Volume 72B, number 3 PHYSICS LETTERS 2 January 1978

WHAT NEUTRAL CURRENT EXPERIMENTS CAN TELL US

ABOUT LEFT-RIGHT SYMMETRY

Vlrendra GUPTA and Prober ROY Tata Institute of Fundamental Research, Bombay 400005, India

Received 27 September 1977

Neutral current consequences of left-right symmetry for the gauge group SUL(2) X SUR(2) X U(1) are derived

m the form of experimentally testable relations AddItional results follow from the hypothesis of no exotic charges

Some of these tests can distmguish such theories from the Weinberg-Salam model

1. Irhductlon and mam results Gauge models with [I] left-right symmetry [2]

provide a rather satisfying answer to the panty puzzle

m unified theories The conservation of parity by the long-range electromagnetism but not by the short- range weak mteractlons follows naturally here since panty-vlolatlon itself ongmates [3] from the sponta- neous breakdown of symmetry This feature 1s absent from the standard SU(2) X U( 1) model of Wemberg and Salam. It has been pointed out [l] that the mcor- poratlon of left-right symmetry (ambidexterity), con- sistent v&h the observed [4] panty-vlolatlon m the hadromc neutral current, requires the mmlmal gauge

@ouP Gm In z SUL(2) X SUR(2) X U( 1) Larger groups * 1 such as SU,(4) X SUR(4) X U( 1) containing G mln have also been considered [5]

The standard model has been quite successful m understanding neutrmo induced neutral current phe- nomena on lsoscalar targets but not atomic parity vlo- latlon [6] provided all atomic physics comphcatlons are assumed to be understood In contrast, ambldex- trous models [l] offer the posablhty of simultaneously explaining both existing neutrmo and atomic neutral current data In this note we present certain new re- sults as general consequences of the left-right symmetry idea m neutral current phenomena, including some which can dlstmgulsh ambidextrous models (based on G,,,) from the standard one Our results would be amenable to experimental verification shortly when data on v, V mcluslve neutral current cross sections

*’ The mamtenance of strict left-right symmetry m the lepto-

nit sector IS difficult with Gmm alone If the known neu-

trinos are taken to be always left-handed [ 51

336

(UT, a, uvn, 0”) as well as atomic panty-violating quantities become available separately for protons and neutrons This 1s note merely a fond hope since the

first set of data on the neutral current mcluslve cross-

section &‘P are already m print [7] We work with a class of ambidextrous models

satisfying certam general requirements rather than wth specific Hlggs schemes as done m ref [l] The gauge group 1s G,,, or, If larger, contains G,,, (vlde ref [5]) m such a way that only the gauge bosons pertaining to Gmln contribute to the effective four- fermlon interaction of the usual quarks and leptons, those outside G,,, being ultra-heavy The lack of exotically charged objects m the model 1s required, restricting one to quarks of charge +i and -3, leptons of charge 0, --1 and Hlggs scalars of charge 0, tl This together with quark-lepton symmetry requires the left-handed and r&t-handed fermlons to belong only to the representations (4, 0), (O,;), (0,O) of G,,, and the Hlggs scalars only to (+, 0), (0, &), (& i), (1, 0), (0,l) and (0,O) The neutrinos v, and up are taken to be always left-handed Lastly, the neutral current 1s required to conserve flavour These condltlons alone imply relations mvolvmg the cross sections ovP etc and the atomic panty-vlolatmg parameters*’ G,,, CAP for the proton, Cvn, CA, for the neutron and Q(2, N) E -2 [CvpZ + Cv,N] for heavy atoms as introduced by Bouchlat [8] To present our results, define

*’ The effective four-fermlon mteractlon IS

2-1’ZG[e?ary5e (CVpF%~ + CVn%,n)

+ FYr”e(CAp%or%P + cAn%or%n)l

Volume 72B, number 3 PHYSICS LETTERS 2 January 1978

2’ z CUT t $p) + cuvn t a”> , (la)

A* 3 (o”~ - act) f (gn ~ $nj , (lb)

r* f yue f uFwe , (ICI

C+ and A+ bemg obtamable from the already existing data on lsoscalar targets, X- and A- are m the process of bemg determined [7,9] and fragmentary mforma- tion 1s available on r’ . In the quark par-ton framework X-, At and A- are determmed solely by the valence quark contnbutlons because of the lsospm and charge conlugatlon mvanance of the “sea” of quark-antrquark parrs Introduce U and D - the momentum fractions

of the u and d quarks m the proton which are known to be 2 0 3 1 and 5 0 20 respectively [lo] from electron scattering experiments Finally, let x (0 <x < 1) describe the mlxmg of the U(1) compo- nent and correspond to sine squared of the Weinberg angle Bw m the standard model In terms of these we have two types of results The ones that are true for an arbitrary Hlggs structure (see sectlon 2) are (me and MN are electron and nucleon masses respectively)

