated by new underlying dynamics, and some

1The theoretical prediction of oe

tt is 6:83 pb for mt = 168:6 GeV. 2We varied the parameter until the O/2 value increased from its minimal value by (1:96)2

units.

new resonances can strongly couple to t_t (e.g., a degenerate, massive color octet of "colorons" and a singlet heavy Z0) or t_b (e.g., a triplet of "top-pions") system. With all these new effects possibly appearing in the top quark system, we conclude that the top quark is likely to be not just another heavy quark.

Is it a SM top quark? What do we know about the interactions of the top quark? Can we learn about them from the radiative effects on the precision LEP/SLC data (physics at the Z-pole)? A few analyses for studying the top quark couplings to the gauge bosons show that current low energy data still allow rooms for new physics [6, 8], and that only the direct measurements (with on-shell top quark produced) of these couplings can be conclusive.

3 Top Quark Physics for the Tevatron at Run-II and

Beyond

To determine how well an observable can be measured at the Tevatron in the Main Injector Era (Run-II and beyond), we need to set up a reference for top quark event rates. For this purpose, we consider a _pp collider with pS = 2 TeV and an integrated luminosity of 2 fb\Gamma 1 (or, 1 fb\Gamma 1 for each experimental group). In the SM, for a 175 GeV top quark, there will be about 1:4 \Theta 104 t_t pairs and 5 \Theta 103 single-t or single-_t events produced. After taking into account the b-tagging efficiency and the detection efficiency [1], there are about 1000 single-b-tagged t_t pairs in the `+ jets sample (among those 600 are also doubleb-tagged), 100 in the dilepton sample, and 250 single-t or single-_t events (in the ` + jets sample) available for testing various properties of the top quark. In the following, we discuss the relevant observables and show that with a 2 fb\Gamma 1 luminosity, many first measurements can already be done to a good accuracy at the Tevatron. With a (10\Gamma 100) fb\Gamma 1 integrated luminosity (beyond Run-II), many further improvements are expected.

3.1 t_t production rate oet_t

At the Tevatron, the dominant t_t pair production mechanism is q _q ! t_t not gg ! t_t, the former contributes about 90% of the rate because the quark luminosities are larger than the gluon luminosities for large x (i.e. for producing heavy top quarks). To test QCD, we need an accurate measurement for oet_t which is experimentally limited by the systematic uncertainties. It is concluded in Ref. [1] that the experimental error in oet_t is ffioet_t ' 10% which is about the same as the theoretical error for calculating oet_t [2]. Assuming the decay branching ratios of the top quarks are as described by the SM, oet_t can also be measured by counting the production rate of dilepton events. Since the

statistical error for the dilepton sample of t_t events is about 1=p100 = 10%, we expect ffioet_t ' 10%, as implied from this measurement.

3.2 Mass of the top quark mt

With enough t_t pair events, the accuracy in measuring mt will be determined by the systematic uncertainty which is dominated by the error in measuring the jet energy scale due to the imperfections in the calorimetry and the effects of initial and final state gluon radiations. The determination on the jet energy scale can be greatly improved by studying the Z + 1 jet and fl + 1 jet events [1]. It is expected that mt can be measured to within a couple percent. So, the uncertainty in measuring mt is ffimt ' (2 \Gamma 4) GeV. With this accuracy on mt, it becomes possible to get a useful constraint (within , 100 GeV) on the mass of the SM Higgs boson.

3.3 Distributions of invariant mass Mt_t and transverse momentum pT (t)

If a heavy new resonance (V ) can be produced in a _pp collision and can strongly couple to t_t [9], then the observed distributions of Mt_t and pT (t) will be different from the SM predictions. (The event rates can either increase or decrease.) By carefully comparing these distributions with the predictions of a given theory, one can then either approve or exclude that theory. Since Mt_t can be reconstructed on an event-by-event basis by requiring that there are two top quarks observed in the event, the shape and the magnitude of this distribution can therefore set a model-independent limit on possible new physics coupled to t_t pairs. Demanding a resonance to be observed at the 5oe level (i.e. S=pB ?, 5) over the t_t continuum in the Mt_t spectrum, one can set the minimum bound on oe(_pp ! V ) \Lambda (V ! t_t) to about (0:4 \Gamma 0:8) pb and (0:1 \Gamma 0:2) pb for MV equal to 500 GeV and 800 GeV, respectively [1].

