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Parity violation experiments at Jefferson Laboratory: HAPPEX and G0
Progress in Particle and Nuclear Physics 55 (2005) 297–307 www.elsevier.com/locate/ppnp
Review
Parity violation experiments at Jefferson Laboratory: HAPPEX and G 0 Jacques Arvieux∗ Institut de Physique Nucléaire d’Orsay (IPN-O), Universite Paris-Sud, Bat.100M, 91406 Orsay-Cedex, France
Abstract A short history of parity violation is given, leading to the present use of parity violating electron scattering for studying the nucleon internal structure. The status of the G 0 and HAPPEX experiments presently running at Jefferson Lab is discussed. Some preliminary results are shown. © 2005 Elsevier B.V. All rights reserved.
1. Introduction The History of Science shows that sometimes long turns and bifurcations are taken before arriving at a complete theory. Moreover it shows that theory by itself, how mathematically beautiful it can be, has to be vindicated by experiments to be accepted. Only when this is done can theory lead to applications in other fields of physics: from object of fundamental studies, it becomes merely a tool. This is particularly true for parity violation, the history of which can be traced back to the 1930’s with the discovery of the β-disintegration of nuclei, showing that the β-spectrum was not due to a two-body decay, but that it must involve a third unknown particle of very small mass, which, after some peripetia, was named neutrino by Fermi. In the 1940’s and 1950’s a series of experiments allowed for studying the weak interaction in many situations besides β-decay, including the weak disintegration of muons, ∗ Tel.: +33 1 6915 6727; fax: +33 1 6915 6470.
E-mail address: [email protected]. 0146-6410/$ - see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ppnp.2005.01.007
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pions, kaons or baryons. Some of these experiments did not produce the expected results, in particular in the kaon sector. The difference with theory was small and subject to experimental criticism, but they led to the conjecture that parity might well be violated. The birth of parity violation is usually attributed to a crucial experiment made in 1956 by Wu [1], following an article by Lee and Yang [2], who proposed a series of experimental tests which could reveal it. At that time, Feymann and Gell-Mann realized that the neutrinos (anti-neutrinos) were only left (right) handed and that the weak interaction had to have an axial coupling besides the usual vector coupling. It took another 20 years or so, before parity violation was put in a strict theoretical framework with the Standard Model of the electroweak interaction of Weinberg, Salam and Glashow. The fundamental idea was that the photon, responsible for the electromagnetic interaction, and the Z 0 , responsible for the weak interactions, were linear combinations of fundamental gauge fields with a mixing angle θW , the Weinberg angle. From then on, parity violation became a tool to measure sin2 θW with a precision higher than that obtained so far in neutrino interactions. This led to the first e–d scattering experiment at SLAC (E-122), which produced one of the best determination of sin2 θW at that time [3]: sin2 θW = 0.20 ± 0.03, in fair agreement with the most recent value sin2 θW = 0.23120(15) [4]. The uncertainty on the measured asymmetry was about 10−5 or 10 ppm. This was followed by two more precise experiments on 9 Be (MAMI-Mainz) [5], where the accuracy reached 1 ppm and 12 C (MIT-Bates) [6] where the accuracy was 0.14 ppm. At that point, sin2 θ was known W to a very high precision, thanks to LEP experiments, and the interest turned to the nucleon internal structure: since the Z 0 -boson couples to the quarks of all flavors, the asymmetry predicted is very different, depending on whether or not there is a strange component in the nucleon sea. The first series of experiments was SAMPLE at MIT-Bates in elastic e– p and quasi-elastic e–d scattering at back angle and low momentum transfer Q 2 [7]. In these kinematical conditions, the asymmetry is essentially sensitive to the strange magnetic moment and axial form-factor. Another experiment, HAPPEX at Jefferson Lab, at small angle and higher energy, measured a combination of the strange electric and magnetic form-factor as discussed below [8]. We report here on the progress of two ongoing experiments at Jefferson Lab: HAPPEX2, a series of experiments at low Q 2 and very forward angle on helium and hydrogen targets, and G 0 , a comprehensive experiment which will be able to do a separation of all three form-factors (strange electric, magnetic and axial form-factors) by performing experiments at forward and backward angles on hydrogen and deuterium targets, with the same apparatus. 2. Parity violation and the nucleon structure The 2004 Nobel Prize in Physics, which recognizes the importance of the “invention” of QCD, reminds us that hadrons in general, and nucleons in particular, have a rather complicated structure with three valence quarks, plus a sea containing, at any time, an indefinite number of gluons which can fluctuate into q q ¯ pairs, as long as the Heisenberg principle is not violated. Among these, strange quarks are special: their mass is of the order of ΛQCD = 200 MeV, so that the probability of finding them in a nucleon may not be
