Understanding Form Factor: A Physical Meaning

[jaleyil]

ıs anyone know about what the physical meaning of form factor is?

 

[Bob S]

The experimental scattering form factor F(q²)² in electron nuclear scattering is the ratio of the observed differential elastic scattering cross section (dσ/dΩ cm² per steradian), corrected for finite mass, to the Mott differential scattering cross section (similar to the Rutherford cross section). See Equation (1) in

http://www.google.com/url?sa=t&sour...x9W5Ag&usg=AFQjCNGiqQANS9CGyQNEuBgQWcxpztMTOQ

The form factor F(q²)² (a function of the momentum transfer q), represents the reduction of the observed cross section due to the finite size of the target proton or nucleus, relative to a point-charge target. For a point-charge target, F(q²) = 1 for all q.

Bob S

 

[tom.stoer]

The form factor is something liek the Fourier transformation of the charge or current density. Attention: this interpretation becomes dangerous in the relativistic domain.

 

[Bob S]

The form factor is something liek the Fourier transformation of the charge or current density. Attention: this interpretation becomes dangerous in the relativistic domain.

Precisely.
See Equations (2) through (4) in

http://www.google.com/url?sa=t&sour...x9W5Ag&usg=AFQjCNGiqQANS9CGyQNEuBgQWcxpztMTOQ

The Appendix gives some interesting useful form factor transformations to/from momentum space from/to physical size. Note that nowhere are any radiative corrections mentioned. The discovery of quarks was based on the extension of form factor analysis of electron-proton scattering at ~ 20 GeV.

Bob S

 

[tom.stoer]

In electron-proton scattering (deep) inelastic scattering becomes important; the structure functions F(Q²,x) are generalizations of form factors.

 

[jaleyil]

can we say hadronic form factor and coupling constant are equivalent concepts or is there any difference between them?

 

[tom.stoer]

There is a difference.

The coupling constant describes how charge and current densities interact. The form factor "is" the (Fourier transform) of the density.

Why do you think they are the same?

 

[Hepth]

Depending on the context, Hadronic Form Factors and DECAY constants are equivalent concepts, where a decay constant for some pseudoscalar meson M:
$$\langle 0| q_1 \gamma^\mu (1-\gamma_5) q_2 | M > = -i f_M p^{\mu}_{M}$$
is part of the parametrization of the matrix, in this case a constant, but say for a vector meson decay
$$\langle \gamma | q_1 \gamma^\mu (1-\gamma_5) q_2 | V > = F_V (q^2) \epsilon^{\mu \nu \alpha \beta} \eta^\nu p_{V\alpha} p_{\gamma \beta} + i F_A (q^2) [\eta^\mu (p_V \cdot p_\gamma ) - p^{\gamma \mu} (p_V \cdot \eta)]$$
Where Fv and Fa are the form factors of the parametrization of this decay. Similar ideas but the "scalars" in the second case are functions of the momentum transfer, while in the first must not depend on momentum, as there is no transfer.
Maybe that's what you meant?

 

[jaleyil]

Thanks a lot Tom. I have another question. Can we measure decay constant directly from high energy experiments ?

 

[tom.stoer]

Which decay constant are you talking about?

 

[jaleyil]

hadronic decay constant