theoretical aspects of searches for time reversal violation in neutron...

THEORETICAL ASPECTS OF SEARCHES FOR TIME REVERSAL VIOLATION IN NEUTRON TRANSMJSSJON

a

'eter Herczeg

rheoretical Division, T-5, Los Alamos National Laboratory, -os Alamos, NM 87545

-

To be published in the Proceed inas of the WorkshoD on 'aritv and Time Reversal Violation In ComDo und Nuclear States and Related Tooicg, October 16-27, 1995, Trento, taly

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THEORETICAL ASPECTS OF SEARCHES FOR TIME REVERSAL VIOLATION IN NEUTRON TRANSMISSION

PETER HERCZEG Theoretical Division, Los Alamos National Laboratory,

Los Alamoe, NM 87545, USA

In nonleptonic nuclear processes one can probe time revend violating interactions which conserve flavor. We discum such interactions and their manifestations in the nucleon-nucleon interaction. Among nuclear physics experiments studies of the transmission of polarized epithermal neutrons appear to be the most sensitive tools to probe for time reversal violation in the nucleon-nucleon interaction. We consider what sensitivitics are required for neutron transmimion experiments to obtain new information on flavor-conacrving time r e v e d violating interactions.

1 Introduction

It has been known for some time that the transmission of low-energy polarized neutrons through oriented targets may provide a sensitive tool to probe for time reversal violating (TV) interactions. Research on this possibility was stimulated by observations of very large parity violating (PV) effects in the transmission of polarized epithermal neutrons at pwave compound nucleus resonances [l]. A PV observable in transmission‘experiments is the quantity

PP = (fl$ - fl’_)/(d+ + g:) > (1) where d+ (d-) is the total neutron-nucleus cross-section for neutrons polarized parallel (antiparallel) to its momentum. A nonzero pp is given rise by the presence of a (8n) + kn term (Zn and kn are the neutron spin and momentum) in the neutron-nucleus elastic forward scattering amplitude. While the characteristic size of P-violating effects in low-energy nucleon-nucleon (N-N) scattering is - [2], values of p p as large as 10” have been observed at some gwave compound resonances [l]. The large effects have been explained [3] as due to “dynamical enhancement” (enhancement resulting from the small difference in the energies of the pwave resonances and the neighboring s-wave resonances) and to “resonance enhancement” (caused by ys >> yp, where yp and ys are the neutron widths of the pwave resonance and of the admixed s-wave resonance, respectively).

In the presence of interactions which violate simultaneously P- and T- invariance, the neutron-nucleus elastic forward scatterin amplitude contains (for polarized targets) a term proportiona1 to (Zn) +in x (J f (f is the spin of the target nucleus) [4]. A P- and T-violating (PVTV) observable is the quantity

4 L

1

c

PP,T (6+ - 6-)/ (6+ -f- 6-) , where a+(a-) is the total neutron-nucleus cross-section for a neutron polarized parallel (antiparallel) to &, x (JJ . The important point which was made [5] is that p p , ~ is enhanced by the same factors as pp. Therefore a measurement of p p , ~ at a resonance which exhibits a large PV effect can be expected to provide a sensitive probe of PVTV interactions.

Experiments which search for PVTV probe also the presence of P-conserving T-violating (PCTV) interactions, since a PCTV interaction combined with the usual weak interaction generates PVTV effects. The resulting limits are considerably weaker than for PVTV interactions because of the participation of the weak interaction. The presence of a PCTV interaction can be probed in neutron transmission experiments also directly, i.e. through a P-conserving T-violating observable. In the presence of PCTV violation the elastic neutron- nucleus forward scattering amplitude contains for targets of spin 2 1 a term of the form (Z,, . x (J l ) (&, + ( J l ) [SI. A PCTV observable is the quantity

pr (a+ - a,)/(a+ + a,), (3) where T+ (a,) is the neutron-nucleus total cross section for neutrons polarized parailel (antiparallel) to g,, x (~1.

