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Isospin Breaking in the Neutron-Proton System

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Isospin Breaking in the Neutron-Proton System Invited paper given at 3rd International Symposium on Pion- TKl-PP-S'J-'J'i Nucleon and Nucleon-Nucleon Physics, Gatchina, May 1989 USSR, Apr. 17-22, 1989 ISOSPIN BREAKING IN THE NEUTRON-PROTON SYSTEM J.A. Nisk&nen" TRIUMF, 4004 Wesbrook Mall, Vancouver, B.C., Canada V6T 2A3 ABSTRACT I review work explaining tne recent TRIUMF measurement of the charge symmetry breaking observable AA = An-Ap in polarized np scattering. In most theoretical models nearly all of this AA can be explained as the np mass difference effect in pion exchange at the zero crossing angle of the experiment, with the more interesting heavy meson exchanges contributing to the angular distribution only outside that angle. Also the reaction np —* dn° is shortly discussed. INTRODUCTION In the absence of any symmetries arbitrary spin-| on spin-^ scattering would have 16 amplitudes, quite a challenge for any attempts of an amplitude analysis. Standard parity and time reversal invariances reduce the number of independent amplitudes to 6. Even this number is further reduced to 5 for identical fermions. The same reduction is achieved in general for nucleons in the isospin formalism. Both the proton and neutron are regarded as states of the same particle species in an abstract isospin space where the strong interaction is rotationally symmetric. Now for both the antisymmetric T = 0 and symmetric T = 1 isospin combination of the two nucleon system there are only 5 independent spin amplitudes. The value of isospin is conserved to good accuracy in strong interactions. The concept of isospin and its conservation have proved to be a very useful simplification in understanding the strong interaction of nucleons. However, from the introduction of the isospin1 it has been clear that rotations and reflections in the isospin space are not exact symmetries. Of course, the proton and neutron do not behave in the same way under the electromagnetic interaction. Even for the strong interaction the symmetry is not exact, because different charge states of the same particle species (e.g. proton and neutron) can have different masses. This means that neither for an arbitrary rotation of the isospin [H,f] = 0 (charge independence) , (1) nor for a rotation by 180° Tl [H,PCS] = 0, Pcs = e" (charge symmetry) , (2) "On leave from Department of Theoretical Physics, University of Helsinki u are exactly valid. Here PCs essentially reverses the "z-axis" of the isospin space, for nucleons it changes protons into neutrons and vice versa. At the hadronic level the reasons for isospin symmetry breaking can be traced to mass differences between different charge states of mesons and baryons, to electromagnetic interaction effects and to the fact that mesons of different isospins mix (ff° and t] or p and u>). Before today's advanced hadron models also the mass differences and meson mixings could have been argued to be of electromagnetic origin. However, in the quark model the u and d quark mass difference can be as fundamentally independent of the electromagnetic interaction as other much larger mass differences, so isospin symmetry breaking may well occur even in the pure strong interaction. At the quark level an obvious reason for isospin symmetry breaking is just this u and d quark mass difference as well as the Coulomb interaction between quarks. One reason for the recent interest in isospin breaking, in particular charge symmetry breaking (CSB), is the hope that its detailed understanding could tell something about the underlying hadron structure in terms of quarks or solitons etc. One should be able to gain information about the strong interaction, which is complementary to the isospin symmetric case. At the very least new constraints on e.g. meson-nucleon couplings could be expected, since meson exchanges appear in different combinations. On the other hand, deviations from the meson exchange picture could be signatures of deeper mechanisms. In the wake of the recent TRIUMF experiment on CSB in np scattering much of the recent work concentrates on the polarization in this scattering and in this talk I shall concentrate on the np system. For earlier and more comprehensive reviews see Refs. 2 and 3. CSB OBSERVABLES IN NEUTRON-PROTON SCATTERING The most obvious CSB interaction is class III in the terminology of Henley and Miller2 and of the form V^'B = (ri + f2)3 v(r). (3) This changes sign in the inversion of the r3 axis. Here v(r) has a similar spin-space structure as the isospin symmetric NN interaction. This type of interaction causes a difference between the pp and nn scattering lengths and affects binding energy differences in mirror nuclei. Due to the presence of the Coulomb interaction extracting reliable information on the strong interaction is quite difficult and model dependent, although