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negligible as will be the case for c-, b- or t-quarks, whose mass is larger than the nucleon itself. On the other hand, strange quarks can only come from the sea since nucleons have no static strangeness. There are essentially three types of matrix-elements involving strange quarks, which can be determined experimentally, albeit more or less indirectly: scalar: N|¯s s|N vector: N|¯s γµ s|N axial-vector: N|¯s γµ γ5 s|N. The scalar matrix element measures the probability of finding s s¯ pairs in the nucleon sea. The vector term measures the strange current: a value different from zero implies there are strange and anti-strange quarks and, moreover, that their spatial and momentum distributions are different. The axial term is directly related to the polarization of the s and s¯ . These are three different quantities and the fact that one is different from zero does not imply that the other ones should also be different from zero and vice versa. Since the s-quark is relatively heavy, its effect on the nucleon mass can be large, even for small s s¯ probabilities. In the SU2 × SU2 limit, the scalar matrix element is related to the Σ -term and to the pion decay constant f π , via low energy theorems [9]. The most recent π–N data [10] seem to indicate values of Σ ≈ 0.6–0.8 from which one can extract a strange 2N|¯s s|N ≈ 0.2–0.6. In conclusion, the scalar term is in favour of quark probability y = N| ¯ uu+ ¯ dd| a large s s¯ -sea but with rather large theoretical uncertainties. The axial term is estimated to be of the order of N|¯s γµ γ5 s|N ≈ −0.1 ± 0.1 from polarised DIS. Note that a recent semi-inclusive K-production experiment at HERMES gives a slightly positive value but with large experimental error bars for s [11]. Concerning the vector-matrix element, the nice thing about it is that its relationship to the strangeness content of the nucleon is essentially void of theoretical uncertainties. In elastic (quasi-elastic) scattering of longitudinally polarized electrons, the asymmetries are given by: A=− ×
G F Q2 √ 4πα 2
γ γ Z − (1 − 4 sin2 θ ) τ (1 + τ )(1 − 2 )G γ G e G E G EZ + τ G M G M W M A γ
θ −1 = 1 + 2(1 + τ ) tan2 2
γ
(G E )2 + τ (G M )2
(2)
τ = −Q 2 /4M 2p , γ
(1)
(3)
γ
where G E and G M are the electric and magnetic electromagnetic form-factors, G EZ and Z are the weak form-factors and G e is the axial form-factor. Using isospin symmetry, GM A the weak form-factors can be related to the quark currents [12]: Z,p
γ,p
γ ,n
G E,M = (1 − 4 sin2 θW )G E,M − G E,M − G sE,M .
(4)
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Note that depending on the authors there might be a difference of a factor of 4 in the definition of the weak form-factors [13]. Assuming that the electromagnetic form-factors are known (within a range of uncertainties), one can deduce the “strange quark formfactors” G sE,M (this is somewhat an abuse of language since the quarks, having no internal structure, have no form-factors as such). 3. Parity violation experiments at Jefferson Lab There are two large experimental set-ups allowing parity violation experiments at JLab: HAPPEX in Hall A and G 0 in Hall C. 3.1. HAPPEX HAPPEX was the first parity violation experiment operational at JLab. The experiment ˇ uses the standard HRS spectrometers, with dedicated Cerenkov detectors made of a Lead/Lucite sandwich. The HAPPEX I experiment used a polarized electron beam of 3.355 GeV. The beam intensity was up to 80 µA and the polarization was of the order of 36% during the first run (with a regular GaAs photocathode) and 75% with a strained GaAs photocathode. The scattered electrons were detected at 12.54◦ giving Q 2 = 0.477 (GeV/c)2 . At this angle, the asymmetry is dominated by the electric term with a large (40%) contribution of the magnetic term. The measured asymmetry is Ath = [−15.05 ± 0.98(stat) ± 0.56(syst)] ppm. The systematic errors are dominated by the neutron electric form-factor uncertainty [14]. From the measured asymmetry one can deduce: G sE + 0.39G sM = 0.025 ± 0.020(stat) ± 0.014(theo) essentially compatible with zero. Following these pioneering experiments, a set of new experiments have been approved by the JLab PAC. 3.1.1. HAPPEX-He This experiment uses a cold gaseous He-target. The 4 He being isoscalar with spin 0, the PV asymmetry depends only on G sE : A00 =
G sE G F Q2 √ (4 sin2 θW ) + γp γn . 2(G E + G E ) α 2
(5)
The experiment has been done at very forward angle (6◦ ) and Q 2 = 0.1 (GeV/c)2 . The experiment aims at a precision of A = 0.18 ppm both in statistics and systematics, resulting in an uncertainty on G sE of 0.015. This has necessitated many improvements as compared to the initial HAPPEX set-up: an improved polarized source using a new superlattice photo-cathode giving a mean polarization of 86%, an improved polarimetry with two polarimeters: Moeller and Compton and the addition of an electron recoil detector to the Compton polarimeter giving a precision of δ P/P ≈ 2% in about one hour, new profile scanners, new beam monitors, new luminosity monitors, a new target cell, new ˇ Cerenkov detectors and finally an improved DAQ.