If the CPT theorem holds, as is the case in gauge theories, T-violating interactions violate also CP-invariance [?I. In the following we shall assume that the terms “CP-violation” and “T-violation” are interchangeable. CP- violation has been seen so far only in the neutral kaon system. The origin of this effect is still unknown. In the KO - K system only the CP-violating parameter E is known to be nonzero, with a magnitude irl H 2 x [8]. The most economical explanation of E is that it is a manifestation of the weak interaction of the Standard Model (SM) [9]. In the SM the coupling of the W to the quarks generates in second order in the weak interaction (fourth order in the W-quark couplings) an effective A S = 2 CP-violating interaction proportional to the Kobayashi-Maskawa (KM) phase 6, which can account for the observed size of e. Alternatively, the observed E may be due to an interaction residing in an extension of the SM. For example, it can be due to the first order effect of a A S = 2 interaction of strength - 10” of the weak interaction (the superweak model [lo]).

The T-violating interactions that can be probed in nonleptonic nuclear processes conserve flavor (strangeness, charm, . . .).

PVTV flavor conserving (Af = 0) CP-violating interactions appear in many models with CP-violation. One such interaction is the @-term present

4

.

2

in the QCD Lagrangian in the SM. The &term has negligible effect on CP- violation in the neutral kaon system, but it can give observable effects else- where, for example a neutron electric dipole moment at the present experimental limit. The KM phase in the SM generates a PVTV Af = 0 CP-violating interaction only in fourth order in the W-quark couplings. The effects of this are too small to be measurable in the foreseeable future. Present searches for PVTV in Af = 0 nonleptonic observables are therefore searches for the #-term and for CP-violating interactions beyond the SM. In many extensions of the SM (e.g. in left-right symmetric models) Af = 0 PVTV interactions occur already in second order in the quark-boson couplings.

In the Standard Model PCTV Af = 0 interactions from the KM phase arise (as PVTV A f = 0 interactions) only in fourth order in the quark-boson couplings. The 9-term generates PCTV interactions only when combined with the weak interaction. Af = 0 PCTV interactions in the SM are therefore too weak to be observable. In extensions of the SM the situation regarding PCTV Af = 0 interactions is different then for PVTV Af = 0 interactions. For PCTV one can prove (111 that in renormalizable gauge theories neglecting the 9-term A f = 0 PCTV quark-quark interactions are absent to order f;, where fy denotes generically the coupling constants of the massive bosons YA(A = 1,2, . . .) to the fermions and the coupling constants of the interactions among the bosons YA. This conclusion holds to all orders in the CP-invariant component of the QCD interactions and to all orders in the QED interactions.

The best limits on T-violating A f = 0 interactions come from experimental limits on the electric dipole moment (EDM) of the neutron and on the EDM’s of atoms and molecules. Note that the A f = 0 T-violating interactions contribute to the EDM’s in the same order as to observables in nonleptonic nuclear processes.

In this talk we shall consider what sensitivities are required for neutron transmission experiments to obtain new information on Af = 0 T-violating interactions. Nonleptonic nuclear proc& are sensitive to T-violation through T-violation in the N-N interaction. In the next section we shall review the description of PVTV in the N-N interaction, consider the limits on the PVTV pion-nucleon coupling constants (which parametrize the PVTV N-N potentials) from the EDM’s, and discuss the implications of the EDM limits for the ratio p p , ~ / p p (see Eqs. (1)-(2)). In Section 3 we consider the same issues for PCTV. In Section 4 we summarize our conclusions.

This talk is based on a recent review article [12] by the author. We refer the reader to this articie for a more detailed discussion and more complete references.

3

2 Parity Violating Time Reversal Violation

PVTV in the low-energy N-N interaction can be described, in analogy with the description of time reversal invariant parity violation [2], in terms of a nonrela- tivitic potential VP,T derived (ignoring two-pion exchange) from one-meson exchange diagrams involving the lightest pseudoscalar and vector mesons. PVTV in the N-N interaction is parametrized in this description by the strength gg$N of the N -b N M matrix elements of the various isospin (I) components H f k of the effective PVTV flavor-conserving nonleptonic Hamiltonian

(4) 40 ( M N I H $ ! & l N ) a g M N N .