@a)

or,

’ (2b)

sign (X-/A’) = sign A- = -ve , (3)

r+-2r--3 t(=,I+o,

Q@,N) Cvp CAP C,, CA,

=(4x-l)ZtN ;-2x

; 2 (-+2x)

(4)

In eq. (5) GA/G, 1s the usual ratio of the axial to the vector couphng m neutron beta decay These relations are also valid m the standard model but with an equa- lity m place of the mequahty of eq (4) Our analysis shows that the experimental vlolatlon of any of eqs. (2)-(5) will rule out all models based on G,,, and fer- mlomc doublets AddItIonal mequahtles follow If there are no exotic Hlggs multlplets, namely

-Q(Z.N) Z(4x - 1) + N’

3n A-‘-A-

G2MNE,, (U+ D) C- l

112

(8)

In the standard model eqs (6)-(8) become equahtles

2 General gauge structure The type of theory we consider has two charged

(Wi, Wi) and three neutral (WL3, WR,, W,) gauge bosons Let the SU,(2), SUR(2) and U(1) subgroup generators and couplings be (TL, gL), (TR, gR) and (Y, gu), respectively The electric charge 1s Q = TL3 + TR3 t f Y and moreover gL = gR = g One may now identify

A~=X112(WL3+WR3)~+(1-2X)1’2~~, (9)

wth the photon and obtain gx1j2= e = (1 - 2x)li2gu

The physical neutral bosons (mass elgenstates) mediating neutral current weak interactions will m general be hnear combmatlons of the massive fields

Z; = 2-1/2(W L3- ‘R3)’ 1 (104

z2” = ($ - x)‘qw,3 + Iv,,)/1 - (2x)1&+$ (lob)

Define the currents

J&j2 = 2 c ~;Y”T~~)& , 0 = 1,X 3) , (11)

where the sum 1s over left-handed or right-handed fer-

mlon doublets $ as the case may be and TLcRj2 = d T~( 1 t (-)yg), 71 berg the Pauh matrices Then Z, and Z2 couple respectively to the pure axial and vector currents

(124

(12b)

Evidently, left-right symmetry and the presence of the usual left-handed fermlomc doublets (as m the standard model) belonging to SU,(2) force the corre-

spondmg right-handed components*3 to appear m

*’ Our results are applicable to other models based on G,,, m

addltlon to those already m the hterature [ 1, 51

337

Volume 72B, number 3 PHYSICS LETTERS 2 January 1978

doublets of SuR(2) Any mixing among the latter due to mass-dlagonahzatlon must leave the neutral current untouched becausepf flavour conservation These facts lead to the simple neutral current couplings gven be- low. For an arbztrary Hlggs structure, the spontaneous breakdown of symmetry will mix Z, and Z, through the squared mass matrix Mi whose inverse IS taken as

(13)

Then the effective four-fermlon interaction causing neutral current phenomena IS

_Q = 2-1/2G go [A( 1 - 2x)J(‘) -J(l) (14)

where go = (fiG)-l e2 [8x( 1- 2x)]-l Owing to equal contrlbutlons to J(l) and Jc2) from

the left-handed neutrinos, the vector and axial

couplings uf and af of a quark or lepton of flavour f Fe, P, u, 4 > *n

X 1 yfr,(uf + afvs)f , 1 (15)

are given by

U,= UP= -igv(l-4x), a,=a,=-+gA, (164

% =+gv<l-$x), a,=38*,

Ud =-f&,(1-&), ad= -$A,

urlth

gv = go [2D + (I- 2~)l/~(B + C)] , (174

~A=~,,[~A(~-~X)+(I-~X)~/~(B+C)] (17b)

The correspondmg standard model couplings are ob- tamed from eq (16) wth gv = 1 = gA and x = sm%+

The quantities descrlbmg panty-vlolatlon m atomic physics are proportional to the off-diagonal matrix elements of Q2, I e B and C The four effective

parity-violating couplings of the electron to the proton and the neutron [8] are

cv,=-igp(l-4x), C,, = 3gp > (18a)

CAP = -CA, = igp( 1 - 4x) GA/G, , (18b)

338

with

gp =go(l -2~)l/~(B +C) = (4;t(;;;N . (19)

In the standard model gp 1s unity From eqs. (16)-( 18) it IS clear that the presence of two neutral bosons m such theories allows [ 1 l] the posslblhty of no parity- vlolatlon m atomic physics (gp = 0) despite its presence m neutrmo-induced processes (gv, gA # 0). The rela- tionship between gv, gA and the neutrmo cross sections may be given as

2- 3ll A+A- g,‘, - ____

G2MNEv(lJ+D)X- (204

gjIg.4 = 3A- --- U-D 1 W’b)

Given the quark parton framework, it IS stralghtfor-

ward to arrive at eqs (2)-(S) directly from eqs (15)- (18) without any speclflcatlon of the Hlggs structure or reference to charged current induced weak mterac- tion. Analogously, one may derive equahtles corre- sponding to +he inequalities of eqs (6), (7) and (8) wth their right-hand sides multlphed by the extra factors gVgA1, i Cgv + gA)2, and gpgA1 respectively The mequalities of eqs (6)-(8) then follow from the additional results

g,>l, gV>gA>O, gV+gAa2, l&?p&& (2l)

which obtam m the absence of exotic Hlggs bosons from the theory. We proceed to establish eq (21).

