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RECEIVEDAUG 291995

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LosAlamosNATIONAL LABORATORY

SEARCHES FOR T-ODD INTERACTIONS IN NUCLEARPROCESSES: REVIEW OF THE THEORY

Peter Herczeg

Theoretical Division, T-5, Los Alamos National LaboratoryLos Alamos, NM 87545

To be published in the Proceed inas of the Moriond ’95orkshog on Dark Matter in Cosmoloav. Clocks and Tests

gf Fundamental Law% Villars-sur-Ollon, Switzerland,January 21-28, 1995, edited by J. Tran Thanh Van,(Editions Frontiers, 1995).

u

.

SEARCHES FOR T-ODD INTERACTIONS IN NUCLEARPROCESSES: REVIEW OF THE THEORY

Peter HerczegThemetical Division

Los A.lamcm National Laboratory, Los Alarms, NM 87545

Am

We review brolly the theoretical aspects of +ime reversal violation in nuclear processes.

1. Introduction

CP-violation has been -n so far only in the neutral km system. Its origin is still un-

known. If the CPT theorem Imlds, as is the case in gauge thmries, CP-violating interactions

viol%e al.w time reversal (T) invariance. Regarding the CPT theorem there is ~me ex-

periment al evidencel J that the interaction responsible for the observed CP-violation violates

T-invarianm.

The obmmed CP-tiolation may just be a manifestation of the weak interaction of the

Standard Model (SM), or it is due to an interaction beyond the SM. In both cases mme of

the new interactions may give rise to observable CP-violation where the SM contribution

is invisible. This underlin~ the importance of searching for CP-violating and T-violating

efkcts in many proc.~.

In this talk2J we shall review what has been learned about T-violating interactions that

can be probed in nuclear processes horn experiments outside of and within nuclear physics,

and consider the role of nuclear physics experiments in obtaining Mher information on such

interactions.

2. T-Violation in

The T-violating

the Nucleon-Nucleon Interaction

part of the N-N interaction has both a parity violating and a parity

conser.hng component. The theoretical feat ur~ of t k are different, and we shall therefore

consider them separately.

2.1. Parity Violating Time Remruel Violation

As time reversal in-variant parity violation (PV) ,3) parity violating time revers41 violation

(PVTV) in the low energy N-N interaction can be described in terms of a nonrelativi~

tic potential Vp,~ derived (ignoring two-pion exchange) horn one-meson exchange diagrams

involving the lightest pseudoscalar and vector mesons. PVTV in the N-N interaction is

parametrized in this d=ription by the strength #~N of the N + NM matrix elements

of the various isospin (I) components of the effective PVTV flavor conserving non.lepton.ic

Hami!totian:

(1)

The set of mesons that can contribute to VP,T includm n*, To, q, p and U. There is a

difference here with respxt to PV, where the exchange of no and q does not contribute to

the P-violating potential VP. Another difference is t hat PVTV pion-exchange exists for all the

pssible (I ~ 2) isospin components of Hp,T, while Vp receives a pion-exchange contribution

only from the iwvector component of Hp, IrI the following we shall consider only the pion-

exchange IWTV potentials, since for comparable PVTV N - N-M coupling constants these

provide the dominant contribution to Vp,T.4)

The PVTV pion exchange potentials51 are generatd

violating rJVN couplings)~g:) = _(o)t

gXNN~~N . ; ,,

by the three independent P, T-

(~)

(3)

#)N , (4)

where the 7’s are the isospin Pad matrices.

2.1.1. Limits on #’N @m non-nuc[ew observable.

The most stringent bounds come born the experimental limits on the electric dipole

moment of the neutron & and on the ektric dipole moment of mme atoms and molecules.

Neutron Electric Dipole Moment.

of the neutron is7)

l(d7Jezptl < l-l

A dimensional argumenta) gives

The experimemal limit on the electric dipole moment

x 10-25 Wm (95% C./. .)

(5)-( )1

for the contribution of g=~~ to & the cize,-(1)1

.. . . . .

& ~ (e/mN) g=NN ~ 2 X 10-14 g~l;N ecm, which would imply 17j\r~Nl s 6 x 10-12.