The lightest, mesons that can contribute to VP,T include the A*, I@, q, p and the w . There is a difference here with respect to PV, where the exchange of TO and 3 does not contribute to the PV potential Vp. Another difference is that PVTV pion-exchange exists for all the possible (I 5 2) isospin components of H ~ , T (see Eqs. (5)-(7) further on), while Vp receives a pion-exchange contribution only from the isovector component of Hp. In the following we shall consider only the contributions from pion-exchange, since the contributions from the heavier mesons are expected to be small [13].

There are three independent PVTV l rNN couplings (with the nucleons and the pion on their mass-shells) [14], which we can write in the form

where the r's are the isospin Pauli matrices. Note that only the no is involved in the I=l coupling.

The couplings (5)-(7) generate PVTV N-N potentials from diagrams where one of the vertices is the strong n N N coupling and the other is the PVTV one. The isoscalar PVTV N-N potential, for example, is given by [15]

where il2 = (?I - ?')/rl2 and f12 = 1.i - p'zl; ?k, & and ii ( h = 1,2) are the coordinates, spin and isospin Pauli matrices of the two nucleons; m~ is

4

.

the mas8 of the nucleon, g r N N is the strong lrNN coupling constant. The isovector and the isotensor potentials have a similar form [IS].

The most stringent bounds on J$TN come from the experimental limits on the electric dipole moment (EDM) of the neutron dn, and on the EDMs of some atoms and molecules.

Neutron Electric Dipole Moment. The experimental limit on the EDM of the neutron is [17]

- I(dn)etptl < 1.1 x ecm (95% C.Z.) . (9)

To obtain from (9) a limit on dzN one has to know the contribution of the ij:JN -coupling to dn .

A defensible calculation of dn in terms of the PVTV coupling of the charged pions to the nucleons was made in Ref. [18], employing sidewise dispersion relations. Sidewise dispersion relations 1191 have been used successfully to calculate the anomalous magnetic moment of the nucleon [20]. In Ref. [20] only the pion- nucleon intermediate state (the lowest mass intermediate state) contributing to the absorptive part of the amplitude was retained and the absorptive integral was cut off near threshold. Thus the input for the calculation was the strong N + Nn amplitude and the pion photoproduction amplitude near threshold. In the analogous calculation of dn the strong N + Nn amplitude is replaced by the PVTV T* N N coupling. The calculation yielded

(10) 4 0 ) ) 4v (dn)rpn N 9 x 1O-l' ( 9 , N N - g X N N ) ecm -

It is interesting to note that this value is very close to the contribution of the R - P loop diagram to dn in the limit m, + 0. The ?r-p loop contribution is the only source of the most singular (in m,) contribution to dn [ 2 1 ] .

The contribution of the PVTV r0nn coupling to dn has not been yet calculated in the dispersion relation approach. Although this contribution to dn is expected to be small relative to the charged pion contribution, it is nevertheless of interest, since the I = l PVTV T N N coupling does not involve the charged pions. The T O contribution is of the form

(11) 4w -0)' (dn),nn = k d (9 x 10'i5) ( - ~ , N N + g r N N - 2 9 ? i ~ )

(originating from the #nn terms in Eqs. (5)-(7)), where lkdl is a constant smaller than unity and, judging from the ratio (- loe2) of the experimental crosbsection for neutral and charged pion photoproduction at threshold [22], possibly as small as - 0.1. Neglecting in Eq. (11) the g r N N and g ,NN terms relative to those in Eq. (lo), we obtain

4 0 ) ) 4 2 ) )

5

The experimental limit (9) implies

(13) 4 0 ) l 4')l 4w b * N N + kd Q r N N - g*NNI c lo-'' *

A new experiment in preparation at the Institut Laue Langevin I231 is expected to improve the current limit on d,, by a factor of 5, and a proposed experimental technique offers the possibility of an additional improvement by about a factor 400 [24].

Atomic and Molecular Electric Dipole Moments. The most stringent experimental limit is on the EDM of the l g 9 H g atom [25]:

ld('99Hg)l < 8.7 x ecm

Atomic physics calculations (261 yielded the relation

(95% c.1.) ,

d ( l g 9 ~ g ) = -4 x 10-17(~s/efm3) ecm (15) between the EDM and the Schiff moment of '"Hg. The Schiff moments of several nuclei have been calculated in Ref. [27] using the PVTV N-N potential

where GF is the Fermi constant, &, ?& and $& (k = a,b; a = n,p; b = n,p) are the spins, coordinates and momenta of the nucleons a and b. For l g9Hg the result is

Q s ( l g 9 H g ) = (-1.4 x qnp efm3 , (17) The contribution of the PVTV noNN couplings to the constants qab can

be obtained by comparing the potential (16) with the zererange limit of the pion-exchange potentials.