3 Symmetry breakdown wzth nonexotzc Hzggs The exclusion of multlplets with members having

charge greater than one umt Implies the followmg forms for vacuum expectation values contributing to the masses of the gauge bosons m terms of certam real parameters (Y, h, /3, y

These correspond respectively to the representations

(i, O), (0, f), (1, O), (0, l), (i, 3) and (i, a) where the reality of the last representation has been made use of Such a structure mixes Wi and Wi as well as Z, and

Z2 The mtroductlon of G through the 2-1/2GJL*J;l

Volume 72B, number 3 PHYSICS LETTERS 2 January 1978

term (Jt = .I,, + 1JL2) III charged current induced

we?k mteractlons implies that

2-l12G =+(2&th; to2 t y2) [(za;+A;)(2+X;)

t(2a~th~t201:+~~)~2+y2)+41j2y21-1 (22)

The elements of MO2 m eq (13) turn out to be

A_4xLY:fak _, B=C=- 4x(1-2x)1/2 +ff;

e2 detf10 e2 detMi ’

_4x(l-2x) ++2P2+2Y2

e2 detMi

(23 a)

detMi = 4c~Lai + 2(0$ + CY~) (J2 + r2) t23b) The use of the above equations and of the definitions

ofgA,gV,gp, 1 e eqs (17) and (19), leads directly to eq. (21) and hence to eqs. (6)-(g) The latter then constitute tests for the nonexotic Hlggs scheme within G mln Note that the presence of more multlplets of one of the given kmds leaves the results unaffected,

e g for y1 left-handed doublets C$ bemg replaced by iX~=lo1~~ and so on We may mention for completeness that the further (UnJustified?) restrlctlon of the Hlggs bosons to doublets (1 e to representations (TL, TR) \nth TL R = 0, 3 so that h, = O= hR) implies gA < 1 and hen;e the result that the right-hand side of eq (2Oa) IS bounded above by unity Eq (8) now implies that -Q(Z,N) < (4x - l)ZtN

The nonexotlclty hypothesis for Hlggs bosons also has an important lmphcatlon regardmg a generalized standard model The parameter z = Mi2Mg cos2fIW, relating the charged and neutral weak boson masses and unity m the standard model, IS forced to be < 1 If one relaxes the Weinberg-&lam doublet restrlctlon for the Hlggs but makes the nonexotlclty hypothesis Thus follows since the only additional Hlggs multlplet allowable into the standard model now 1s the triplet (q+, cp”, cp-) and the only nonzero vacuum expectation value (cp”) contributes to MW but not to M, One IS then led to gv = gA = gp = z-l 2 1 for such a theory so that, while eq (7) holds*’ as an mequahty eqs (6)

and (8) reduce to z-independent equalities as before Eqs (2)-(5), of course hold here also with the mequa- hty of eq (4) replaced by an equality However, m

*4 Eq (7) is vahd m an SU(2) X U(1) model with arbitrary right-

handed couplmg [ 121 with z < 1,i e nonexotlc Hlggs bosons

contrast with the last result of the previous paragraph, the right-hand side of eq (20a) IS bounded below by unity An experimental comparison of this combma- tion of cross sections with the bound will therefore be very interesting

4 Dmusslon and conclusion To compare our results with experimental data the

most unambiguous procedure would be to determine x independently of the quark-antiquark “sea” from A-/A+ and then verify the other predictions In par- ticular, eq (21) can be checked directly through the use of eqs (20) Eqs (2) and (5) are tests not only of the standard model but also of G,,, Given nonexotl- city and the generalized standard model, the same statement can be made about eq (7) On the other hand, if eq (4) IS verified as a strict mequahty, models based

On Gmm will be favoured over the standard one (even allowing z < 1) The same can be said about eqs (6) and (8) wlthm the aegis of the nonexotlclty hypothesis It may be noted that eqs (5) and (8) imply certain upper

bounds on Cvp, CAP, Cvn, CA, To summarize, although the posslblhty of an “eawer”

explanation of small atomic parity-violation in left- nght symmetric theories based on G,,, has been noted by many, we emphasize that several results m neutrmo mcluded neutral current processes on separate proton and neutron targets can test theories of this type Moreover, the observation of certain strict mequahtles can serve to dlstmguish between such theories and the standard model.

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