Ⅰ. HIGHLIGHTS OF THE YEARRIKEN Accel. Prog. Rep. 50 (2017)

Disentangling transverse single spin asymmetries for forward
neutrons in high-energy polarized-proton–nucleus collisions
G. Mitsuka∗1red line) and a one-pion exchange model (OPE) that represents hadronic interactions occuring at b < R p + RA (solidblack line). AN originating in OPE well explains thePHENIX result in pp collisions but does not in pA collisions. In this study, the Glauber multiple scattering modelis applied to OPE to account for nuclear effects. Here weﬁnd that UPCs have a positive and large AUPC
compared
Nwith AOPE= −0.05 of hadronic interactions.
NIn Fig. 1 (b), ﬁlled black circles indicate AN inclusively
measured by the PHENIX zero-degree calorimeter1) . These
AN values can be compared with open red circles that correspond to the sum of UPCs and OPE MC simulations, denoted as AUPC+OPEand calculated as
N

It is reported from the PHENIX experiment at BNLRHIC that the transverse single spin asymmetry, denoted
as AN , for forward neutrons measured in transversely√
polarized-proton–nucleus (pA) collisions atsNN =200 GeV is far
different
fromthatinproton–proton(pp)√collisions at s = 200 GeV1) (see panel (b) of Fig. 1.)
In this report, I present an important but rather unknown mechanism: ultra-peripheral pA collisions (UPCs,also known as Primakoff effects). UPCs contribute to themeasured AN modestly in pAl collisions and signiﬁcantly
in pAu collisions. UPCs occur when the impact parameterb is larger than the sum of the radii of each colliding particle, namely b > R p + RA (R p and RA are the radius of theproton and nucleus, respectively). In UPCs, virtual photons(γ ∗ ) emitted from the relativistic nucleus interact with thepolarized protons and then produce the neutrons and otherparticles.
The differential cross section for single pion and neutron
production, dominant among many other channels, in UPCs
is given bydW db2 dΩn=2where d 3 Nγ ∗ /d ωγrest∗ db is the double differential photon
ﬂux due to the fast-moving nucleus, W is the γ ∗ p center-ofmass energy, dΩn = sin Θ dΘ dΦ with the neutron scattering polar angle Θ and azimuthal angle Φ in the γ ∗ p centerof-mass frame, and Phad (b) is the probability of having nohadronic interactions in pA collisions at a given b. Single neutron and pion productions from the γ ∗ p interaction
are simulated following the differential cross sections predicted by the MAID 2007 model.2) The cross section of theγ ∗ p → π + n interaction is approximated as

8dσ/dΦ [mb]d σγ ∗ p→π + n
R0yT
1+cosΦ∝ R00
TdΩπR00T,(2)(a) p+Au → n+X(b) A as a function of Z0.2OPE × Glauber

NUPC

6PHENIX pp
PHENIX pA
Simulation (UPC + OPE)

0.1

4020ywhere R00
T and RT are the response functions for pion photoproduction. AN for forward neutrons in UPCs (hereafter0y00
AUPCN ) inherits the target asymmetry T (π −Θ) ≡ RT /RT inEq. (2), which is ∼ 0.7 at W < 1.3 GeV and ∼ −0.2 at W >1.3 GeV within the PHENIX detector acceptance. Owing tothe virtual photon ﬂux leading to low-energy photons andthe pion photoproduction cross section via a Δ (1232) resonance, UPCs accordingly provide AUPC
∼ 0.35 for forward
Nneutrons.
Figure 1 (a) shows the differential cross section in pAucollisions, d σ /dΦ, as a function of Φ, for UPCs (dashed∗1(3)where σUPC and σOPE are the cross sections of UPCs andOPE, respectively. In pAu collisions, since σUPC  σOPE ,we obtain AUPC+OPE= 0.16, which is consistent with theN
PHENIX result. Consistency between our simulation result
AUPC+OPE= −0.02 and the PHENIX data is also found inNpAl collisions, where σUPC is 8 % of σOPE .
In the MC simulations discussed in this report, electromagnetic effects (UPCs) and hadronic effects (OPE) aretaken into account independently. However, the interference between these two effects, called the Coulomb-nuclear
interference, would have nonzero amplitudes in the verysmall momentum-transfer region. The imprementation of
the Coulomb-nuclear interference will be a topic of future
investigation.

d 3 Nγ ∗ d σγ ∗ p→π + n (W )Phad (b), (1)dW db2dΩnOPEσUPC AUPC
N + σOPE AN,
σUPC + σOPEAN4d σUPC(pA→π + n)

AUPC+OPE=N0−0.1−20Φ [rad.]20204060
Atomic number Z

80Fig. 1. Left: d σ /dΦ distributions for UPCs and OPE. Right:
Comparison of AN as a function of Z.

References
1) I. Nakagawa et al. (PHENIX Collaboration), J. Phys. Conf.
Ser. 736, 012017 (2016).
2) D. Drechsel, S. S. Kamalov, L. Tiator, Eur. Phys. J. A 34, 64(2007).

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