Polarization-transfer measurement to a large-virtuality bound proton in the deuteron
A1 Collaboration, I. Yaron, D. Izraeli, P. Achenbach, H. Arenhövel, J. Beričič, R. Böhm, D. Bosnar, L. Debenjak, M. O. Distler, A. Esser, I. Friščić, R. Gilman, I. Korover, J. Lichtenstadt, H. Merkel, D. G. Middleton, M. Mihovilovič, U. Müller, E. Piasetzky, S. Širca, S. Strauch, J. Pochodzalla, G. Ron, B. S. Schlimme, M. Schoth, F. Schulz, C. Sfienti, M. Thiel, A. Tyukin, A. Weber
PPolarization-transfer measurement to a large-virtuality bound proton in the deuteron
I. Yaron, ∗ D. Izraeli, ∗ P. Achenbach, H. Arenh¨ovel, J. Beriˇciˇc, R. B¨ohm, D. Bosnar, L. Debenjak, M. O. Distler, A. Esser, I. Friˇsˇci´c, † R. Gilman, I. Korover,
1, 6
J. Lichtenstadt, H. Merkel, D. G. Middleton, M. Mihoviloviˇc, U. M¨uller, E. Piasetzky, S. ˇSirca,
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S. Strauch, J. Pochodzalla, G. Ron, B. S. Schlimme, M. Schoth, F. Schulz, C. Sfienti, M. Thiel, A. Tyukin, and A. Weber (A1 Collaboration) School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel. Institut f¨ur Kernphysik, Johannes Gutenberg-Universit¨at, 55099 Mainz, Germany. Joˇzef Stefan Institute, 1000 Ljubljana, Slovenia. Department of Physics, University of Zagreb, HR-10002 Zagreb, Croatia. Rutgers, The State University of New Jersey, Piscataway, NJ 08855, USA. Department of Physics, NRCN, P.O. Box 9001, Beer-Sheva 84190, Israel. Department of Physics, University of Ljubljana, 1000 Ljubljana, Slovenia. University of South Carolina, Columbia, South Carolina 29208, USA. Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel. (Dated: August 12, 2018)Possible differences between free and bound protons may be observed in the ratio of polarization-transfer components, P (cid:48) x /P (cid:48) z . We report the measurement of P (cid:48) x /P (cid:48) z , in the H( (cid:126)e, e (cid:48) (cid:126)p ) n reaction atlow and high missing momenta. Observed increasing deviation of P (cid:48) x /P (cid:48) z from that of a free protonas a function of the virtuality, similar to that observed in He, indicates that the effect in nucleiis due to the virtuality of the knock-out proton and not due to the average nuclear density. Themeasured differences from calculations assuming free-proton form factors ( ∼ The proton elastic electric and magnetic form factors(FFs) describe the distributions of electric charge andmagnetization inside the proton and thus are intimatelyrelated to its internal structure [1]. Scattering polarizedelectrons off protons and simultaneous measurement oftwo polarization-transfer components allow one to deter-mine the ratio of the electric to magnetic FF [2]. Thismethod eliminates many potential sources of systematicuncertainties and allows for high-precision measurementsof this ratio.In nuclei, the effects of the strong nuclear field on abound nucleon are an interesting issue: Do bound nucle-ons have the same properties as free ones [3]? Measure-ment of the polarization of a proton that was knocked outof a nucleus by a polarized electron (quasi-elastic scatter-ing) and the comparison to that of a free proton enableto probe possible changes in the FF ratio and may pointto changes in the internal structure of a bound proton.It is particularly interesting to measure such effects inthe deuteron which is the most weakly bound nuclearsystem, and is frequently used as a ‘free-neutron’ target.Changes in the FF of ‘off-the-mass-shell’ nucleons maybe relevant even in the deuteron.We report here measurements of the transverse andlongitudinal polarization-transfer components of theknocked out proton in the quasi-free H( (cid:126)e, e (cid:48) (cid:126)p ) n reactionas a function of the proton missing-momentum ( p miss )compared to those of the free proton [4]. The data arealso compared to calculations [5], as well as to exist-ing similar data from the He( (cid:126)e, e (cid:48) (cid:126)p ) H reaction [6, 7].The comparison of data from a loosely bound nucleus (deuteron) to the data from the high density He wasmade as a function of the proton virtuality defined as: ν ≡ (cid:16) M A − (cid:113) M A − + p (cid:17) − p − M p , (1)where M A , M A − and M p are the target, residualnucleus, and proton masses, respectively p miss is themissing-momentum in the reaction, (cid:126)p miss = (cid:126)q − (cid:126)p p , (cid:126)q is the momentum transfer and (cid:126)p p is the out-going protonmomentum. The good agreement between the deuteronand He data, shown below, indicates that the devia-tions from the free proton ratio do not originate fromthe average nuclear density (which is vastly different inthese nuclei) but rather from the ‘off shell’ effects of theknocked out proton, as reflected by its virtuality.In the elastic H( (cid:126)e, e (cid:48) (cid:126)p ) reaction there are two beamhelicity dependent, non-vanishing polarization-transfercomponents: transverse ( P (cid:48) x , perpendicular to the protonmomentum in the scattering plane defined by the inci-dent and scattered electron), and longitudinal ( P (cid:48) z , alongthe proton momentum). In the one photon exchange ap-proximation their ratio ( P (cid:48) x /P (cid:48) z ) H is directly related tothe ratio of elastic electric G pE ( Q ) to magnetic G pM ( Q )FF at a given four-momentum transfer Q [2]: (cid:18) P (cid:48) x P (cid:48) z (cid:19) H = − M p ( E + E (cid:48) ) tan( θ e / · G pE ( Q ) G pM ( Q ) , (2)where E ( E (cid:48) ) is the incident (scattered) electron energy,and θ e is the electron scattering angle.For quasi-free elastic scattering off a bound nucleon,the knock-out proton is in general not ejected in the a r X i v : . [ nu c l - e x ] F e b e'e ⃗ Scattering Plane k ⃗ k ⃗ ' θ e p ⃗ ' Reaction Plane ɣ * ɸ pq q ⃗ p x ̂ y ̂ z ̂ θ pq p ⃗ p FIG. 1. The kinematics for quasi-elastic scattering of a boundproton in a nucleus, defining scattering and reaction planes. momentum-transfer ( (cid:126)q ) direction (and in the scatteringplane) due to its initial momentum. This introduces anadditional plane, the reaction plane, spanned by the mo-mentum transfer ( (cid:126)q ) and the outgoing proton momentum( (cid:126)p p ), characterized by the spherical angles θ pq and φ pq asshown in Fig. 1. Following the convention of [7] the polar-ization components are the ones in the scattering planealong ( z ) and perpendicular ( x ) to (cid:126)q .Changes in the structure of a bound nucleon may be re-flected in the measured ratio ( P (cid:48) x /P (cid:48) z ) of knocked-out nu-cleons. Other effects may influence this ratio as well. Wecompare the measurement to state of the art calculationsof the deuteron that take into account meson-exchangecurrents (MEC), isobar currents (IC), relativistic contri-butions of lowest order (RC), and final-state interactions(FSI) [5]. We observe significant differences between thecalculation and the measured results.The experiment was performed at the Mainz Microtron(MAMI) using the A1 beam-line and spectrometers [8].For the measurements 600 and 630 MeV CW polarizedelectron beams of 10 µ A current were used. The aver-age beam polarization was 80%, measured with a Møllerpolarimeter. The beam helicity was flipped at a rateof 1 Hz. The target consisted of an oblong shaped cell(50 mm long, 11 . − − Q ranges and two missing-momentum ranges each. Details of the kinematic set-tings are summarized in Table I, where p p and θ p ( p e and θ e ) are the knock-out proton (scattered electron) mo-mentum and angle. The missing momentum is taken to -200 -100 0 100 z / P x P -1-0.8-0.6 ] = 0.40 [GeV (a) Q [MeV/c] miss p -200 -100 0 100-1.4-1.2-1-0.8 ] = 0.18 [GeV (b) Q H, setup A H, setup B H, setup C H, setup D Calculation [5]
FIG. 2. The measured ratio of helicity dependent polariza-tion components, P (cid:48) x /P (cid:48) z , versus the missing-momentum. Thedata are compared to the calculations based on the theoreticalframework of Ref. [5]. The uncertainties are statistical only,and the horizontal bars indicate the p miss standard deviationin each bin. be positive (negative) if a component of (cid:126)p miss is paral-lel (anti-parallel) to the momentum-transfer vector ( (cid:126)q ). TABLE I. The kinematic settings in the experiment. Theangles and momenta represent the center values for the twospectrometer set-ups.Setup Setup Setup SetupKinematic A B C D E beam [MeV] 600 600 630 630 