arXiv:hep-ph/0601127v1 17 Jan 2006 0 Hadronic Parity Violation: a New View through the Looking Glass Michael J. Ramsey-Musolf Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, CA 91125 USA and Shelley A. Page Dept. of Physics & Astronomy, Univ. of Manitoba, Winnipeg, MB R3T 2N2 Canada February 2, 2008 Abstract Studies of the strangeness changing hadronic weak interaction have produced a number of puzzles that have so far evaded a complete explanation within the Stan- dard Model. Their origin may lie either in dynamics peculiar to weak interactions involving strange quarks or in more general aspects of the interplay between strong and weak interactions. In principle, studies of the strangeness conserving hadronic weak interaction using parity violating hadronic and nuclear observables provide a complementary window on this question. However, progress in this direction has been hampered by the lack of a suitable theoretical framework for interpreting hadronic parity violation measurements in a model-independent way. Recent work involving effective field theory ideas has led to the formulation of such a framework while motivating the development of a number of new hadronic parity violation experiments in few-body systems. In this article, we review these recent develop- ments and discuss the prospects and opportunities for further experimental and theoretical progress. 1 Contents 1 Introduction 3 2 Weak Meson Exchange Model Meets the End of the Road 7 2.1 Meson Exchange Model of the Weak N-N Interaction . . . . . . . . . . . 8 2.2 Experimental Progress . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.1 Longitudinal Analyzing Power in pp Scattering . . . . . . . . . . . 13 2.2.2 Progress in the np System . . . . . . . . . . . . . . . . . . . . . . 18 2.2.3 Neutron Spin Rotation Experiments . . . . . . . . . . . . . . . . 21 2.2.4 Nuclear Anapole Moments . . . . . . . . . . . . . . . . . . . . . . 23 2.2.5 Parity Violation in Compound Nuclei . . . . . . . . . . . . . . . . 25 2.3 The End of the Road . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3 Effective Field Theory Framework 27 3.1 The Pionless Effective Field Theory . . . . . . . . . . . . . . . . . . . . . 28 3.2 PV EFT with Pions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3 Recent Theoretical Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.4 Experimental Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4 Beyond Hadronic Parity Violation 47 5 Summary and Conclusions 49 6 Acknowledgements 50 2 1 Introduction Explaining the weak interactions of quarks in terms of the dynamics of the Standard Model (SM) has been an area of vigorous research in nuclear and particle physics for several decades. Experimentally, the hadronic weak interaction (HWI) is probed by observing non-leptonic, flavor changing decays of mesons and baryons and by measur- ing observables that conserve flavor but violate the parity symmetry of the strong and electromagnetic interactions. Theoretically, the problem has been a particularly chal- lenging one, requiring the computation of low-energy weak matrix elements of the HWI in strongly interacting systems. Although the structure of the weak quark-quark inter- action in the SM has been well established for some time, its manifestation in strongly interacting systems remains only partially understood. The stumbling block has been the non-perturbative nature of quantum chromodynamics (QCD) at low energies. In contending with it, theorists have resorted to a variety of approximation schemes to ob- tain physically reasonable estimates of HWI observables. Ultimately, however, arriving at definitive, SM predictions requires that one treat the non-perturbative QCD dynamics in a rigorous way. In the case of the flavor changing decays of mesons, use of effective field the- ory (EFT) techniques – chiral perturbation theory (χPT), heavy quark effective the- ory (HQET), and recently, soft collinear effective theory (SCET) – have led to enormous progress. In each instance, the presence of distinct physical scales at play in the processes of interest allows one to carry out a systematic expansion of the effective Lagrangian in powers of scale ratios while incorporating the symmetries of QCD into the structure of the operators. The operator coefficients that encode the non-perturbative QCD dy- namics are obtained from measurement, and the structure of the EFT is then used to translate this information into predictions for other observables. Moreover, a meaning- ful confrontation of experiment with QCD theory can be made, as computations of the operator coefficients can in principle