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LOW ENERGY AND NUCLEAR PHYSICS, P AND T VIOLATION
C. Kim
To cite this version:
C. Kim. LOW ENERGY AND NUCLEAR PHYSICS, P AND T VIOLATION. Journal de Physique Colloques, 1973, 34 (C3), pp.C3-33-C3-37. �10.1051/jphyscol:1973304�. �jpa-00215274�
LOW
ENERGY AND NUCLEAR PHYSICS,P
ANDT
VIOLATION*C. W. KIM (**)
Service de Physique ThCorique, Centre &Etudes NuclCaires de Saclay, BP 2, 91 190 Gif-sur-Yvette, France
RBsumB. - L'objet de ce rapport est de faire le bilan actuel sur les invariances P et T dans les interactions forte, Blectromagn6tique et faible, en particulier dans les domaines kle basse energie ou de physique nuclkaire. L'influence & l'introduction d'un potentiel nucleon-nuclkon violant la parite et les cons6quences qui en dkcoulent pour la physique nucleaire, sont discutks tout specia- lement.
Abstract. -A brief review of the present status on P and Tinvariance in strong, electromagnetic and weak interactions is presented. Emphasis is laid on the low energy and nuclear phenomena, in particular on the discussion of the parity violating nucleon-nucleon potential due to P violation in weak interactions and its effects on nuclear physics.
1. Introduction. - Tnvariances of physical laws under the discrete symmetry operators such as P, C and T are related to the impossibility of objectively defining the concept of right or left handedness, particle or antiparticle, and positive or negative flow of time, respectively. This impossibility, on the other hand, imposes on theories that describe physical laws certain restrictions so that the theories become simplified.
Ever-improving experimental techniques have reveal- ed that some of the supposedly non-observables turn out to be measurable, implying the break down of symmetry principles. The well-known examples are the violation of P, C and C P in weak interactions.
The purpose of this report is to review [I] the pre- sent status of P and T invariance in strong, electro- magnetic and weak interactions (in what follows, we assume the validity of the CPT theorem ; this is the reason why the invariance under C i s not discussed here). We shall discuss, in particular, various experi- ments that have been used and can be used in the future to test the symmetries, with special emphasis on low energy and nuclear phenomena.
In section 2, a summary of experiments to test P invariance is given. Emphasis will be on the dis- cussions of the parity-violating nucleon-nucleon potential due to the P violation in weak interactions and its effects on nuclearphysics. In section 3, we review
(*) Work supported in part by the National Science Foun- dation.
(**) On leave from Department of Physics, The Johns Hopkins University, Baltimore, Maryland, USA.
the present status of Tinvariance in strong, electroma- gnetic and weak interactions.
2. P invariance. - The concept of parity as a good quantum number for physical systems was introduced by Wigner in 1927 in connection with the selection rule for atomic spectra. However,, serious consideration had never been given to parity until the discovery of the violation of P invariance in weak interactions. Since then, various experiments have been performed to test P invariance in the strong, electro- magnetic and weak interactions.
The test is based on essentially two methods.
The first method is to look for the violation of a parity selection rule flue to the presence of the parity- violating ~amiltoni'an. This approach has been 'used to test parity violation in the strong interaction.
The best known (and the most recent) example of this type, which looked- for the decay
(normal a decay <s absolutely forbidden if P is con- served), indicates that P invariance is valid to
The second method is to look for a pseudoscalar interference term of the type p . q in the differential transition rate (p and a are, respectively, the momen- tum and the spin angular momentum) of one (not necessarily the same particle) of the particles involved in a reaction. The presence of this term implies, for example, a longitudinal (or circular) polarization of final particles with non-zero spin or anisotropic
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973304
C3-34 C . W. KIM angular distribution of a final particle with respect to the spin direction of another particle.
The original experiment of Wu and her collaborators employed this method to show that the violation of P is indeed maximal (in the sense that the coefficient of the a.p term takes the value maximally allowed) in P-decay.
Tests of P invariance in the electromagnetic inter- actions of hadrons are also based on this method, for example, the measurement of asymmetries in nuclear y-ray emission due to the admixture of the regular, say, M 1 transition and the irregular (parity- violating) E 1 transition. The admixture leads to an asymmetry in y-rays emitted by a random assembly of nuclei. The experiments on the transitions in '14Cd, 17'Lu, lS1Ta,
...
indicate that P invariance is also valid to lov6 [I].It is, therefore, safe to conclude that P invariance holds to a high degree of accuracy
-
lod7)in the strong and electromagnetic interactions, while P violation in the weak interaction is maximal. It is crucial to notice that the accuracy of P invariance in the strong and electromagnetic interaction is, in fact, consistent with the order of magnitude of P violation in nuclear levels due to the P violation in weak interactions. Therefore, if P invariance for the strong and electromagnetic interactions is assumed, positive results of P violation experiments can be used to investigate a parity-violating nucleon potential arising from the weak Hamiltonian and eventually the weak Hamiltonian itself. In the following we shall discuss this subject in detail.