3.4 Top quark decays and FCNC decay modes of top

Because the top quark is heavy, it will decay via weak interaction before it feels non-perturbative strong interaction. This is the first opportunity we have for studying the properties of a bare quark. In the SM, the total decay width of a SM top quark is \Gamma t ' 1:6 GeV(mt=180 GeV)3, and the branching ratio of the weak two body decay t ! bW + is about one hundred percent. In this decay mode the top quark will analyze its own polarization [10]. If t is found dominantly decaying to bW +, the second top (_t) in each t_t event should be carefully studied as a window for small non-SM decay modes of top quarks. For instance, in the Minimum Supersymmetric Standard Model (MSSM), t

can decay into bH+, t ! ~t1 ~O/01, or R-parity violating channels, etc., and their branching ratios depend on the detailed parameters of the model. With enough t_t events, one can tag one t and study the detailed properties of another t for each t_t event. We call this t-tagging.

In the SM, the branching ratios for the FCNC decay modes were found to be too small to be detected, for instance, Br(t ! cH) , 10\Gamma 7, Br(t ! cg) , 10\Gamma 10, Br(t ! cZ) , 10\Gamma 12, and Br(t ! cfl) , 10\Gamma 12. However, in some models, the FCNC decay modes of the top quark can be observable [11]. Consider the MSSM with light chargino and top-squark. One of the t in the t_t event decays to ~t1 ~O/01, and ~t1 subsequently decays to c ~O/01. The signature of this event is W + 2 jet+ 6ET which is not included in the counting experiments that only count events with W + * 3 jets. A careful study on this signature can approve the MSSM or set limit on the MSSM parameters [4]. Other studies [1] show that a 2 fb\Gamma 1 luminosity can be sensitive to BR(t ! cZ) , 2% (from 3` + 2 jets or 2` + 4 jets sample) and BR(t ! cfl) , 0:3% (from ` + fl + 2 jets or fl + 4 jets sample).

3.5 Ratios of branching ratios: R` and Rb

Define R` to be the ratio of the t_t cross sections measured using dilepton events to that measured using ` + jets events. If R` differs from the SM prediction, then it will imply new physics that will allow t to decay without a W boson in the final state, as in a charged Higgs decay (t ! bH+ [12]), or a top-squark decay (t ! ~t1 ~O/01). Hence, R` measures BR(t ! bW ). With 2 fb\Gamma 1, the error on BR(t ! bW ) is about 10% [1]. Another useful ratio Rb is that of the t_t cross section measured by using double-b-tagged events to the one measured by using single-b-tagged events. This determines the upper limit on the branching ratio of t ! X where X does not contain any b-quark. This method can be applied to both ` + jets and dilepton samples, from a known b-tagging efficiency. With 2 fb\Gamma 1, this upper limit can be set to about (3 \Gamma 5)% [1]. This result can be interpreted as the error on measuring BR(t ! bW ) if a W boson is confirmed in t decay.

With a large t_t event rate, one can use R` and Rb to select events in which the top quark decays to a W -boson and a b-quark, and then redo the study as done in Ref. [4] for obtaining the best fit on oet_t, mt and BR(t ! bW ). Generally speaking, a small BR(t ! X) is better measured from direct search of the rare decay mode than from the measurements of R` and Rb.

3.6 Partial decay width \Gamma (t ! bW ) and the lifetime of top

The total decay width \Gamma t of a SM top quark cannot be measured from the invariant mass of t reconstructed in the t_t events [13]. An elegant way

to determine the lifetime (the inverse of the total decay width \Gamma t) of the top quark is to measure the partial decay width \Gamma (t ! bW ) and the branching ratio BR(t ! bW ). This is because \Gamma t = \Gamma (t ! bW )=BR(t ! bW ).

As discussed above, BR(t ! bW ) can be determined from measuring R` and Rb. The width \Gamma (t ! bW +) can be measured by counting the production rate of top quarks from the W -b fusion process which is equivalent to the W -gluon fusion process by properly treating the bottom quark and the W boson as partons inside the hadron [13]. Consider the q0b ! qt process. It can be viewed as the production of an on-shell W -boson which then rescatters with the b-quark to produce the top quark. This is known as the "effectiveW approximation". Although some assumptions about the dynamics of the hard scattering (for approximating an off-shell W -boson by an on-shell W boson) need to be made for applying such an approximation, the kinematics of this factorization is exactly the same as that in the deep-inelastic scattering processes. The analytic expression for the flux (f*(x)) of the incoming W*- boson (* = 0; +; \Gamma for longitudinal, right-handed, or left-handed polarization) to rescatter with the b-quark can be found in Ref. [14]. The constituent cross section of ub ! dt is given by

^oe(ub ! dt) = X

*=0;+;\Gamma

f* x = m

2t

^s ! "

16ss2m3t ^s(m2t \Gamma M 2W )2 # \Gamma (t ! bW

+ * ) ;

where MW is the mass of W +-boson and p^s is the invariant mass of the hard part process. Hence, the production rate of single-top event from the W -gluon fusion process measures the partial decay width of the top quark \Gamma (t ! bW +).

