This talk summarizes recent progress in top quark physics studies for high
energy linear electron-positron colliders as presented at the LCWS2000 Workshop
at Fermilab. New results were presented for top pair production at threshold
and in the continuum, as well as for top production at $\gamma\gamma$
colliders.Comment: 7 pages, Latex, uses aipproc.sty; plenary talk presented at Linear
  Collider Workshop 2000, Fermilab, Batavia, IL, Oct. 24--28, 200

Orr, Lynne H.

English

arXiv

Lynne H. Orr

Crossref

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January 2001
Top Quark Physics: Summary
Lynne H. Orr∗
∗Department of Physics and Astronomy
University of Rochester
Rochester, NY 14627-0171
Abstract. This talk summarizes recent progress in top quark physics studies for high
energy linear electron-positron colliders as presented at the LCWS2000 Workshop at
Fermilab. New results were presented for top pair production at threshold and in the
continuum, as well as for top production at γγ colliders.
INTRODUCTION
Top quark production promises to provide an excellent system in which to study
the physics of the Standard Model and beyond, and a linear e+e− collider provides
an excellent environment in which to do so. The top quark’s mass of 174 GeV gives
it a number of unique features. Its decay width Γt = 1.4 GeV is so large that top
decays before hadronizing [1], unlike the lighter quarks. This rapid decay causes
the top quark’s spin information to be passed to its decay products. Top also has
the largest coupling to the Higgs sector of all the fermions; indeed the fact that
its Yukawa coupling is very close to unity suggests that the top quark may play a
special, fundamental role in Electroweak Symmetry Breaking. The importance of
the top quark to new physics studies is indicated by the fact that the top quark
was featured in talks at this conference not only in the present session but also
in the Higgs, Electroweak, New Phenomena, and Supersymmetry sessions. This
underscores the point that in order to get at physics beyond the SM, we must
understand the physics of the top quark in detail.
Here we summarize the work that was presented in the Top Quark session. Sig-
nificant progress has been made in a number of areas since LCWS99 at Sitges (see
[2] and [3] for summaries of theoretical and experimental aspects of top physics
at LCWS99), including top production at threshold, at high energies, and in γγ
collisions. Threshold studies by the European Working Group were not presented
here but will be included in the TESLA TDR to be released in Spring 2001 [4].
TOP AT THRESHOLD
A linear e+e− collider operating in the threshold region for top pair production
(around 350 GeV in the center of mass) allows us to make precise measurements
of the top quark mass and the strong coupling constant αs. The top width and
couplings can be measured to a lesser extent. Top-antitop pairs cannot form topo-
nium because they decay too fast, but there is still a Coulomb-like QCD interaction
between the t and t̄ which results in notrivial structure in the top production cross
section at threshold. Experimental simulations indicate that a threshold scan could
give a top mass measurement with an experimental uncertainty as low as 40 or 50
MeV [3]. This would be an improvement over the LHC, where we can expect to
measure the top mass to a GeV or two at best. This presents a challenge to theorists
to achieve comparable precision in threshold cross section predictions.
Theoretical Issues
NNLO calculations of the top threshold cross section were presented at Sitges,
and the results did not at first bode well for the prospect of achieving the desired
theoretical precision [2]. There were several problems: the NNLO corrections to
the normalization were unexpectedly large, the 1S peak position (used to deter-
mine mt) shifted with respect to NLO by large amounts (600–800 MeV), and the
renormalization scale dependence was no better at NNLO than at NLO.
The situation was already improving around the time of the Sitges meeting, and
it has been further clarified since then. The resolution of the peak position–mass
problem was discussed in talks here by Sumino [5] and Yakovlev [6], and a summary
of the situation can be found in [7]. The problem arose from the top mass definition
used in the calculations. Specifically, if one calculates in terms of the familiar pole
mass — the position of the pole in the top quark propagator and the mass measured
in top quark reconstruction (for example by CDF and D∅) — one is sensitive to
effects associated with long distance/low energy phenomena such as hadronization.
This so-called renormalon ambiguity gives rise to uncertainties of order ΛQCD and
results in a shift in the NNLO peak position.
The solution is to switch to a mass definition that is appropriate for short dis-
tances, such as the 1S mass; see [7] for a discussion of the various possibilities.
The renormalon contribution to the relation between the pole mass and the short
distance mass is exactly canceled by a corresponding contribution in the relation
between pole mass and the binding energy of the tt̄ state. The resulting NNLO
peak shift is well under control, and one can realistically expect much-improved
theoretical precision.
Just what it would take to achieve 50 MeV theoretical precision was the sub-
ject of the talk by Sumino [5]. It requires higher-order calculations in which the
renormalons continue to cancel. There was some confusion at Sitges about order
counting in the cancellation, but this has since been clarified: the cancellation takes
place at different orders in αs in the binding energy and the mpole–mM̄S relation;
one has to go one order higher in Ebinding. For the desired theoretical precision,
one needs O(α4s) in the mass and O(α5s) in Ebinding. Sumino reported results for
