The Black Body Limit in DIS.

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

2. The Dipole model: Hadronic Cross Section of size, r. For small size quark-antiquark pairs, the result is derived at leading log order: (See Frankfurt et. al. Phys.Rev.D55:98-104,1997) 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). DIS 2004

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

4. matching region hard regime soft regime DIS 2004

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

6. Interpolation: Now invert the defining equation: DIS 2004

7. 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. DIS 2004

8. Proton target. DIS 2004

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

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

11. Fraction of s due to G > Gh. DIS 2004

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

13. Fraction of s DIS 2004

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

15. Longitudinal Structure Functions of MFGS without fitting. DIS 03 H1prelim-03-043 E.Lobodzinska DIS 2004

16. 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: DIS 2004

17. 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 • The saturation scale, R0, is fixed by the small size dipole behavior as well as the maximum cross section, s0. • 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 Q2. DIS 2004

18. 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.) • Both models have strong dependence upon quark masses at large hadronic sizes. DIS 2004

19. Reading from Bottom to top, X = .0001 X = .001 X = .01 Already significant variation with mass at 1 GeV2. DIS 2004

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

21. The mean squared dipole size. Factors of d2 appear in the diffractive cross sections like r-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 DIS 2004

22. Summary: • At HERA, DIS with Q2=2 GeV2, and x=10-4,about 1/5 of the total cross section is due to interactions with G>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/y 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.) DIS 2004