Q [GeV ] 0.40 0.40 0.18 0.18 p miss [MeV] -80 to 75 75 to 175 -80 to -15 -220 to -130 p e [MeV] 384 463 509 398 θ e [deg] 82.4 73.8 43.4 49.4 p p [MeV] 668 495 484 665 θ p [deg] -34.7 -43.3 -53.3 -39.1 In the analysis, cuts were applied to identify coincidentelectrons and protons that originate from the deuteriumtarget, and to ensure good reconstruction of tracks in thespectrometer and FPP. Only events that scatter by morethan 10 ◦ in the FPP were selected (to remove Coulombscattering events).Helicity-independent corrections to the measured ra-tios (acceptance, detector efficiency, target density, etc.)cancel out by the frequent flips of the beam helicity. Theuncertainties in the beam polarization, carbon analyz-ing power, and efficiency are also canceled by taking the P (cid:48) x /P (cid:48) z ratio. The total systematic uncertainty in the P (cid:48) x /P (cid:48) z ratio is estimated to about 1 −
2% (mainly from re-action vertex reconstruction and spin precession estima-tion) and is small compared to the dominant statisticaluncertainty.The data for both squared four-momentum transfersare presented in Fig. 2 as a function of the missing-momentum. The data are compared to a calculation of P (cid:48) x /P (cid:48) z for the deuteron [5] that takes into account FSI,MEC, IC and RC. The calculations presented here (andthe hydrogen values used below) use the free proton FFsof Bernauer et al. [4]. The theoretical results shown inFig. 2 were obtained by averaging calculations on theevent-by-event basis over the entire data sample in eachbin. We note that the theoretical results depend on thesign of the missing momentum.Figure 3 shows the double-ratio of the deuteron datato hydrogen, ( P (cid:48) x /P (cid:48) z ) H / ( P (cid:48) x /P (cid:48) z ) H , as a function of thevirtuality. Our data are supplemented with higher Q deuteron data measured at Jefferson Lab [10]. The dataare shown separately for positive and negative missingmomenta to show a possible dependence (as suggestedby the calculation).Our new measurements double the virtuality rangecovered by the previous experiments. Within the overlap, the data are consistent. The data show strong deviationsof ( P (cid:48) x /P (cid:48) z ) H from that of a free proton which are in-dicated by the decrease of the double-ratio well belowunity at large virtuality. The higher-momentum data ofJLab, (up to Q =1.6 GeV ) suggest that the deviationis independent of Q .The deuteron double-ratio data are compared withthose of proton knock-out from He measured at JLab [7].The deuteron is the least bound nucleus in nature withthe largest average distance between nucleons and thelowest average nuclear density. On the other hand He isa very strongly-bound nucleus with a very high averagedensity.The excellent agreement between the deuteron and He data, with the same behavior of the double ratio( P (cid:48) x /P (cid:48) z ) A / ( P (cid:48) x /P (cid:48) z ) H , Fig. 3, suggests that the deviationsfrom the free proton value due to nuclear effects do notdepend on the nuclear average density. It is the virtu-ality, rather than the nuclear density, that determinesthe double-ratio behavior, while the latter would affectthe number of protons of a given virtuality (i.e. a given‘off-shellness’) in the nucleus. ] [GeV n -0.10 -0.08 -0.06 -0.04 -0.02 0.00 -0.02 -0.04 -0.06 H ) z / P x / ( P A ) z / P x ( P <0 miss p >0 miss p H, This work H, JLab He, JLab H Calculation FIG. 3. The measured double-ratio ( P (cid:48) x /P (cid:48) z ) A / ( P (cid:48) x /P (cid:48) z ) H ( A = H , He) as a function of the proton virtuality, ν , for deuteron(this work and [10]) and for He [7]. The virtuality dependence is shown separately for positive and negative missing momenta.The symbols for the data of this work correspond to those in Fig. 2. Also shown are calculations for deuteron case (see textfor details). ] [GeV n -0.10 -0.08 -0.06 -0.04 -0.02 0.00 -0.02 -0.04 -0.06 H c a l c ) z / P x / ( P H e x p ) z / P x ( P <0 miss p >0 miss p FIG. 4. The double-ratio of the measured ( P (cid:48) x /P (cid:48) z ) exp to thetheoretical ( P (cid:48) x /P (cid:48) z ) calc (full calculation of [5]). The symbolsrefer to the different experimental set-ups defined in the leg-end of Fig. 2. The high precision data reported here allow a mean-ingful comparison to calculations. The calculations [5]consider medium effects but assume unmodified