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The preliminary results obtained in July 2004 give APV = [−7.40 ± (0.89)stat ± 0.57(syst)] ppm to be compared to the SM prediction without strangeness A0 = −7.82 ppm, from which one can extract G sE = −0.019 ± 0.041(stat) ± 0.026(syst) at Q2 = 0.1 (GeV/c)2 . 3.1.2. HAPPEX-H This is an extension at Q2 = 0.1 (GeV/c)2 of the HAPPEX-I experiment. It will complement, in different kinematics, the PVA4 experiment and allow one to perform a Rosenbluth separation with the SAMPLE experiment at backward angle. The Standard Model asymmetry without strangeness is very small (A0 = −1.6 ppm) and the precision aimed at is δ(G sE +0.08G sM ) = 0.010. A first run has taken place in July 2004 with limited statistics. The combined preliminary He and H results at Q2 = 0.1 (GeV/c)2 are shown in Fig. 1, combined with the SAMPLE and PVA4 [17] results. G sE is compatible with zero but G sM is slightly positive at a 1–2 standard deviation level. Besides these experiments, aimed at studying the nucleon structure, there is a proposal (PREX, JLab E00-003) to measure the neutron distribution in 208 Pb by using parity violation since the Z 0 couples essentially to neutrons. 3.2. The G 0 experiment The G 0 experiment is an ambitious undertaking aiming at separating the three components G sE , G sM and G eA in a large domain of Q2 = 0.12–1.00 (GeV/c)2 . This is done by performing three separate experiments with the same apparatus: elastic ep scattering at forward angle (around 65◦ ) and backward angle (around 115◦) plus ed quasi-elastic at backward angle. The experiment takes place in JLab Hall C. The proposal (spokesperson: D. Beck) was first submitted in 1991 but it took some time before the financing was acquired. The years 1998–2002 were devoted to design, development, building and testing the various components. The size of the collaboration is about 100 physicists and engineers, coming from some 20 laboratories in the USA, Canada, France and Armenia. More details can be found on the G 0 web site http://g0web.jlab.org/. 3.2.1. Forward angle measurements In the forward angle set-up, the protons recoiling from ep elastic scattering at a fixed electron energy of 3 GeV are detected at θ p = 65◦ ± 10◦ , corresponding to a rather small electron scattering angle (around θe = 6–15◦ ). The asymmetries to be measured lie in the range −3 to −40 × 10−6 . The beam intensity is 40 µA and the polarization of the order of 75%. The experiment aims at a statistical precision A A ≤ 5%, which requires −13 −14 2 counting statistics of the order of 10 –10 counts per Q setting. This has necessitated the construction of a dedicated apparatus with large acceptance and high counting rate detectors and electronics. It is based on a superconducting toroidal magnet (SMS) of 1.6 T.m. having eight coils which was designed to focus particles of the same momentum and angle to a single point on the focal plane, wherever they originate from an extended target (L = 20 cm). Individual particles are counted in a set of 16 pairs (in coincidence)
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Fig. 1. Preliminary result of the new HAPPEX experiment at Q2 = 0.1 (GeV/c)2 combined with SAMPLE and PVA4 results at Q2 = 0.1 (GeV/c)2 .
Fig. 2. Schematics of the electron detection in the G 0 forward running mode (right) and of the Focal Plane Detectors or FPDs (left).
of scintillators per octant (the FPDs or Focal Plane Detectors) placed in the focal plane at various Q 2 positions (see Fig. 2). The recoiling protons are identified by a combination of magnetic momentum selection by the SMS and time-of-flight information. The solid angle is of the order of 0.5–0.9 sr depending on momentum transfer. Heavy collimators protect
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Fig. 3. Time-of flight spectrum on a log scale. The horizontal axis is the channel number (full scale = 32 ns). The G 0 recoil protons are superimposed on the leakage spectrum from the other halls.
the detectors from a direct view of the beam. Overviews of the G 0 experimental set-up are given in [15,16]. Various contributions on the G 0 experimental set-up can be found in the proceedings of the International Workshops on Parity Violation and Hadronic Structure in 2002 (Mainz) and 2004 (Grenoble). Commissioning of the apparatus started in August 2002, and by January 2003 the G 0 experiment had met the specifications for all the instrumentation, allowing some preliminary data to be taken during about 50 h or 5% of the statistics. The data showed that everything was OK at a level of precision of a few ppm. A second commissioning run was scheduled in October to December 2003, immediately followed by data taking, which ended in May 2004. During this period and as the statistics was improved, reaching the final goal of 1 ppm per detector or better, various problems were found and solved. Among these, there was the problem of leakage from the other halls. The G 0 beam structure is unconventional, with one burst every 32 ns (31.25 MHz) as compared with 2 ns (499 MHz) for the conventional JLab beam. This was required by a proton time-of-flight between target and detector of the order of 20 ns. During the course of the experiment, G 0 has taken data under various conditions: Hall C alone (rarely), together with Hall B (most of the time) and with Hall B and Hall A (for limited periods of time). Each hall uses a different laser with different helicity correlated properties. It was well known that there is some leakage between the different halls, but as long as their time structure is identical, it is rather straightforward to minimize the helicity correlated asymmetry of the combined beams. This was not the case for G 0 and there was a residual, uncorrected 2 ns time structure under the G 0 32 ns time-of-flight spectra and in particular under the elastic peak (Fig. 3). The leakage current is small (of the order of 40 nA at 40 µA), but its asymmetry can reach 500 ppm, so that the overall contamination would be have been of the order of 0.5 ppm. After a series of tests near the end of the data taking period, a method was found which allows for the correction of the leakage asymmetries directly from the time-of-flight spectra, and the residual uncertainty is presently less than 0.1 ppm.
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Fig. 4. Estimated combined statistical and systematical G 0 uncertainties as a function of Q 2 .