For the constant qnp we find

-(O)' -(1)/ ('7nP) ,o = -(fi S * N N / G F m z ) ( g , N N + g r N N + &:$N). (18)

In the zenrange limit the potential (16) accounts also for the charged-pion contribution, if in the momentum-space PVTV N-N amplitude terns higher

6

than linear in the momentum variables are neglected [27]. This contribution to the constants f7,b and ?&, has not been worked out yet. Ignoring the charged- pion contributions, we obtain from Eqs. (15) (17) and (18)

~f(~"Hg) -5.0 x 10 -17 (grNN - ( O ) l +B!11?)~ + &:$N) ecm (19) Equation (19) and the experimental limit (14) imply

An improvement of the limit (20) by a factor of 10 seems possible [28]. A calculation of ~f('~'Hg) using the pion-exchange potentials is in progress [29].

The limits (13) and (20) are the most stringent limits on the PVTV pion- nucleon coupling constants. The next best limit, which comes from a measurement of a PVTV effect in a nuclear y-decay, is weaker by 4-5 orders of magnitude.

What are the implications of the limits (13) and (20) for the size of the cross-section asymmetry p p , ~ ? To give an answer, we shall estimate the ratio

in the idealized case when the admixtures of opposite parity states in the given pwave compound nucleus resonance are dominated by the contribution of a single s-wave resonance. Then X is given by [30]

where $, and &, are 5- and pstates of the compound nucleus, and nJ is a factor which depends on the pwave compound resonance spin and on the ratio of the neutron widths of the pwave resonance for the different channel spins [31].

The absolute values of the matrix element of VP,T and Vp between com- and pound nuclear states can be approximated by I(VP,,T),.~.IN~

I ( V P ) ~ . ~ . ] NC-l'l, where (VP,,T)..~. and (VP)~.~. are average single-particle matrix elements, and Nc is the number of single-particle states contained in the expansion of states of the compound nucleus [32]. We shall approximate the potentials Vp,r and Vp by effective one-body potentials.

The one-body potential corresponding to the sum of the PVTV pion- exchange potentials in the approximation when the two-body potentials are taken to be of zero range is [33]

-112

7

where

In Eq. (23) I: = F/r, r = Id; F, a‘ and r, are single-nucleon operators, and pn is the nucleon density in the nucleus. For Vp we shall take the I=O pexchange potential. The corresponding one-body potential is given by [34]

where g p N N is the strong p N N coupling constant, pv is the isovector anomalous magnetic moment of the nucleon, and WP 21 0.8. For the coupling constant g r g N we shall take in the following g$.gN = 2 x [34].

From Eqs. (23) and (25) we obtain for the ratio r in Eq. (22)

where

In Eq. (27) we have included some extra factors: the factor F(m,R)(R = nuclear radius), which accounts for the nonzero range of the pion-exchange potentials 1351, and the factors SjR and wP which account, respectively, for the suppression of the matrix element of the PVTV pion-exchange potentials and of the PV pexchange potential due to the short-range repulsion in the strong N-N interaction; the quantity /? is given by

Taking F(m,R) = 0.7 (valid for A ;L 170, which is satisfied for the cases we shall discuss), wp = 0.84 [36], g p N N = 2.79, g r N N = 13.45, z* = 0.95 [35], and U P = 1/3.6 [36], we obtain

K 2: 31.7p . (29) Investigations of the quantity p [37] led to the conclusion that a reasonable

value to use for A N 150 to 200 is /? N 0.2. A special case where /? is of the order

8

A

'hc

of 10 was pointed out recently in Ref. [38]. This occurs in the mixing between the states of parity doublets in nuclei with intrinsic octupole deformations. The PV matrix elements between such states are small due to specific cancellations [391*

The ratio A is given by

where

In Eqs. (31)-(33) we have assumed that n5 N 1 (see Eq. (22)). If this is not so, the limits given below can be easily adjusted.

