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The 1986's publication "A measurement of the space-like pion electromagnetic form factor" (http://dx.doi.org/10.1016/0550-3213(86)90437-2) starts with:

The pion form factor has been measured in the space-like $q^2$ region $0.014$ to $0.26 (GeV/c)^2$ by scattering $300 GeV$ pions from the electrons of a liquid hydrogen target.

The process under consideration is the elastic scattering of a charged pion with an electron. They conventionally refer to $q^2$ for a space-like photon momentum and to $t=-q^2$ for a time-like photon momentum.

Why does this energy range for the photon correspond to being "space-like"?

As far as I know one can only talk about being "space-like/time-like/light-like" for the separation of two space-time points or events (in 4D Minkowski space). What would be the two points here?

What energy would be the time-like regime for $q^2$ in the context of 300 GeV pions used to measure the e.m. form factor?

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    $\begingroup$ You can of course talk about a spacelike distance, but more generally it refers to a spacelike vector. In -+++, a timelike vector has negative Minkowski norm. A spacelike one has positive norm. $\endgroup$
    – Ryan Unger
    Commented Jan 26, 2015 at 19:49
  • $\begingroup$ @0celo7 That's an answer. Why not post it as one. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Jan 27, 2015 at 0:17
  • $\begingroup$ @dmckee: I'm not sure how it pertains to this question though. If the four-momentum is not null, then the photon has to be virtual. I'm not sure what the physical meaning of space-like energy is. $\endgroup$
    – Ryan Unger
    Commented Jan 27, 2015 at 0:56
  • $\begingroup$ Of course, one can also talk about a vector being space/time/light-like; same as two points in a vector space always define a vector, namely the one pointing from the first to the second point. $\endgroup$
    – ritter
    Commented Jan 27, 2015 at 20:50
  • $\begingroup$ I believe the vector $q$ connects the first scattering vertex (incoming pion, photon, outgoing pion) with the second vertex (incoming e, photon, outgoig e). Thus, the question is, why is this energy range considered as being space-like? $\endgroup$
    – ritter
    Commented Jan 27, 2015 at 20:52

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I believe that by saying

in the space-like $q^2$ region $0.014$ to $0.26 GeV^2$

the authors meant that they are talking about scattering here. It's not this particular energy region that makes it spacelike. More generally one knows that in scattering the momentum transfer is negative $q^2<0$. This means $q$ is a spacelike vector.

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