A second problem which was underestimated is that of the background. This background ranges from a few % (for low Q 2 ) to about 25%. Part of it comes from the Al windows of the target. During the first commissioning run, the Al exit window was about 280 µm. It was reduced to 75 µm for the second commissioning and data taking runs. To estimate this background, data were taken with a pure Al target but a fraction of the background comes from inelastic reactions in the hydrogen target. This has been estimated by a Monte Carlo simulation before the experiment. The dominant reaction is π 0 production for which theoretical calculations [18,19] show that the asymmetry has the same sign as the elastic asymmetry, therefore simplifying in principle the subtraction procedure (if the asymmetries were identical in the elastic and inelastic regions, the problem would reduce to estimating a dilution factor). The difficulties that are being faced are (1) that the background is underestimated by the simulation and (2) that its asymmetry varies drastically with Q 2 , even changing sign for large Q 2 . This will have consequences on the accuracy of the high Q 2 final data whose estimated error bars are shown in Fig. 4. The curve is the Standard Model prediction without strangeness. It is now believed that part of this background comes from hyperon production and subsequent decays for which simulations are under way. The preliminary results are shown in Fig. 5 for detectors 1–12 blinded by an overall normalization factor whose value lies in the range 0.75–1.25 [20]. These data show that the asymmetry increases as a function of Q 2 (the Q 2 varies from 0.12 for detector 1 to about 1 (GeV/c)2 for the high end of detector 15) but no comparison can be made yet with theoretical predictions. The analysis effort is now concentrating on the high Q 2 region and especially on detector 15 which contains all Q 2 values ranging from 0.5 to 1.0 (GeV/c)2 , making the background
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Fig. 5. Preliminary results from G 0 . The horizontal scale is the detector number ranging from 1 to 15, the vertical scale is the asymmetry in ppm.
subtraction more delicate. The analysis of the small detector data (low Q 2 ) is almost complete, and final data should be available by the end of 2004. 3.2.2. Backward angle measurements In the backward angle configuration, the scattered electrons are detected instead of the recoil protons as shown in Fig. 6. Since the scattered electrons have energies of the order of a few hundreds of MeV, they are all relativistic and a measurement of their time-of-flight spectra is of limited interest. The beam structure can therefore be the JLab standard one at 499 MHz (2 ns between pulses), eliminating the leakage problem. Moreover, the intensity can be increased from 40 to 80 µA since tests done during the forward angle data taking period have shown that the target should stand such an intensity without significant boiling. The detection will be based on coincidences between 14 FPDs (FPDs 1 and 2 having been removed) and a set of 9 new counters, the CEDs (or Cryostat Exit Detectors). Appropriate combinations of FPD–CED coincidences will allow the separation of elastic and inelastic events. The inelastic data are of particular interest as their weak asymmetry A of the N– transition. will give access to the axial form-factor G N GEANT simulations have shown that, with a deuterium target, there will be a large π − ˇ background coming from the en → epπ − reaction. Therefore a set of Cerenkov detectors have been built and they are presently at JLab for final testing before mounting. Due to the limited kinematical range, each Q 2 requires a different incident electron energy. The G 0 collaboration has requested three energies (424, 585 and 799 MeV),
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Fig. 6. Schematics of the electron detection in the G 0 backward running mode. The black arrow indicates the direction of the incident electron beam.
corresponding to Q 2 = 0.3, 0.5 and 0.8 (GeV/c)2 , for both hydrogen and deuteron targets. These values may change slightly for operational reasons. At the time of this writing (November 2004) only the 0.8 (GeV/c)2 run has been approved by the Jefferson Lab PAC. Since the end of the forward angle data taking run, the SMS magnet and Ferris Wheel have been put to the side of the beam line in Hall C and they have been rotated by 180◦. The first G 0 backward angle run is scheduled for the end of 2005. 4. Conclusion Parity violating electron scattering has become a standard tool for studying the nucleon inner structure and Jefferson Lab is playing a preeminent role in this field. The first results obtained at selected values of Q 2 show that the strange vector currents are small. The most recent round of experiments at Jefferson Lab aim at getting a very high precision in a limited Q 2 domain (HAPPEX) or at getting comprehensive data over a wide Q 2 range from 0.12 to 1.0 (GeV/c)2 , with an emphasis on a complete separation of the three form-factors G sE and G sM and G eA at 0.3, 0.5 and 0.8 (GeV/c)2 . Acknowledgements I would like to express thanks to all my colleagues from G 0 for their constant dedication and to D. Armstrong and D. Lhuillier from HAPPEX for their help in gathering information and material. References [1] C.S. Wu, Phys. Rev. 105 (1957) 1413. [2] T.D. Lee, C.N. Yang, Phys. Rev. 104 (1956) 254. [3] C. Prescott et al., Phys. Rev. Lett. B 77 (1978) 347.
