Bled Workshops in Physics Vol. 18, No. 1 P. 6 A Proceedings of the Mini-Workshop Advances in Hadronic Resonances Bled, Slovenia, July 2 - 9, 2017 The role of nucleon resonance via Primakoff effect in the very forward neutron asymmetry in high energy polarized proton-nucleus collision I. Nakagawa for the PHENIX Collaboration RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Abstract. A strikingly strong atomic mass dependence was discovered in the single spin asymmetry of the very forward neutron production in transversely polarized proton-nucleus collision at y/s = 200 GeV in PHENIX experiment at RHIC. Such a drastic dependence was far beyond expectation from conventional hadronic interaction models. A theoretical attempt is made to explain the A-dependence within the framework of the ultra peripheral collision (Primakoff) effect in this document using the Mainz unitary isobar (MAID2007) model to estimate the asymmetry. The resulting calculation well reproduced the neutron asymmetry data in combination of the asymmetry comes from hadronic amplitudes. The present EM interaction calculation is confirmed to give consistent picture with the existing asymmetry results in pT + Pb —> n0 + p + Pb at Fermi lab. 1 Nuclear Dependence of Spin Asymmetry of Forward Neutron Production Large single spin asymmetries in very forward neutron production seen [1] using the PHENIX zero-degree calorimeters [2] are a long established feature of transversely polarized proton-proton collisions at RHIC in collision energy y/s = 200 GeV. Neutron production near zero degrees is well described by the one-pion exchange (OPE) framework. The absorptive correction to the OPE generates the asymmetry as a consequence of a phase shift between the spin flip and non-spin flip amplitudes. However, the amplitude predicted by the OPE is too small to explain the large observed asymmetries. A model introducing interference of pion and a -Reggeon exchanges has been successful in reproducing the experimental data [3]. The forward neutron asymmetry is formulated as where ^flip (^non-flip) is spin flip (spin non-flip) amplitude between incident proton and out-going neutron, and 6 is the relative phase between these two amplitudes. Although the OPE can contribute to both spin flip and non-flip amplitudes, resulting AN is small due to the small relative phase. The decent amplitude can be generated only by introducing the interference between spin flip n exchange and spin non-flip a -Reggeon exchange which has large phase shift in between [3]. An 0.5 1 0.3 n is calculated using SOPHIA model [9]. The neutron energy cut xF = En/Ep > 0.4 is applied to be consistent with the experiment [4] where En is the energy of the outgoing neutron and Ep is the incident proton beam energy. As can be seen, the prominent peak is located slightly below A(1232MeV) peak since the equivalent photon yield is weighted to lower energy in the nuclear Coulomb field [10]. The momentum transfer are defined t' = t — (W2 — m2)2/4P2 for the Fermi experiment1, whereas t is defined as —t = m^(1 — xF)2/xF + /xF for the RHIC experiment, where mn is neutron mass, and Pt is the transverse momentum of neutron. Unfortunately, the momentum transfers are not defined consistently between two experiments due to undetected tt+ in the RHIC experiment. -t GeV2 Fig. 4. (Top) The t distributions of the n0p system in pT + Pb n0 + p + Pb for W < 1.36 GeV and 1.36 < W < 1.52 GeV, respectively. The finite asymmetry was observed in the region |t' | < 1 x 10-3 (GeV/c)2 of panel (b) [7]. (Bottom) The experimental momentum transfer distributions of the RHIC experiment for 3 different trigger selections. (Color online) 1 See reference [7] for the definition. The role of nucleon resonance via Primakoff effect 11 Table 1. The difference of experimental conditions between RHIC [4] and Fermi [7] experiments. Fermi RHIC Beam Energy Ep [GeV] 185 100 V [GeV] 19.5 200 Target nucleus Pb Au