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Deep inelastic muon scattering as a test of gauge theories
Volume 76B, number 1
PHYSICS LETTERS
8 May 1978
DEEP INELASTIC MUON SCATTERING AS A TEST OF GAUGE THEORIES M. KLEIN and T. RIEMANN 1 Joint Institute for Nuclear Research, High Energy Laboratory, Dubna, USSR
Received 14 February 1978
Different asymmetries in polarized lepton scattering are shown to be remarkably dependent on the valence quark and lepton multiplet structure in currently discussed gauge theories. Therefore deep inelastic muon experiments at SPS energies can contribute significantly to the investigation of neutral currents.
In the near future high energy deep inelastic muon experiments will be performed probing the nucleon structure at m o m e n t u m transfers, Q 2 of a few hundreds (GeV/c) 2 [1]. For muons and electrons both having electromagnetic and weak interactions, neutral current effects are expected to be of the order of K = a 2 G / ( v ~ . 2 r r o O ~ 1.8 X 10-4Q 2 ,
atomic experiments could require to extend the gauge group. As corresponding examples, we consider SU(2)L X SU(2)R X U(1) theories which predict the absence [6] *2 or a reduced size [7] of parity violation in atoms although having a rich V, A structure. The weak current coupling to the Z-field is given by
(1)
resulting from the interference of the one-photon exchange with the Z-boson exchange [2,3]. A measurement of these effects yields new and independent information on the structure of neutral currents which is very desirable considering the rather ambiguous experimental situation [4]. Therefore we perform a comprehensive quark parton model evaluation of different cross section asymmetries in polarized ~+- scattering for various gauge theories * 1. The main question involved concerns the extent to which the predictions of currently discussed gauge models differ from one another. Assuming natural flavour conservation, any neutral current process in the valence quark approximation is sensitive only to the £, u, d sector of corresponding models. Based on SU(2) × U(1) invariance, there are eight possibilities to arrange ~, u, d in righthanded (r.h.) singlets or doublets, respectively, which are included in the following discussion. The contradiction between neutral current results from neutrino and ,1 On leave of absence from: Institut ftir Hochenergiephysik tier Akademie der Wissenschaften der DDR, Berlin-Zeuthen. ,1 See ref. [5] for a recent investigation of the influence of electromagnetic corrections.
i2gz~'I'm(vff - a ~ ' ~ s ) ~ Z m .
(2)
Here ff is ta(e), u or d and gz is the coupling constant. In the SU(2) X U(1) theories under consideration one has for the conventional Higgs structure g2 = 2 M 2 G / v~and %=I L+I R-2Qsin20,
aqj = I L - I R,
(3)
where 1LfR) denotes the third component of the weak SU(2) in the corresponding 1.h. (r.h.) doublet, Q is the electric charge and sin20 the unification angle. Using the above definitions, we can calculate d ~ , the deep inelastic cross section of scattering leptons with charge -v, and an averaged beam helicity ~ off nucleons. Normalizing to the one-photon exchange cross section do 0, one has for any SU(2) X U(1) theory do~/do0 = 1 - K [uu V(x) T- a u A ( x ) g ( y )
(4)
+ ~ ( ~ a V(x) + u A ( x ) g ( y ) ) ] ,
with g(y) = y ( 2 - y ) / ( 1 + (1 ._y)2). Here V(x) and +2 Note some printing errors in ref. [6]. 79
Volume 76B, n u m b e r 1
PHYSICS LETTERS
A ( x ) are ratios of structure functions defined as in ref.
[3], which are independent o f x for an isoscalar target V=(2vu - v d ) . 6 / 5 ,
A=(a d-2au).6/5.
(5)
According to eq. (4) several asymmetry parameters can be measured: (i) parity violation asymmetries varying only the helicity: A ~ - do~(~>0) - da*(~<0) da~(~ > 0 ) + da~(~ < 0 )
(6)
= _• I~l(;-aV+v~zag(.y)) ;
(ii) a "beam conjugation" asymmetry varying both the beam charge and the helicity: a - da+(~ > 0 ) - d a - ( ~ < 0 ) do+(~ > 0) + d a - ( ~ < 0 )
(7)
= _ ~(a u + [ ~ [ o u ) A g ( y ) ;
(iii) charge asymmetries varying only the beam charge: D = .d°+(~) - do- (~) _
K a u ( A g ( y ) + ~V) ,
do+(~) + do-(G)
(8)
c= D(~=O). Note that certain ratios of asymmetries measure purely leptonic or purely hadronic couplings, i.e. C/B=au/(a
+ I~lvu),
C/O=Zg(y)/(Zg(y)+~V).