be performed on the lattice. The situation involving the HWI of baryons is far less satisfactory, and decades of experimental and theoretical work have left us with a number of unresolved puzzles. In the case of hyperon non-leptonic decays, for example, one has not yet been able to find a simultaneous accounting of both the parity conserving P-wave and parity violating (PV) S-wave decay amplitudes. Similarly, the PV asymmetries associated with the radiative decays of hyperons are anomalously large. In the limit of degenerate u-, d-, and s- quarks, SU(3) flavor symmetry implies that these asymmetries must vanish. Given the known mass splitting between the strange and two light flavors, one would expect the asymmetries to have magnitudes of order m /M 0.15, where M 1 GeV is a s B B ∼ ∼ typical hyperon mass. The experimental asymmetries, in contrast, are four-to-five times larger in magnitude. Even the well-known ∆I = 1/2 rule that summarizes the observed dominance of the I = 1/2 channel over the I = 3/2 channel in strangeness changing nonleptonic decays remains enigmatic, as no apparent symmetry favors either channel. In short, consideration of QCD symmetries and the relevant physical scales does not suffice to account for the observed properties of the ∆S = 1 HWI. While the puzzles surrounding the strangeness changing HWI have been discussed extensively elsewhere, the ∆S = 0 HWI has generally received less attention. Nonethe- 3 less, since we do not know whether the breakdown of QCD symmetry-based expectations in the ∆S = 1 sector results from the presence of a dynamical strange quark or from other, yet-to-be-uncovered dynamics, consideration of the ∆S = 0 HWI – for which the strange quark plays a relatively minor role – is no less important. In the following review, we focus on this component of the HWI. According to the SM, the structure of the low-energy ∆S = 0 HWI is relatively simple: G 1 ∆S=0 = F JCC†JλCC + JNC†JλNC (1) HHWI √2 λ 2 λ (cid:18) (cid:19) where G is the Fermi constant and where JCC and JNC are the weak charged and F λ λ neutral currents, respectively. The theoretical challenge is to find the appropriate effec- tive interaction ∆S=0 eff(N,π,∆,...) that best describes the hadronic manifestation of HHWI ∆S=0. Because JCC transforms as a doublet under strong isospin while JNC contains HHWI λ λ I = 0 and I = 1 components, the current-current products in ∆S=0 contain terms that HHWI transform as isoscalars, isovectors, and isotensors. Consequently, ∆S=0 eff must contain HHWI the most general set of operators having the same isospin properties. In what follows, we review the theoretical efforts to determine this effective interaction. Experimentally, the ∆S = 0 HWI can be isolated solely via hadronic and nuclear physics processes that violate parity, thereby filtering out the much larger effects of the strangeness conserving strong and electromagnetic interactions. Efforts to do so are not new. Soon after the 1957 discovery of parity violation in µ-decay and nuclear β- decay, the search was on for evidence of a PV weak nuclear force that would result in small, parity violating effects in nuclear observables. That year, Tanner reported the first experimental search for a PV nucleon-nucleon (NN) interaction (1). Subsequently, Feynman and Gell-Mann (2) predicted that the four fermion interactions responsible for leptonic and semi-leptonic weak decays should have a four nucleon partner that is similarly first order in G . A decade later, Lobashov et al. produced the first definitive F evidence for the existence of a first order weak NN force in radiative neutron capture on 181Ta that was consistent with the Feynman and Gell-Mann hypothesis (3, 4). The pursuit of this evidence in the Tanner, Lobashov and subsequent experiments was challenging, as one expected the magnitude of the PV effects to be (10 7). Along − O the way, it was realized that certain accidents of nuclear structure in many-body nuclei could amplify the expected PV effects by several orders of magnitude, and a 10% PV ∼ effect was, indeed, observed in 139La (5). The amplification arises from two sources: the presence of nearly degenerate opposite parity states that are mixed by the HWI, and the interference of an otherwise parity forbidden transition amplitude with a much larger parity allowed one. Subsequent experiments then yielded a mix of PV measurements in nuclei, where one expected amplification factors of order 102 to 103, as well studies of PV observables in the scattering of polarized protons and neutrons from hadronic targets. Theoretically, however, the use of nuclear systems