J. Arvieux / Progress in Particle and Nuclear Physics 55 (2005) 297–307 [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
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Review of Particle Physics, Phys. Lett. B 592 (2004) 1. W. Heil et al., Nucl. Phys. B 327 (1989) 1. P.A. Souder, Phys. Rev. Lett. 65 (1990) 695. D.T. Spayde et al., Phys. Lett. B 583 (2004) 79. K.A. Aniol et al., Phys. Rev. C 69 (2004) 065501. J. Glaser, H. Leutwyler, M. Saino, Phys. Lett. B 253 (1991) 252. M.G. Olsson, W.B. Kaufmann, PiN Newsletter 16 (2002) 382. B. Seitz et al., EPJA 17 (2003) 369. M.J. Musolf et al., Phys. Rep. 239 (1994) 1. D.T. Spayde et al., Phys. Rev. Lett. 84 (2000) 1. K. Aniol et al., Phys. Lett. B 509 (2001) 211. J. Roche, Contribution to 9th International Conference on the Structure of Baryons, Baryons2002, 3–8 March 2002, Newport News, USA, 2002, p. 355. D.H. Beck, Prog. Nucl. Part. Phys. 50 (2003) 429. F. Mass et al., Phys. Rev. Lett. 93 (2004) 022002. M.P. Rekalo, J. Arvieux, E. Tomasi-Gustafsson, Phys. Rev. C 5 (2002) 035501. H.W. Hemmert, D. Drechsel, Z. Phys. A 353 (1995) 321. P.G. Roos, (for the G 0 Collaboration), Contribution to Parity Violation and Hadronic Structure, PAVI04, Grenoble, 8–11 June, 2004, Europhys. J. A (in press).
Review
Parity violation experiments at Jefferson Laboratory: HAPPEX and G 0 Jacques Arvieux∗ Institut de Physique Nucléaire d’Orsay (IPN-O), Universite Paris-Sud, Bat.100M, 91406 Orsay-Cedex, France
Abstract A short history of parity violation is given, leading to the present use of parity violating electron scattering for studying the nucleon internal structure. The status of the G 0 and HAPPEX experiments presently running at Jefferson Lab is discussed. Some preliminary results are shown. © 2005 Elsevier B.V. All rights reserved.
1. Introduction The History of Science shows that sometimes long turns and bifurcations are taken before arriving at a complete theory. Moreover it shows that theory by itself, how mathematically beautiful it can be, has to be vindicated by experiments to be accepted. Only when this is done can theory lead to applications in other fields of physics: from object of fundamental studies, it becomes merely a tool. This is particularly true for parity violation, the history of which can be traced back to the 1930’s with the discovery of the β-disintegration of nuclei, showing that the β-spectrum was not due to a two-body decay, but that it must involve a third unknown particle of very small mass, which, after some peripetia, was named neutrino by Fermi. In the 1940’s and 1950’s a series of experiments allowed for studying the weak interaction in many situations besides β-decay, including the weak disintegration of muons, ∗ Tel.: +33 1 6915 6727; fax: +33 1 6915 6470.
E-mail address: [email protected]. 0146-6410/$ - see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ppnp.2005.01.007
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J. Arvieux / Progress in Particle and Nuclear Physics 55 (2005) 297–307
pions, kaons or baryons. Some of these experiments did not produce the expected results, in particular in the kaon sector. The difference with theory was small and subject to experimental criticism, but they led to the conjecture that parity might well be violated. The birth of parity violation is usually attributed to a crucial experiment made in 1956 by Wu [1], following an article by Lee and Yang [2], who proposed a series of experimental tests which could reveal it. At that time, Feymann and Gell-Mann realized that the neutrinos (anti-neutrinos) were only left (right) handed and that the weak interaction had to have an axial coupling besides the usual vector coupling. It took another 20 years or so, before parity violation was put in a strict theoretical framework with the Standard Model of the electroweak interaction of Weinberg, Salam and Glashow. The fundamental idea was that the photon, responsible for the electromagnetic interaction, and the Z 0 , responsible for the weak interactions, were linear combinations of fundamental gauge fields with a mixing angle θW , the Weinberg angle. From then on, parity violation became a tool to measure sin2 θW with a precision higher than that obtained so far in neutrino interactions. This led to the first e–d scattering experiment at SLAC (E-122), which produced one of the best determination of sin2 θW at that time [3]: sin2 θW = 0.20 ± 0.03, in fair agreement with the most recent value sin2 θW = 0.23120(15) [4]. The uncertainty on the measured asymmetry was about 10−5 or 10 ppm. This was followed by two more precise experiments on 9 Be (MAMI-Mainz) [5], where the accuracy reached 1 ppm and 12 C (MIT-Bates) [6] where the accuracy was 0.14 ppm. At that point, sin2 θ was known W to a very high precision, thanks to LEP experiments, and the interest turned to the nucleon internal structure: since the Z 0 -boson couples to the quarks of all flavors, the asymmetry predicted is very different, depending on whether or not there is a strange component in the nucleon sea. The first series of experiments was SAMPLE at MIT-Bates in elastic e– p and quasi-elastic e–d scattering at back angle and low momentum transfer Q 2 [7]. In these kinematical conditions, the asymmetry is essentially sensitive to the strange magnetic moment and axial form-factor. Another experiment, HAPPEX at Jefferson Lab, at small angle and higher energy, measured a combination of the strange electric and magnetic form-factor as discussed below [8]. We report here on the progress of two ongoing experiments at Jefferson Lab: HAPPEX2, a series of experiments at low Q 2 and very forward angle on helium and hydrogen targets, and G 0 , a comprehensive experiment which will be able to do a separation of all three form-factors (strange electric, magnetic and axial form-factors) by performing experiments at forward and backward angles on hydrogen and deuterium targets, with the same apparatus. 2. Parity violation and the nucleon structure The 2004 Nobel Prize in Physics, which recognizes the importance of the “invention” of QCD, reminds us that hadrons in general, and nucleons in particular, have a rather complicated structure with three valence quarks, plus a sea containing, at any time, an indefinite number of gluons which can fluctuate into q q ¯ pairs, as long as the Heisenberg principle is not violated. Among these, strange quarks are special: their mass is of the order of ΛQCD = 200 MeV, so that the probability of finding them in a nucleon may not be
