1. T. Csörgő 1, R. J. Glauber 2, F. Nemes 1, J. Velasco 3 1 Wigner RCP, Budapest, Hungary 2 Harvard University, Cambridge, MA, USA 3 IFIC, University of Valencia, Valencia, Spain

2. Introduction to Diffraction Glauber-Velasco model Some Old-New Results Non-exponential behaviour of d  /dt at low-t Analysis of TOTEM/LHC p+p @ 7 TeV New results, generalized Glauber & Velasco Imaging with shadow profile functions from ISR to LHC Summary arxiv:1306.4217 arxiv:1311.2308

3. Diffraction – Hofstadter, Nobel (1961) Diffraction – Hofstadter, Nobel (1961) Diffractive electron scattering on nuclei and the resulting charge density distributions, images of spherical nuclei

4. Diffraction in pA, Diffraction in pA, Glauber and Matthiae, NPB21 (1970) 135 Glauber and Matthiae, NPB21 (1970) 135 Diffractive proton scattering on nuclei confirms the charge density distributions of spherical nuclei

5. Diffraction – What have we learned? Diffraction – What have we learned? The volume of spherical nuclei is proportional to A The surface thickness is constant, independent of A → Central charge density of large nuclei is approx constant R. Hofstadter, Nobel Lecture (1961)

6. What have we learned since WPCF2013? What have we learned since WPCF2013? t dip  tot ~ C geometric scaling at LHC C = 54.8 ± 0.7 mbGeV 2 (data) C ≠ 35.9 mbGeV 2 (black disc) NOT in black disck limit arxiv:1311.2308 BEL effect expected: proton becomes Blacker, Edgier, Larger, with increasing √s

7. Glauber – Velasco model summary Glauber – Velasco model summary BSWW EM form factors G E R.J. Glauber and J.Velasco Phys. Lett. B147 (1984) 380 F(t): f. sc. amplitude (b): opacity, complex f(t): cluster averaged parton- parton scattering amplitude d/dt: diff. cross-section elastic pp scattering -t = q 2 : momentum transfer b: impact parameter

8. First results @ Low-X 2013: GV works for d  /dt dip First results @ Low-X 2013: GV works for d  /dt dip Glauber-Velasco (GV) (original) describes d/dt data Both at ISR and TOTEM@LHC in the dip region arxiv:1311.2308 Note: at low-t GV is ~ exponential Really? Lower energies?

9. News in 2014: non-exponential at low-t News in 2014: non-exponential at low-t TOTEM preliminary similar to non-Gaussian features of HBT correlations

10. Non-exponential at low-t, details Non-exponential at low-t, details TOTEM preliminary similar to non-Gaussian features of HBT correlations

11. Diffraction in pp @ ISR, Diffraction in pp @ ISR, Glauber and Velasco, PLB147 (1984) 380 Glauber and Velasco, PLB147 (1984) 380 Illustration: elastic pp at the ISR energy range 13.7 – 62.7 GeV well described by Glauber-Velasco

12. Diffraction in pp @ ISR Diffraction in pp @ ISR Glauber and Velasco, PLB147 (1984) 380 Glauber and Velasco, PLB147 (1984) 380 Illustration: elastic pp at the SppS energy range 546-630 GeV well described by Glauber-Velasco _ _ _

13. Non-exponential pp in GV model Figure 4 from Glauber-Velasco PLB 147 (1984) 380 Slope is not quite exponential (for femtoscopy: a non-Gaussian behaviour) _

14. Imaging with shadow profile Imaging with shadow profile

15. at 7 TeV proton becomes Blacker, but NOT edgier, and Larger BEL BNeL effect Saturation from shadow profiles Saturation from shadow profiles ISR and SppS: R.J. Glauber and J.Velasco Phys. Lett. B147 (1987) 380 b 1,b 2 fixed apparent saturation: proton is ~ black at LHC up to r ~ 0.7 fm see also Lipari and Lusignoli arXiv:1305.7216arXiv:1305.7216 Kohara, Ferreira, Kodama arXiv:1408.1599arXiv:1408.1599

16. proton becomes Blacker, but NOT edgier, and Larger BNeL effect BNeL effect BNeL effect This work Lipari and Lusignoli arXiv:1305.7216arXiv:1305.7216Kohara, Ferreira, Kodama arXiv:1408.1599arXiv:1408.1599 see also

17. Shadow imaging in p+p at ISR Proton image: gray (n=1) edge, dark (n~3) center Opacity expansion of order n: exp(-) = 1-   

18. Shadow imaging in p+p at LHC Proton at 7 TeV: gray (n=1) edge, very dark (n ≥ 4) center Opacity expansion of order n: exp(-) = 1-   Simple choice for the generalization of GV: f(t)/f(0) = exp(i b 1 |t| + i b 2 |t| 2 ) / sqrt( 1 + a t)  f(t)/f(0) = exp(i b 1 |t| + i b 2 |t| 2 ) / sqrt( 1 + a|t| + a 1 |t| 2 + a 2 |t| 3 + …) More systematic expansions and further improvements are under investigation.

19. Picture of proton Picture of proton Investigation of Glauber-Velasco model works well in the dip region at LHC but needs extension in low-t TOTEM: non-exponential behaviour geometric scaling but not in the Black Disc limit generalized Glauber-Velasco works well at low-t also at dip-t, but … from BEL to BNeL effect Grey at r~ 1 fm, black up to r~0.7 fm

20. Shadow imaging in p+p at LHC The BNeL effect. Thank You!

21. Summary Summary Collectivity in Collision in Kolymbari Collectivity in Collision in Kolymbari C 2 K 65th birthday of László Csernai 65th birthday of László Csernai 65 L C 2 K = 65 L C 2 K = 65 L Happy Birthday ! Happy Birthday !

22. Backup slides Backup slides

23. Multiple Diffraction Theory of Elastic proton-proton scattering Multiple Diffraction Theory of Elastic proton-proton scattering

24. Multiple Diffraction Theory of Elastic proton-proton scattering: Glauber-Velasco Multiple Diffraction Theory of Elastic proton-proton scattering: Glauber-Velasco

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