Semileptonic Processes Research Articles

A Divergence of Semileptonic processes in Current Algebra of Gauge Theories

A Divergence of Semileptonic processes in Current Algebra of Gauge Theories

Renormalizable SU(3) × SU(3) Model of the Weak Interaction

A new model of the weak interaction is presented. The renormalizable model, which is based on an SU(3) \ifmmode\times\else\texttimes\fi{} SU(3) intermediate scalar boson coupling scheme, reproduces the successes of the standard ($V\ensuremath{-}A$) theory for leptonic and semileptonic processes. Hadronic $\ensuremath{\Delta}Y=1$ processes arise in the model exclusively from finite one-loop diagrams and obey an exact octet rule. The analogous $\ensuremath{\Delta}Y=0$ graphs renormalize the quark masses to give finite mass differences within isotopic spin multiplets; when added to the electromagnetic mass differences within multiplets, this effect gives a good account of these mass splittings.

Higgs scalars in semileptonic processes

Interactions of Higgs scalars are discussed in a gauge theory of weak interactions. The construction of the mass matrix for fermions in vector-like theories similar to the gauge theory is also discussed, a few possible extensions of the gauge model to include hadrons and corrections to interactions of weak charged currents due to exchanges by Higgs S± -scalars. It was shown that due to these corrections apparent breaking of the Callen-Freiman relation for Ke3 form factors is possible, but the GoldbergerFreiman relation survives in its original form.

Unified Weak-Electromagnetic Gauge Schemes Based on the Three-Dimensional Unitary Group

SU(3)\ifmmode\times\else\texttimes\fi{}U(1) and chiral SU(3)\ifmmode\times\else\texttimes\fi{}SU(3)\ifmmode\times\else\texttimes\fi{}U(1)\ifmmode\times\else\texttimes\fi{}U(1) models for the weak and electromagnetic interactions of leptons and hadrons are proposed. The usual quark model for hadrons as well as the usual Cabibbo rotation scheme is assumed. Symmetry-breaking effects due to inequalities in the masses of the gauge bosons are considered. By making a simple choice of the gauge boson masses based on the $U$-spin subgroup of SU(3), the undesired $|\ensuremath{\Delta}S|=2$ weak nonleptonic transitions can be completely eliminated and the undesired $|\ensuremath{\Delta}S|=1$ neutral current semileptonic transitions drastically suppressed. These models can reproduce the ordinary phenomenological weak interaction but are sufficiently flexible to give the possibility of interesting new effects for neutral leptonic and semileptonic processes, as well as to allow the possibility of an over-all arbitrariness in normalization for the effective nonleptonic interaction. Another consequence of the present scheme is the existence of very heavy leptons. A brief discussion of including the strong interactions in a grand unification is also presented.

CP-Violation in the Renormalizable Theory of Weak Interaction

In a framework of the renormalizable theory of weak interaction, problems of CP-violation are studied. It is concluded that no realistic models of CP-violation exist in the quartet scheme without introducing any other new fields. Some possible models of CP-violation are also discussed. When we apply the renormalizable theory of weak interaction1l to the hadron system, we have some limitations on the hadron model. It is well known that there exists, in the case of the triplet model, a difficulty of the strangeness chang­ ing neutral current and that the quartet model is free from this difficulty. Fur­ thermore, Maki and one of the present authors (T.M.) have shown2l that, in the latter case, the strong interaction must be chiral SU ( 4) X SU ( 4) invariant as precisely as the conservation of the third component of the iso-spin 13 • In addi­ tion to these arguments, for the theory to be realistic, CP-violating interactions should be incorporated in a gauge invariant way. This requirement will impose further limitations on the hadron model and the CP-violating interaction itself. The purpose of the present paper is to investigate this problem. In the following, it will be shown that in the case of the above-mentioned quartet model, we cannot make a CP-violating interaction without introducing any other new fields when we require the following conditions: a) The mass of the fourth member of the quartet, which we will call (, is sufficiently large, b) the model should be con­ sistent with our well-established knowledge of the semi-leptonic processes. After that some possible ways of bringing CP-violation into the theory will be discussed. We consider the quartet model with a charge assignment of Q, Q -1, Q -1 and Q for p, n, A. and (, respectively, and we take the same underlying gauge group SUweak (2) X SU(1) and the scalar doublet field cp as those of Weinberg's original model.1l Then, hadronic parts of the Lagrangian can be devided in the following way:

Possible inconsistencies in calculations of semi-leptonic processes involving charged Higgs-Kibble scalars

Recently calculations have been made on various models of unified theories of weak and electromagnetic interactions. The Salam-Weinberg (1) model is essentially in difficulty owing to the existence of neutral currents, while the Georgi-Glashow (2) fivequark model gives an unacceptably large value for KL--> ~ . Models incorporating the cancellation mechanism of Glashow-Maiani-Iliopoulos (GMI)(8) give a zero value for KL-+ ~ t when there is an S U 4 invarianee among the quarks. The Lee-Prentki-Zumino model (LPZ)(4) is one such model. Some authors assume that the charmed and corresponding uneharmed quarks have a nonzero mass difference. Given this assumption, the data for K L ~ t and K1-K 2 mass difference give incompatible bounds on the quark mass differences (5). However since strong-interaction effects are appreciable in the K1-K 2 mass difference such considerations do not rule out the model completely. In this note we discuss how plausible any quanti tat ive calculations are for models such as LPZ for semi-leptonic processes. I t seems to us that present calculations should be regarded with some scemptieism. We find that we are unable to calculate ]~ and ]z mutually consistently. Unfortunately purely leptonic processes yield rather trivial constraints on the model. An analysis of ~.-e scattering data gives a lower bound on the mass of the charged Higgs-Kibble (6) scalar of 3 MeV! We consider K h and Kt~ decays since the data are reasonably good. In addition to vector-boson exchanges, Higgs-Kibble particles can be exchanged (eft Fig. 1, 2 and 3)

Muon pair creation via two-photon exchange in charged-particle collisions. II.—Hadron collisions

Muon pair creation via two-photon exchange in charged-hadron collisions is discussed on the basis of a numerical calculation as well as an analytical formula. The form factor and also the large mass of hadrons make this cross-section very small for a large invariant mass of the muon pair at low energies. However, at extremely high energies and for not so massive muon pairs the present process becomes comparable with other semi-leptonic processes. This process may be measurable at NAL energies. We also briefly discuss theq 2 dependence of the missing-mass spectrum in the ordinary deep inelastic process on the basis of a muon-parton analogy.

Neutral-Current Effects in a Class of Gauge Field Theories

Neutral-current couplings constitute a distinctive feature of certain models of weak interactions based on the idea of broken gauge symmetry. We discuss the observational implications for semileptonic processes; in particular, the relations among the inclusive ($\ensuremath{\Delta}S=0$) reactions $\ensuremath{\nu}+N\ensuremath{\rightarrow}\ensuremath{\nu}+X$, $\ensuremath{\nu}+N\ensuremath{\rightarrow}\ensuremath{\mu}+X$, $e+N\ensuremath{\rightarrow}e+X$. For $I=0$ targets, and with no further dynamical assumptions, we find the theoretical bound $\frac{{\ensuremath{\sigma}}^{(\ensuremath{\nu}\ensuremath{\rightarrow}\ensuremath{\nu})}}{{\ensuremath{\sigma}}^{(\ensuremath{\nu}\ensuremath{\rightarrow}\ensuremath{\mu})}}\ensuremath{\gtrsim}0.14$ for neutrino energies above a few GeV. Additional theoretical input increases this lower bound to 0.24.

Experimental limit on the neutral current in the semileptonic processes

We have searched for example of the reactions v μ + n → v μ + n + π° and v μ + p → v μ + p + π° in a large optical spark chamber as a test for the presence of neutral currents in semi-leptonik weak interactions. No candidate for either reaction was observed. With 90% confidence, the upper limit for the neutral current reactions was found to be: ⦅σ(v n + p → v μ + π° + p) + σ(v μ + n → v μ + π° n)⦆ / 2σ(v μ + n → μ − + π° + p) < 0.14 .

Leptonic and semi-leptonic weak interactions

New results on leptonic and semi-leptonic weak processes are reviewed. Recent references on this subject are accumulated.

Effects of a Neutral Intermediate Boson in Semileptonic Processes

The observable effects of a neutral intermediate vector boson in semileptonic processes are considered in the context of a proposed renormalizable theory of the weak and electromagnetic interactions. With strange particles neglected, this theory allows the calculation of neutral-current form factors in terms of charged-current form factors and electromagnetic form factors. The results are neither confirmed nor refuted by present data. One possible method of incorporating the strange particles is briefly discussed.