Detected particle(s) p + n0 n Momentum transfer (GeV/c)2 | t' I < 0.001 0.02 < —t < 0.5 Invariant mass W [GeV] 1.36 < W< 1.52 An —0.57 ± (0.12)sta + 0.21 — 0.18 +0.27 ± 0.003 4 Asymmetry Induced by Photo-Pion Production Pion production reaction from nucleon are intensely studied in various medium energy real photon and electron beam facilities. See reference [11] as one of review articles. The present forward neutron asymmetries via UPC effect corresponds to the photo-pion production from a transversely polarized fixed target. The polarized y*p cross section is given as Eq. (4): n = _lqL{R00 + Py RTy} (3) Iql [RT0{1 + P2 cos ^„T (en)}] (4) where R00 is the unpolarized, while R°y is target polarized response functions, respectively. T(en) corresponds to the definition of the present analyzing power An = T(en) = R°y/R00. en represents production angle of n in the center-of-mass system. There are several theoretical/phenomenological fitting models available to describe photo-pion production observables. Here I quote Mainz unitary isobar model, namely MAID2007 [12] to calculate the asymmetries in the present kinematics. Shown in Fig. 5 is the MAID prediction of the unpolarized response function R00 plotted as a function of the invariant mass W of pion and nucleon systems at Q2 = 0(GeV/c)2 and en = 40°. The multipoles are weak function of Q2(= —t) and only moderately change within our kinematic coverage —t < 0.5 (GeV/c)2. The leading order multipole decomposition following the notation of reference [13] is given in Eq. (5): R?° = 5I Mi + I 2 + MÎ+MT- + 3M|+E1+ + ... (5) 2 where Mi+ is famous magnetic dipole transition amplitude from the nucleon ground state to the A(P33) resonance state. As blue curve indicates, the y*p —» LUy* 12 I. Nakagawa 25 20 15 g 10 t£ R00 (Q2=0, theta*pi=40deg) 1100 1200 1300 1400 Invariant Mass [MeV] 1500 n + pi + p + pi0 5 0 Fig. 5. (Color online) Unpolarized R0O(W) response function at Q2 = 0(GeV/c)2 and = 40° plotted as a function of the invariant mass W [MeV]. Red and blue curves represent MAID predictions for y*p —> + n and y*p —> n0 + p decay channels, respectively. n0p channel shows distinctive peak around well known A resonance region (W = 1232 MeV) in Fig. 5. This is mainly driven by the dominant |M1+|2 term in Eq. (5). On the contrary, the A peak is not as distinctive as n0 channel for the channel and shows rather larger cross section in the threshold pion production region below A. This is due to enhanced charge coupling of photon to the pion field in the target proton which doesn't exist for n0 channel. This is known as KrollRudermann term [14] as shown in the diagram (d) in Fig. 3. Shown in Fig. 6 is the target polarization response function R°y (W) of the MAID predictions for —» n+n (red) and y*p^ —» n0p (blue) decay channels, respectively. The leading order multipole decomposition of RTy is denoted as Eq. (6): R0y = Im{E0+(E1+ - M1 + )-4cos0n(E1+M1 + )....} (6) The asymmetries show peak structure around A region for both and n0 channels, while the sign is opposite. The magnitude of asymmetry is substantially as large as RTy - 15[^b/st] for channel compared to n0 channel. This is because of the strong interference between E0+ and M1+ channel in channel as appears in the first term in Eqn.6. The amplitude of E0+ is much greater in channel compared to n0 channel due to aforementioned Kroll-Rudermann term. Although dominant A amplitude, i.e. M1+ is even stronger in n0 channel, this interference is relatively minor due to smallness of E0+ for n0 channel. The obtained analyzing power AN for MAID predictions by taking the ratio of response functions RTy (W) and R00 (W) are shown in Fig. 7 plotted as a function of the invariant mass W at Q2 = 0(GeV/c)2 and 0^ = 40°. Note there are distinctive difference between and n0 channels in AN as a function of W according to the MAID model. shows remarkably large asymmetry over AN > 0.8 The role of nucleon resonance