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Weinberg's gauge model for weak and electromagnetic interactions with Han-Nambu quarks
Nuclear Physics B56 (1973) 635-641 North-Holland Pubhshmg Company
WEINBERG'S GAUGE MODEL FOR WEAK AND ELECTROMAGNETIC INTERACTIONS WITH HAN-NAMBU QUARKS Yoav ACHIMAN * Instltut fur Hochenergwphystk, UmversltatHeMelberg Recewed 29 December 1972 (Revised 5 March 1973) Abstract A version of the Wemberg model is constructed using Han-Nambu quarks, m order to obtain the conventional classification of hadrons The use of Han-Nambu quarks leads to a suppression of neutrmos coupled to the AS = 0 hadromc current, while the coupling to neutral leptomc currents remains as m Wemberg's theory. Wemberg's renormahzable gauge theory of weak and electromagnetic interactions was originally [ 1 ] apphed to leptons only. In order to generahze the model for hadrons, m a way that avoids unwanted AS ~ 0 transitions, Wemberg [2] used the idea of Glashow-Ihopoulos-Malm [3], winch amounts to the introduction of a new charmed p-like quark. The same method allows also the cancelation of Adler-BeilJacklw [4, 5] anomalies, winch may Interfere w~th the renormallzatlon programme. However, the observed spectrum o f hadrons, winch is so well generated by the different versions o f the quark model, does not find a simple interpretation m terms of this model. Another weak point of Welnberg's model is that the couphng o f neutrinos to the neutral AS = 0 hadronic current is on the edge of inconsistency with experiment [6] To avoid the second difficulty, new models were set forward. An 0(3) model was proposed by Georgl and Glashow [7] and improved by Blorken [8], tins model avoids completely the use of a weak neutral current. Prentkl and Zumino [9] and Lee [10] suggested SU(2) X U(1) models m winch the neutral weak currents do not contain a ~-v term. Other possible models of tins kind were discussed by Bjorken and Llewelyn Smith [8, 11 ]. Recently Llpkm [12] suggested that the charmed quarks m the Georgl and Glashow model may f'md a natural place in the family of Han-Nambu quarks [13]. If Han-Nambu quarks are used as basic hadrons the good predictions of the naive quark model_are incorporated in the_ model without difficulties wxth the statistics o f quarks or with the n 0 -~ 77 amplitude. Georgl and Glashow [14] gave an exphclt * Volkswagenstiftung fellow.
Y. Achtman, Wemberg's gauge model
636
version of their 0(3) model [7] using Han-Nambu quarks This is, however, done m a rather comphcate way *. It should be desirable to have a version of Wemberg's model using Han-Nambu quarks as this Is the simplest and most economical gauge model. It wall be shown that this can be done m a way that avoids the apparent inconsistency of the original model with experiment [6]. This model will be of special interest if neutral leptomc currents will be observed while the AS = 0 neutral hadromc currents remain relatively suppressed. The mass of the vector mtermedmte bosons is reduced by a factor three with respect to Welnberg M w ~> 12 4 GeV. The nine Han-Nambu quarks constitute the followmg three triplets under the conventmnal strong mteractmns SU(3)
:i1 :i1 f °l The p-quarks (p~, p~, pO) are assumed to constitute a triplet under another SU(3) (SU(3)'), and this is true for the triplets of n-quarks and X-quarks, SU(3)' Is also assumed to be an apprommate symmetry o f the strongmteractmns. (In particular we want 13' and Y' to be good quantum numbers under the strong interactmns) [ 14]. All observed hadrons are taken to be slnglets under SU(3)' and their properties are the same as in the quark model. To obtain a Wemberg-hke gauge model, we need two doublets under the SUL(2 ) X U(1) gauge group A natural way to do this is as follows Pl
--
_
(1,
,
(2)
L
() P2
_
where C
n l = c o s 0 c n 1 + s i n 0 c x 1, X~ = - s i n 0 c n 1 + c o s 0 c x 1 The corresponding nght-handed particles we take to be smglets All the other quarks are also scalars under SUL(2), and they enter the weak interactions currents only vla * A version of the Georgl-Glashow model with Han-Nambu quarks was also suggested by Mohapatra [ 15 ] This version leads to a great rate of KL --*/~+t~-(ref. [ 16] ) m contradiction with experiment