A defensible calculation of & in terms of the PVTV mNN constants was made in Ref. 9

employing sidewise dispersion relations. The dominant contribution corms from the PVTV

m+ NN couplings The calculation yidded & = 9 x lo-15(~)jN –_(2)tg=~N) ecm. The contri.

bution of the rON intermediate state h= not beeri yet calculated. Although this contribution

to & is expectd to be small relative to the chargtxi pion contribution (owing to the small-

ness of the experimental cro~-sect ion for neutral pion photoproduct ion at threshold), it is

nevertheless of interest, since the I= 1 PVTV coupling does not involve the charged pions.

horn ‘he two independent nOhrNcoupling constants

15’ (1)1 -(2)fmnn = (-gy~N + ?mNN - 29=NN)

(6)

(’7)

(wLich are the coefficient of the row and r“nn terms in Eqs. (2)-(4)) only ~.nn contribut~

to &, Including formally this contribution, w have

(& & 9 X 10-15 (~$’N + k3#~N – r~2]N) , (8)

where k is a constant smaller than unity, possibly as small as N 0.1. The experimental limit

(5) implies

‘2)! ] <1.2 x 10-11. (9)1#/N + ‘&N - ~.IvN7rIn Ref. 10 it was shown that in the mm + O limit the most singl.d~ contribution to & arises

solely from the n-p intermediate state. The sme of this contribution Lurns out to be very

close to the value in (8).

11, is expected to improveA new experiment in prepar~tion at the kstitu~ Laue Langevin

the current limit on & by a factor of 5, and a proposed experimental technique offers the

possihlity of an additional improvement by about a factor of 400 (Ref. 12).

Atomic and Molecular Electric Dipole Moments. The electric dipole moments (EDM) of

atoms and molecules are sensitive to PVTV in the N-N interaction through the Schiff moment

of the nucleus, which ;s induced by the nuclear electric dipole moment, and (for nuclei with

ground state spin larger than ~) through the nuclear magnetic quadruple ~oment. 13’14)-(I)/

The most stringent limit on the constants gnNN comes from the experiment a] limit on

the EDM of the lWHg atom15)

ld(lwHg)l <9 x 10-28 ~m (95% C.L) . (lo)

Atomic calculations 1416) yield the relation d(l WHg) = -4 x 10–17Q~(1WHg) ecm (efm3)’1

betwmn the lWHg electric dipole moment and Sch.i.flrx.ament. Q$(19gHg) has been calculated

in Ref. 14 using the PVTV N-N potential

WA = (cJr /2/3 rn~) [(q~ &a – ~ qJ5a d(~~ – Fb) (11)

+ ~~ dax db{fla‘~,,6(f’a – ~~)}+] ,

where ~&, ?& and $&(k = a,b; a = n,p; b = n, p) are the spin, coordinates and momenta of

nuclems a and b, obtaining

Q~(lgglYg) = 1.4x 10-8 ~P efh3 . (12)

The contribution of the PVTV nONN couplings to the constants q~ and q~ can be ob-

t aind by comparing the potential (11) with the zero-raage limit of the PVTV pion exchange

potentials given in Ref. 5. We find

(r?PP)7r” = -(%lp).o = (A 9~xvN/GF d) #rm I (13)

(q~)mo = o (a=n, p; b=n, p) , (15)

where g=~N is the strong ~NN coupling constant, and ?nw and ?mntl me given in Eqs. (6)

and (7). In the local (zer~range) limit the potential (11) accounts also for the charged pion

contribution, 14) but the corresponding constants q~ and id have not been worked out yet.

Ignoring the cha.rged-pion contribution, we obtain from Eqs. (12) (13) and (10) the bound

i~:)jv+#;jv+~:2;Nl<1.8x10-11. (16)

An improvement of the limit (16) by a factor of 10 seems possible. 12) A new calculation

17) Experimentalof d( lggHg) using the twm’body pion exchange potentials is in pr( gross.

limits18) and the pertinent calculations 14, are available also for the elect ric dipole moment’

of the 12gXe atom and of the ‘T/F’ molaule. The corresponding bounds on the PVTV mNN

constants are weaker than the bound in (16) by factors of -300 and * 25, respectively. It

should be notd however that d(TW) probes a combination of the PVTV nNN constants

which is differeut from the one in (16).

