Form Factors and Transverse Charge Densities

Siddharth Venkat

UW REU 2010

Scattering Theory

Scattering Theory (cont.)

Born approximation

Gives a differential cross section

which can be experimentally determined

The Form Factor

Electric potential

where

On the Light Front

Why?

Relativistic Form Factor

After some math:

Finite Radius Approximation

Densities can be approximated by zero far from the particle

Density is the Fourier transform of the form factor → F is band limited

Can use the sampling theorem

The Result

Where:

Data

More form factors

Transverse Densities

0.0 0.5 1.0 1.5 2.0b fm0.5

1.0

1.5

2.0

m bfm 2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4b fm0.5

1.0

1.5

2.0chbfm 2

Calculation of error

Get dF1 from propagation of errors

Assume errors in ρch add

Error

Final Result

Conclusion

• Random error is small

• What about higher Q2?

Acknowledgements

• Jerry Miller

• REU

• NSF