We start with the conventional Cabibbo current- current weak Hamiltonian density [2]
Ja(x) = lF)(x)
+
lp)(x)+
cos 0 j?=O(x)+
+
sin 0jp=
'(x),
(2) where G = 1.02 x 10-~/m; and 6 0.2 is the Cabibbo angle. In eq. (2) the lepton current isand j r Z 0 ( x ) and j,d"='(x) are, respectively, the stran- geness-conserving and strangeness-changing hadron currents which consist of the vector and axial-vector currents. The weak Hamiltonian in eq. (1) and (2) leads to a weak (parity-violating) nucleon potential
vPV,
whose strength is of the order-
lo-'compared to the usual strong interaction potential V.
This parity-violating potential VPV is responsible for parity impurities in nuclear levels and is also respon- sible for the observed <c parity-forbidden )) a-decay of 160(2-), mentioned above. In the case of electro-
magnetic interactions, the matrix elements of the hadron electromagnetic current j;'"'(x) are modified in two ways :
where $, and t,bi. are eigenstates of the original parity- conserving Hamiltonian, and j,"m'PV(x) is the effective parity-violating current simulated by the weak Hamiltonian and has the strength of
-
times j,"."'(x) if the origin of this current is from the weak Hamiltonian of eq. (1). The effects of j,"'m.Pv(x) in nuclear matrix elements are, in general, negligible because of its divergencelessness 131. The states
JIi
and $; are eigenstates of the new total Hamiltonian including VPV and thus are admixtures of opposite parity states (see eq. (10) below).
2.1 PARITY-VIOLATING NUCLEON POTENTIAL. - First we shall discuss VPv. The AS = 0 part of Hw(x) responsible for VPV is given by (we are concerned only with the parity-violating part)
Since jfO(x) and j/=l(x) transform, respectively, as AI = 1 and AI =
4
objects, the cos2 0 term has AI = 0 and AI = 2 pieces, while the sin2 0 term has only a AI = 1 piece. It seems, from inspection of eq. (5), that the sin2 0 term may be negligible compared to the cos2 0 term. However, this is not the case since the contribution of the cos2 0 term to VpV is of rela- tively short range and hence also suppressed due to the hard core nature of the nucleon potential.The deduction of VPV from eq. (5) can be done by estimating the exchange of various mesons between two nucleons. In the case of the exchange of a single meson, one vertex is a weak one and the other a strong one. The exchange of no, a, yo,
...
does not give rise to any VPV if CP invariance is assumed and if off-shell effects of the nucleons are ignored [4].The exchange of a single n* gives contributions only to the AI = 1 part of VPV [l] ;
= f
8 J2-9
nm, ( c 1 + a 2 ) .whereg2/4n: = 1 4 . 6 , ~ ~ ~ = p1
-
p, a n d r =1
r, - r2 I.The coefficient f i n eq. (6) can be calculated, for example, from the value of the S-wave (parity-violating) amplitude for the process n + p
+
n', a(n?). Theamplitude a(n!-) is related to the experimentally observable amplitudes, a(=:) and a(&), by SU(3) 151,
where A is a constant which depends on the details of HW(x).
Using the experimental values of a(S1) and a ( k ) and eq. (7), one obtains
f z 2.7 x 1 0 - ' ~ . (8) It should be noted that the dependence of A on the details of Hw(x) is rather sensitive and, in fact, this sensitivity can be used to rule out immediately a number of specific models of Hw(x) when
v,PV
(in particular, f ) is known from experiment. For example, we have [6]
A = - (2)- '1' tan 0 g - 0.14
for the Cabibbo theory, A = 0 for the y,-invariant model of Segri and A is of order unity if the neutral currents are introduced. In spite of the reduction due to the sin2 0 factor, ViV remains important because of its long range nature.