2.1.2. Nuclear Physics Probes of P VTV in the N-N Interaction.

Among nuclear processes the most promising candidate for investigation of PVTV in the

N-N interaction is the transmission of polarized neutrons through polarized targets. In the

presence of a PVTV interaction the neutron-nucleus forward scattering amplitude contains a

term proportional to (&n) “In x (~) (dn and in are the neutron spin and momentum, ~ is the

spin oft he target nucleus). 19) A PVT’V obswwable is the quantity pp,T s (o+ –0–)/(o++u– ),

where o+ (a_) is the total neutron-nucleus scattering cross-section for a neutron polarized

parallel (antiparallel) to in x (~). A PV effect (due to the (dn) . ~ term) is the quantity

pp = (o: – d_)/ (a\ + L), where a! (a:) is the total neutron-nucleus cross-section for

neutrons polarized parallel (antiparallel) to its momentum. ‘Jery large values of pp have

been observd near pwave compound nucleus resonances (7x 10–2 for the 0.734 eV pwave

resonance in 13gLa).ml Such large effects are the result of “dynamical” and “resonance”

enhancements.21) These enhancement factors are effective also for pp,T, and therefore one

can expect that the best candidates for PVTV searches are resonances for which pp Is large.

Assuming tw~state mixing the ratio ~ = pp,T/pp is given by21,2’2) ~ =

nJ(@S lVp,Tl~p)/ (09 lVpltiP), where VS and @p are s- and p-states of the compound nucleus,

and 7’LJis a factor which depends on the p-wave compound resonance spin and on the ratio

of the neutron width of the pwave resoxiance for the different channel spins.23)

‘(1 ) For VP it is adequateLet us consider A for the 1=1 PVTV pion exchange potential VP,T .

‘(o) Wc shall as-me that nJto take tht~ 1=0 P-violating p-exchange. potential Vp . a 1 and

write

A =

-(o)fwhere gpNN 22X

~(l) -(1)’ (0)1A(l) R (@slv;:)l@p)/(@slvf(0) l@p) = %NN/gpNN ‘ (17)

10-6 is the ~& PV pNN coupling constant. Assuming that V~,~) and

V$O) can be approximated by one-body otent ials, the constant K(1, is given by24)fJ ) ~31m7~ , (18)

where

0 = (’lJsl~” (f’/r) (~Pn/~r) ‘~lt’p)/(@sl~” 7*14%) s (19)

In Eq. (19) p~ is the nucleon density in the nucleus, and 6, ~, F and T. are single-particle

operators; r = Ifl. Based on the imwstigations in the first papa of Ref. 4 and in Refs. 25

and 26, a reasonable wdue of ~ to use for estimates appears to be 9 = 0.2. With this value

the limit (16) implies(20)J(lI ~ 6 x 10-5.

For tile #{N and ~~~i~ interactions the limits on the corresponding A’s are stronger than

(20) by factors of A/(N-Z) and A/2( N-Z), respectively. Assuming that there are no cancel-

lations in Eqs. (9) and (16), the implication is that to compete with the limit (16), pp,T has

to be measured for pp = 7 x 10-2 with a seni~ivity of 4x 10-6.

A measurement of pp,T was carried out in the experiment of Ref. 21, using a polarized

165H0 target and 7-12 MeV incident neutrons. The experiment yielded lpp,~l <5 x 10-3

(95% cl.). A measurement of the P-violating effect has also bwn performed, with the result

IPPI ~ 5 x 10-4 (95% c.1.). The implications for the P,T-violating nNN constants are not

krowmi A neutron spin rotation experiment to search for PVTV is under preparation at

KEK.28)

In ~-decay and p-decay PVTV in the N-N interaction gives rise to contributions to T-odd

correlations in the decay probability. In -pdecay PVTV has b-n searched for in a transition

in *wHf (Ref. 29), where the PV effmt is unusually large. For the ~~~~ interaction the

sensitivity of this experiment woldd have to be improved by four elders of magnitude to

compete with the limit (16:1.24) This appears to be beyond reacn in the foreseeable futwe.ml

The same is true for a.n cthenvise attractive case in 182W (Ref. 30).