Violation of the|ΔI→|=12Rule in theKl3Decays

The violation of the $|\ensuremath{\Delta}\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}|=\frac{1}{2}$ rule in the ${K}_{l3}$ decays is discussed in detail. The effect of broken symmetry on weak hadron currents is taken into account by applying the hypothesis of asymptotic SU(3) and SU(2) symmetries. No assumption is made about the mechanism of the SU(3) and SU(2) breakings except that both of them belong to an octet. The main effect turns out to be described essentially by the effect of the particle mixings which take place among the ${\ensuremath{\pi}}^{0}$, ${\ensuremath{\eta}}^{0}$, and ${{\ensuremath{\eta}}^{\ensuremath{'}}}^{0}$ (958) mesons. It is shown that one of the solutions for these mixing parameters, which is compatible with the SU(3) and SU(2) mass splittings between the members of the pseudoscalar nonet, gives rise to a rather sizable violation of the $|\ensuremath{\Delta}\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}|=\frac{1}{2}$ rule in the branching ratios, and in particular, the sign of the violation is opposite to the one obtained by the usual consideration of the electromagnetic correction involving charged leptons. The solution predicts ${R}_{e}\ensuremath{\simeq}\frac{\ensuremath{\Gamma}({K}_{L}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{e}^{\ensuremath{\mp}}\ensuremath{\nu})}{2\ensuremath{\Gamma}({K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{e}^{+}\ensuremath{\nu})}\ensuremath{\simeq}0.94$ and also ${R}_{e}\ensuremath{\simeq}{R}_{\ensuremath{\mu}}$, where ${R}_{\ensuremath{\mu}}$ is the corresponding branching ratio for the muon decays. This seems to be consistent with the latest compilation of world data. A remark is also added on the semileptonic baryon processes in broken SU(3) and SU(2) symmetries.

Test of Lepton Quantum Numbers by Muon Capture

It is shown that the $\ensuremath{\Delta}Q=2$ semileptonic process can be tested by experiments on muonic atoms. The $\ensuremath{\Delta}$ resonances in nuclear ground states will lead to a ${\ensuremath{\mu}}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{+}$ reaction presently observable if the $\ensuremath{\Delta}Q=2$, $\ensuremath{\Delta}S=0$ interaction is within about two orders of magnitude of the ordinary strangeness-conserving interactions. The consequences for various lepton schemes is discussed.

Current-Current Interaction and Calculation of the Nonleptonic Baryon Decays

Arguments are given why the nonleptonic weak interaction should, in a quark model with neutral-vector-boson strong interaction, be calculable in terms of low-energy contributions, which can be estimated from the knowledge of semileptonic processes. Fair agreement with experiments seems to support this possibility. The suggestion is also made that this model could be very helpful in understanding many properties of electromagnetic and weak interactions.

Status of the Cabibbo theory

Abstract The Cabibbo theory of semi-leptonic processes is examined on the basis of recent experimental and theoretical results. Although the gross features of the experimental situation conform with the theory, the detailed analysis is not completely satisfactory at the present time. Thus, the Ke3 decay rates, the neutron lifetime, the Ξ− beta-decay rate, the asymmetry αΣ−e(Σ− → n + e + ν), and the 26Al ft value require explanation or further precise experimentation. The problem of universality of weak interactions is discussed on the basis of two models which assume the validity of current algebra at small distances and for which the secondorder radiative corrections to GV/Gμ are finite: the first assumes a special form for the space-space part of the current algebra, the second assumes the existence of the intermediate boson. Although the present experimental situation as described by the 14O data is consistent with both models, it is possible that a clarification of the Ke3 decay rates and the “26Al problem”, as well as precise calculations of symmetry-breaking corrections to Ke3 amplitudes, may discriminate against one of them. The need for accurate calculations of second-order symmetry-breaking effects to vector matrix elements and of electromagnetic corrections of order Zα2 is emphasized.

The selection rules in the feinberg and pais field theory of weak interactions

The peratization method of Feinberg and Pais is applied to semi-leptonic processes. A matrix formalism is presented which makes it possible to treat these processes in a way closely similar to what is done in the simpler case of the purely leptonic processes. It is shown that, when peratization is applied to contributions of the higher order graphs,a) the concept of universality and the CVC theory remain meaningful andb) the set of selection rules implied by a one-boson-exchange approximation remains unchanged to the orderg2. In particular, if the fundamental Lagrangian involves no ΔS=−ΔQ or |ΔS|=2 currents, such selection rules as ΔS/ΔQ 1 and ΔS≠2 are still valid.