For an I = 1 PVTV N-N interaction the limit (20) from d( lg9Hg) yields for A(') (taking p = 0.2, gpZN = 2 x

lA(')l < 6 x . (34) For the I = 0 and I = 2 interactions the best limits on A = A(') and A = A(2) are from d, (Eq. (13)). They are (taking (N-Z)/A = 0.18, which is the value for 13'La, and approximately the value for A z 130-170)

I A ( ~ ) I < 1.4 x 10-~ . t 36) The implication of Eq. (34) is that, barring a cancellation in Eq. (20),

p p , ~ has to be measured for p p = 10" with a sensitivity of 6 x to provide the same limit on 3tiN as d(lg9Hg).

In using the limits (34) - (36) it has to be kept in mind that they are based on a rough estimate, in which the theoretical uncertainty may be large.

It is intersting to note that if a nonzero d ( l g 9 H g ) is observed, then ac- cording to the results (34) - (36) a measurement of p p , ~ would enable one to tell whether the source of PVTV is an I=O or 2 PVTV interaction (e.g. the @-term), or an 1=1 PVTV interaction.

9

4

The first (and the only so far) measurement of p p , ~ was carried out in the experiment of Ref. [40], using a polarized lssHo target and 7-12 MeV incident neutrons. The experiment yielded ( p p , ~ ( < 5 x (95% c.1.). A measurement of the P-violatingeffect has also been performed, with the result (ppl < 5 x (95% c.1.). The implications for the PVTV nNN constants are not known. A neutron spin rotation experiment to search for PVTV is under preparation at KEK [41]. Note that the ratio of the P,T-violating and P-violating rotation angles is for twwtate mixing again proportional to ( ~ s , s l V p , , ~ l ~ ~ ) / ( l s ~ V p ~ ~ p }

-(I)' * In models with CP-violation given a limit on g r N N one is interested in the implied limit on the fundamental parameters of the models [42].

As we have mentioned earlier, in the SM there are two sources of CP- violation: the KM phase S in the quark mixing matrix, and the PVTV @-term in the QCD Lagrangian.

Since the contribution of the KM phase to the PVTV Af = 0 interaction is second order in the weak interaction, the one-boson exchange diagrams which generate the PVTV N-N interaction can include diagrams involving the K-mesons. The dominant diagrams have been found to be the K-exchange diagrams involving weak baryon 3 nucleon transitions. The resulting PVTV N-N interaction can be represented by a potential of the form (16) with 1431

1301.

qcb 5 10'' (37) and &b = 0 (a=n,p; b=n,p). The present upper limits are about 6 orders of magnitude weaker than (37). In Eq. (37) the equality signs would apply if 6 is responsible for the observed value of e.

The constant 4 0 ) ' grNN due to the &term has been calculated in Ref. E211 using PCAC and current algebra (note that 4 1 ) ' g r N N = g p i N = 0, since the &term is isoscalar. This approach yields

From Eq. (38) and the limit (13) one obtains

fel c 4 x 10-l~ . (39) In many extensions of the SM there are new CP-violating interactions. An example is the class of left-right symmetric models based on the gauge group S u ( 2 ) ~ x su(2)RX U ( ~ ) B - L [44). In these models A f = 0 PVTV a r k already in second order in the quark-gauge boson couplings. The part of the PVTV Af = 0 charged current nonleptonic interaction involving the u,d

10

quarks (which presumably dominates the N + Nlr matrix elements) con- tributes only to -41P gINN [16]. -41)' gINN is given by

JfiN = GF rn: k Cge sin(a + w ) , where is proportional to the Wt - WR mixing angle (WL and WR are the gauge bosons associated with SU(2)t and SU(Z)R, respectively), a and w are CP-violating phases, and k is a constant. The bound (20) from d(lg9Hg) implies

*ICge sin(a +w) l < 8.5 x lO"/k . Calculations find values of k in the range from - 4 to - 270. The limit (41) and a comparable limit from €' /e are the most stringent limits on ego

present experimental limit on gtLN. sin (a + w ) . Thus in left-right symmetric models 41)l gINN can be as large as the

3 Parity Conserving Time Reversal Violation

PCTV in the low-energy N-N interaction can again be described by an N-N potential (VT) derived from onemeson exchange diagrams. The strength of PCTV is characterized by the effective coupling constants &iN defined by

( M N I H ~ ) I N ) a # f ) N N . (42) Unlike for PVTV, one-pion exchange does not contribute to the PCTV N-N interaction [45]. Also, there is no contribution from pO-exchan e [45]. The

change of p* generates an isovector potential, and AI-exchange potentials of all possible (I 5 2) isospins [45,46].