In ~-decay an enhancement by 2-3 orders of magnitude of the effect due to ?VTV in the

N-N interaction can occur in some cas~ for first forbidden beta decays where the beta decay

horn the admixed state is superallowed or allowed.31J The implication of the bounds (9) and

(16) is that even with such enhancements the expected size of the PVTV effmt would be

about four ~rd~is of magnitude below where the effects of the final state interactions can be

expected.

2.!. 9. PVTV in the IV-N Interaction in Mtidels with CP- Violation.

The Standard Mode(. In the SM tb.en are two sources of CP-violatiom the Kobayashi-

Maskawa (KM) ph~ 6KM in the quar~ -Ixing matrix and the PVTV (?-term in the QCD

Langrangian.

The KM phase contribut~ to PVTV in the N-N interaction only L1 saond order in the

weak interaction. The dominant diagrams have been found to be the K-exchange diagrams

involving weak baryon-nucleon transitions. 32) The strength of the corresponding four-nucleon

interaction is z 10‘g GF, to be compared with the prmmt limit of N 10–3 GF from cf(lgQHg).

The O-term is isospin Lwariant, and therefore it induces only an isoscalar nNN coupling.

The constant ~~~~ has been calculated in Ref. 10 using PCAC and current algebra, obtaining

lF~#N I = 0.02W The b=t ~t on 117f~Nl is from & (Eq. (9)), which implies

Iel <4 x 10-10. (21)

Left-Right Symmetric Models. These m.odels33) provide a framework for the under-

s~,anding of parity violation in the weak interactions. The simplest models are based on the

gauge group SU(2)~x SU(~)RX U(l)~_~. In SU(2)~x SU(?)RX U(l)B_L models there is a

PVTV flavor cwwewing nonleptonic interaction first order in the weak interaction. The part

of this interaction involving the u, d quarks, which presumably dom.inat~ the N ~ Nn ma-

trix elements, is a pure isovector. ‘) The constant ##N is of the

sin (c! + w), where k is a constant, (go = (flR/g~)(cO@~/cOsfl~)~,

angle, OF and tl~ are. quark n;ixing anglti in the right-handed and

w are CP-violating phases. I he bound (16) implies

l<~d sin(a + w)[ < &5 x 10-5/k.

form &=l$N = GF m~k(~g

< is the WL - WR mixing

left-handed smtors, a and

(22)

CalcJatims ‘) find values of k in the range from z 4 to -270. Quark model calculations of

dn lead to upper limits on I(ge sin(a+w)l as weak as N 10-3 ad as strong as x 3x 10-5. The

experimental limit on Rec’/c and the calculation in Ref.

upper limit of 10-3 on I<ge sin(a + u)!, wluch is free of

by beta decay (see Section 3).

36 yields l(~e sin(a+w)l s 10--- An

theoretical u.ncertaint ies, is providd

Models with Exotic Fermio~. A PVTV flavoi conwwing nordeptcmic interaction for the

u, d qu~rks of the same structure u in left-right symmetric models can arisen) akw in

models wit h exotic fermions (ferrnions with noncanonical SU(2) ~ x U(1) assigmnents).~)

The parameter ~ge sin(a -+ w) is replaced in this c- by ~m[SfiS~(V’)U~], where sfid s

sin#, L9# are light-heavy mixing angles, and VR is a generation mixing matrix. The limits

on ~m[9~9~(VR)Ud] are the same as on @ sin(a + w).

Multi-Higgs Models. Higgs .wtors containing two or more Higgs doublets arise in many

extensions of the Standard Model. Such models can contain CP-violating interactions me

diated by Higgs bosons. An example is the Weinberg model,w) which contains three Higgs

doublets. In this model flavor changing neutral current Hi- interactions are absent, and

therefore the Higgs bosons can be relatively light, and with unsupp- couplings. Both

& and d(lggHg) can have values near the present experimental Limits (SXXRef. 40).

Supwsymmetric Models. In supersymmetric models there are new CP-virdating ph-s,

which can contribute to the el=tric dipole moments. In the supersymmetric standard model

& and d(lggHg) can have values near the present experimental limits (see Ref. 40).