Ebinding to O(α5s) in the large-β0 approximation, which is sufficient to demonstrate
the renormalon cancellation. He obtained the following masses for the “toponium”
1S state (keeping the contributions from individual orders in αs separate):
M1S = 2× (174.79− 0.46− 0.39− 0.28− 0.19) GeV (1)
= 2× (165.00 + 7.21 + 1.24 + 0.22 + 0.052) GeV (2)
where the first result is for the pole-mass scheme and the second is for the M̄S-
mass scheme; the improvement in convergence in the latter scheme is clear. The last
number in each line is a new result reported here at LCWS2000. This represents
significant progress; still needed for the desired theoretical precision are theO(α4sm)
relation between mpole and mM̄S (a four-loop calculation), inclusion of final-state
interactions and electroweak corrections, and a determination of the effect of initial
state radiation on the position of the 1S peak.
Yakovlev also discussed top production at the threshold [6]. He introduced a
new short-distance mass definition, the P̄ S mass, which is a modification of the PS
(potential-subtracted) mass defined in [8]. The P̄ S mass includes recoil corrections
of order 1/m and further improves the behavior of the cross section. Yakovlev also
reported that nonfactorizable corrections to the threshold cross section cancel at
NNLO.
The peak position problems with the top threshold are therefore now solved,
paving the way for a precise threshold mass measurement. The problems associated
with the overall normalization and renormalization scale dependence must also be
resolved if we wish to measure top couplings at the threshold. Fortunately, there
was some good news on this front about the time of this workshop. Although
it was not presented here, a new threshold calculation appeared recently which
involves resumming logarithms of the top velocity. The calculation results in a vast
reduction of the theoretical uncertainty to the few percent level. Details can be
found in [9].
Experimental Issues
Ikematsu discussed experimental aspects of top momentum reconstruction near
threshold [10]. Previous studies have focused on threshold scans (see [3] for a status
report) which measure the total top production cross section. But as Ikematsu
pointed out, we can extract additional information by examining threshold top
events in more detail. For example, anomalous CP-violating gluon EDM couplings
are enhanced at the threshold. To study these, we need to measure the momentum
of the top quark. Ikematsu presented results of an experimental simulation at
√
s =
2mt + 2 GeV including ISR, beamstrahlung, and QCD threshold corrections for
lepton plus jets events. He compared a traditional direct momentum reconstruction
algorithm to a kinematic fitting technique that incorporated a likelihood function.
The kinematic fit significantly improves energy resolution and resolution in the
direction of the top momentum. Extension of the study to energies below threshold
and incorporation of an improved jet clustering algorithm are in progress.
CONTINUUM TOP PRODUCTION
Anomalous Couplings
At center of mass energies well above threshold, a linear collider allows us to
probe the couplings associated with the top production and decay vertices. The
production vertex involves the couplings of top to the photon and Z0, which are
difficult-to-impossible to measure at the LHC. The decays are sensitive to the cou-
pling of top to the W boson and b quark. In both of these processes we can look for
CP-violating couplings in electric and weak dipole moments. The work reported
here [11,13] focused on the top production vertex.
Kiyo [11] discussed the effects of anomalous γ and Z0 couplings in spin corre-
lations in top production and decay. Using the off-diagonal spin basis of Parke
and Shadmi [12], Kiyo showed that the azimuthal angle dependence of final-state
leptons can be very sensitive to CP-violating effects. Let the coupling at the top
production vertex be given by
gttγ,Z = gV {Qγ,ZL γµL+Qγ,ZR γµR +
(pt − pt̄)µ
2mt
[Gγ,ZL L+G
γ,Z
R R]} (3)
with anomalous couplings GL,R. With if3 = GR −GL, |f3| = 1 corresponds to an
electric dipole moment of 10−16e cm. One can define a leptonic azimuthal asym-
metry as a function of the top quark scattering angle. This asymmetry vanishes in
the SM but can be as large as 5 or 10% for |f3| of the order of 0.2. In addition, one
can distinguish between the various couplings (γ vs. Z and positive vs. negative)
by adjusting the polarization of the initial electrons and positrons.
This method does require reconstruction of the top quark direction. Being able
to distinguish the up- vs. down-type decay products of the W boson is also helpful;
in leptonic W decays this information is given by the lepton charge.
M. Iwasaki addressed these experimental issues associated with measuring the
couplings at the top production vertex [13]. The particular questions of interest
were how well we can reconstruct the t and t̄ quarks (and identify which is which),
whether we can identify Iz of the W decay products, and to what extent we can use
this information to constrain couplings. She presented results from an LCD fast
simulation using Pandora-Pythia, with ISR, beamstrahlung, and QCD radiation
included.
The presence of two neutrinos in dilepton events makes it difficult to obtain the
t and t̄ momenta, so this mode was not included in Iwasaki’s studies. For lepton
plus jets events, jet energies were obtained with a combination of tracking (for
charged particles) and calorimetry (for neutrals) rather than straight calorimetry.
b-tagging was performed by requiring that the pT -corrected mass at the vertex be
greater than 1.8 GeV, and by cutting on the number of significant tracks in the jet.
The resulting flavor tag dramatically improved W and top mass reconstruction.
The lepton charge provided Iz information.
Flavor tagging played an even more important role in the all-jets mode, with