via Primakoff effect 13 R0y (Q2=0, theta*pi=40deg) 20 15 10 5 2 o -5 -10 n + pi + p + piO 15OO Invariant Mass [MeV] Fig. 6. (Color online) Polarized R0y (W) response function at Q2 = 0(GeV/c)2 and = 40° plotted as a function of the invariant mass W [MeV]. Red and blue curves represent MAID predictions for y*pT —> n+n and y*pT —> n0p decay channels, respectively. just below A(1232 MeV) due to the interference between E0+ of Kroll-Rudermann and A dipole resonance Mi+ terms. The contribution of this invariant mass region to the observed neutron is large due to matching peak of the invariant mass yield as shown in the right panel of Fig.2. Analyzing Power (Q2=0, theta*pi=40deg) Fig. 7. (Color online) Analyzing power AN(W) at Q2 = 0(GeV/c)2 and 6^ = 40° plotted as a function of the invariant mass W [MeV]. Red and blue curves represent MAID [12] predictions for y*pT —> n+n and y*pT —> n0p decay channels, respectively. The MAID is in general known to fit reasonably well to photo-pion production data in low to medium energy region. Shown in Fig. 8 is the analyzing power T(= An) of MAID (red curve) fits to —> n+p reaction data observed in PHOENICS experiment at ELSA [15]. For the comparison, Argonne-Osaka [16] 14 I. Nakagawa model fits are also shown in blue curve. Although some model dependence is seen in higher energies W > 1365 MeV in the region where no data, two models are fairly consistent to each other in lower energies W < 1319 MeV. Although the ELSA data is not necessarily perfect overlap with the kinematic range of the present RHIC data, the extrapolation of data by MAID seem to give reasonable estimate since the data coverage is sufficiently large in W bins below A which are rather weighted for the present neutron data. - - 5: : 5 ' ■ 5. - 05/TSs^n 'E, = 220 MeV ' -W = 1137 MeV 0 50 100 150 5 'E, = 241 MeV " - W = 1154 MeV 0 50 100 l50 0 5'E, = 262 MeV ' -W = 1171 MeV 0 50 100 l.0 0 5'E, = 282 MeV ' -W = 1187 MeV 0 50 100 l.0 5 'E, = 303 MeV ' - W = 1203 MeV 0 50 100 l.0 05 'E, = 324 MeV ■ W = 1219 MeV 0 50 100 l.0 'E, = 345 MeV ' -W = 1236 MeV 0 50 100 150 5 'E, = 366 MeV " " W = 1251 MeV 0 50 100 l.0 0 5 "E, = 393 MeV ' -W = 1271 MeV 0 50 100 l.0 0 5 "E, = 425 MeV ' -W = 1295 MeV 0 50 100 l.0 5"E, = 458 MeV " - W = 1319 MeV 0 50 100 l.0 05"E, = 49l MeV ' W = 1342 MeV 0 50 100 l.0 ■ . 'E, = 524 MeV ' -W = 1365 MeV 5 'E, = 557 MeV ' -W = 1387 MeV 0 5 "E, = 589 MeV ' W = 1409 MeV 0.5 • I • 0- ^ - ^ 0 5'E, = 620 MeV ' -W = 1429 MeV 5'E, = 650 MeV ' -W = 1449 MeV W = 1466 MeV s, s, 0, 0, 0, 0, Fig. 8. (Color online) Analyzing power T(= AN) of MAID (red curve) and Argonne-Osaka [16] model (blue curve) fit to y*pT —> n+p reaction data observed in PHOENICS experiment at ELSA [15]. In reference [17], an attempt is made to evaluate average AN within the present RHIC experiment using so evaluated MAID AN. Shown in the left panel of the Fig.9 is the analyzing power T(= AN) as a function of pion production angle 0^ and the invariant mass W of —> n. The region between thin and thick curves are the rapidity range of the present RHIC experiment and each curves corresponds to the rapidity boundaries of n = 8.0 and n = 6.8, respectively. As can be seen in the figure, the large AN >0.8 is distributed in 0^ <1 [rad] around W ~ 1.2 GeV and this is where the peak of the neutron yield is located as shown in the right panel of Fig.2 according to EM interaction Monte-Carlo. The yield weighted average of AN within the acceptance between 6.8 < n < 8.0 and xF > 0.4 is plotted as open square in the right panel of Fig.9. The analyzing power via EM interaction are very similar between p+Al or p+Au because the slope of the photon yield as a function of photon energy is very similar. On the other hand, resulting AN will be quite different between them due to the fraction of hadronic interaction and the EM interactions are quite different. In fact, the EM cross section grows square function of atomic number Z. The