We note yet that stringent limits from the elatric dipole moments are available on the

coefficients of various effective PVTV operators.41)

2.2. Pmity Conserving TirLIeRevemal Violation

The lightest meson contributing to the parity conserving time reversal violat ing (PCTV)

N-N potentials is the p+ (Ref. 42). The PCTV pNN coupling has the form43JJ#W

= k7pNN/2~N) ~~A” q.(p~ r- – pi T+)N , (23)

where ~~N~ is the PCTV pNN coupling constant. The next meson-exchange contribution+,0is from the Al .

A dimensional argument8) sugg=ts for the contribution of (23) the size & s (e/m,v)

(GFmfi/4~)3pNN = 2 x 10-m ~~,~pJ, which would imply [?jP~Nl ~ 6x 10-6. A calculation44)

of the contribution of ~PNN to & gives @pN~l s 1 x 10-2 (95Y0 c.l. ). The limits from

d(lggHg) are weaker.44)

From nuclear process= a limit of l~A, NNI ~ 0,17 (95% c.1.) is implied by a study of

a 7-transition in 57Fe (Ref. 45). The limit from studies of detailed balance and nuclear

energy-level fluctuations in compound nuclei is \~P~~~ s 2.5. An experknent46) me=~ing

1S5H0 yields l~p~N I S 23 (Ref. 47).neutron transmission (the (i?n . ~n x J~(~n “J~ term] in

It is anticipated that the latter limit will be irnprovd by a factor of N 150. In suppressed

beta decays it may be posible to obtain limits on ~PNpJ similar. to those from ~-dec~y.qsl

An example of a PCTV flavor conserving inte~actjo~l at the quark level is

H = (91 /m\)(~ /~~fd)~ui~~pvi75u)~~1475~ ! (24)

where mx is the mass of the boson mdiating the interaction. In Ref. 49 a limit of g~ ~

4 x 10-6 has been ~ on g~ tiom tw-loop contributions to& involving the interaction (24)

and Z-exchange. Similar limits fol’bw for other PCTV interactions. If PP~N = (g~/m~)m~,

this implies 1~~~] S (2 x 10‘6 GeV2)/m~ (l~fl~~l ~ 3 x 10-10 for m,. ~ m~).

In renormalizable gauge theories flavor-co~ing (43/ = O) PCTV quark-quark (q-q)

interact ions are fundamentally different from A~ = O PVTV q-q interactions: while in some

extensions of the SM (e.g. in left-right symmetric models) A~ -= O PVTV q-q intcmctions

can occur in second order in the boson-fermion couplings, this is not so for Aj = O PCTV q-q

‘) that neglecting the e-term A~ = O PCTVinteractions. For the PCTV c= one can prove(i) (j)

q-q interact ions are absent to order g= g= , where Ya is any boron m~igenstate other

than a gluon and a photon from the set {Ya} (a =(i)

1,2. ..) in the theory, and g= and g~)(i =

1,2,...; j=l,2 ,. ..) are the coupling constants of Y. to the bilinears involving the fermion

m~igenstates. This conclusion holds to all orders in the CP-invariant component of the

QCD interwtions and to all orders in the QED interactions. Consequently, without the Oterm

the lowest order in which A~ = O PCTV q-g interactions can be induced is the fourth order

in the boson-ferrnion and boson-boson coupling constant~: through diagrams involving three

Y=-fermion and one thrdmson couplings (triangle-type diagrams), or through diagrams

with four Ya-fermion couplings (box diagrams). For example, the interaction (24) can be

‘) The t-loop contributions of (24) toinduced by a triangletype X~xchange diagram.

~ become thea thra+loop diagrams and, as we note in Ref. 50, the corresponding limit

from & will have to be therefore reexamined. The maxirnd size of the strength of a triangle

diagram is of the order of (1/87r2)(q/iM)( l~41/kf~), where M is the m= of the heaviest

particle in the triangle, and ~4 is a product of four coupling constants. A rough estimate of

17pNN is ?7pNN = (1/8m2)(m,~/M)( m~/m~)l@14 sin+, where @ is a CP-violating phase. With

1914= (4in@w)4 one ~~d have ITPNNI S 2 x 10-9 for ~ Z ~w, Jfx 2 mw- P=nthwe are investigating the constraints on some models where X is very light, with a mass of

the order of a few GeV (Ref. 51).

