# How can the proton include top quarks, if a top quark is heavier than the proton?

A proton have mass $938~\mathrm{MeV/c^2}.$ How is it possible that a proton can include the heavier quarks with much higher mass like top quark with $173~\mathrm{GeV}\;?$

• For people who think this is false: the OP is talking about the proton's parton distribution functions. The top quark PDF is not zero. – knzhou Aug 24 '16 at 2:14
• The proton consists of valence quarks, gluons, and virtual quark/antiquark pairs that have a fleeting existence. The top quark contributes to this latter category. – Lewis Miller Aug 24 '16 at 2:58
• How do we know an electron has gluons, and virtual quark/antiquark pairs that have a fleeting existence? How do we know there's more than just three quarks? – Bill Alsept Aug 24 '16 at 5:54

Your confusion arises because the quark content of a proton is composed of virtual quarks.

In physics, a virtual particle is a transient fluctuation that exhibits many of the characteristics of an ordinary particle, but that exists for a limited time. The concept of virtual particles arises in perturbation theory of quantum field theory where interactions between ordinary particles are described in terms of exchanges of virtual particles. Any process involving virtual particles admits a schematic representation known as a Feynman diagram, in which virtual particles are represented by internal lines

Particles are represented by lines with arrows to denote the direction of their travel, with antiparticles having their arrows reversed. Virtual particles are represented by wavy or broken lines and have no arrows.

In quantum mechanics one calculates probabilities for interaction. When probing the proton by scattering experiments, the solutions fit the data with the proton having a content of a large number of virtual particles , consistent with the standard model of particle physics.

The proton "bag"

mathematically can be described by the virtual existence of the three valence quarks, and the virtual existence of innumerable quark and gluon particles off mass shell.

Virtual particles have the quantum number attributes of the named particle, but are off mass shell mathematical representations of the particles. They are mathematically represented by a propagator function, which has the named mass in its denominator. The further from the pole the energies probed are the smaller the contribution from the particle described by the propagator.

As you observe the masses of the charmed, bottom and top quarks are so large that any contribution from the propagators to the scattering crossection probing the proton will be very small. Still they have been fitted as a virtual contributions because it is allowed by the symmetries of the standard model.

The answer to the "how" is ," because they are off mass shell".