The agreed top mass for now is 173 GEV/c2 so that is the pole mass? And this pole mass is derived from some calculation using the measured mass?Reggid said:For the top quark in some measurements the pole mass is used, in other measurments other mass schemes are used.
Inclusive processes involving massive quarks are an important ingredient of LHC physics, not least because of their role in determining PDFs. Uncertainties in heavy quark masses can lead to substantial contributions to PDF uncertainties, and thus to uncertainties in predictions for LHC crosssections for a wide range of processes.
Perturbative coefficient functions can be renormalized to depend on either the pole mass m or the MS running mass m(µ). The perturbative relation between them is now known to four loops, and for top the choice is essentially immaterial. However for charm and beauty nonperturbative corrections are more substantial, and while the MS charm and beauty masses can be determined rather precisely (to a few tens of MeV) through nonperturbative lattice or sum rule calculations, their pole masses are subject to large uncertainties (a few hundreds of MeV).
The conclusion of the paper explains that:Global PDF fits traditionally use pole masses. This is because the experimental observables used in the fits are generally inclusive, to avoid large uncertainties from final state effects. Heavy quarks in the final state are dealt with in the perturbative calculations by putting them on-shell: hadronisation corrections are then of relative order Λ/m, and thus power suppressed. The on-shell condition naturally leads to the mass dependence from heavy quarks in the final state being expressed in terms of the pole mass. In this short note, we will re-examine the possible use of the MS running mass in PDF determinations, and consider other ways in which uncertainties due to charm mass dependence might be reduced at LHC.
We have shown that, while for processes with only internal charm quark lines (such as processes with no charm in the final state, or semi-inclusive processes) it is straightforward to calculate using either pole mass or running mass in the hard cross-section, for inclusive processes with charm in the final state there no advantage to using the running mass, since the kinematics produces a nontrivial dependence on the pole mass which cannot be avoided without spoiling the factorized perturbative expansion. It follows that any empirical determination of the charm quark mass from inclusive charm production data has an intrinsic limitation due to nonperturbative corrections of a few hundred MeV. It is easy to see that these considerations generalise straightforwardly to inclusive hadronic processes such as W c or Z c-anti-c production, and indeed to inclusive beauty production, though here the effect will be less significant.
Pole mass is ill defined for the up quark, down quark and strange quark, because due to the mass of the lightest hadrons in which they are valence quarks, and the reality of quark confinement, these quarks are never observed at energy scales remotely close to their inferred MS mass from QCD. Instead, the masses of these three light quarks is customarily quoted at the 1 GeV or 2 GeV energy scale, usually using the MS bar scheme.A number of recent perturbative determinations of the MS charm mass from inclusive data claim an uncertainty as small as 50 MeV, competitive with the nonperturbative results. The reason for this small uncertainty is probably the use of the theoretical assumption that charm is produced entirely perturbatively, which greatly increases sensitivity to the charm mass. However it is clear from the poor convergence of Equation (4) that perturbation theory close to the charm threshold is unreliable: charm production is subject to large nonperturbative corrections. Relaxing the assumption by fitting a charm PDF, significantly reduces the dependence of the PDFs on the charm mass. This in turn reduces the dependence of high energy cross-sections required at LHC on the charm mass, and thus increases their precision. It will also presumably increase the uncertainty on any empirical determination of the charm mass from inclusive data to a few hundred MeV.
Pole mass is the mass of a particle when it is at rest, while non-stationary mass takes into account the particle's motion and energy. Non-stationary mass is also known as relativistic mass.
Pole mass is typically measured using scattering experiments, where the mass of a particle can be determined by analyzing its interactions with other particles.
Pole mass is an important concept in particle physics as it helps us understand the fundamental properties of particles and their interactions. It also plays a crucial role in the development of theories such as the Standard Model.
Yes, the pole mass of a particle can change depending on its interactions with other particles and its energy. This is due to the effects of relativity, where the mass of a particle is not a fixed quantity but can vary with its velocity and energy.
The concept of non-stationary mass is important in understanding the behavior of particles at high energies, where the effects of relativity become significant. It also helps us reconcile the differences between theoretical predictions and experimental observations in particle physics experiments.