april 15-19, 2007m. block, aspen workshop cosmic ray physics 2007 1 imposing the froissart bound on...
Post on 21-Dec-2015
220 views
TRANSCRIPT
![Page 1: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/1.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
1
Imposing the Froissart Bound on Hadronic Interactions:
Part II, Deep Inelastic Scattering & new structure functions for ultra-high energy -n cross sections
Martin Block
Northwestern University
![Page 2: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/2.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
2
Prior Restraint! the Froissart Bound
![Page 3: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/3.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
3
1) The Proton Structure Function F2p(x,Q2) : “Small-x Behavior
of Parton Distributions from the Observed Froissart Energy Dependence of the Deep-Inelastic-Scattering Cross Sections”, M. M. Block, Edmund L. Berger and Chung-I tan, Phys.Rev. Lett. 308 (2006).
2) Global Structure Function Fit and Predictions for Ultra-high Energy Neutrino-nucleon Cross Sections,
Work in progress for this meeting ! M. M. B, Edmund L. Berger and Chung-I Tan
Outline
![Page 4: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/4.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
4
Deep inelastic electron scattering
e e’
*
p
*p scattering
![Page 5: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/5.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
5
p log2(s/s0) fit, compared to the p even amplitude fit
M. Block and F. Halzen,
Phys Rev D 70, 091901, (2004)
Now employ same formalism for p scattering!
![Page 6: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/6.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
6
Proton Structure Function F2(x,Q2), from Deep Inelastic Scattering, Block, Berger & Tan, PRL 99, 88 (2006).
Bjorken xVirtuality
![Page 7: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/7.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
7
Reduced Virtual Photon Total Cross Section
![Page 8: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/8.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
8
![Page 9: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/9.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
9
Only ln2(s/s0) term needed!
![Page 10: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/10.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
10
![Page 11: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/11.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
11
![Page 12: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/12.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
12
Froissart bound fit, ln2 W, to reduced cross sections
![Page 13: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/13.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
13
Individual fits of the proton structure F2(x,Q2) vs. x, for 15 different Q2 values, in GeV2
Bjorken x
ONE functional form, ln2 s, fits ALL!
![Page 14: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/14.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
14
![Page 15: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/15.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
15
![Page 16: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/16.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
16
Scaling Point
Global (Simultaneous) Fit of F2(x,Q2) to x and Q2
![Page 17: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/17.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
17
F2(x, Q2): Global Fit Parameters for Q2/x >>m2, x<0.09
0.11 < Q2 < 1200 GeV2
Excellent 2/d.f. for 169 degrees of freedom
![Page 18: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/18.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
19
![Page 19: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/19.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
20
Predictions are made using ZEUS data in
global fit
Experimental data are from H1 collaboration
NO RENORMALIZATION
made!
1 Q2 GeV2
![Page 20: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/20.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
21
Comparing ln2x and CTEQ6.5 fits
![Page 21: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/21.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
22
Factor of 8 !
Standard CTEQ3 n
Froissart Bound n
n estimates, courtesy F. Halzen
![Page 22: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/22.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
23
SUMMARY
![Page 23: April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering](https://reader030.vdocuments.us/reader030/viewer/2022033104/56649d5f5503460f94a3ed46/html5/thumbnails/23.jpg)
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
24
To be done:
1. Include H1 in global fit, simultaneously fitting F2 and
dF2 /d(logQ2), d(logF2) /d(log x)
2. Constrained gluon particle distribution functions (p.d.f.’s)
for LHC &ILC
3. Constrained quark p.d.f’s for LHC & ILC
4. Recalculate cosmic ray neutrino cross sections using
bounded p.d.f.’s; current values are much too big!
Needs x~10-8 and Q2~6400 GeV2 . Enormous extrapolation !