The parity-violating nucleon potential from the vector meson (JP = 1-) exchange, e. g.
vY,
can beobtained from the cos2 0 part of H~"(X) in eq. (5) based on either the factorization approach or the current field identity and field algebra. The two methods give the same result [I] for the exchange of p* :
where g~ = 1.24 and pV is the isovector anomalous magnetic moment of the nucleons. It is to be noted that
vBv
has both A 1 = 0 and A1 = 2 pieces, and, as mentioned already, its effectiveness is reduced by the strong repulsion between nucleons. The contribution from the neutral p exchange vanishes in the factori- zation approach, but is non-zero, in general.There will also be contributions from heavier mesons. However, the resulting potentials are of very short range because of their masses (> m,), so that their contributions are negligible due to the pre- sence of the hard core effect of the nucleon forces.
The two-body potentials due to the multi-meson exchange 171 (e. g. v;:) and to the three-body parity- violating forces [8] (F'ZV (3 body)) have been discussed in the past with some unsettled questions. In parti- cular, the two pion exchange effects lead to a potential
which is more effective than that of p exchange due to its long range. However, in order to avoid double counting, the p-exchange part must be extracted from this. The AI = 1 part of the two pion exchange potential is roughly of the same order of magnitude as that of one pion exchange or less.
Finally, an isovector potential VPV (2nd class) due to the presence of possible second class currents [9]
has also been discussed. Calculations indicate that the contribution of VPV (2nd class) is comparable to that of
v,!"
(AI = 1) if the upper limit which is allowed by the present experiments such as the ratios of the ft-values is used.2 . 2 NUCLEAR STATES WITH MIXED PARITY. - In the presence of VPv, any nuclear state
I
$a>
can beexpressed as, in the first order (in G ) perturbation theory,
where $LP) represents the eigenstates of the parity- conserving part of the total Hamiltonian with parity P is then the wrong parity state) and
The presence of the wrong parity states in eq. (10) gives rise to the violation of a parity selection rule and a pseudoscalar component in a transition amplitude, as mentioned earlier. We shall discuss the following three examples of relative importance.
2 . 3 EXAMPLES. - 2.3.1 160 -+ 12C
+
a. - The transition rate of 160(2-) -t 12C(O')+
a(O+)is given by
(12)
<
b ; 2 '1 vPV
12-(8.87MeV)>
3i,b = E(8.87 MeV) - Eb 7
where
I
b ; 2'>
are the JP = 2' states of 160 which are admixed into the original JP = 2-, 1 = 0 state by VPV, S is a strong interaction decay operator, andI
$f>
= 1 12C+
CI>.
In this case only the AZ = 0 part of VPV contributes to the decay (predominantly p exchange). The theoretical calculations 1101 with the use of :V in eq. (9) give the values,depending on the nuclear models used, while the most recent experimental value is [8]
This may be regarded as an agreement between theory and experiment, giving some support to the p-exchange potential in eq. (9). However, independent experi-
C3-36 C. W. KIM mental confirmation and more refined calculations are desirable.
2.3.2 n
+
p -+ d+
y. - The parity-violating potential VPV gives rise to a circular polarization, P,,, of the emitted photon. The circular polarization is, in general, given bywhere
<
OL>
is the dominant regular electro- magnetic multipole amplitude and (((3c
)) is thecorresponding irregular multipole amplitude. In the reaction, n
+
p + d+
y ,<
M 1>
is the dominant amplitude and only the AI = 0 part of VPV contributes.Furthermore, only the first term in eq. (14) contributes.
Since the binding energy of the deuteron is small, the two nucleons involved are essentially free and thus this reaction is particularly simple from a theo- retical point of view. The observed value of P, in recent experiments [I I]
is, however, in poor agreement with the theoretical estimates, the theoretical values [12] being roughly one to three orders of magnitude smaller than eq. (15).
The origin of the discrepancy is not clear at the moment.
2 . 3 . 3 Transition in '"Ta. - The 482 keV transi- tion in 18'Ta is the most intensively studied example in the parity-violating effect. The transition is a mixture of M 1 and E 2 to which VPV admixes E 1. Numerous experimental values cluster around the value [8]
On the other hand, various calculations [8] with eq. (6) and (9) and with the use of the best available nuclear waves functions and short range correlations seem to fail to reproduce the experimental value in eq. (16), the theoretical values based on the Cabibbo theory being typically one order of magnitude smalle~
than eq. (16). In this transition; as in most complek nuclear cases all three parts of
vP\
AI = 0, 1, 2 contribute so that boeh VZV and V; are expected to play roles. Before we conclude hastily that the conventional Cabibbo theory fails (e. g. the need for neutral currents) it is necessary to further investigatevPV
as well as nuclear physics problems. Several attempts [13] (e. g. a giant dipole dominance approach) are in progress to sharpen up the nuclear physics part. Attempts [14] to account for the discrepancy by modifying VPV, in particular,VF
andv;:
arestill unsatisfactory. More theoretical and experimen- tal investigations of n
+
p ++ d+
y andn+
d ++ 3H+
yare also desirable to pin down the cause of the problem.