introduces an additional level of complication in the interpretation of experiments, as one must contend with both nu- clear structure effects as well as the dynamics of non-perturbative QCD. For over two decades now, the conventional framework for carrying out this interpretation has been a meson exchange model, popularized by the seminal work of Desplanques, Donoghue, and 4 Holstein (DDH) (6). The model assumes that the PV nucleon-nucleon (NN) interaction is dominated by the exchange of the pion and two lightest vector mesons (ρ and ω), and its strength is characterized by seven PV meson-nucleon couplings: h1, h0,1,2, h1 π ρ ρ′ and h0,1, where the superscript indicates the isospin1. DDH provided theoretical “rea- ω sonable ranges” and “best values” for the hi using SU(6) symmetry, constraints from M non-leptonic hyperon decay data, and the quark model to estimate the experimentally unconstrained terms. Despite various attempts to improve upon the original DDH work, the results of their analysis still remain as the benchmark, theoretical targets for the PV meson-nucleon couplings. The experimental results from nuclear and hadronic PV measurements have been analyzed using the DDH framework, leading to constraints on combinations of the hi M that typically enter PV observables. The results are in general agreement with the DDH reasonableranges,thoughtherangesthemselvesarequitebroad,andtheconstraintsfrom different experiments are not entirely consistent with each other. A particular quandary involves h1: the γ-decays of 18F imply that it is consistent with zero, while the analysis π of the 133Cs anapole moment differs from zero by several standard deviations (7). More to the point, the connection between the PV experiments and SM expectations is far from transparent. Indeed, in order to draw this connection using the meson-exchange framework and nuclear PV observables, one has to sort through a number of model dependent effects involving nuclear structure, hadron structure, and the meson exchange model itself. Whether one has a reasonable hope for doing so in a systematic manner is debatable at best. At the end of the day, the goal of studying the ∆S = 0 HWI with hadronic and nuclear PV is to help determine the degree to which the symmetries of QCD characterize the realization of the HWI in strongly interacting systems and, as a corollary, to shed light on the long standing puzzles in the ∆S = 1 sector. To that end, one would ideally formulate the problem to make the contact with the underlying SM as transparent as possible while avoiding hadronic model and nuclear structure ambiguities. Recently, a framework for doing so has been formulated in Reference (8) using effective field theory ideas. That work builds on the extensive developments in the past decade of an EFT for the strong NN interaction that has been applied successfully to a variety of few-body nuclear phenomena. In the case of the PV NN force, two versions of the EFT are useful, depending on the energy scales present in the process under consideration: (I) Forenergieswellbelowthepionmass,theEFTcontainsonlyfour-nucleonoperators and five effective parameters, or “low-energy constants”, that characterize the five independent low-energy S-wave/P-wave mixing matrix elements: λ0,1,2, λ , and s t ρ . Relative to the leading order parity-conserving four nucleon operators, the PV t operators are (Q), where Q is a small energy scale. In this version of the EFT, O the pion is considered to be heavy and does not appear as an explicit, dynamical degree of freedom. (II) At higher energies, the the pion becomes dynamical and three additional constants 1In the literature,the isovector,PVπNN couplingis oftendenotedf . Here,however,weadoptthe π h1 notation to avoid confusion with the pion decay constant. π 5 associated with π-exchange effects appear at lowest order: h1, along with a second π parameter in the EFT potential, k1a, and a new meson-exchange current opera- π ¯ tor characterized by C . Moreover, the EFT incorporates the effects of two-pion π exchange forthe first timein asystematic way, leading to predictions fora medium- range component of the PV NN interaction. The essential differences between the PV EFT and the meson-exchange frameworks – as well as their similarities – are summarized in Figure 1. π,ρ,ω π π (a) (b) (c) (d) Figure 1: Comparison of (a) meson-exchange and (b-d) effective field theory (EFT) treat- ments of the parity-violating NN interaction. Panels (b), (c), and (d) give illustrative contributions to short, medium, and long-range components, respectively . Clearly, implementing the EFT approach to