I know that under normal circumstances the top quark does not have the time to hadronize. Under what conditions would it be possible to hadronize?
Obviously adding more energy to the top (if that was possible) is not the solution. Is it possible to create a top with less energy? If so, would it live longer? Or is the top simply too massive to ever do anything but decay?
I will address these:
Is it possible to create a top with less energy?
The top is uniquely characterized by its mass. If another particle were detected with a different mass, close by , it would not be the top. ( and the whole symmetry scheme for the quarks would have to be rethought). This means that in the center of mass system of the top where the decays can be simply studied the only energy available is the mass of the top, so there is no meaning to this question.
If so, would it live longer? Or is the top simply too massive to ever do anything but decay?
All higher generation quarks decay to either up or down (lowest generation). This in the end creates stable protons as the final hadronic system which conserves the baryon number . Hadronic decays are a subset of all decays: they are decays where quark goes only into hadrons, instead of a lepton and some hadrons.
I know that under normal circumstances the top quark does not have the time to hadronize.
Reference: "Top-quark physics at the Large Hadron Collider" by Markus Cristinziani and Martijn Mulders 2017 J. Phys. G: Nucl. Part. Phys. 44 063001:
Page 28: "The average lifetime of top quarks is a factor of $\sim10$ smaller than the hadronization timescale $(1/\Lambda_{QCD} \sim 10^{-24} s)$, ...".
In addition,
Page 26: "4.7. Interpretation of the top-quark mass measurements
With a precision below 0.5% in the best results it is important to define exactly what quantity is measured. All measurements discussed so far, and included in the combinations, are calibrated using Monte Carlo simulations and thus measure the Monte Carlo top mass parameter as a matter of definition. A proper relation between this Monte Carlo mass parameter and the SM $m_t$ parameter used in field theoretical calculations is lacking. For the top quark mass the choice of a renormalisation scheme for the theoretical mass definition is known to have large effects on the numerical value of the obtained mass. The difference between two popular schemes, $\overline{\rm MS}$ and the pole mass, is as large as 10 GeV. Once the mass is known in a short-distance scheme like the $\overline{\rm MS}$ scheme, however, it can be transferred to a different short-distance mass scheme with good precision, typically well below 50 MeV $^{[129]}$. However, the pole mass scheme is not a short-distance scheme and it is affected by the so-called renormalon ambiguity which limits the precision of its translation to other mass schemes to about 70 MeV at best $^{[129, 130]}$. It has been argued that the Monte Carlo mass parameter is expected to be close in numerical value to the pole mass definition, with an unknown offset that is thought to be up to 1 GeV, and that it would be preferable to avoid the use of the pole mass scheme all-together and directly relate the Monte Carlo mass to a short distance mass definition like the MSR mass $^{[131–133]}$. For a proper choice of scale parameter this scheme could have a numerical value close to the pole mass, without suffering from renormalon ambiguities.
To establish quantitatively the size of a possible offset between the Monte Carlo mass and a suitable theoretical mass definition it is useful to compare the Monte Carlo prediction for a physical observable to a prediction from a first-principles QCD calculation with corrections up to the level of stable particles after radiation and hadronisation. In principle the offset can be different for different observables, so the calibration would have to be performed for each observable of interest.
One could also argue that in practice the differences between the MC mass and a pole mass definition are related to perturbative and non-perturbative QCD corrections that are to first approximation described by the MC simulations and to some extent already covered by systematic uncertainties related to theoretical modelling already assigned. If this is true, different methods using different observables should yield top mass results that are compatible within the assigned uncertainties.
Either way, a possible bias in the mass definition could depend in principle on the observable, and it is therefore useful to measure the top mass with as many different observables as possible, and to explore alternative methods that allow the use of a well defined QCD calculation without the use of a Monte Carlo program as intermediate step.".