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negligible as will be the case for c-, b- or t-quarks, whose mass is larger than the nucleon itself. On the other hand, strange quarks can only come from the sea since nucleons have no static strangeness. There are essentially three types of matrix-elements involving strange quarks, which can be determined experimentally, albeit more or less indirectly: scalar: N|¯s s|N vector: N|¯s γµ s|N axial-vector: N|¯s γµ γ5 s|N. The scalar matrix element measures the probability of finding s s¯ pairs in the nucleon sea. The vector term measures the strange current: a value different from zero implies there are strange and anti-strange quarks and, moreover, that their spatial and momentum distributions are different. The axial term is directly related to the polarization of the s and s¯ . These are three different quantities and the fact that one is different from zero does not imply that the other ones should also be different from zero and vice versa. Since the s-quark is relatively heavy, its effect on the nucleon mass can be large, even for small s s¯ probabilities. In the SU2 × SU2 limit, the scalar matrix element is related to the Σ -term and to the pion decay constant f π , via low energy theorems [9]. The most recent π–N data [10] seem to indicate values of Σ ≈ 0.6–0.8 from which one can extract a strange 2N|¯s s|N ≈ 0.2–0.6. In conclusion, the scalar term is in favour of quark probability y = N| ¯ uu+ ¯ dd| a large s s¯ -sea but with rather large theoretical uncertainties. The axial term is estimated to be of the order of N|¯s γµ γ5 s|N ≈ −0.1 ± 0.1 from polarised DIS. Note that a recent semi-inclusive K-production experiment at HERMES gives a slightly positive value but with large experimental error bars for s [11]. Concerning the vector-matrix element, the nice thing about it is that its relationship to the strangeness content of the nucleon is essentially void of theoretical uncertainties. In elastic (quasi-elastic) scattering of longitudinally polarized electrons, the asymmetries are given by: A=− ×
G F Q2 √ 4πα 2
γ γ Z − (1 − 4 sin2 θ ) τ (1 + τ )(1 − 2 )G γ G e G E G EZ + τ G M G M W M A γ
θ −1 = 1 + 2(1 + τ ) tan2 2
γ
(G E )2 + τ (G M )2
(2)
τ = −Q 2 /4M 2p , γ
(1)
(3)
γ
where G E and G M are the electric and magnetic electromagnetic form-factors, G EZ and Z are the weak form-factors and G e is the axial form-factor. Using isospin symmetry, GM A the weak form-factors can be related to the quark currents [12]: Z,p
γ,p
γ ,n
G E,M = (1 − 4 sin2 θW )G E,M − G E,M − G sE,M .
(4)
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Note that depending on the authors there might be a difference of a factor of 4 in the definition of the weak form-factors [13]. Assuming that the electromagnetic form-factors are known (within a range of uncertainties), one can deduce the “strange quark formfactors” G sE,M (this is somewhat an abuse of language since the quarks, having no internal structure, have no form-factors as such). 3. Parity violation experiments at Jefferson Lab There are two large experimental set-ups allowing parity violation experiments at JLab: HAPPEX in Hall A and G 0 in Hall C. 3.1. HAPPEX HAPPEX was the first parity violation experiment operational at JLab. The experiment ˇ uses the standard HRS spectrometers, with dedicated Cerenkov detectors made of a Lead/Lucite sandwich. The HAPPEX I experiment used a polarized electron beam of 3.355 GeV. The beam intensity was up to 80 µA and the polarization was of the order of 36% during the first run (with a regular GaAs photocathode) and 75% with a strained GaAs photocathode. The scattered electrons were detected at 12.54◦ giving Q 2 = 0.477 (GeV/c)2 . At this angle, the asymmetry is dominated by the electric term with a large (40%) contribution of the magnetic term. The measured asymmetry is Ath = [−15.05 ± 0.98(stat) ± 0.56(syst)] ppm. The systematic errors are dominated by the neutron electric form-factor uncertainty [14]. From the measured asymmetry one can deduce: G sE + 0.39G sM = 0.025 ± 0.020(stat) ± 0.014(theo) essentially compatible with zero. Following these pioneering experiments, a set of new experiments have been approved by the JLab PAC. 3.1.1. HAPPEX-He This experiment uses a cold gaseous He-target. The 4 He being isoscalar with spin 0, the PV asymmetry depends only on G sE : A00 =
G sE G F Q2 √ (4 sin2 θW ) + γp γn . 2(G E + G E ) α 2
(5)
The experiment has been done at very forward angle (6◦ ) and Q 2 = 0.1 (GeV/c)2 . The experiment aims at a precision of A = 0.18 ppm both in statistics and systematics, resulting in an uncertainty on G sE of 0.015. This has necessitated many improvements as compared to the initial HAPPEX set-up: an improved polarized source using a new superlattice photo-cathode giving a mean polarization of 86%, an improved polarimetry with two polarimeters: Moeller and Compton and the addition of an electron recoil detector to the Compton polarimeter giving a precision of δ P/P ≈ 2% in about one hour, new profile scanners, new beam monitors, new luminosity monitors, a new target cell, new ˇ Cerenkov detectors and finally an improved DAQ.