Y. Achtman, Wemberg'sgauge model
637
the electromagnetic one (prowdes they are charged). This procedure do not lead to any difficulty as the new mass terms are independent of the Higgs scalar bosons. As leptons we use the following left-handed doublets and slnglets t
~L
e-
L (3)
/js
/L P
~'~ = ( - sin a ve + cos ¢xve ) L ,
~'= (- sm ~
(4)
~. + cos ~ ~'. )L" I
t
All right-handed leptons e R,/JR, VeR and VuR are scalars Notice that we have used the same mixing for electrons and muons in order to obtain e - / j umversahty. As m all SU L (2) X U(1) gauge theories [ 11], the mteracuon Lagranglan of the fermlons w~th the Yang-Mdls vector bosons A x and B x ~s m the form
t' = ½gA~,• .f'+½g'B~,(J~ -
2J~~,'m)'
(5)
where g, g' are arbitrary couphng constants. Wemberg's theory involves one Hlggs scalar doublet
(°-)
¢~= ~o
'
whose vacuum expectation value
will break spontaneously the SUL(2 ) X U(1) gauge symmetry down to the electromagnetic one. The charged weak currents can be written exphcltly in the hadromc and the leptonic spaces in the following way
f~W =l Pl 7X( 1 + 75) n~ + i if2 'Yh(1 + 3'5) 2~,
(7)
J~W = cos a [i V-e 7x( 1 + 75) e- + l vu 7h(1 + 75)/j-] + sm a [i Su ~/r'(1 + , s ) e - + i-~, 3,x(1 + "rS)'-],
(8)
while the neutral weak currents take the followmg form ]~Z =½ [iPl 7h( I + 'Y5)Pl + iP2 7X( 1 + "Y5)P2- i n l Th( 1 + 3'5)nl -- t X-I 7X( 1 + "}'5)X1] -- 2 sin 2 ~ow (IXe,m)h ,
(9)
638
Y Achtman, Wemberg's gauge model
]~Z = ½{- iT- 7}'(1 + 75)e- + i cos 2 a v-e 7}'(1 + 75)re + i sm 2 ¢~ v-e 7}'(1 + 75)Ve + sin a cos a ~e 7}'(1 + 75)Ve
(10)
+ v-~ 7}'(1 + 75)vel + (e -+ p)} - 2 sin 2 ~ow (/'eX,,m),g_., where r
_g tg ~W - ~" As In the other models based on Han-Nambu quarks [12, 14], the slnglet part under SU(3)' of the hadromc current will contribute to the semfleptonic interactions of hadrons. In the charged current only the first term revolves a singlet part i,e. i p 1 3'}'(1 + 75)n] = xl ]-}`Cablbbo+ telms trans, as I~, Y'.
(11)
In view of the assumption that 13' and Y' are good quantum numbers of the strong interactions, this decomposition will not be altered by strong Interactions symmetry breaking. It also ensures that CVC will be a good symmetry, as long as the interactions do not involve unobserved charmed hadrons, which are presumably very heavy, ff they exast. The non-slnglet term of the charged hadronic current will play the usual role as in the Glashow-Ihopoulos-Mianl method, Le It will cancel effective AS 4= 0 second-order contributions m the SU(3) X SU(3)' symmetry hmit. To obtain hadron-lepton umversal coupling to Wx, the mlxmg angle of neutrinos is fixed to be COS
Ot = I
(12)
.
The effective coupling of the charged currents is in our model
Left
_
charg.
9 8/142
[e- ')'}`(1 + 75)Ve + ~ 7}`(1 + 75)/)# +]~ab,bbo l }`
X [Ve "r}`(1 + 75)e + ~-u 3'}`(1 + 75)ta +ICablbbo]
(13)
+ terms involving charmed hadronic currents and/or heavy leptons. The effective Fermi couphng constant is therefore G
1
e2
(14)
- 9 8 M~V sin 2 Cw '
I.e. MW -
12 4 GeV sin @W
(15)
The neutral currents effective coupling is as follows Left n G-G----rx j}`J" neut = y N/r2 a T ~ T + h c
(16)
639
Y Achiman, ICemberg's gauge model
In pamcular, the effective interaction of the neutral hadronlc current with leptons is 9G ~l ' ~ 19 ~ "YX(1 + 75)re + ~ u--u7x( 1 + 7 5 ) u
(17)
- e- 7x(1 + 75)e - ~ 7x(1 + "/5)#+ 2 sm29w (TTXe + ffTx#)] I h + h.c. We see that the hadromc neutral current couples to neutrino terms with the Fermi couphng constant. The coupling to the charged leptons is enhanced by a factor 9, but this interaction is masked by the electromagnetic one. Using the exphclt form of the hadromc neutral current, eq. (18), one obtains the following expression (/XhZ)uncharmed= !2 [A~ + (I - 4 sm 2 ~0W)V~] + lsoscalar terms,
(18)
where A 3 and V3_are the lsovector axaal and vector currents respectively. This expresslon is chfferent from the hadromc neutral current of Wemberg's original model, which may be written as follows
(/~Z)Wemberg = A~ + (1 - 2 Sln2 tpW) V~ + lsoscalar terms.