Above references:
[129] Marquard P, Smirnov A V, Smirnov V A and Steinhauser M 2015 Phys. Rev. Lett. 114 142002
[130] Beneke M, Marquard P, Nason P and Steinhauser M 2016 On the ultimate uncertainty of the top
quark pole mass arXiv:1605.03609
[131] Hoang A H 2014 The top mass: interpretation and theoretical uncertainties 7th Int. Workshop on
Top Quark Physics (TOP2014) (Cannes, France) arXiv:1412.3649
[132] Moch S et al 2014 High precision fundamental constants at the TeV scale arXiv:1405.4781
[133] Hoang A H, Jain A, Scimemi I and Stewart I W 2008 Phys. Rev. Lett. 101 151602
Second source
"The Top Mass in Hadronic Collisions" by Paolo Nason (19 Jan 2018):
Page 7: "There are several followups of the work in ref.$^{[18]}$. In ref.$^{[19]}$, it was argued that, in general, an additional uncertainty of 1 GeV should be accounted for in top mass measurements at hadron colliders. It is also argued that the top pole mass in general cannot be determined with a precision better than 1 GeV because of the mass renormalon problem. Although it is stated somewhere in this paper that 1 GeV “is the energy value I use in this talk for what theorists call hadronization scale”, this value, quoted in the abstract and in many places in the paper, has been echoed as is in several other publications and talks, to be taken as a serious hard limit on the precision that can be achieved in the measurement of the top mass by direct methods.".
[18] A. H. Hoang and I. W. Stewart, Top Mass Measurements from Jets
and the Tevatron Top-Quark Mass, Nucl. Phys. Proc. Suppl. 185
(2008) 220–226, [0808.0222].
[19] A. H. Hoang, The Top Mass: Interpretation and Theoretical
Uncertainties, in Proceedings, 7th International Workshop on Top
Quark Physics (TOP2014): Cannes, France, September 28-October 3,
2014, 2014. 1412.3649.
Under what conditions would it be possible to hadronize?
Obviously adding more energy to the top (if that was possible) is not the solution. Is it possible to create a top with less energy? If so, would it live longer?
Or is the top simply too massive to ever do anything but decay?
[Note: I believe Anna has kindly answered your other questions, I'll add a small improvement to my answer.]
In Quantum Chromodynamics (QCD) a Chiral perturbation theory (ChPT) is not available to create a 'top Quark condensate' where one could extend the top Quark's lifetime. Source: Wikipedia - ChPT - Mesons and Nucleons:
"Since chiral perturbation theory assumes chiral symmetry, and therefore massless quarks, it cannot be used to model interactions of the heavier quarks.".
Use of Lattice QCD to model these hypothesis is expensive, and difficult.
"Analytic or perturbative solutions in low-energy QCD are hard or impossible to obtain due to the highly nonlinear nature of the strong force and the large coupling constant at low energies.
...
In lattice QCD, fields representing quarks are defined at lattice sites (which leads to fermion doubling), while the gluon fields are defined on the links connecting neighboring sites. This approximation approaches continuum QCD as the spacing between lattice sites is reduced to zero. Because the computational cost of numerical simulations can increase dramatically as the lattice spacing decreases, results are often extrapolated to $a = 0$ by repeated calculations at different lattice spacings a that are large enough to be tractable.
Numerical lattice QCD calculations using Monte Carlo methods can be extremely computationally intensive, requiring the use of the largest available supercomputers. To reduce the computational burden, the so-called quenched approximation can be used, in which the quark fields are treated as non-dynamic "frozen" variables.".
Further references:
Deconfinement and color confinement is not well understood, finding papers documenting experiments and explaining the relevant portions is also challenging. Here's what the link on color confinement has to offer:
"There is not yet an analytic proof of color confinement in any non-abelian gauge theory. The phenomenon can be understood qualitatively by noting that the force-carrying gluons of QCD have color charge, unlike the photons of quantum electrodynamics (QED). Whereas the electric field between electrically charged particles decreases rapidly as those particles are separated, the gluon field between a pair of color charges forms a narrow flux tube (or string) between them. Because of this behavior of the gluon field, the strong force between the particles is constant regardless of their separation.
Therefore, as two color charges are separated, at some point it becomes energetically favorable for a new quark–antiquark pair to appear, rather than extending the tube further. As a result of this, when quarks are produced in particle accelerators, instead of seeing the individual quarks in detectors, scientists see "jets" of many color-neutral particles (mesons and baryons), clustered together. This process is called hadronization, fragmentation, or string breaking.".
In one answer to this question: "About free quarks and confinement" it is noted:
"As J. Rennie points out, none of this is completely understood and a full mathematical description of confinement would be the biggest breakthrough in quantum theory in decades.".