FFs forthe proton in the deuteron. They show (see Fig. 3) a clearvirtuality dependence of the ratio ( P (cid:48) x /P (cid:48) z ) H to that ofthe free proton which depends on the sign of the miss-ing momentum. The contributions of the different cor-rections in the calculation are not shown in the figurefor simplicity. However, there is a significant differencebetween the plane wave impulse approximation and the‘full’ calculation, mainly due to FSI. Relativistic correc-tions do not alter the slope of the virtuality dependence.The calculated contributions of MEC and IC are small.There is an overall deviation of about 10% betweenthe calculation and the data as shown in Fig. 4. It maysuggest that additional corrections, such as modificationsin the bound nucleon structure may still be required. Thetheoretical results are different for positive and negative p miss kinematics. This may also be observed also in the He data [7]. This trend should be confirmed for thedeuteron with additional data at larger positive p miss .To summarize, the new data of the polarization-transfer double-ratios ( P (cid:48) x /P (cid:48) z ) H / ( P (cid:48) x /P (cid:48) z ) H extend theprevious measurements and almost double the virtualityrange. The measurements are consistent with the pre-vious H and He data sets (obtained in different kine-matics). They clearly show that the effect of the nuclearmedium on ( P (cid:48) x /P (cid:48) z ) H depend strongly on the virtual-ity of the bound proton and are almost independent ofthe average nuclear density and Q . The calculationsfollow a similar trend as the data and deviate from hy- drogen results as the virtuality increases. However, tak-ing the form-factors for a bound proton to be those of afree proton, the calculations do not fully reproduce thestrong virtuality dependence observed in our measure-ment. This may indicate the need to invoke in-mediumform factor modifications. It clearly suggests extendingthe measurements on the deuteron in the positive p miss sector, as well as extending both the He and deuterondata to larger virtuality. Indeed, such measurementswere proposed [11] and approved by the Jefferson LabProgram Advisory Committee. It would be interestingto further examine the effect of virtuality on the protonproperties in heavier nuclei.Notice that in the definition of virtuality Eq. (1), thefull ‘off-shellness’ is associated with the struck proton. Ifone assumes equal sharing between the proton and theneutron, none of the essential conclusions of this workwill be changed. However, for heavier nuclei, the waythe ‘off-shellness’ will be split between nucleons mightyield a large difference.We would like to thank the Mainz Microtron opera-tors and technical crew for the smooth and reliable op-eration of the accelerator. This work is supported bythe Israel Science Foundation (Grant 138/11) of the Is-rael Academy of Arts and Sciences, by the DeutscheForschungsgemeinschaft (SFB 1044) with the Collabora-tive Research Center, and by the U.S. National ScienceFoundation (PHY-1205782). ∗ These authors contributed equally to this work. † Present address: MIT-LNS, Cambridge, MA 02139, USA.[1] C. F. Perdrisat, V. Punjabi, and M. Vanderhaeghen,Prog. Part. Nucl. Phys. , 694 (2007).[2] A. I. Akhiezer and M. P. Rekalo, Fiz. Elem. Chast. Atom.Yadra , 662 (1973), translated in Sov. J. Part. Nucl. ,277 (1974).[3] M. Sargsian et al. , J. Phys. G , R1-R45 (2003), andreferences therein.[4] J. C. Bernauer et al. , Phys. Rev. C , 015206 (2014).[5] H. Arenh¨ovel, W. Leidemann, and E. L. Tomusiak, Eur.Phys. J. A , 147 (2005).[6] S. Dieterich et al. , Phys. Lett. B , 47 (2001).[7] S. Strauch et al. , Phys. Rev. Lett. , 052301 (2003); M.Paolone et al. , Phys. Rev. Lett. , 072001 (2010).[8] K. I. Blomqvist et al. , Nucl. Instrum. Methods Phys.Res., Sect. A , 263 (1998).[9] T. Pospischil et al. , Nucl. Instrum. Methods Phys. Res.,Sect. A , 713 (2002).[10] B. Hu et al. , Phys. Rev. C73