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The preliminary results obtained in July 2004 give APV = [−7.40 ± (0.89)stat ± 0.57(syst)] ppm to be compared to the SM prediction without strangeness A0 = −7.82 ppm, from which one can extract G sE = −0.019 ± 0.041(stat) ± 0.026(syst) at Q2 = 0.1 (GeV/c)2 . 3.1.2. HAPPEX-H This is an extension at Q2 = 0.1 (GeV/c)2 of the HAPPEX-I experiment. It will complement, in different kinematics, the PVA4 experiment and allow one to perform a Rosenbluth separation with the SAMPLE experiment at backward angle. The Standard Model asymmetry without strangeness is very small (A0 = −1.6 ppm) and the precision aimed at is δ(G sE +0.08G sM ) = 0.010. A first run has taken place in July 2004 with limited statistics. The combined preliminary He and H results at Q2 = 0.1 (GeV/c)2 are shown in Fig. 1, combined with the SAMPLE and PVA4 [17] results. G sE is compatible with zero but G sM is slightly positive at a 1–2 standard deviation level. Besides these experiments, aimed at studying the nucleon structure, there is a proposal (PREX, JLab E00-003) to measure the neutron distribution in 208 Pb by using parity violation since the Z 0 couples essentially to neutrons. 3.2. The G 0 experiment The G 0 experiment is an ambitious undertaking aiming at separating the three components G sE , G sM and G eA in a large domain of Q2 = 0.12–1.00 (GeV/c)2 . This is done by performing three separate experiments with the same apparatus: elastic ep scattering at forward angle (around 65◦ ) and backward angle (around 115◦) plus ed quasi-elastic at backward angle. The experiment takes place in JLab Hall C. The proposal (spokesperson: D. Beck) was first submitted in 1991 but it took some time before the financing was acquired. The years 1998–2002 were devoted to design, development, building and testing the various components. The size of the collaboration is about 100 physicists and engineers, coming from some 20 laboratories in the USA, Canada, France and Armenia. More details can be found on the G 0 web site http://g0web.jlab.org/. 3.2.1. Forward angle measurements In the forward angle set-up, the protons recoiling from ep elastic scattering at a fixed electron energy of 3 GeV are detected at θ p = 65◦ ± 10◦ , corresponding to a rather small electron scattering angle (around θe = 6–15◦ ). The asymmetries to be measured lie in the range −3 to −40 × 10−6 . The beam intensity is 40 µA and the polarization of the order of 75%. The experiment aims at a statistical precision A A ≤ 5%, which requires −13 −14 2 counting statistics of the order of 10 –10 counts per Q setting. This has necessitated the construction of a dedicated apparatus with large acceptance and high counting rate detectors and electronics. It is based on a superconducting toroidal magnet (SMS) of 1.6 T.m. having eight coils which was designed to focus particles of the same momentum and angle to a single point on the focal plane, wherever they originate from an extended target (L = 20 cm). Individual particles are counted in a set of 16 pairs (in coincidence)
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Fig. 1. Preliminary result of the new HAPPEX experiment at Q2 = 0.1 (GeV/c)2 combined with SAMPLE and PVA4 results at Q2 = 0.1 (GeV/c)2 .
Fig. 2. Schematics of the electron detection in the G 0 forward running mode (right) and of the Focal Plane Detectors or FPDs (left).
of scintillators per octant (the FPDs or Focal Plane Detectors) placed in the focal plane at various Q 2 positions (see Fig. 2). The recoiling protons are identified by a combination of magnetic momentum selection by the SMS and time-of-flight information. The solid angle is of the order of 0.5–0.9 sr depending on momentum transfer. Heavy collimators protect
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Fig. 3. Time-of flight spectrum on a log scale. The horizontal axis is the channel number (full scale = 32 ns). The G 0 recoil protons are superimposed on the leakage spectrum from the other halls.
the detectors from a direct view of the beam. Overviews of the G 0 experimental set-up are given in [15,16]. Various contributions on the G 0 experimental set-up can be found in the proceedings of the International Workshops on Parity Violation and Hadronic Structure in 2002 (Mainz) and 2004 (Grenoble). Commissioning of the apparatus started in August 2002, and by January 2003 the G 0 experiment had met the specifications for all the instrumentation, allowing some preliminary data to be taken during about 50 h or 5% of the statistics. The data showed that everything was OK at a level of precision of a few ppm. A second commissioning run was scheduled in October to December 2003, immediately followed by data taking, which ended in May 2004. During this period and as the statistics was improved, reaching the final goal of 1 ppm per detector or better, various problems were found and solved. Among these, there was the problem of leakage from the other halls. The G 0 beam structure is unconventional, with one burst every 32 ns (31.25 MHz) as compared with 2 ns (499 MHz) for the conventional JLab beam. This was required by a proton time-of-flight between target and detector of the order of 20 ns. During the course of the experiment, G 0 has taken data under various conditions: Hall C alone (rarely), together with Hall B (most of the time) and with Hall B and Hall A (for limited periods of time). Each hall uses a different laser with different helicity correlated properties. It was well known that there is some leakage between the different halls, but as long as their time structure is identical, it is rather straightforward to minimize the helicity correlated asymmetry of the combined beams. This was not the case for G 0 and there was a residual, uncorrected 2 ns time structure under the G 0 32 ns time-of-flight spectra and in particular under the elastic peak (Fig. 3). The leakage current is small (of the order of 40 nA at 40 µA), but its asymmetry can reach 500 ppm, so that the overall contamination would be have been of the order of 0.5 ppm. After a series of tests near the end of the data taking period, a method was found which allows for the correction of the leakage asymmetries directly from the time-of-flight spectra, and the residual uncertainty is presently less than 0.1 ppm.
