![Page 1: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/1.jpg)
Exclusive Vector Meson Production in eA Collisions
F.S. Navarra
IFUSP/São Paulo/Brazil
based on:
V.P. Gonçalves, M.S. Kugeratski, M.V.T. Machado and F.S. Navarra,
arXiv:0905.1143
![Page 2: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/2.jpg)
Introduction
eA collisions : good place to look for the Color Glass Condensate
Saturation scale is large :
A. Deshpande, R. Milner, R. Venugopalan and W. Vogelsang,
Ann. Rev. Nucl. Part. Sci. 55 165 (2005)
x
xQAQs
020
3/12
The Electron-Ion Collider (EIC) :
![Page 3: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/3.jpg)
Observables to be measured at eRHIC
Kugeratski, Gonçalves, Navarra , EPJC (2005) , EPJC (2006)
Cazaroto, Carvalho, Gonçalves, Navarra, PLB (2008) , PLB (2009)
is reduced with respect to the linear case by up to 50 %
totdiff / falls with x and grows with W and A up to 0.30
)3(2D
P Fx becomes flat in Px, with increasing A
gqq| changed by saturation effects
)3(,2
)3(,2 21/ D
ADA FFR very flat in Px,
2F
2Q
No “smoking gun” !
![Page 4: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/4.jpg)
LFcF2and
With dipoles:
With nuclear PDF´s:
Altarelli Martinelli (1978)
![Page 5: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/5.jpg)
![Page 6: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/6.jpg)
Vector meson production in the dipole approach
Proportional to the square of the dipole cross section : more sensitive to non-linear effects !
![Page 7: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/7.jpg)
Coherent and incoherent nuclear diffraction :
Vector meson production off nuclei :
Kopeliovich, Nemchik. Schmidt, Phys. Rev. C76 025210 (2007) Kopeliovich, Nemchik. Schäfer, Tarasov, Phys. Rev. C65 035201 (2002) Ivanov, Kopeliovich, Tarasov, Hüfner, Phys. Rev. C66 024903 (2002)
Coherent : Incoherent :
Light cone Green function formalism
22
2
Vc mQl
Ac Rl High energy limit : large coherent
length
Not too large dipoles...
![Page 8: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/8.jpg)
Coherent Production
dp
Photon wave function: QED (back-up slide)
Meson wave function: Boosted gaussian (back-up slide)
Dipole-nucleon cross section
K. Tuchin, arXiv:0812.1519
Compare with the Glauber approach :
C. Marquet, R. Peschanski, G. Soyez, hep/ph/0702171
Barone , Predazzi (2002), Nikolaev, Zakharov (1991)
![Page 9: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/9.jpg)
Incoherent Production
2GeV
A. Caldwell, M. Soares, Nucl. Phys. 696 (2001)
![Page 10: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/10.jpg)
K. Golec-Biernat, M. Wüstoff, Phys. Rev. D59, 014017 (1998)
Dipole cross section
GBW
![Page 11: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/11.jpg)
E. Iancu, K. Itakura, S. Munier, Phys. Lett. B590, 199 (2004)
G. Watt, H. Kowalski, Phys. Rev. D78, 014016 (2008)
IIM
bCGC
![Page 12: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/12.jpg)
Linear limit
GBW, IIM and bCGC cross sections include non-linear effects
To define signatures of saturation we need to know the linear background
0r 2Q DGLAPBKJIMWLK ,
Turn off non-linear effects in the nucleon
![Page 13: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/13.jpg)
Results
We expect:
grows with W because doesdp
falls with Q because does
grows with the size of the meson
coherent grows with the size of the nucleus
incoherent grows weakly with the size of the nucleus
![Page 14: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/14.jpg)
![Page 15: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/15.jpg)
![Page 16: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/16.jpg)
![Page 17: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/17.jpg)
![Page 18: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/18.jpg)
![Page 19: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/19.jpg)
![Page 20: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/20.jpg)
Conclusions
Predictions for the coherent and incoherent cross sections
Coherent cross sections are much larger in all cases
V.P. Gonçalves, M.V. Machado, Eur. Phys. J. C38, 319 (2004)
Update and improvement of previous estimates
Ratio inc/coh weakly dependent on W, Q and dipole cross section
Ratio inc/coh strongly dependent on A and on the vector meson
Nucleon non-linear effects are small
Kopeliovich, Nemchik. Schmidt, Phys. Rev. C76, 025210 (2007)
![Page 21: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/21.jpg)
F. Dominguez, C. Marquet, B. Wu, Nucl. Phys. A823, 99 (2009)
Our results agree qualitatively with other approaches
To be done: theoretical error bars, improve on the dipole cross section,
compute the t dependence
![Page 22: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/22.jpg)
Nuclear X nucleon effects
![Page 23: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/23.jpg)
![Page 24: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/24.jpg)
![Page 25: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/25.jpg)
Meson wave functions Boosted gaussian
![Page 26: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/26.jpg)
![Page 27: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/27.jpg)
Photon wave function
Spin and polarization are the same for the photon and the meson
![Page 28: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/28.jpg)
Polarization and helicityNormalization of wave function: not 1 for photons
F.~Dominguez, C.~Marquet and B.~Wu, %``On multiple scatterings of mesons in hot and cold QCD matter,'' Nucl.\ Phys.\ A {\bf 823}, 99 (2009) [arXiv:0812.3878 [nucl-th]].
![Page 29: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/29.jpg)
![Page 30: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/30.jpg)
![Page 31: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/31.jpg)
Differential equation depends on the equation of state !
Korteweg - de Vries (KdV)
Breaking wave equation
EOS:
Euler
If:
0...2 If:
![Page 32: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/32.jpg)
How to get the Laplacian ?
In nuclear matter mean field theory (non-linear Walecka) :
Usually: 002 V and
Equations of motion
Mean fieldLagrangian
![Page 33: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/33.jpg)
BV
V
m
gV 2
202
Compute the Lagrangian, energy-momentum tensor and obtain the EOS :
But we can estimate the Laplacian :
![Page 34: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/34.jpg)
Dipole approach
![Page 35: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/35.jpg)
M.S. Kugeratski, V.P. Gonçalves, F.S. Navarra, Eur. Phys. J. C44 577 (2005)
M.S. Kugeratski, V.P. Gonçalves, F.S. Navarra, Eur. Phys. J. C46 413 (2006)
M.S. Kugeratski, V.P. Gonçalves, F.S. Navarra, Eur. Phys. J. C46 465 (2006)
F. Carvalho, F.O. Durães, F.S. Navarra, S. Szpigel, Phys. Rev. C79 035211 (2009)
E.R. Cazaroto, F. Carvalho, V.P. Goncalves , F.S. Navarra, Phys. Lett. B671 233 (2009)
E.R. Cazaroto, F. Carvalho, V.P. Goncalves, F.S. Navarra, Phys. Lett. B669 331 (2008)
![Page 36: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/36.jpg)
![Page 37: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/37.jpg)
![Page 38: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/38.jpg)
Dipole approach
![Page 39: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/39.jpg)
M.S. Kugeratski, V.P. Gonçalves, M.V. Machado, F.S. Navarra, Phys. Lett. B44 577 (2006)
![Page 40: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/40.jpg)
XI HADRON PHYSICSMarch, 22 - 27, 2010, São Sebastião, Brazil
![Page 41: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/41.jpg)
![Page 42: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/42.jpg)
É difícil acreditar...
![Page 43: Exclusive Vector Meson Production in eA Collisions](https://reader036.vdocuments.us/reader036/viewer/2022081513/568159c4550346895dc71615/html5/thumbnails/43.jpg)