t. csörgő 1, r. j. glauber 2, f. nemes 1, j. velasco 3 1 wigner rcp, budapest, hungary 2 harvard...
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Diffraction – Hofstadter, Nobel (1961) Diffraction – Hofstadter, Nobel (1961) Diffractive electron scattering on nuclei and the resulting charge density distributions, images of spherical nucleiTRANSCRIPT
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MULTIPLE DIFFRACTION THEORY OF ELASTIC PP SCATTERING, WITH APPLICATIONS TO 7 TEV PP DATA
T. Csörgő1, R. J. Glauber2, F. Nemes1 , J. Velasco3
1 Wigner RCP, Budapest, Hungary2 Harvard University, Cambridge, MA, USA3 IFIC, University of Valencia, Valencia, Spain
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Introduction to DiffractionGlauber-Velasco modelSome Old-New Results
Non-exponential behaviour of ds/dt at low-t Analysis of TOTEM/LHC p+p @ 7 TeV
New results, generalized Glauber & Velasco
Imaging with shadow profile functionsfrom ISR to LHC
Summary
arxiv:1306.4217arxiv:1311.2308
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Diffraction – Hofstadter, Nobel (1961)
Diffractive electron scattering on nuclei and the resulting charge density distributions, images of spherical nuclei
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Diffraction in pA, Glauber and Matthiae, NPB21 (1970) 135
Diffractive proton scattering on nuclei confirms the charge density distributions of spherical nuclei
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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)
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What have we learned since WPCF2013? tdip stot ~ C
geometric scaling at LHC
C = 54.8 ± 0.7 mbGeV2 (data)
C ≠ 35.9 mbGeV2
(black disc)
NOT in black disck limitarxiv:1311.2308
BEL effect expected:
proton becomesBlacker,Edgier,Larger,
with increasing √s
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Glauber – Velasco model summary
BSWW EM form factors GE
R.J. Glauber and J.Velasco Phys. Lett. B147 (1984) 380
F(t): f. sc. amplitudeW(b): opacity, complex
f(t): cluster averaged parton-parton scattering amplitude
ds/dt: diff. cross-section elastic pp scattering
-t = q2: momentum transferb: impact parameter
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First results @ Low-X 2013: GV works for ds/dt dip
Glauber-Velasco (GV)(original)
describes ds/dt dataBoth at ISR andTOTEM@LHC
in the dip region
arxiv:1311.2308
Note: at low-tGV is ~ exponential
Really? Lower energies?
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News in 2014: non-exponential at low-t
TOTEM preliminarysimilar to non-Gaussian
features of HBT correlations
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Non-exponential at low-t, details
TOTEM preliminarysimilar to non-Gaussian
features of HBT correlations
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Diffraction in pp @ ISR, Glauber and Velasco, PLB147 (1984) 380
Illustration: elastic pp at the ISR energy range 13.7 – 62.7 GeV well described by Glauber-Velasco
Glauber and Velasco, IFIC preprint, 1996, unpublished
Glauber and Velasco, Phys. Lett. B147 (1984) 380
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Diffraction in pp @ ISR Glauber and Velasco, PLB147 (1984) 380
Illustration: elastic pp at the SppS energy range 546-630 GeV well described by Glauber-Velasco
_
_ _
Glauber and Velasco, Phys. Lett. B147 (1984) 380
Glauber and Velasco, IFIC preprint, 1996, unpublished
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Non-exponential pp in GV model
Figure 4 fromGlauber-Velasco
PLB 147 (1984) 380Slope is not quite
exponential
(for femtoscopy:a non-Gaussian behaviour)
_
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Imaging with shadow profile
Glauber and Velasco, Phys. Lett. B147 (1984) 380
Glauber and Velasco, IFIC preprint, 1996, unpublished
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at 7 TeV
proton becomes
Blacker, butNOT edgier,and Larger
BEL BNeL effect
Saturation from shadow profiles
ISR and SppS:R.J. Glauber and J.Velasco
Phys. Lett. B147 (1987) 380 b1,b2 fixed
apparent saturation:proton is ~ black at LHC
up tor ~ 0.7 fm
see alsoLipari and Lusignoli arXiv:1305.7216
Kohara, Ferreira, Kodama arXiv:1408.1599
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proton becomes
Blacker, butNOT edgier,and Larger
BNeL effect
BNeL effect
This work
Lipari and Lusignoli arXiv:1305.7216 Kohara, Ferreira, Kodama arXiv:1408.1599see also
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Shadow imaging in p+p at ISR
Proton image: gray (n=1) edge, dark (n~3) center
Opacity expansion of order n: exp(-W) = 1- W + W2/2! - ...
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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(-W) = 1-W + W2/2! - ...
Simple choice for the generalization of GV:f(t)/f(0) = exp(i b1 |t| + i b2 |t|2 ) /
sqrt( 1 + a t)f(t)/f(0) = exp(i b1 |t| + i b2 |t|2 ) / sqrt( 1 + a|t| + a1 |t|2 + a2 |t|3 + …)More systematic expansions and further improvements are under investigation.
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Picture of proton Investigation of Glauber-Velasco model
works well in the dip region at LHCbut needs extension in low-t
TOTEM: non-exponential behaviour
geometric scalingbut not in the Black Disc limit
generalized Glauber-Velasco
works well at low-talso at dip-t, but …
from BEL to BNeL effect
Grey at r~ 1 fm, black up to r~0.7 fm
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Shadow imaging in p+p at LHC
The BNeL effect.Thank You!
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Summary
Collectivity in Collision in KolymbariC2K
65th birthday of László Csernai65 L
C2K = 65 L
Happy Birthday !
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Backup slides
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Definitions and derivations from (1) Glauber and Velasco, Harvard Print 88-0344, Phys. Lett. B147 (1984) 380(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
Multiple Diffraction Theory of Elastic proton-proton scattering
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Multiple Diffraction Theory of Elastic proton-proton scattering: Glauber-Velasco
(1) Glauber and Velasco, Harvard Print 88-0344, Phys. Lett. B147 (1984) 380(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Multiple Diffraction Theory of Elastic proton-proton scattering: Glauber-Velasco(1) Glauber and Velasco, Harvard Print 88-0344, Phys. Lett. B147 (1984) 380(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 1 from (1)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 2 from (1)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 3 from (1)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 4 from (1)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 1 from (2)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 2 from (2)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 3 from (2)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 4 from (2)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 5 from (2)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 6 from (2)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 7 from (2)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 8 from (2)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 9 from (2)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 10 from (2)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 11 from (2)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 12 from (2)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 13 from (2)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 14 from (2)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 15 from (2)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished
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Figure 16 from (2)
Figures from (1) Glauber and Velasco, Harvard Print 88-0344, PLB 147(1984) 380 and(2) Glauber and Velasco, IFIC preprint, 1996, unpublished