the ∆S = 0 HWI requires carrying out new experiments in few-body systems for which ab initio structure computations can be performed. As outlined in Reference (8), a program of such measurements exists in principle. From a practical standpoint, carrying it out will involve meeting a number of experimental challenges. In light of these new theoretical developments and experimental opportunities, we believe it is time to review the field of hadronic PV anew. Comprehen- sive reviews of the subject have appeared over the years, including the influential Annual Reviews article by Aldelberger and Haxton completed two decades ago (9). In what follows, we hope to provide the “next generation” successor to that work, updating the authors’ analysis in light of new theoretical and experimental progress. Since our focus will be on new developments, we touch only lightly on older work that has been reviewed in Reference (9) and elsewhere (10). Before doing so in detail, however, we find it useful to summarize the primary developments and shifts in emphasis that have occurred since Reference (9) appeared: Theextensive development ofχPTandNNEFT,togetherwithsubstantialprogress • in performing lattice QCD simulations, has revolutionized our approach to treating hadronic physics. While the use of hadronic models can provide important physical insights, the present day “holy grail” is to derive first-principles QCD predictions for hadronic phenomena. At the time of the Adelberger and Haxton review, the quark model was still in vogue, whereas lattice QCD and hadronic EFTs had yet to realize their potential. Today, the situation is reversed. Indeed, in the case of ∆S = 0 HWI, the use of a meson-exchange model for the NN interaction that entails a truncation of the QCD spectrum and contains effective couplings that 6 likelyparameterizemorephysicsthantheelementarymeson-nucleonPVinteraction (e.g., 2π-exchange) obscures rather than clarifies the connection with the SM. We now know how to do better. Newexperimental andtechnologicaldevelopments haveopenedtheway toperform- • ing PV experiments in few-body systems. The landscape now differs substantially from that of the 1980’s, at which time it appeared that measuring a number of (10 7) effects in few-body processes was impractical. Indeed, two decades ago, − O the presence of the nuclear enhancement factors made experiments with many- body nuclei such as 18F more attractive than those in few-body systems. Since then, precise new measurements of 10 7 PV observables in p~p scattering, ~nα spin − rotation, and polarized neutron capture on hydrogen have either been completed or are in progress, and plans are being developed for other similarly precise few-body measurements at NIST, LANSCE, the SNS, and IASA (Athens). As we discuss below, completion of a comprehensive program of few-body measurements is now a realistic prospect. Enormous progress has been made in performing precise, ab initio calculations in • the few-body system using Green’s function and variational Monte Carlo methods. These computations start with state-of-the-art phenomenological potentials that incorporate our present knowledge of NN phase shifts and include minimal three- body forces as needed to reproduce the triton binding energy and other three-body effects. A marriage between the NN EFT methods and these few-body computa- tional approaches is also being developed. As a result, a realistic prospect exists for performing precise computations with the PV EFT for few-body observables, leaving one free from the nuclear structure questions that enter the interpretation of many-body PV observables. In short, the frontier today for understanding the ∆S = 0 HWI lies in the few-body arena, for which a combination of precise experiments and first-principles theory provide new tools for making the most direct possible confrontation with the interplay of the strong and electroweak sectors of the SM. In the remainder of this article, we elaborate on this view. 2 Weak Meson Exchange Model Meets the End of the Road While the era of the meson-exchange framework for hadronic PV is drawing to a close, it has played such a central role in the field that its development and use following the publication of Reference (9) calls for a brief review. The primary theoretical develop- ments have included updated theoretical “reasonable ranges” and “best values” for the hi provided by DDH and others (6, 11, 12), the analysis of nuclear anapole moments M extracted from atomic PV experiments, computations of nuclear PV contributions to PV electron scattering asymmetries, and new global fits of the hi