(18W)
Our cross sections of neutnno-nucleon scattermg are therefore generally suppressed by a factor ¼, with respect to Wemberg's ones In parncular, if one recomputes the results of Albright, Lee and Paschos [6] using our current, eq. (18), the lower bound
on o ( v p ~ mOp) + o ( v n ~ vlr°p)
R =
2 o(vun ~/aTr0p)
is consistent with zero, under their approxtmations. Hence, the inconsistency of their lower bound with the experimental value [17], is not valid in our versmn. An analogous expression to eq. (17) describes pure leptonlc interactions. Hence, neutrinos scatter on charged leptons with the same couphng strength as m Wemberg's model The quarks have the same mass terms as m Wemberg's model, apart from additional terms hke - mq~Lq R + h.c.),
(19)
whach generate the masses of the scalar quarks under the weak gauge symmetry. The leptonlc mass terms wdl have m our model the following expressions me
rove'
-e
,
~. ~b-~e R $ - - - ~ - - sm a ~LVeR ~b+, - mve,
cos a ~ ' PeR + (e ~/2) + h.c.
(20)
The Adler-Bell-Jacklw [4, 5] anomalies are canceled out in our versmn also This Is because we add to the original Welnberg's theory only quarks which are scalars under the gauge group and Leptons which are neutrally charged. Also, the use of
640
Y Achtman, lqemberg's gauge model
Han-Nambu quarks insures the correct magnitude and sign of the n o -~ 77 amplitude. We have assumed, as m Wemberg's theory, that the model involves only one Hlggs doublet This is obviously a minimal assumption. We expect, however, that when the model will become a part of the complete theory of all interactions, including the strong ones more multlplets of Hlggs fields will be needed. This fact is known from gauge mvanant schemes where the minimal gauge group is enlarged, e.g. to SUL(3 ) × SUR(3 ) (ref [18]). This wtll also be the case in a theory which is able to predict definite relations between the masses of the fermlons *. In such a case it is possible that M Z is enhanced with respect to the value obtained using only one doublet of Hlggs fields Note, however, that we cannot enhance M z by a large amount without introducing a large family of Hlggs bosons (e.g. for (Mz/M0z) 2 ~ 100 one needs roughly 100 Hlggs bosons) [11]. To conclude, while other Han-Nambu versions of gauge models are aimed to obtam the conventional classification of hadrons only, we have here a new result namely, the suppression of terms which led to the apparent inconsistency of the original Wemberg model with experiment Notice also that this version is the only model consistent with experiment (and the usual classification of hadrons) that predicts neutral current effects in the near future neutrino experiments. The author would hke to thank Prof J. Prentkl for careful reading of the manuscript and especially for remarks and suggestions which play an important role m the present version of the paper. Note added zn p r o o f After submitting the paper for pubhcatlon we learned about other preprmts concerning the application of Han-Nambu quarks to gauge models [ 19, 20] Han-Nambu quarks are not used m those versions m the content of Wemberg's model. Also, the model of Rawls and Yu revolves an addlttonal nonet of charmed quarks Our version is simpler and more economical Very recently one serious vv + e- -~ vv + e- event was observed by the Gargamelle neutrino collaboration [21 ]. If the observation of neutral leptomc currents wall be confirmed, all models other than the Wemberg one will be excluded If at the same time AS = 0 neutral currents wall stay relatively suppresses [ 17], than the version of Wemberg's model with Han-Nambu quarks will be favoured.
References
[1] S Wemberg, Phys Rev. Letters 19 (1967) 1264. [2] S Wemberg, Phys. Rev 5D (1972) 1412. [3] S.L Glashow, J Ihopoulos and L Maml, Phys. Rev. D2 (1970) 1285. * The posslbfl:ty of postulating a larger number of Hlggs multlplets was already dascussed by Lee [11].
