Ⅰ. HIGHLIGHTS OF THE YEAR
RIKEN
Accel. Prog. Rep. 56 (2023)

RIKEN Accel. Prog. Rep. 56 (2023)

Measurement of ﬂavor asymmetry of light-quark sea in the proton withDrell-Yan dimuon production in p + p and p + d collisions at 120 GeV†
K. Nakano,∗1,∗2 Y. Goto,∗2 Y. Miyachi,∗3 K. Nagai,∗4 S. Sawada,∗2,∗5 and T.-A. Shibata∗2,∗6for the E906/SeaQuest Collaboration

2

1.5

CT18
NNPDF4.0

1.4
1.3
1.2
σpd / 2σpp

Evidence for a ﬂavor asymmetry between the ū andd¯ quark distributions in the proton has been found indeep-inelastic scattering and Drell-Yan experiments.1,2)
The asymmetry observed in the E866 experiment3) suggested a drop of the d¯(x) /ū (x) ratio in the x > 0.15
region, where x means the fraction of nucleon momentum carried by partons. Here, we report results fromthe SeaQuest experiment, with improved statistical precision, for the ﬂavor asymmetry in the large x region up
to x = 0.45.
The SeaQuest experiment detects µ+ µ− pairs(dimuons) produced in the Drell-Yan process.4) The differential cross section at leading order is given by:

1.110.9
Mass-Fit method
Systematic uncertainty
Intensity-Extrapolation method
Systematic uncertainty

0.8
0.7
0.6
0.5
0.05

0.1

0.15

0.2

0.25

2d σ4πα(1)=dx1 dx2
9x1 x2 s∑][×e2i qiA (x1 ) q̄iB (x2 ) + q̄iA (x1 ) qiB (x2 ) ,

x2

0.3

0.35

0.4

0.45

0.5

Fig. 1. The cross section ratio versus x2 obtained with thetwo extraction methods.

i∈u,d,s,...

The data that SeaQuest recorded between June 2014
and July 2015 were analyzed.
The result of σ pd /2σ pp using the “IntensityExtrapolation” (IE) method was reported in Refs. 5)
and 6). We developed another method of extracting
σ pd /2σ pp , called “Mass-Fit” (MF) method, in order
to conﬁrm that the systematic uncertainty of the IE
method has been properly evaluated. The results ofσ pd /2σ pp using the two methods are shown in Fig. 1.
They are in excellent agreement.
¯The ratio of d(x)/ū(x)was derived from σ pd /2σ pp
and reported in Refs. 5) and 6). Using d¯(x) /ū (x) asinput, we can determine the diﬀerence, d¯(x) − ū (x).
It provides a direct measure of the contribution from
non-perturbative processes, since perturbative processes
†

∗1
∗2
∗3
∗4
∗5

∗6

Condensed from the article in arXiv:2212.12160 (2022)
Department of Physics, University of Virginia
RIKEN Nishina Center
Faculty of Science, Yamagata University
High Energy Nuclear Physics, Los Alamos National Lab
Wako Nuclear Science Center (WNSC), IPNS, KEK
College of Science and Technology, Nihon University

should cancel out in d¯(x) − ū (x). Figure 2 showsd¯(x) − ū (x) at Q2 = 25.5 GeV2 over the region 0.13 <x < 0.45. For comparison, experimental data and theoretical calculations are overlaid. The SeaQuest data
have better uncertainty than the existing data, and arein good agreement with the two calculations.
0.4
SeaQuest

0.35

Systematic uncertainty

0.3

NuSea/E866 (Q2 = 54 GeV2)

0.25

HERMES (Q2 = 2.3 GeV2)

0.2
d−u

where α is the ﬁne-structure constant, ei is the chargeof a quark with ﬂavor i, and qiA,B (x1,2 ) are the quark
distribution functions in hadrons A and B for quarks
carrying a momentum fraction x1 and x2 , respectively.
SeaQuest utilized the 120-GeV proton beam at Fermilab
for hadron A and liquid hydrogen and deuterium targets
for hadron B. The cross-section ratio of the two targets¯
has a direct sensitivity to d(x)/ū(x)
as[]
σ pd
1d¯(x2 )
1+.
(2)
≈
2σ pp
2ū (x2 )

0.15
0.1

Q2 = 25.5 GeV20.05
0−0.05−0.1
0.1

Alberg, Ehinger and Miller
Basso, Bourrely, Pasechnik, and Soffer

0.15

0.2

0.25

0.3x0.350.40.45

Fig. 2. Result of d¯(x) − ū (x).

References
1) P. Amaudruz et al., Phys. Rev. Lett. 66, 2712 (1991).
2) A. Baldit et al., Phys. Lett. B 332, 244 (1994).
3) R. S. Towell et al., Phys. Rev. D 64, 052002 (2001).
4) S. D. Drell et al., Phys. Rev. Lett. 25, 316 (1970).
5) J. Dove et al., Nature 590, 561 (2021).
6) Y. Goto et al., RIKEN Accel. Prog. Rep. 55, S16 (2022).

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