3. Time Reversal Violation in Beta Decay

T-violating contributions to beta decay can wi~ also Erom T-violating charged current

quark-lepton interactions. Experimental information is a~ailable on the coefficients D and R

of the correlations ($

spin), respectively.

The D-Coefficient.

Dt to the D-coefficient

~’ x &/J13eEv and (F) . (~) x ~./JEe(6 - electron spin, ~s nuclear

To lowest order in the new interactions the T-violating contribution

is given by52)

(25)

where qLR is the strength of an interact ion involving a V-A leptonic and a V+A ]uark current

relative to GF/fi, and aD is a constant involving the nuclear matrix elements. The present

experimental limit on ~mqLR from beta decay is

l.ffiba~~l <1.1 x 10-3 (95% C.lm) (26)

In the Standard \fodel T-violating leptcmquark interactions arise only in second order

in the wak interaction or in order OGF, and therefore they are expected to be unobservably

small. A non.zero ~mv~R can arise at the t- level in models imching right-handed gauge

bosons (e.g. in left-right symmetric models), in models with exotic fermions, and in models

with leptoquarks. 521 In left-right symmetric models and in exotic fwnion models one has

lmqLR = – c@in(~ + U) ami lm~LR = ~m[9~s~(Vi&d], rvtively. h we have noted in

*tion 2.1.3, there are stringent limits on these parameters from the dipole moments, and

from #/c. Unlike the limit (26), these limits may involve unknown theoretical uncertainties.

For the leptoquark contributions to .~m~LR there an no si~cant limits from the electric

dipole moments, nor from </c. New experiments to search for T-violation in l~eutron decay53)

and lgNe decay ~) are under preparation, aiming at improving the limit (26) by about an

order of magnitude.

The R-Coefficient. The R-coefficient is sensitve to T-violating scalar and tensor inter-

act ions. Scalar interactions can arise from charged Higgs exchange, slepton exchange (in

R-parity violating supersymmetric models) and ~om Ieptoquark exchange.521 A rment mea-

surement of R in 8Li decay yielded a limit of z 10-2G~ on tensor interactions.=) Indirect

limits on scalar am! tensor imeractions derivw!56’41J from the experimental bcunds on PVTV

e-N interactions are more stringent by -- 2 and z 3 Grders of magnitude, respectively. How-

ev,~r the theoretical ~~rtainti~ ~ciated with the h~ts co~d be large.56’41 )

4. Conclusions

The PVTV 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 lWHg atom set stringent limits on the PVTV nNN coupling constants. It appears that

horn nuclear physics proc- only neutron transmission remains as a possible candidate for

improving these limits. Fhsed on the existing calculations, and barring cancellations i:~ &

and d(lggHg), in a case where the PV asymmetry is 7 x 10-2 the PVTV asymmetry would

have to be measured with a sensitivity of 4 x 10-6 to compete with the existing limits.

The PCTV N-N interaction is governed by p+-exchange and the exchange of he-wier

m~ns. The best ;mit on the PCTV pNN coupling constant (l~p~~ I ~ 10-2, and possibly

a much more stringent limit) comes from the electric dipole moment of the neutron. The

theoretical expectation for PCTV in the N-N interaction is that it is small, most likely below

the strength oft he weak interaction, and probably considerably so.

Searches for the D-coefficient in beta decay constrain left-right symmetric models, models

with exotic fermions, and models with leptoquarks. The leptoquark contribution to D can

be as large as the present experimental limit for D. In the other models more stringent limits

9

on ImqLR (~ Fq. 25) than horn the D-coefficient have been derived hmm the experimental

bounds on d(lWHg), & and #/c. Howevertk linits are not as rehable as the direct limits,

in view of the uncertainty= in the calculations.

Searches for the R-me.f6cient provide information on scalar- and tensor-type T-violating

interactions. For such interactions stringent limits have km deduced born the experimental

bound on the PVTV tensor e-~ interactkm. Homwr the thmretical uncertainties awiated

with th~ limits may be large.

Acknowledgments

I would liLa to thank Geoffrey Greene for inviting me to give this talk. This work was

supported by the United States Department of Ener~.

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