1. Masanori HIRAI 2006, Nov 9, Tokyo-u
Observation on dA scattering at forward rapidities V. Guzey, M. Strikman, and W. Vogelsang Phys. Lett. B603 (2004)
Masanori HIRAI
2006, Nov 9,　Tokyo-u

2. Introduction BRAHMS at RHIC ? PRL93,24303 (2004) Deuteron-Au collision
RdAu , Rcp
Forward rapidity
h=2.2, 3.2 for negatively charged hadron
Suppression of RdAu increasing hadron rapidity
Nuclear effect of initial condition in target nucleus
Shadowing effect ? ?
Expectation of enhancement of h- in dAu experiment, However..
Isospin considerations [p: up(x)>dp (x), d:ud(x)=dd(x)]
NLO pQCD calculation
Parton moment fraction x for hadron production at BRAHMS
Effect of leading-twist nuclear shadowing

3. NLO pQCD calculation Success for RHIC experiment
pp  0 X at s=200 GeV
PHENIX collaboration, PRL91, (2003)
dAu for central rapidity h=0
D. de Florian, R. Sassot, PRD69, (2004)
Prediction for hadron production
High precision
Ambiguity of initial and final distributions
PDF and FF obtained by global analysis
Forward region ?
STAR collaboration, PRL92, (2004)
3.4<h<4.0, h=3.8: good agreement
BRAHMS ?

4. Kinematics and x ranges probed in forward scattering
Cross section by pQCD
Theoretical uncertainty
mR,F=pT (pT/2..2pT)
Non-perturbative part
Parton distribution function f(x)
Fragmentation function D(z)
Perturbative part
Partonic cross section
22 process
gggg, ggqq,qgqg
qqqq, qq’qq’
qqqq, qqgg, qqq’q’

5. Kinematics and x ranges probed in forward scattering
Kinematics for hadron production

6. Kinematics and x ranges probed in forward scattering
Cross section for 22 process
Integration of phase space for the parton d

7. Kinematics and x ranges probed in forward scattering
Another integration for zc
23 process in NLO

8. Kinematics and x ranges probed in forward scattering
Central rapidity: h=0
Symmetric x1 and x2, pT/s
Forward scattering h>0
Asymmetric
x1 covering the large-x region, x2 at small-x
How small x2 in forward region
x2 > 0.01, pT=1.5 GeV
The shape depends on the PDF sets
Increasing x2 with pT
One of estimation for average <x2>
CTEQ6M
GRV98

9. Influence of leading-twist nuclear shadowing
Nuclear target d & Au
Nuclear effect on PDFs
Shadowing effect, x<0.1
Antishadowing, 0.1<x<0.2
EMC effect, 0.2<x<0.8
Fermi motion, x>0.8
BRAHMS kinematics
Averaged x2=0.01: shadowing effect ?
Leading-twist NPDF
Diffractive
L. Frankfurt, V. Guzey, M. Strikman, PRD71, (2005)
Global fit with nuclear DIS and DY data
M.H, S. Kumano, N. Nagai, PRC70, (2004)
D. de Florian, R. Sassot, PRD69, (2004)

10. Leading-twist nuclear shadowing
Gribov’s theorem:Sov. Phys. JETP29, 483 (1969)
Relation between nuclear shadowing and diffraction
Factorization of diffraction process: J. C. Collins,PRD57, 3051 (1998)
Diffractive PDF fD(b,Q2,xp,t) obtained by HERA measurement
NPDF taking account of shadowing effect
Neglected nuclear effect of deuteron: d=(p+n)/2
A few % correction
Q2 evolution given by DGLAP equation
NPDF at initial scale Q2=2 GeV
Large effect of gluon shadowing
Diffractive constitute, 10%(quark), 30%(gluon)
Satisfying conservation low
Baryon number, momentum conservation
Antishadowing effect from momentum cons
Enhancement: x=0.1(quark), x=0.03(gluon)

11. Other nuclear PDFs
Pb/D
valence
antiquark
gluon
Ca/D

12. Nuclear PDFs by DS Valence- and anti-quark distributions
Ca/D
Valence- and anti-quark distributions
are very similar.
Gluon shadowing is fairly small, but
it is within the HKN uncertainties.

13. Nuclear effect on p0 production
D(x1)-Au(x2)  p0 + X
Suppression at small-x
Shadowing effect
Enhancement at x=0.1
Antishadowing effect
pT increasing
Decreasing shadowing effect
Shad.1 & shad.2
Enhancement at x, #1:x=0.03, #2:x=0.1
Suppression RdAu due to shadowing
Forward rapidity  small value of x2
Low pT

14. Isospin consideration for the ratio of dA and pp cross section
BRAHMS data
h=0, 1: (h++h-)/2
h=2.2, 3.2: h-
Charged hadron
Assuming pion dominant
qg process
d:f(x1), Au:g(x2)
Enhancement of RdAu of negative hadron
p: p+>p-, u-quark dominates
d: p+=p-, ud(x1)= dd(x1)=[dp (x1) +up (x1)]/2
Valence quark distribution in d and p
Important role in forward h- production

15. Ration RdAu(pT) Charged hadron Negative charged hadron
Moderate pT dependence
Negative charged hadron
h=2.2, 3.2
Increasing RdAu with pT
Difference of dv quark contribution
Suppression in low-pT
Shadowing effect
Positive charged hadron
s(dAu h+X)> s(dAu h-X)
Factor 3 at pT=3 GeV ?
Challenging to understanding it in terms of a non-perturbative effect

16. Conclusion and outlook
Intrinsic enhancement of RdAu for negative hadron
Different nature of the “projectile” (deuteron vs. proton)
Suppression of RdAu for summed charged hadron
Impossible to explain RdAu suppression at forward rapidity
NLO pQCD+ Leading-Twist NPDF(shadowing& antishadowing)
Suppression of 15% due to shadowing effect
Positive charged hadron vs. negative charged hadron
Enhancement of proton production ?
Experimental data is quite challenging to understanding
Energy loss effect
Initial state only: 10%
Initial & final state: 3%