1. 4/14/2004DIS 2004 The Black Body Limit in DIS. Ted Rogers, Mark Strikman, Vadim Guzey, Xiaomin Zu Penn State University Based on hep-ph/0309099 plus further studies.

2. 4/14/2004DIS 2004 The Dipole model: Hadronic Cross Section of size,  For small size quark-antiquark pairs, the result is derived at leading log order: The dipole model we use (see, e.g., McDermott, et. al. Eur.Phys.J.C16;641,2000) interpolates the cross section between the hard regime to the soft regime. This is the Leading Twist dipole model of McDermott, Frankfurt, Guzey and Strikman (MFGS). (See Frankfurt et. al. Phys.Rev.D55:98-104,1997)

3. 4/14/2004DIS 2004 The perturbative regime: With a matching ansatz:

4. 4/14/2004DIS 2004 hard regime soft regime matching region

5. 4/14/2004DIS 2004 t-dependence for dipole-nucleon elastic scattering: Small Size/Hard Limit: Large Size/Soft Limit: (Frankfurt,Strikman Phys.Rev.D;66,2002)

6. 4/14/2004DIS 2004 Interpolation: Now invert the defining equation:

7. 4/14/2004DIS 2004 The Black Limit: If the amplitude is assumed to be purely imaginary, then unitarity requires, If, then the target is totally absorbing (black) at impact parameter, b.

8. 4/14/2004DIS 2004 Proton target.

9. 4/14/2004DIS 2004 Contributions from different q: The profile function obtained By integrating up to U.

10. 4/14/2004DIS 2004 Lead target. Dotted line: x = 10 -2 Dashed line: x = 10 -3 Lower solid line: x = 10 -4 Upper solid line: x = 10 -5 Leading TwistGlauber Model

11. 4/14/2004DIS 2004 Fraction of  due to  h 

12. 4/14/2004DIS 2004 Comparison with factor of 9/4 for octet dipole-nucleon scattering. Red line is the profile with a factor of 9/4.

13. 4/14/2004DIS 2004 Fraction of  

14. 4/14/2004DIS 2004 Comparison with factor of 9/4 for octet dipole-nucleon scattering. Red line is the profile with a factor of 9/4.  Fraction of 

15. 4/14/2004DIS 2004 Longitudinal Structure Functions of MFGS without fitting. DIS  H1prelim-03-043 E.Lobodzinska

16. 4/14/2004DIS 2004  Comparison between the MFGS model and one that uses vector meson production data alone. (S. Munier et. al. Nucl. Phys.B603:427,2001.) Note relation:

17. 4/14/2004DIS 2004 The saturation scale, R 0, is fixed by the small size dipole behavior as well as the maximum cross section,  0. In order for the perturbative regime to match data, the quark mass must be less than about 140 MeV. That is much less than.3 GeV for all values of Q 2. Quark mass in other models: For example, the Golec-Biernat and Wusthoff (GBW) model: K. Golec-Biernat and M. Wusthoff Phys.Rev.D59:014017,1999

18. 4/14/2004DIS 2004 Both models have strong dependence upon quark masses at large hadronic sizes. Quark mass dependence in the MFGS model: The masses in the soft regime are set equal to about.3 GeV which is consistent with estimates from instanton models and lattice QCD. (There is no sensitivity to mq in the hard regime.)

19. 4/14/2004DIS 2004 Reading from Bottom to top, X =.0001 X =.001 X =.01 Already significant variation with mass at 1 GeV 2.

20. 4/14/2004DIS 2004 Distribution over sizes with large tails for small masses.

21. 4/14/2004DIS 2004 The mean squared dipole size. Factors of d 2 appear in the diffractive cross sections like  meson photoproduction and Compton scattering. This behavior in the GBW model persists in its more recent version: J. Bartels et. al., Phys.Rev.D66:014001,2002

22. 4/14/2004DIS 2004 Summary: At HERA, DIS with Q 2 =2 GeV 2, and x=10-4,about 1/5 of the total cross section is due to interactions with  >0.5. Corrections to the model from spin flip and a real part of the amplitude are small. Inelastic diffraction tends to speed up the approach to the unitarity limit. J/  data must be used for t-dependence because a significant contribution to the small size cross section comes from large -t. The quark mass in the soft regime must be chosen carefully. Note that instanton models and lattice QCD support the use of masses around.3 GeV. (See, e.g. D. Diakonov, Instantons at Work, hep-ph/0212026.)