At the Run-II of the Tevatron (with an integrated luminosity of 2 fb\Gamma 1), we expect that the lifetime of the top quark will be known to about 20% , 30%. Here, we have assumed that the branching ratio for t ! W b can be measured to about 10% and the cross section for W -gluon fusion process is known to about 15% , 20% [13]. The total cross section for the W -gluon process was calculated by applying the QCD subtraction procedure described in Ref. [15] to properly resum all the large logs of the form [ffs ln(Q=mb)]n from n-fold collinear gluon emission.

3.7 Form factors of t-b-W , Vtb and mt

The most general operators for the t-b-W coupling are [10]:

gp

2 ^W

\Gamma _ _bfl_(f L

1 P\Gamma + f R1 P+)t \Gamma 1MW @* W

\Gamma _ _boe_* (f L

2 P\Gamma + f R2 P+)t*

+ gp2 ^W +_ _tfl_(f L1

\Lambda P

\Gamma + f R1

\Lambda P

+)b \Gamma 1M

W @

* W

+_ _toe_* (f R

2

\Lambda P

\Gamma + f L2

\Lambda P

+)b*

+ @_W \Gamma _ _b(f L3 P\Gamma + f R3 P+)t + @_W +_ _t(f R3

\Lambda P

\Gamma + f L3

\Lambda P

+)b ;

where P\Sigma = 12 (1 \Sigma fl5), ioe_* = \Gamma 12 [fl_; fl* ] and the superscript \Lambda denotes the complex conjugate. In the SM, the only nonvanishing form factor at tree level is f L1 = 1. These form factors will have different values if new physics exists. The typical energy transfer scale for the t-b-W coupling in the decay of the top quark (in either the t_t pairs or the single-top events) is of the order MW . In the W -gluon fusion process, the W -boson is not on-shell, but under the "effectiveW approximation" this scale is again of order MW . (This is why the production rate of this process can be related to the decay width \Gamma (t ! bW +).) In the Drell-Yan type single-top production process, qq0 ! W \Lambda ! t_b, the typical energy transfer scale is of order the invariant mass of the t_b pair which is larger than mt. Hence, for instance, if there is a new heavy resonance that couples to the t_b pair, it will be likely to enhance the production rate of singletop events at the Tevatron from the W \Lambda process. However, in this case, neither the decay width of the top quark nor the single-top production rate from the W -gluon fusion process will be largely modified. Therefore, to fully explore the form factors for the interaction of t, b and W , all these processes have to be detected.

Using the invariant mass (mb`) of b and `, one can determine the polarization of the W boson which depends on the values of these form factors. A study [15] shows that if f L1 ss 1 and f R1 and f L;R2 are almost zero (SM values), then the errors ffif L1 , (2 \Gamma 3)% and ffif R1 , 0:2. The measurement of f L1 can be interpreted as the measurement of the CKM element Vtb which is therefore known to within 3%. (We note that this result is more accurate than that obtained from measuring the qq0 ! W \Lambda ! t_b production rate which yields a 10% error in measuring Vtb [1].) Furthermore, the fraction (FL) of longitudinal W 's

from top decays is equal to 12 m

2 tM 2

W , and is independent of f

L;R 1 , it is therefore a

good tool for measuring mt [10]. (The quadratic dependence of FL on mt helps in ffimt by a factor of 2.) A 2% accuracy in determining FL yields a , 2 GeV error in measuring mt.

3.8 Exotic production mechanism and testing CP violation in

top

If new physics modifies strongly the t-c-g coupling, then the production rate of t-c pairs from q _q ! g ! t_c can be largely enhanced. By measuring this production rate at high Mtc, one can set the minimum energy scale \Lambda tcg at which new physics must set in. A study in Ref. [16] showed that \Lambda tcg ?, 4 TeV if no signal is found at a 3oe level. For this value of \Lambda tcg, the branching ratio t ! cg should be less than about 10%.

Besides all the potential physics discussed above, the Tevatron, as a _pp collider, is unique for being able to test CP violation by measuring the production rates of single-top events. A nonvanishing asymmetry (At) in the

inclusive production rates of the single-t events and the single-_t events signals CP violation [17]. With 2 fb\Gamma 1, it is possible to observe this asymmetry forA

t ?, 20% [17].

This work is supported in part by the NSF under grant no. . We thank our colleagues who contributed to the studies in Ref. [1].

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