3. T invariance. - First serious attention has been paid to the validity of T invariance only after the discovery of P violation. In addition the discovery of C P violation in the neutral K-decays has.simulated much interest in T invariance since the violation of CP, together with the C P T theorem, clearly indicates the violation of T in the decays.
We shall again discuss two methods of test. The first method makes use of microreversability based on T invariance. If the Hamiltonian commutes with T, it can be shown that the transition rate A (i -+ f ) is the same as the transition rate A (f, -+ i,) where i, and f, are, respectively, the time-reversed initial and final states. Some care must be taken, however, since in the case when the reaction can be described by the Born approximation one can show from the hermiticity of the Hamiltonian alone that
even if T is violated. Thus, a negative experimental result does not necessarily imply T invariance unless experimental accuracy exceeds that of the Born approximation.
This method is widely used in testing T invariance in strong interactions. Experiments [15] with the processes such as a
+
2 4 ~ g o 27Al+
p,suggest that T invariance holds to -- in the strong interactions. Recent detailed balance tests with the reactions, y -i d o n
+
p and y+
n o n-+
p, are still inconclusive [I 61.The second method is to look for a correlation of the type a.(p x p'). This triple product changes the sign under T (both angular and linear momenta change sign under T). The classic example of this type of the test is the measurement of the electron- neutrino angular correlation with respect to the spin direction of the neutron in neutron P-decay. Recent experiments [I71 have set the limit on the coefficient D of the triple product :
D = 0.01
+
0.01 for n -+ p+
e-+
= 0.002f 0.014 for ' ' ~ e -+
+
e'+
v,.
(19) It has been pointed out [18], however, that such P-decay tests between mirror pairs of nuclei only test T invariance due to first class currents, but not second class ones. In order to test unambiguously 'the presence of T violating second class currents, one must look for the triple product in the processes where initial and final states are not the members of the same isomultiplets, e. g.
The contribution ,t the second class currents, both T conserving arLd T violating, is, in general, suppressed either by some symmetries or by kinematics. In the
case of 32P decay, the unusual suppression of the Gammow-Teller matrix element enhances the effect of the T-violating second class current. The calculated asymmetry coefficient D based on the maximal T violation is of order
-
10-I [lg], [I91 which can be detected with the present experimental technique.Other tests of this type are the studies of the corre- lation 6,. (p, x p,) in the decay K -, n
+
p+
v [20]and the correlation a,.(o, x p,) in the decay A -, .n-
+
p [21] ; the latter, however, is difficult to analyze because final states interactions are impor- tant. The present results indicate that there is no evidence of T violation in weak interactions except in the neutral K-decays. In some decays, even maxi- mal violation of T is not ruled out experimentally.T invariance (or its violation) in the electroma- gnetic interactions has also been a subject of consi- derable interest since the discovery of C P violation in the K-decays. It has been proposed that the C P violation effects in the neutral K-decays could be due to a break-down of C (or T since P is known to be conserved to a high degree of accuracy) in the electromagnetic interactions of hadrons. So far, no violation of T has been found within the experimental error of about one per cent in the experiments which involve elementary particles [22].
Nuclear tests of T invariance essentially look for a phase difference in a mixed y-transition (e. g. M 1
+
E 2). If T invariance holds, then the relative phase angle cp between the mixed multipoles is 0 or n. As mentioned already, the effect of the phase difference introduces asymmetry terms into expres- sions for angular correlations ; e. g. the correlation a.(kl x k,), whose coefficient is proportional to sin 9, is measured using an initially polarized nucleus which decays by a y-y cascade. The most recent measu- rement yields [23]s i n q
-
(4 f 5) xin the P-decay of lg21r.
The T-violating (or C-violating) electromagnetic currents have no consequences for nucleons on their mass shell because of the requirement of the hermi- ticity and conservation of the current [24]. Conse- quently, T-violation, if any, would appear through the off-mass shell effects of the nucleons inside the nucleus and hence the effect is strongly suppressed.
Several calculations [25], though difficult because of the lack of an adequate theory, indicate that the T-violating effects are typically of order
-
evenfor the cc maximal )) violation of T in the electro- magnetic interactions, at least in nuclear cases.
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