1. Improved Measurement of d/u Asymmetry in the Nucleon Sea
核子中の sea quark における d/u 非対称の改良測定
Phys. Rev. D 64, (2001).
R. S. Towell et al.
FNAL E866 / NuSea Collaboration
Contents
1. Introduction
2. Experiment
3. Analysis
4. Results
5. Summary
I will report on a paper titled as “Improved Measurement of anti-d over anti-u Asymmetry in the Nucleon Sea”.
This paper was published by Towell et al., in Physical Review, in two-thousand one.
The contents of my talk are Introduction, Experiment, Analysis, Results, and Summary.
Jinnouchi / Shibata Lab.
06_ Ryo Nagai
2009/07/07 1

2. 1. Introduction
This experiment measured dimuon momentum from Drell-Yan process (see next page).
The goal—
This paper presents improved analysis results by using the previous data.
determine spd/2spp over a wide kinematic range
determine d/u in the proton u
proton
valence quark
The usual assumption
Sea quark-antiquark pair is produced perturbatively from gluon splitting.
The numbers of uu and dd pairs should be approximately equal, because the mass difference of u and d is small. d
sea quarks d
This is Introduction.
This experiment measured dimuon momentum from Drell-Yan process.
The goal is to determine Drell-Yan cross section ratio (sigma-pd over two sigma-pp) over a wide kinematic range and also to determine anti-d over anti-u in the proton.
This paper presents improved analysis results by using the previous data.
The usual assumption is as follows. Sea quark anti-quark pair is produced perturbatively from gluon splitting. The number of uu-bar and dd-bar quark pair should be approximately equal, Because the mass difference of u-quark and d-quark is small.
This experiment is effective to verify this assumption in the proton. d d
gluon splitting
gluon u
sea quarks
This experiment is effective to verify this assumption. u d u
valence quark
valence quark 2

3. Drell-Yan process At nucleon level At quark level
proton-beam
(1-x1) p1
At quark level
X: hadrons, p: proton, q: quark
g*: virtual photon, m: muon
Fig. shows Drell-Yan process in the actual experiment.
This experiment used proton and deuteron as targets.
4-momentum of the muon pair was measured.
x1, x2 : Bjorken-x of the quarks from the beam and target
The figure shows Drell-Yan process.
At nucleon level, pp annihilate to mu-plus mu-minus. At quark level, quark and anti-quark annihilate to a virtual photon. The virtual photon decay mu-plus mu-minus.
The figure shows Drell-Yan process in the actual experiment.
This experiment used proton and deuteron as fixed targets. Proton-beam hit the fixed target. 4-momentum of the muon pair (p3, p4) was measured.
Here, x1 and x2 are Bjorken-x of the quarks from the beam and target, respectively.
(1-x2) p2
fixed target
(proton or deuteron)
Drell-Yan process
(Feynman diagram) 3

4. Measured—muon 4-momentum p3=(E3, p3), p4=(E4, p4)
The Feynman-x (xF) and dimuon mass (M) are defined as:
s=(p1+p2)2~2E1mp : the total 4-momentum squared of the initial nucleons
pg || : the center-of-mass longitudinal momentum of the virtual photon
Thus, x1 and x2 are determined by the measurement.
The p-d Drell-Yan cross section can be expressed as spd~spp+spn.
For x1>>x2, Drell-Yan cross section ratio is expressed
The right side was simplified further assuming d(x)<<4u(x).
The equation shows that spd/2spp is closely related to d/u.
Muon 4-momentum p3, p4 was measured.
The Feynman-x and dimuon mass are defined as following equations. They are related to Bjorken-x.
So, x1 and x2 are determined like this.
Here, s is the total 4-momentum squared of the initial nucleons. p-gamma-parallel is the center-of-mass longitudinal momentum of the virtual photon.
Next, the proton-deuteron Drell-Yan cross section can be expressed as the equation.
If x1 is much larger than x2, Drell-Yan cross section ratio is expressed like this. The right side was simplified further assuming this condition.
The equation shows that the Drell-Yan cross section ratio (sigma-pd over 2 sigma-pp) is closely related to anti-d over anti-u. 4

5. The FNAL E866 / NuSea Spectrometer
2. Experiment
This experiment used 800 GeV proton beam extracted from the Fermilab Tevatron accelerator.
SM0, SM12, SM3 (dipole magnets)
SM0 & SM12 … reject hadrons
SM3 … measure the muon momentum
Detector
Station
detector
What to measure 1 2 3
drift
chambers
hodoscopes
position of
muons
(trigger) 4
proportional
tubes
This is the detector.
This experiment used eight-hundred GeV squared proton-beam extracted from the Fermilab Tevatron accelerator.
The figure shows the detector of the experiment.
Proton-beam hit the target.
SM0 and SM12 are dipole magnets. Here is Hadron absorber. It reject hadrons. SM3 is also dipole magnet. It is used to measure the muon momentum.
Station 1, 2, 3 are drift chambers and hodoscopes. Station 4 is proportional tubes and hodoscopes. They measure position of muons.
The FNAL E866 / NuSea Spectrometer 5