Y. Achtman, lfemberg 's gauge model
641
[4] S.L. Adler, Phys. Rev. 177 (1969) 2426, J.S. Bell and R. Jacklw, Nuovo Omento 60 (1969) 47. [5] C. Bouchlat, J. lllopoulos and Ph. Meyer, Phys. Letters 7 (1972), D Gross and R. Jacklw, Phys. Rev. D6 (1972) 477. [6] B.W. Lee, Phys. Letters B40 (1972) 420, Phys Letters B40 (1972) 423, E.A Paschos and L. Wolfenstem, NAL preprint, NAL-THY-69; C.H. Albnght, B.W Lee and E.A. Paschos, NAL preprmt, NAL-THY-86. [7] H. Georgl and S L Glashow, Phys Rev Letters 28 (1972) 1494. [8] J.D. Bjorken and C.H. LleweUyn Smith, SLAC prepnnt SLAC-PUB-1107 [9] J Prentkl and B. Zummo, Nucl Phys. B47 (1972) 99. [10] B.W. Lee, Phys. Rev D6 (1972) 1188 [11] B.W Lee, Report to a plenary session of the 16th Int. Conf on High energy physics, NAL, September, 1972, B Zummo, Lectures gwen at the Carges Summer Institute, July, 1972 TH-1550 CERN [12] H J. Dpkln, NAL report NAL-THY-85 [13] M.Y Han and Y. Nambu, Phys Rev 139B (1965) 1006. [14] H Georgl and S.L Glashow, Harvard prepnnt [15] R N. Mohapatra, Maryland report No 72-022 [16] B.W. Lee, J.R. Prlmack and S P Trelman, NAL preprmt, NAL-THY-74. [17] B.Y Lee in ref [6], and report by the CERN neutnno group of the 16th Int Conf on high energy physics, Batavia, Sept. 6 - 1 3 , 1972. [18] Y. Achiman, Heidelberg IHEP prepnnt. [19] A Love and G.G Ross, Rutherford Lab preprmt PPP/T/33. [20] J.M. Rawls and L.P Yu, San I~ego preprmt UCSD-10P10-118 [21] Von Krogh, Invited talk at the 1973 German Physical Soe. meeting, Heidelberg.
WEINBERG'S GAUGE MODEL FOR WEAK AND ELECTROMAGNETIC INTERACTIONS WITH HAN-NAMBU QUARKS Yoav ACHIMAN * Instltut fur Hochenergwphystk, UmversltatHeMelberg Recewed 29 December 1972 (Revised 5 March 1973) Abstract A version of the Wemberg model is constructed using Han-Nambu quarks, m order to obtain the conventional classification of hadrons The use of Han-Nambu quarks leads to a suppression of neutrmos coupled to the AS = 0 hadromc current, while the coupling to neutral leptomc currents remains as m Wemberg's theory. Wemberg's renormahzable gauge theory of weak and electromagnetic interactions was originally [ 1 ] apphed to leptons only. In order to generahze the model for hadrons, m a way that avoids unwanted AS ~ 0 transitions, Wemberg [2] used the idea of Glashow-Ihopoulos-Malm [3], winch amounts to the introduction of a new charmed p-like quark. The same method allows also the cancelation of Adler-BeilJacklw [4, 5] anomalies, winch may Interfere w~th the renormallzatlon programme. However, the observed spectrum o f hadrons, winch is so well generated by the different versions o f the quark model, does not find a simple interpretation m terms of this model. Another weak point of Welnberg's model is that the couphng o f neutrinos to the neutral AS = 0 hadronic current is on the edge of inconsistency with experiment [6] To avoid the second difficulty, new models were set forward. An 0(3) model was proposed by Georgl and Glashow [7] and improved by Blorken [8], tins model avoids completely the use of a weak neutral current. Prentkl and Zumino [9] and Lee [10] suggested SU(2) X U(1) models m winch the neutral weak currents do not contain a ~-v term. Other possible models of tins kind were discussed by Bjorken and Llewelyn Smith [8, 11 ]. Recently Llpkm [12] suggested that the charmed quarks m the Georgl and Glashow model may f'md a natural place in the family of Han-Nambu quarks [13]. If Han-Nambu quarks are used as basic hadrons the good predictions of the naive quark model_are incorporated in the_ model without difficulties wxth the statistics o f quarks or with the n 0 -~ 77 amplitude. Georgl and Glashow [14] gave an exphclt * Volkswagenstiftung fellow.