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Fig. 4. Estimated combined statistical and systematical G 0 uncertainties as a function of Q 2 .
A second problem which was underestimated is that of the background. This background ranges from a few % (for low Q 2 ) to about 25%. Part of it comes from the Al windows of the target. During the first commissioning run, the Al exit window was about 280 µm. It was reduced to 75 µm for the second commissioning and data taking runs. To estimate this background, data were taken with a pure Al target but a fraction of the background comes from inelastic reactions in the hydrogen target. This has been estimated by a Monte Carlo simulation before the experiment. The dominant reaction is π 0 production for which theoretical calculations [18,19] show that the asymmetry has the same sign as the elastic asymmetry, therefore simplifying in principle the subtraction procedure (if the asymmetries were identical in the elastic and inelastic regions, the problem would reduce to estimating a dilution factor). The difficulties that are being faced are (1) that the background is underestimated by the simulation and (2) that its asymmetry varies drastically with Q 2 , even changing sign for large Q 2 . This will have consequences on the accuracy of the high Q 2 final data whose estimated error bars are shown in Fig. 4. The curve is the Standard Model prediction without strangeness. It is now believed that part of this background comes from hyperon production and subsequent decays for which simulations are under way. The preliminary results are shown in Fig. 5 for detectors 1–12 blinded by an overall normalization factor whose value lies in the range 0.75–1.25 [20]. These data show that the asymmetry increases as a function of Q 2 (the Q 2 varies from 0.12 for detector 1 to about 1 (GeV/c)2 for the high end of detector 15) but no comparison can be made yet with theoretical predictions. The analysis effort is now concentrating on the high Q 2 region and especially on detector 15 which contains all Q 2 values ranging from 0.5 to 1.0 (GeV/c)2 , making the background
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Fig. 5. Preliminary results from G 0 . The horizontal scale is the detector number ranging from 1 to 15, the vertical scale is the asymmetry in ppm.
subtraction more delicate. The analysis of the small detector data (low Q 2 ) is almost complete, and final data should be available by the end of 2004. 3.2.2. Backward angle measurements In the backward angle configuration, the scattered electrons are detected instead of the recoil protons as shown in Fig. 6. Since the scattered electrons have energies of the order of a few hundreds of MeV, they are all relativistic and a measurement of their time-of-flight spectra is of limited interest. The beam structure can therefore be the JLab standard one at 499 MHz (2 ns between pulses), eliminating the leakage problem. Moreover, the intensity can be increased from 40 to 80 µA since tests done during the forward angle data taking period have shown that the target should stand such an intensity without significant boiling. The detection will be based on coincidences between 14 FPDs (FPDs 1 and 2 having been removed) and a set of 9 new counters, the CEDs (or Cryostat Exit Detectors). Appropriate combinations of FPD–CED coincidences will allow the separation of elastic and inelastic events. The inelastic data are of particular interest as their weak asymmetry A of the N– transition. will give access to the axial form-factor G N GEANT simulations have shown that, with a deuterium target, there will be a large π − ˇ background coming from the en → epπ − reaction. Therefore a set of Cerenkov detectors have been built and they are presently at JLab for final testing before mounting. Due to the limited kinematical range, each Q 2 requires a different incident electron energy. The G 0 collaboration has requested three energies (424, 585 and 799 MeV),
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Fig. 6. Schematics of the electron detection in the G 0 backward running mode. The black arrow indicates the direction of the incident electron beam.
corresponding to Q 2 = 0.3, 0.5 and 0.8 (GeV/c)2 , for both hydrogen and deuteron targets. These values may change slightly for operational reasons. At the time of this writing (November 2004) only the 0.8 (GeV/c)2 run has been approved by the Jefferson Lab PAC. Since the end of the forward angle data taking run, the SMS magnet and Ferris Wheel have been put to the side of the beam line in Hall C and they have been rotated by 180◦. The first G 0 backward angle run is scheduled for the end of 2005. 4. Conclusion Parity violating electron scattering has become a standard tool for studying the nucleon inner structure and Jefferson Lab is playing a preeminent role in this field. The first results obtained at selected values of Q 2 show that the strange vector currents are small. The most recent round of experiments at Jefferson Lab aim at getting a very high precision in a limited Q 2 domain (HAPPEX) or at getting comprehensive data over a wide Q 2 range from 0.12 to 1.0 (GeV/c)2 , with an emphasis on a complete separation of the three form-factors G sE and G sM and G eA at 0.3, 0.5 and 0.8 (GeV/c)2 . Acknowledgements I would like to express thanks to all my colleagues from G 0 for their constant dedication and to D. Armstrong and D. Lhuillier from HAPPEX for their help in gathering information and material. References [1] C.S. Wu, Phys. Rev. 105 (1957) 1413. [2] T.D. Lee, C.N. Yang, Phys. Rev. 104 (1956) 254. [3] C. Prescott et al., Phys. Rev. Lett. B 77 (1978) 347.
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