six jets and no leptons. Here Iwasaki used the mass tag for b tagging and added
a measurement of vertex charge to distinguish b from b̄. A charm tag — using
a combination of pT corrected mass and vertex momentum — was also shown
to be reasonably effective (28% efficiency and 69% purity) in obtaining detailed
information about the W decays. Note that such a charm tag would be very
difficult at the LHC.
The result of the lepton plus jets analysis is that we can expect measurements
to about 2–4 × 10−2 in the axial couplings F γ,Z1A . Vector coupling studies are in
progress, as studies of the top decay vertex. An analysis for the all-jets mode is
also on the way.
QCD
Precision measurements require precision predictions that include QCD correc-
tions. Progress was reported here on fixed-order QCD corrections to top production
and decay [14] and improvements in parton shower Monte Carlos to take the top
mass into account [15,16].
QCD corrections to top processes have previously been performed for the produc-
tion and decay processes separately or combined in the on-shell approximation. As
of the Sitges meeting [2], real gluon corrections to the full top production and decay
process with off-shell top quarks were calculated. Macesanu discussed the calcula-
tion of virtual corrections to top production and decay for off-shell top quarks [14]
with all interferences, including so-called nonfactorizable corrections that contain
diagrams with gluons connecting different parts of the process (t production and t̄
decay, for example). The computation is being performed in the double-pole ap-
proximation, keeping only contributions from terms which contain two resonant top
quarks, in analogy to the RacoonWW approach [17] to corrections to W pair pro-
duction. The loop corrections are nearly complete and will be combined with the
result for real gluon radiation [18] to give a complete NLO description of off-shell
top production and decay.
In Monte Carlo programs, gluon radiation is often treated in the parton shower
approximation, using parton splitting functions. This involves soft and collinear
approximations for the radiated gluons. The shower approximation incorporates
the leading QCD effects to high orders in αs and works well for massless particles.
Radiation from massive particles like the top quark is more complicate, however.
In particular, from massless particles is characterized by a collinear singularity,
whereas the mass of a heavy particle suppresses collinear radiation, creating a
“dead cone” in the vicinity of the radiating particle. Parton showers have difficulty
approximating the dead cone, and in addition they have difficulty populating large
angles.
The solution is to incorporate matrix element corrections to the parton shower
approach, and corrections to the programs HERWIG [15] and Pythia [16] were re-
ported at this workshop. Corcella showed results for matrix element corrections
to top decays in HERWIG; the program now reproduces the matrix element cal-
culation for radiation in top events at linear colliders not too far above threshold.
Corrections for radiation in top production are in progress, for hadron colliders
as well. Also underway are the incorporation of spin correlations, and ISR and
beamstrahlung for linear colliders.
Sjöstrand reported on improvements to Pythia [16], including matrix element
corrections to radiation from all heavy particles: not only for top and the other SM
particles but for supersymmetric particles as well. For radiation in top production
at Ecm = 500 GeV, the corrections increase emissions off the tt̄ pair but decrease
emissions in the top decays, for a net decrease in the entire production and decay
process. An interesting point to note about the corrections is a strong dependence
of the radiation on the spin structure of the underlying process, in constrast to the
universal behavior of massless splitting functions.
Corcella also discussed briefly some studies of top mass reconstruction in dilep-
ton events using HERWIG and Pythia [15]. The lepton energy and bl invariant
mass spectra were not very sensitive to mt, but the Eb spectrum near threshold
appeared more promising. However he also showed that differences between HER-
WIG and Pythia can amount to hundreds of MeV, which already saturates the
desired uncertainty in the mass.
TOP AT γγ COLLIDERS
Finally, Boos gave a very nice review of top physics at γγ colliders [19]. Many
processes and measurements are similar to those at e+e− colliders. The pair pro-
duction cross section can be higher at γγ colliders for some polarizations and center
of mass energies, and NLO corrections increase the γγ cross section. The threshold
has similar NNLO problems to e+e− colliders, but these presumably can also be
resolved.
A variety of top couplings and non-SM effects can be studied at a photon collider.
The γtt coupling, for example, enters top pair production to the fourth power, and
is already separate from the top coupling to the Z. Boos showed that CP properties
of the Higgs boson can be studied, as can effects of large extra dimensions. Single
top production probes the Wtb vertex and is sensitive to some technicolor models;
ironically, its biggest background is tt̄ pair production.
SUMMARY
We have seen at this workshop a lot of progress in top studies as we move
from looking primarily at the big picture to performing more detailed analyses.
Some very good news was that the theory of top production at threshold is once
more under control. In continuum production, calculations of QCD corrections are
becoming more sophisticated, and anomalous couplings are being studied in more
detail. In addition, the experimental side of top reconstruction is becoming better
understood. Much work is still under way, so we anticipate even more progress
soon.
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