Y. Achtman, Wemberg's gauge model
636
version of their 0(3) model [7] using Han-Nambu quarks This is, however, done m a rather comphcate way *. It should be desirable to have a version of Wemberg's model using Han-Nambu quarks as this Is the simplest and most economical gauge model. It wall be shown that this can be done m a way that avoids the apparent inconsistency of the original model with experiment [6]. This model will be of special interest if neutral leptomc currents will be observed while the AS = 0 neutral hadromc currents remain relatively suppressed. The mass of the vector mtermedmte bosons is reduced by a factor three with respect to Welnberg M w ~> 12 4 GeV. The nine Han-Nambu quarks constitute the followmg three triplets under the conventmnal strong mteractmns SU(3)
:i1 :i1 f °l The p-quarks (p~, p~, pO) are assumed to constitute a triplet under another SU(3) (SU(3)'), and this is true for the triplets of n-quarks and X-quarks, SU(3)' Is also assumed to be an apprommate symmetry o f the strongmteractmns. (In particular we want 13' and Y' to be good quantum numbers under the strong interactmns) [ 14]. All observed hadrons are taken to be slnglets under SU(3)' and their properties are the same as in the quark model. To obtain a Wemberg-hke gauge model, we need two doublets under the SUL(2 ) X U(1) gauge group A natural way to do this is as follows Pl
--
_
(1,
,
(2)
L
() P2
_
where C
n l = c o s 0 c n 1 + s i n 0 c x 1, X~ = - s i n 0 c n 1 + c o s 0 c x 1 The corresponding nght-handed particles we take to be smglets All the other quarks are also scalars under SUL(2), and they enter the weak interactions currents only vla * A version of the Georgl-Glashow model with Han-Nambu quarks was also suggested by Mohapatra [ 15 ] This version leads to a great rate of KL --*/~+t~-(ref. [ 16] ) m contradiction with experiment
Y. Achtman, Wemberg'sgauge model
637
the electromagnetic one (prowdes they are charged). This procedure do not lead to any difficulty as the new mass terms are independent of the Higgs scalar bosons. As leptons we use the following left-handed doublets and slnglets t
~L
e-
L (3)
/js
/L P
~'~ = ( - sin a ve + cos ¢xve ) L ,
~'= (- sm ~
(4)
~. + cos ~ ~'. )L" I
t
All right-handed leptons e R,/JR, VeR and VuR are scalars Notice that we have used the same mixing for electrons and muons in order to obtain e - / j umversahty. As m all SU L (2) X U(1) gauge theories [ 11], the mteracuon Lagranglan of the fermlons w~th the Yang-Mdls vector bosons A x and B x ~s m the form
t' = ½gA~,• .f'+½g'B~,(J~ -
2J~~,'m)'
(5)
where g, g' are arbitrary couphng constants. Wemberg's theory involves one Hlggs scalar doublet
(°-)
¢~= ~o
'
whose vacuum expectation value
will break spontaneously the SUL(2 ) X U(1) gauge symmetry down to the electromagnetic one. The charged weak currents can be written exphcltly in the hadromc and the leptonic spaces in the following way
f~W =l Pl 7X( 1 + 75) n~ + i if2 'Yh(1 + 3'5) 2~,
(7)
J~W = cos a [i V-e 7x( 1 + 75) e- + l vu 7h(1 + 75)/j-] + sm a [i Su ~/r'(1 + , s ) e - + i-~, 3,x(1 + "rS)'-],
(8)
while the neutral weak currents take the followmg form ]~Z =½ [iPl 7h( I + 'Y5)Pl + iP2 7X( 1 + "Y5)P2- i n l Th( 1 + 3'5)nl -- t X-I 7X( 1 + "}'5)X1] -- 2 sin 2 ~ow (IXe,m)h ,
(9)
638
Y Achtman, Wemberg's gauge model
]~Z = ½{- iT- 7}'(1 + 75)e- + i cos 2 a v-e 7}'(1 + 75)re + i sm 2 ¢~ v-e 7}'(1 + 75)Ve + sin a cos a ~e 7}'(1 + 75)Ve
(10)
+ v-~ 7}'(1 + 75)vel + (e -+ p)} - 2 sin 2 ~ow (/'eX,,m),g_., where r
_g tg ~W - ~" As In the other models based on Han-Nambu quarks [12, 14], the slnglet part under SU(3)' of the hadromc current will contribute to the semfleptonic interactions of hadrons. In the charged current only the first term revolves a singlet part i,e. i p 1 3'}'(1 + 75)n] = xl ]-}`Cablbbo+ telms trans, as I~, Y'.