In the following we shall consider for simplicity only the #-exchange contribution. The PCTV p N N coupling constant TpNN is defined by

lightest contributing meson is therefore the p*, and then the A, 8 , O . The ex-

The coupling constants q5p and gp ( $ p 3 gP) defined in Ref. [46] and Ref. [47], respectively are related to the coupling constant gpNN in Eq. (43) as gpNN = SpNN k ~ g p 14.6 g p -

The best direct limit on gpNN comes from the neutron EDM. The contribution to d, of the one-loop diagram involving the JpNN-coupling and the PV

-

11

n N N coupling constant g:NN [34] (which provides the parity violation) has been calculated in Ref. [48]. The result and the experimental limit (13) imply

where ( g : N N ) D D H (z 2.3 x is the recommended value of g:NN [48] based on the calculations in Ref. [48]. The experimental information on g:NN is IgkNNI < 6 x [%I. As noted in Ref. [47], independently of the value of g:NN an upper limit of a few times on (gpNNI from d,, probably cannot be evaded, since there are other diagrams involving g p N N , in which parity- violation comes from parity violating vector meson-nucleon-nucleon couplings.

A limit of (gpNN I ;S 0.7 follows from the experimental limit (20) on d ( l g 9 H g ) [47]. From nuclear physics experiments the best limit is IgpNNI s 1, obtained from the experimental limit on a PCTV effect in a y-decay of 57Fe [49].

An experiment to search for the PCTV cross-section asymmetry pr (Eq. 3) in neutron transmission (the only experiment of this kind so far) was carried out recently using 2 MeV polarized neutrons and an aligned l s sHo target [50]. An analysis [51] of the results of this experiment in terms of a PCTV opti- cal potential for neutron-nucleus scattering, generated by the gPNN-coupling, yielded the limit IgpNN I s 22. It is anticipated that this limit will be improved by a factor of - 150 [51].

PCTV A f = 0 four-quark interactions can be written in the form

where i = 1,2, j = 1,2; i # j [52]. Considerably stronger limits than (44) on g p N N induced by the interactions (45) have been derived from short-distance contributions of (45) to the neutron EDM [52,53]. In Ref. [53] a limit of g i 6 4 x has been set on 9% from tweloop contributions to dn involving an interaction of the type (45) and %exchange. Assuming that gpNN is of the order of (&/m%)m$, this implies IgpNN1 5 2 x GeVa/m$(IgpNNI S 3 x lo-'' for mx 2 mw). The limits from dn for operators involving quark currents which do not flip the chirality of the quarks are weaker. Such operators exist, but their dimension is eight and higher [54]. An analysis in the framework of effective Lagrangian indicates, assuming for the high-energy scale A (the scale associated with the unknown physics) the value A z 100 GeV, that for such operators ITpNN\ S [54].

In the Standard Model PCTV in the N-N interaction due to the KM phase b is expected to be of about the same size as the size of PVTV, i.e. - 10'' relative to the weak interaction (if 6 accounts for e), since both arise in 4th

12

order in the W-quark couplings. For le1 = 4 x 1O'O (the present experimental upper limit) the contribution of the 6-term would be expected to be also of the order of lo-' relative to the weak interaction, since to generate a P-conserving interaction the participation of the weak interaction is necessary.