fraction of the hadronic and EM interactions are estimated by the cross section ratio of them assuming one pion exchange (OPE) for the hadronic interaction. The is simpler hadronic interaction model than the reference [5]. However, the cross section of The role of nucleon resonance via Primakoff effect 15 the hadronic interaction for the leading neutron production in this very forward rapidity range 6.8 < n < 8.0 is known to be dominated by OPE [3]. On the other hand, the nuclear absorption effect is claimed to play important role in the reference [5] and is not considered in reference [17] though, the absorption effects are somewhat canceled when one take ratio between the hadronic and the EM interactions. Details are discussed in the reference [17]. So obtained hadron/EM cross section weighted AN are plotted as open circles in the right panel of Fig.9 and are compared with experimental analyzing power data (solid symbols). Solid circle and squares are inclusive and BBC vetoed data, respectively. The calculated AN open circles are to be compared with inclusive data points (solid circle) and they are in very good agreement. 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 0.4 0.2 1.2 1.4 1.6 1. W (GeV) □ □ ■ Simulation (UPC) Simulation (UPC + Hadronic) q —•— PHENIX (pA, inclusive) - —■— PHENIX (pA, veto) —A— PHENIX (pp) 50 100~ Atomic number Z 3 2 1 0 0 0 Fig.9. (left) Analyzing power T(= An) as a function of pion production angle in and the invariant mass W of y*pT —> n+n. The region between thin and thick curves are the rapidity range of the present RHIC experiment and each curves corresponds to the rapidity boundaries of n = 8.0 and n = 6.8, respectively. (right) Comparison of experimental analyzing power data (solid symbols) and model predictions (open symbols) plotted as a function of atomic number Z. Solid circle and squares are inclusive and BBC vetoed data, respectively. Open square is kinematically averaged AN prediction over RHIC acceptance by MAID. Open circles are weighted mean prediction of MAID and one pion exchange AN for Al and Au. Both plots are quoted from reference [17]. 5 Summary A theoretical attempt was made to explain strong A-dependence in the very forward neutron asymmetry recently observed in transversely polarized proton-nucleus collision at a/s=200 GeV in PHENIX experiment at RHIC [4]. The drastic A-dependence in the forward neutron asymmetry AN cannot be explained by the conventional hadronic interaction model [5] which was successful to explain the asymmetries observed for p + p collision [3]. In this document, possible major contribution in the asymmetry from the UPC (Primakoff) effect via one photon 16 I. Nakagawa exchange from the nuclear Coulomb field is discussed. The Mainz unitary isobar (MAID2007) model [12] was used to estimate the asymmetry by the EM interaction which fit past y * pT —> n+n reaction data [15] well. The MAID predicts large asymmetry below A region for n+n-channel due to the interference between non-resonance contact Eo+ (non-spin flip) and A resonance Mi+ (spin flip) amplitudes. Once kinematic average within the detector acceptance and kinematic cuts, the resulting asymmetries overshot both inclusive AN data for both p + Al and p + Au data. Once these average EM asymmetries are further taken weighted mean by cross section ratio with hadronic asymmetries, the resulting asymmetries reproduced both p + Al and p + Au data well [17]. The importance of the interference in non-resonance and A resonance contradicts from the large asymmetry observed in pT + Pb —» n0 + p + Pb at Fermi lab [7] which is interpreted mainly due to the interference between A and N*(1440) and higher resonances. This difference can be explained by the relatively strong Kroll-Rudermann term [14] contribution for n+ channel, and which raises the importance of the interference below A unlike n0 channel. 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