6. The dimuon distribution for x1 versus x2
3. Analysis
x1 … Bjorken-x of the beam
x2 … Bjorken-x of the target
The resulting dimuon distributions, x1 versus x2 .
Blank region in Fig.
cut to remove unwanted events (ex. U and J/y resonance families …)
beam
7500 x1 Υ
The figure shows counts as a function of dimuon mass.
The peaks are U resonances.
5000
counts / 0.1 GeV/c2
This is Analysis.
The figure is the resulting dimuon distributions versus x1 and x2.
Blank region in the figure shows the result to cut to remove unwanted events, such as upsilon and j-psi resonance families.
Also, the figure shows counts with dimuon mass. The two peaks are upsilon resonances. This experiment unwanted these peaks.
These black points in the figure were used for the analysis. Υ’
2500
J/y 5 10 15
dimuon mass (GeV/c2)
J/y resonance x2
target
U resonance
These black points in Fig. were used for the analysis.
The dimuon distribution for x1 versus x2

7. The Drell-Yan cross section ratio versus x2
4. Results (1)
spd/2spp moves up and down along x2.
It shows large x-dependence of the Drell-Yan cross section ratio.
spd/2spp
This is results.
Figure four shows the Drell-Yan cross section ratio versus Bjorken-x, x2.
Vertical bar is statistical error. Systematic uncertainty is less than 1% error.
This shows the Drell-Yan cross section ratio moves up and down along x2.
It shows large x-dependence of the Drell-Yan cross section ratio.
Next, we converted the data with the following relation.
Next, convert the data with the following relation, x2
The Drell-Yan cross section ratio versus x2
( x2 … Bjorken-x of the target ) 7

8. d/u versus x2 shown with statistical and systematic uncertainties
4. Results (2)
converted using the relation between spd/2spp and d/u.
The graph shows d/u increases at 0< x<0.2 and decreases at 0.2 < x.
d >u for x < 0.25.
The expected value was d/u = 1
d/u
large deviation from 1
The figure shows anti-d over anti-u versus Bjorken-x.
Vertical bar is statistical error. This band shows systematic uncertainty.
The graph shows anti-d over anti-u increases here, and decreases here.
It shows that there is large deviation from 1. At this region, anti-d is larger than anti-u.
The expected value by the usual assumption about the sea quark production was that anti-d over anti-u equal 1.
It is about 70% difference.
There is large asymmetry of u anti-u and d anti-d pairs.
About 70% difference !! x2
There is large asymmetry of uu and dd pairs.
d/u versus x2 shown with statistical and systematic uncertainties

9. 5. Summary
This paper reports improved analysis of the measurement of the Drell-Yan cross section ratio per nucleon of p+d to p+p.
The experiment used 800 GeV proton beam and measured 4-momentum of dimuon.
From this measurement the large asymmetry of the uu and dd pairs in the nucleon sea is extracted as a function of x.
This result is different from the expectation, “the same numbers of uu and dd pairs are produced perturbatively”.
The result suggests possibility that there is a non-perturbative origin for the production of the uu and dd pairs.
This is summary.
This paper reports a mesurement of the Drell-Yan cross section ratio per nucleon of proton-deuteron to proton-proton.
The experiment used eight hundred GeV per c proton beam and measured four-momentum of dimuon.
From this measurement the large asymmetry of the anti-u quark and anti-d quark in the nucleon sea is extracted as a function of Bjorken-x.
The result suggests possibility that there is a non-perturbative origin for the production of the sea quarks pairs from gluon splitting. 9

11. Passive origin of d/u asymmetry
Perturbative origin
Pauli blocking…less than 1%
Non-perturbative origin
Meson cloud model
express the physical proton as the combination of a proton with a symmetric sea and a series of virtual meson-baryon state
Chiral quark model
Similar to the meson model
Except the virtual meson couples directly to a quark (not to the nucleon)

12. Meson Cloud Model proton p-meson Light gray region… p-meson cloud u u
sea quarks u d u d d
Light gray region…
p-meson cloud d d d u u u d u
valence quark d d

13. The center-of-mass 4-momentum
Feynman-x (xF)
Feynman-x (xF) is defined as :
The center-of-mass 4-momentum
The center-of-mass longitudinal momentum is
Invariant mass (center-of-mass) is
Using these expressions,

14. Dimuon mass (M) Dimuon mass (M) is defined as: Invariant mass
The law of conservation of energy and momentum is
Using the law, M is calculated as
p1 = (E1, p1) : 4-momentum of the beam
p2 = (E2, p2) : 4-momentum of the target
p2 = 0 (fixed target)
m1, m2 ~ mp
mp << E1
(experimental condition)
Using the expression of the invariant mass,

15. Detector Drift chamber : Hodoscope : Proportional tube :
A multiwire chamber
Spatial resolution is achieved by measuring the time electrons need to reach the anode wire.
measured from the moment that the ionizing particle traversed the detector.
Hodoscope :  
A combination of multiple detector elements arranged in space and connected by logic circuitry such that particle tracks can be identified .
used for triggering purposes
Proportional tube :
drift tube read out without measurement of drift time.

16. J/y and U resonance J/y particle : consist of cc
Mass : 3.1 GeV/c2
U particle : consist of bb
Mass : 9.5, 10.0, 10.4, 10.5 GeV/c2 16