progress has been made."11" Class III forces (proportional to the total isospin operator) 'Note lhat the difference with the np scattering length in the same singlet stale is mainly due to the class II isotensor interaction ex ( 3rJ3r23 - 1). This arises from meson mass differences, in particular from m,± - m»o Though this is charge dependent, it is invariant in the reversal of the r3 axis and so charge symmetric. conserve the isospin and vanish in the neutron-proton interaction. In the np system the nonzero CSB interaction compatible with space inversion and time reversal invariancea and with the generalized Pauli principle must be of the forms = (nXT2)3S1xS2Lv(r)> (4) (rl-T1)3(al-S2)-Lw{r). (5) called class IV forces. Both of these necessarily change the spin and isospin. Therefore they must vanish for pp and nn states and cannot directly affect e.g. mirror nucleus energy differences. It is also clear that the first form requires an exchange of a charged meson (notably ir±), whereas the second needs a neutral one (most importantly a photon or pu> meson mixing). It is of practical importance that in partial waves the only difference between these two forms is a phase factor (-1)J. This causes the CSB exchange of charged and neutral mesons to be qualitatively different. Because of spin mixing and conservation of parity and angular momentum, it is immediately clear that these forces can only contribute to the mixing of spin singlets with triplets which are not tensor coupled (i.e. J — L). This mixing is now a sixth independent amplitude in np scattering. Assuming only Lorentz invariance, parity conservation and time reversal invariance, the scattering matrix of two spin-j particles is standardly expressed in terms of six am- plitudes as5 a M = 2 K + f>) + (a- b)aXna2n + (c + d)aXmo2m + (c - d)ouo2l + e(<7ln + <72n)+/(<Tln-<7jn)] . (6) Here / mixes the triplet and singlet states (n normal to the scattering plane), whereas a...e are the usual isospin honouring mplitudes. The unit vectors are defined in terms of the incident and final momenta as (7) The mixing amplitude / is conventionally presented in terms of partial wave mixing angles similar to the tensor coupling as5'6 S6) (8) with Pl(cos9) = sin0 P'L(cos0) the associated Legendre polynomial. To make the series converge the long ranged magnetic interaction amplitude fem is normally separated as an exact plane wave amplitude. The same can be done with OPE to improve the convergence. The parameter fj is defined similarly to the tensor coupling by / COS27JC1"-' \ii2 ^'*'") coa2fj The isospin violating part is the nondiagonal elements of the S-matrix. These are so called 'bar' phase shifts, although the bar ii omitted. The simplest CSB observable is the difference of the neutron and proton analyzing powers in polarized scattering AA = An-A, = 2Re(b'f)/a0. (10) This is nonzero, if and only if the neutron and proton are distinguishable. Typically this is a very small effect. In a recent TRIUMF experiment7 AA was measured at 477 MeV for the angle at which A crosses through zero, with the result A^(72°) = 0.0047 ± 0.0022 ± 0.0008 , (11) thereby for the first time establishing the existence of this new class of nuclear force. The restriction to the zero crossover angle was necessary to eliminate the major systematic errors, but as will be seen later, unfortunately misses some most interesting piece of CSB in np scattering. A new measurement at 350 MeV extending somewhat off the zero crossing angle has been proposed at TRIUMF.8 Another experiment is already in the analysis stage at IUCF to also measure the shape of the angular distribution of AA at 183 MeV.9 The only other experimentally feasible CSB observable is Ak, -A.k = 2Im(c-f)/o0, (12) but this is predicted to be small in Ref. 13 for most angles. THEORETICAL INTERPRETATION Considerable amount of theoretical work has been done to explain or predict the TRIUMF result by nonrelativistic DWBA calculations,10"14 a relativistic i-matrix ap- proach,15 or quark clusters.16 All DWBA calculations agree that at the zero-crossing angle the effect of the np mass difference in the OPE is the dominant effect and enough to explain the data point obtained at TRIUMF. They use some more or less phenomeno- logical potential to produce nucleon wave function distortions, whereupon the isospin breaking amplitude is treated perturbatively. This CSB contribution arises in the Dirac formalism from the charge and mass changing «•* exchange in the following way. The pion-nucleon coupling is s si\ P </>• . (13) if the np mass difference is taken into account and E ss M assumed. Keeping the terms of first order in 6 = (Mn - Mp)/(Mn + Mp) and using the commutation rules of the Pauli matrices gives the coupling in the form In pion exchange between two nucleons the second term leads to a class III interaction, the third one combines to give a nonrelativistic CSB potential of type of eq.
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