As we have mentioned in Section 1, in any renormalizable gauge model neglecting the Pterm PCTV in the Af = 0 quark-quark interactions can be generated only in higher than second order in the non-QCD and non-QED couplings [ll]. The interaction (45), for example, can be induced by a triangle-type diagram involving a three-boson coupling and three boson-fermion couplings 1111. The twdoop contributions of (45) to dn become then three-loop diagrams and, as we note in Ref. 1111, the corresponding limit from dn will have to be therefore reexamined. The maximal strength of a triangle diagram is of the order of (1/8r2) ( q / M ) (1j41/Mi), where M is the mass of the heaviest particle in the triangle, and ij4 is a product of four coupling constants. A rough estimate of gpNN is therefore ~ , , N N 2: (1/8r2) ( ~ N / M ) (mz/m$)lij14 x sinqi, where qi is a CP-violating phase. With = ( e / s i n e ~ ) ~ one would have IgpNNI 5 2 x for M 2 mw, M x 2 mw. Presently we are investi- gating the constraints on some models where X is very light, with a mass of the order of a few GeV (Ref. 1551).

4 Conclusions

In nonleptonic nuclear processes one can probe T-violating interactions which conserve flavor. In this talk we discussed what sensitivities are required for neutron transmission experiments to obtain new information on such interactions.

Nonleptonic nuclear processes are sensitive to T-violation through T- violation in the N-N interaction. The parity violating time reversal violating N-N interaction is dominated (for comparable coupling constants) by pion exchange. The experimental bounds on the electric dipole moment of the neutron and of the Ig98g atom set stringent limits on the PVTV lrNN coupling constants. It appears that from nuclear physics processes only neutron transmission r e m a b aa a possible candidate for improving these limits. Based on the existing calculations and on a rough estimate of the ratio of the matrix elements of the PVTV and PV potentials, and barring cancellations in d( '99H9), in a case where the PV asymmetry is 10'' the PVTV asymmetry would have to be meaaured with a sensitivity of 6 x to compete with the existing limits. The neutron EDM sets at present the best limit on the @-parameter. The PVTV n N N coupling constants can be as large as the experimentd limits also in several extensions of the Standard Model. The contribution of the

13

Kobayashi-Maskawa phase to PVTV in the N-N interaction is about six orders of magnitude (if 6 accounts for e) below the present limits.

The parity conserving time reversal violating N-N interaction is governed by @-exchange and the exchange of heavier mesons. The best limit on the PCTV pNN coupling constant comes from the electric dipole moment of the neutron. The contributions of the KM phase and of the @-term to PCTV in the N-N interaction are expected to be at most of the order of relative to the strong N-N interaction. Theoretical investigations lead to the expectation that PCTV in the N-N interaction is small in any model, with a strength relative to the strong N-N interaction which is most likely below the strength of the weak interaction, and probably considerably so.

Acknowledgments

I would like to thank N. Auerbach for asking me to give this talk, and to J. D. Bowman for enlightening conversations. This work w8s supported by the United States Department of Energy.

References

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[31

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[51

The first observation of a large effect was reported in V. P. Alhenkov et al., Pis’ma Zh. Eksp. Teor. Fiz. 35, 42 (1982) [JETP Lett. 35, 51 (1982)]. Large effects were observed later in a number of other cases. For a review see J. D. Bowman, G. T. Garvey, M. B. Johnson, and G. E. Mitchell, Annu. Rev. Nucl. Part. Sci, 43, 829 (1993). For a review see W. Haeberli and B. R. Holstein, in Symmetries and Fundamental Interactions in Nuclei, edited by W. C. Haxton and E. M. Henley (World Scientific, Singapore, 1995), p. 17. 0. P. Sushkov and V. V. Flambaum, Pis’ma 2%. Eksp-. Teor. Fix. 32, 377 (1980) [JETP Lett. 32, 352 (1980)j; V. E. Bunakov and V. P. Gudkov, Z. Phys. A303, 285 (1971); Nucl. Phys. A401, 93 (1983). P. K. Kabir, Phys. Rev. D 25, 2013 (1982); L. Stodolsky, Nucl. Phys. B197, 213 (1982). V. E. B d o v and V. P. Gudkov, Pis’ma Zh. Eksp. Teor. Fiz. 36, 268 (1982) [JETP Lett. 36, 329 (1982)l; Z. Phys. A308, 363 (1982); Nucl. Phys. A401, 93 (1983). V. G. Baryshevsky, Yad. Fiz. 38, 1162 (1983) [Sov. J. Nucl. 699 (1983)); P. K. Kabir, in The Investigation of h h e n tions with Cold Neutrons, edited by G. L. Green, NBS Special Publication No. 711 (U.S. GPO, Washington, D.C. 1986), p. 81.