(11)
In view of the assumption that 13' and Y' are good quantum numbers of the strong interactions, this decomposition will not be altered by strong Interactions symmetry breaking. It also ensures that CVC will be a good symmetry, as long as the interactions do not involve unobserved charmed hadrons, which are presumably very heavy, ff they exast. The non-slnglet term of the charged hadronic current will play the usual role as in the Glashow-Ihopoulos-Mianl method, Le It will cancel effective AS 4= 0 second-order contributions m the SU(3) X SU(3)' symmetry hmit. To obtain hadron-lepton umversal coupling to Wx, the mlxmg angle of neutrinos is fixed to be COS
Ot = I
(12)
.
The effective coupling of the charged currents is in our model
Left
_
charg.
9 8/142
[e- ')'}`(1 + 75)Ve + ~ 7}`(1 + 75)/)# +]~ab,bbo l }`
X [Ve "r}`(1 + 75)e + ~-u 3'}`(1 + 75)ta +ICablbbo]
(13)
+ terms involving charmed hadronic currents and/or heavy leptons. The effective Fermi couphng constant is therefore G
1
e2
(14)
- 9 8 M~V sin 2 Cw '
I.e. MW -
12 4 GeV sin @W
(15)
The neutral currents effective coupling is as follows Left n G-G----rx j}`J" neut = y N/r2 a T ~ T + h c
(16)
639
Y Achiman, ICemberg's gauge model
In pamcular, the effective interaction of the neutral hadronlc current with leptons is 9G ~l ' ~ 19 ~ "YX(1 + 75)re + ~ u--u7x( 1 + 7 5 ) u
(17)
- e- 7x(1 + 75)e - ~ 7x(1 + "/5)#+ 2 sm29w (TTXe + ffTx#)] I h + h.c. We see that the hadromc neutral current couples to neutrino terms with the Fermi couphng constant. The coupling to the charged leptons is enhanced by a factor 9, but this interaction is masked by the electromagnetic one. Using the exphclt form of the hadromc neutral current, eq. (18), one obtains the following expression (/XhZ)uncharmed= !2 [A~ + (I - 4 sm 2 ~0W)V~] + lsoscalar terms,
(18)
where A 3 and V3_are the lsovector axaal and vector currents respectively. This expresslon is chfferent from the hadromc neutral current of Wemberg's original model, which may be written as follows
(/~Z)Wemberg = A~ + (1 - 2 Sln2 tpW) V~ + lsoscalar terms.
(18W)
Our cross sections of neutnno-nucleon scattermg are therefore generally suppressed by a factor ¼, with respect to Wemberg's ones In parncular, if one recomputes the results of Albright, Lee and Paschos [6] using our current, eq. (18), the lower bound
on o ( v p ~ mOp) + o ( v n ~ vlr°p)
R =
2 o(vun ~/aTr0p)
is consistent with zero, under their approxtmations. Hence, the inconsistency of their lower bound with the experimental value [17], is not valid in our versmn. An analogous expression to eq. (17) describes pure leptonlc interactions. Hence, neutrinos scatter on charged leptons with the same couphng strength as m Wemberg's model The quarks have the same mass terms as m Wemberg's model, apart from additional terms hke - mq~Lq R + h.c.),
(19)
whach generate the masses of the scalar quarks under the weak gauge symmetry. The leptonlc mass terms wdl have m our model the following expressions me
rove'
-e
,
~. ~b-~e R $ - - - ~ - - sm a ~LVeR ~b+, - mve,
cos a ~ ' PeR + (e ~/2) + h.c.
