Elastic Scattering and Unitarity Constraints on Semi-Hard Jet Production

1. Elastic Scattering and Unitarity Constraints on Semi-Hard Jet Production Ted C. Rogers The Pennsylvania State University In collaboration with Anna Stasto and Mark Strikman:arXiv:0801:0303 Forward Physics at LHC with TOTEM, Penn State University, April 30, 2008

2. Impact Parameter Picture

3. Modelling pp x-sections at very high energies • Assume dominantly imaginary amplitude (real Γ) - Unitarity constraint on profile: • Extrapolation to very high energies: • Use extrapolation of elastic differential cross section. = (e.g., Islam, Luddy, Prokudin (2003))

4. Modelling pp x-sections at very high energies • Extrapolation to very high energies. • Important component of cosmic ray event generators. • Both hard and soft contributions: • Typically modelled in an eikonal/parton picture: • Hard part modeled by pQCD dijet formula. • Impact parameter dependence modeled / obtained from fits. • Soft part modelled with Regge theory; fits from elastic and total cross sections. (Recall P. Sommers talk) hard soft (DPMJET, QGSJET, SIBYLL…) (Review: Engel (2003))

5. Hard Scattering • At least one (semi-)hard jet pair. distribution function P Hard scattering:use pQCD + … P

6. Hard Scattering

7. i n c ¾ j 2 t e s Hard Scattering

8. Information from DIS: GPDs • The generalized gluon PDF and deep inelastic J/ψ production. • Impact parameter space gluon distribution function. Describes transverse distribution of hard partons -Recall talk of C. Weiss.

9. Information from DIS: GPDs • Frankfurt, Strikman, Weiss (FSW(2004)): fit to 2-gluon form factor from J/ψ production: • In impact parameter space:

10. Information from DIS • pp 2jet + X cross section in impact parameter space.

11. Information from DIS

12. Inelastic 2-jet profile function exclusive probability

13. Inelastic 2-jet profile function

14. p T V 1 4 s e = Comparison with extrapolation • Large contribution from large impact parameters. • Identical partons, • CTEQ6M gluon PDF extrapolated profile function using elastic cross section Small effect from correlations

15. Comparison with extrapolation:UHE • Identical partons, • CTEQ6M gluon PDF ptc = 3.5 GeV ptc = 2.5 GeV Islam et al.

16. Comparison with extrapolation • Sensitivity to large-b at -t = .02 GeV2. • Integrand of Fourier transform to t-space. • Integrate to b = 1.5 fm. Percent of integral; • ptc = 1.5 GeV: 65 % • ptc = 2.5 GeV: 80 % • ptc = 3.5 GeV: 87 %

17. Comparison with extrapolation • Sensitivity to large-b at -t = .1 GeV2. • Integrand of Fourier transform to t-space. • Oscillations at large b.

18. Comparison with extrapolation • Transition from small to large b, affects cross section at t = 0. • Fraction of differential inelastic cross section from dijet production to expectation from Islam,Luddy,Prokudin fit. 1.5 GeV 2.5 GeV 3.5 GeV

19. Source of low-pt taming: • Very rapid growth of gluon distribution at small-x. • Below some value of x, non-linear effects come into play, growth is tamed. • In pp 2jets + X jets x-section, what is the role “saturation” of the gluon distribution? • Look at jet rapidity distribution. • Compare with Golec-Biernat-Wustoff model in DIS to estimate “saturation” scale.

20. Source of taming: Region where gluon PDF would lead to saturation in dipole-proton scattering • Apparently small effect from gluon saturation. (solid line for octet dipoles) • Dominant effect from multiple parton scattering.

21. Summary • s-channel unitarity provides a general consistency relationbetween the hard dijet component of the cross section, and extrapolations to high energies. • At large b, correlations expected to be small. Can useGPDs extracted from DIS in the dijet formula. • pt cutoff should be chosen to avoid inconsistency – precise t-dependence needed at LHC energies. • Large part of taming due to multiple scattering (i.e. having two PDFs in the jet formula) rather than from gluon saturation in the PDFs. • Given a model of correlations, analysis can be extended to smaller b. (e.g. Treleani (1999))