- 14

[7] Regarding the CPT theorem there is experimental evidence that the interaction responsible for the observed CP-violation violates T-invariance; see M. D&jardin, in Dark Matter in Cosmology, Clocks, and Tests of Fun- damental Lows, proceedings of the XXXth Rencontre de Moriond, edited by B. Guiderdoni, G. Greene, D. Hinds, and J. Trh Thanh Vin (Edi- tions F’rontieres, 1995), p. 571.

[8] For a review see B. Winstein and L. Wolfenstein, Rev. Mod. Phys. 65, 1113 (1993).

[9] The electroweak component of the Standard Model will be understood here to be the minimal version of the S u ( 2 ) ~ x U(l) gauge theory, con- taining three families of leptons and quarks, one Higgs doublet, and only left-handed neutrinos.

*

[lo] L. Wolfenstein, Phys. Rev. Lett. 13, 562 (1964). [ll] P. Herczeg, J. Kambor, M. Simonius, and D. Wyler, “Parity Conserv-

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[17] I. S . Altarev et al., Phys. Lett. B 276, 242 (1992); K. F. Smith et al., Phys. Lett. B 234, 191 (1990); see also L. Montanet et al. (Particle Data Group), Phys. Rev. D 50, 1173 (1994).

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15

(Editiona F'rontieres, 1995), p. 589. 1241 See S. K. Lamoreaux and R. Golub, in Dark Matter in Cosmology, Clocks,

and Tests of Fundamental Laws, edited by B. Guiderdoni, G. Greene, D. Hinds, and J. Trh Thanh V b (Editions F'rontieres, 1995), p. 597. See also R. Golub and S. K. Lamoreaux, Phys. Rep. 237, 1 (1994).

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[27) V. V. Flambaum, I. B. Khriplovich, and 0. P. Sushkov, Ref. [26]. [28] S. K. Lamoreaux and R. Golub, the first paper in Ref. [24]. [29] W. C. Haxton and K. Lee, in preparation, reported in W. C. Haxton,

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[30] V. E. Bunakov and V. P. Gudkov, Z. Phys. A308, 363 (1982); Nucl. Phys. A401, 93 (1983). For a review see V. P. Gudkov, Phys. Rep. 212, 77 (1992).

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[32] For a discussion of this approximation and references see B. Desplanques, J. de Phys. 45, C3 (1984).

[33] P. Herczeg, Ref. [16]. The onebody potentials given in this reference are in error by a factor of 4, as found in A. Griffiths and P. Vogel, Phys. Rev. C 43, 2844 (1991). We have included this factor in Eq. (23). The presence of the factor (N-Z)/A in the onebody potential corresponding to the I=O PVTV two-body force was noted already in W. C. Haxton and E. M. Henley, Ref. [15].

[34] See E. G. Adelberger and W. C. Haxton, Annu. Rev. Nucl. Part. Sci. 35, 501 (1985). The data require only the existence of an I = 0 PV N-N interaction. A fit to the data [E. G. Adelberger, in Proceedings of the International Symosium in Weak and Electromagnetic Zntemctions in Nuclei; Heidelberg, 1986, edited by H. V. Klapdor (Springer-Verlag, 1986), p. 592) in terms of the I = 0 PV p N N coupling constant g p N N and the PV r N N coupling constant g k N N (in the notation of Adelberger

and an upper limit of IgLNNI < 6 x for &NN' The latter bound is

4w

and Haxton, g p N N (0 ) l = h!, g:NN = f w / 2 ) yielded Q p ~ ~ (0)' 2 (2 - 3) x

16

such, that the pion-exchange term in V' is not more important for our estimate than the term proportional to g:sN.

(35) A. Griffiths and P. Vogel, Ref. [33]. I361 E. G. Adelberger and W. C. Haxton, Ref. [a]. [37] V. P. Gudkov, Ref. [31]; A. Griaths and P. Vogel, Phys. Rev. C 44,

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(421 Calculations of the PVTV pion-nucleon coupling constants in models were reviewed in our session at the Workshop by V. Gudkov.

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(1996).

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theoretical aspects of searches for time reversal violation in neutron...

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