(20)
The Adler-Bell-Jacklw [4, 5] anomalies are canceled out in our versmn also This Is because we add to the original Welnberg's theory only quarks which are scalars under the gauge group and Leptons which are neutrally charged. Also, the use of
640
Y Achtman, lqemberg's gauge model
Han-Nambu quarks insures the correct magnitude and sign of the n o -~ 77 amplitude. We have assumed, as m Wemberg's theory, that the model involves only one Hlggs doublet This is obviously a minimal assumption. We expect, however, that when the model will become a part of the complete theory of all interactions, including the strong ones more multlplets of Hlggs fields will be needed. This fact is known from gauge mvanant schemes where the minimal gauge group is enlarged, e.g. to SUL(3 ) × SUR(3 ) (ref [18]). This wtll also be the case in a theory which is able to predict definite relations between the masses of the fermlons *. In such a case it is possible that M Z is enhanced with respect to the value obtained using only one doublet of Hlggs fields Note, however, that we cannot enhance M z by a large amount without introducing a large family of Hlggs bosons (e.g. for (Mz/M0z) 2 ~ 100 one needs roughly 100 Hlggs bosons) [11]. To conclude, while other Han-Nambu versions of gauge models are aimed to obtam the conventional classification of hadrons only, we have here a new result namely, the suppression of terms which led to the apparent inconsistency of the original Wemberg model with experiment Notice also that this version is the only model consistent with experiment (and the usual classification of hadrons) that predicts neutral current effects in the near future neutrino experiments. The author would hke to thank Prof J. Prentkl for careful reading of the manuscript and especially for remarks and suggestions which play an important role m the present version of the paper. Note added zn p r o o f After submitting the paper for pubhcatlon we learned about other preprmts concerning the application of Han-Nambu quarks to gauge models [ 19, 20] Han-Nambu quarks are not used m those versions m the content of Wemberg's model. Also, the model of Rawls and Yu revolves an addlttonal nonet of charmed quarks Our version is simpler and more economical Very recently one serious vv + e- -~ vv + e- event was observed by the Gargamelle neutrino collaboration [21 ]. If the observation of neutral leptomc currents wall be confirmed, all models other than the Wemberg one will be excluded If at the same time AS = 0 neutral currents wall stay relatively suppresses [ 17], than the version of Wemberg's model with Han-Nambu quarks will be favoured.
References
[1] S Wemberg, Phys Rev. Letters 19 (1967) 1264. [2] S Wemberg, Phys. Rev 5D (1972) 1412. [3] S.L Glashow, J Ihopoulos and L Maml, Phys. Rev. D2 (1970) 1285. * The posslbfl:ty of postulating a larger number of Hlggs multlplets was already dascussed by Lee [11].
Y. Achtman, lfemberg 's gauge model
641
[4] S.L. Adler, Phys. Rev. 177 (1969) 2426, J.S. Bell and R. Jacklw, Nuovo Omento 60 (1969) 47. [5] C. Bouchlat, J. lllopoulos and Ph. Meyer, Phys. Letters 7 (1972), D Gross and R. Jacklw, Phys. Rev. D6 (1972) 477. [6] B.W. Lee, Phys. Letters B40 (1972) 420, Phys Letters B40 (1972) 423, E.A Paschos and L. Wolfenstem, NAL preprint, NAL-THY-69; C.H. Albnght, B.W Lee and E.A. Paschos, NAL preprmt, NAL-THY-86. [7] H. Georgl and S L Glashow, Phys Rev Letters 28 (1972) 1494. [8] J.D. Bjorken and C.H. LleweUyn Smith, SLAC prepnnt SLAC-PUB-1107 [9] J Prentkl and B. Zummo, Nucl Phys. B47 (1972) 99. [10] B.W. Lee, Phys. Rev D6 (1972) 1188 [11] B.W Lee, Report to a plenary session of the 16th Int. Conf on High energy physics, NAL, September, 1972, B Zummo, Lectures gwen at the Carges Summer Institute, July, 1972 TH-1550 CERN [12] H J. Dpkln, NAL report NAL-THY-85 [13] M.Y Han and Y. Nambu, Phys Rev 139B (1965) 1006. [14] H Georgl and S.L Glashow, Harvard prepnnt [15] R N. Mohapatra, Maryland report No 72-022 [16] B.W. Lee, J.R. Prlmack and S P Trelman, NAL preprmt, NAL-THY-74. [17] B.Y Lee in ref [6], and report by the CERN neutnno group of the 16th Int Conf on high energy physics, Batavia, Sept. 6 - 1 3 , 1972. [18] Y. Achiman, Heidelberg IHEP prepnnt. [19] A Love and G.G Ross, Rutherford Lab preprmt PPP/T/33. [20] J.M. Rawls and L.P Yu, San I~ego preprmt UCSD-10P10-118 [21] Von Krogh, Invited talk at the 1973 German Physical Soe. meeting, Heidelberg.