to nuclear and hadronic M 7 PV data. Experimentally, one has seen the completion of the TRIUMF 221 MeV p~p scattering experiment and a neutron spin rotation experiment at NIST, the launching of an ~np dγ experiment at LANCSE, and the first non-zero result for a nuclear anapole → moment in an atomic PV experiment with 133Cs. 2.1 Meson Exchange Model of the Weak N-N Interaction The meson-exchange, PV NN potential, VPV , is generated by the meson-exchange dia- DDH grams of Figure 1a, wherein one meson-nucleon vertex is parity conserving and the other parity violating. The Lagrangians for each set of interactions have been written down on numerous occasions in the literature, so we only give the final form of the static potential: h1g m τ τ ~p p~ VPV (~r) = i π A N 1 × 2 (~σ +~σ ) 1 − 2,w (r) DDH √2Fπ (cid:18) 2 (cid:19)3 1 2 ·" 2mN π # τ +τ (3τ3τ3 τ τ ) g h0τ τ +h1 1 2 +h2 1 2 − 1 · 2 − ρ ρ 1 · 2 ρ(cid:18) 2 (cid:19)3 ρ 2√6 ! p~ p~ p~ ~p 1 2 1 2 (~σ ~σ ) − ,w (r) +i(1+χ )~σ ~σ − ,w (r) 1 2 ρ ρ 1 2 ρ − ·( 2mN ) × ·" 2mN #! τ +τ g h0 +h1 1 2 − ω ω ω 2 (cid:18) (cid:18) (cid:19)3(cid:19) p~ p~ ~p ~p 1 2 1 2 (~σ ~σ ) − ,w (r) +i(1+χ )~σ ~σ − ,w (r) 1 2 ω ω 1 2 ω − ·( 2mN ) × ·" 2mN #! τ τ ~p ~p g h1 g h1 1 − 2 (~σ +~σ ) 1 − 2,w (r) −(cid:16) ω ω − ρ ρ(cid:17)(cid:18) 2 (cid:19)3 1 2 ·( 2mN ρ ) τ τ ~p p~ g h′1i 1 × 2 (~σ +~σ ) 1 − 2,w (r) . (2) − ρ ρ (cid:18) 2 (cid:19)3 1 2 ·" 2mN ρ # Here ~p = i~ , with ~ denoting the gradient with respect to the coordinate ~x of the i i i i − ∇ ∇ i-th nucleon, r = ~x ~x is the separation between the two nucleons, 1 2 | − | exp( m r) i w (r) = − (3) i 4πr is the standard Yukawa function, and the strong πNN coupling g has been expressed πNN in terms of the axial-current coupling g using the Goldberger-Treiman relation: g = A πNN g m /F , with F = 92.4 MeV being the pion decay constant. The g , V = ρ,ω, are A N π π V the strong vector meson-nucleon Dirac couplings, and the χ give the ratio of the strong V Pauli and Dirac couplings. The terms in Eq. (2) display different dependences on isospin and spin, so that various observables are sensitive to distinct linear combinations of the hi . A notable feature is the absence of a neutral π-exchange component. Indeed, the M only manifestation of π-exchange appears in the first term of Eq. (2) that contains only products of the isospin raising and lowering operators for the two nucleons. This feature reflects a more general theorem by Barton that forbids a neutral pseudoscalar-exchange component in the PV potential when CP is conserved (13). 8 Table 1: Theoretical reasonable ranges (second column) and best values (columns 3-5) for the PV meson-nucleoncouplings (15), hi , from DDH (6), Dubovic and Zenkin (DZ)(11), M and Feldman et al. (12). All values are quoted in units of g = 3.8 10 8. π − × PV Coupling DDH Range DDH Best Value DZ FCDH h1 0 30 + 12 +3 +7 π → h0 30 -81 -30 -22 -10 ρ → h1 -1 0 -0.5 +1 -1 ρ → h2 -20 -29 -25 -18 -18 ρ → h0 15 -27 -5 -10 -13 ω → h1 -5 -2 -3 -6 -6 ω → The values of the hi appearing in VPV are most conveniently expressed in units M DDH of g , the natural strength for the weak ∆S = 1 B B π couplings2: π ′ → G F2 g = 3.8 10 8 F π . (4) π − × ≈ 2√2 The original DDH reasonable ranges and updated best values are given in Table 1. Note that no prediction for h1 appears, as DDH were unable to compute this constant in ρ′ Reference (6). Subsequently, Holstein (14) used a 1/2 pole model to estimate this − parameter. Using the quark modelto compute the 1/2 1/2+ mixing matrix elements, − ↔ he obtained h1 1.8 g . Henceforth, we will not refer to this prediction when referring ρ ′ ≃ π to the DDH values. The various SU(6) symmetry arguments, current algebra techniques, and quark w model estimates that lead to the values in Table 1 have been discussed in detail elsewhere (6, 12), and since our emphasis lies on a new formulation in which these couplings do not appear, we do not revisit those discussions here. Instead, we concentrate on new applications of this framework. Anapole Effects Two particularly novel uses of the PV meson-exchange framework have been in the analysis of atomic PV experiments and PV electron scattering. Shortly after PV was observed in µ-decay and β-decay, Zeldovich and Vaks pointed out that weak interactions could also induce a PV coupling of the photon and fermion (16). Electromagnetic (EM) gauge invariance implies that the lowest dimension effective operator for this coupling has the form (17) F ffγ = A ψ¯ γ γ ψ ∂ Fµν , (5) LPV Λ2 f µ 5 f ν where Fµν is the EM field strength tensor, F is the anapole coupling, and Λ is an A 2Here, B and B′ denote octet baryons. 9