(9)
The SU(2)L × SU(2)R × U(1) model of Mohapatra and Sidhu (MS) [6] having two Z-bosons predicts A + = A - = 0 and B = C = D = - a ( 1 ) A ( 1 ) g ( y ) • 2~/(1 + e) #
(10)
a~(1) = _ 1/2,A (1) = - 9 / 5 , e m 0.1) because Z 1 has only axial couplings and Z2 only vector couplings to massive particles. In the model of De ROjula, Georgi and Glashow (DGG) [7], Z 1 corresponds to the neutral gauge boson in the Salam-Weinberg]GIM-theory (SW) and Z 2 has again only vector couplings. Asymmetries arise in DGG which are about one half of those predicted by SW. Deep inelastic muon experiments at the CERN SPS
80
8 May 1978
will reach a Q2 of about 200 (GeV/c)2 with an accuracy of 1% for the asymmetries using a 50 m carbon target [1,8]. Adopting this Q2 as a reasonable value for illustration, we study A - D as functions of the relative energy transfer y, the helicity ~ and the unification angle sin20. In fig. 1 the y-dependence ofA - D is shown at sin20 = 1/4 +3 and ~ = 1 for the gauge models considered disregarding the pure vector model where all asymmetries are zero. As can be seen, different models yield remarkably different predictions all being only weakly dependent on y. The strongest differences are revealed by the parity violation asymmetry A + and the beam charge asymmetry D. Evidently, experinaental errors smaller or about 1%, i.e. (5 × 10-3Q2)%, are necessary to decide whether the lepton is in a r.h. doublet or not. If ~ occurs only in l.h. doublets (solid curves), the quark couplings can be determined from the asymmetry D. On the other hand, one easily realizes that an improved accuracy of at least 1/2% is required to resolve the quark coupling structure if there is a r.h. lepton doublet (dashed curves). The behaviour of the SU(2) L X SU(2)R X U(1) models considered is shared by none of the SU(2) X U(1) models. Note the particularly large charge asymmetry in MS. Additional informations arise from the helicity dependence ofA - D . The slopes and intercepts of the straight lines a +b~ can be determined by varying ~, i.e. varying the momentum of the n,K parent beam and keeping the muon momentum fixed [9]. The asymmetries depend linearly on sin20. Therefore in fig. 2, the angular dependence of A - D is given for y = 3/4 and ~ = 1. One can distinguish three groups of asymmetry parameters. The information being extractable from A - is nearly independent of sin20. For A+ and B the mean spacing between different predictions decreases with increasing sin20. Note, however, that even the exotic value of sin20 ~ 0.5 would allow one to determine the coupling of the muon in SU(2) X U(1) models from A +. Finally, the usefulness of C and D is the same for any sin20 fixed. Thus, if nature prefers another unification angle than 1/4 analogous conclusions can be drawn. *3 Taken seriously, the value of sin20 = 1/4 [4] implies v• = 0 in the standard model (eq. (3)). T h u s in the f r a m e w o r k of SU(2) X U(1) invariance, the recent CDHS neutrino experiment is most contradictory to atomic parity experiments indicating a~ = 0,
Volume 76B, n u m b e r 1
PHYSICS LETTERS
A-
A-"
B
*/* 4
(u~d)
2
d
I
-
C
S W
.
.
.
t
-
lu,d) .
D (%d)
MS 0
8 May 1978
(u,)u~qd~L);)I/.ilU/J)
.
,,-
4 5 J(u,d) 0.5
\.
\
"..MMSj 0.75
1 0.5
0.75
0.5
0.75
1 0.5
0.75
~.MS 0.5
0.75
1
Y Fig. 1. A s y m m e t r i e s (cqs. ( 6 ) - ( 8 ) ) as functions o f y at sin20 = 1/4, Q2 = 200 (GeV/c) ~ and ~ = 1 for various gauge theories. The SU(2) X U(1) curves are denoted by the particles occuring in r.h. doublets. SW is Salam-Weinberg/GIM, MS is ref. [6]. DGG [7] n o t shown here yields about one half o f SW.
It is evident that the complete set of asymmetries can be studied only for muons, where positively and negatively charged polarized beams are available. Deep inelastic electron experiments measure only A - (eq. (6)) and must be combined with other reaction channels as the elastic one to draw definite conclusions on the weak couplings [10].
A-
A "+
To summarize, deep inelastic polarized muon experiments reaching momentum transfers, Q2, of sever. al hundred (GeV/c) 2 can be considered as a new and independent source of information on the isospin structure of weak neutral currents of leptons and of hadrons. They are expected to be able to distinguish between currently discussed classes of gauge theories
B
C
_10
0.1
D
iu,~),~,~.);~, ;Cu,d) /
0.3
0.5
0.1
0.3
0.5
0.1
0.3
0.5
0.1
0.3
0.5
~,~"~.~,~;
0.1
0.3
0.5
sin2 e
Fig. 2. A s y m m e t r i e s (eqs. ( 6 ) - ( 8 ) ) as functions of sin20 at y = 3]4, Q2 = 200 (GeV/c) 2 and ~ = 1 for various gauge theories. The SU(2) X U(1) curves are denoted b y the particles occuring in r.h. doublets. SW is Salam-Weinberg/GIM, MS is ref. [6]. DGG [7] n o t shown here yields about one half of SW.
81
Volume 76B, number 1
PHYSICS LETTERS
provided the experimental accuracy for corresponding observables is smaller than (5 × 10-3Q2)% which appears to be reachable at the CERN SPS. We are indebted to D. Yu. Bardin, S. M. Bilenky, A. De Rfijula, W. -D. Nowak, I. A. Savin, and N. M. Shumeiko for valuable discussions and suggestions.
References [1 ] CERN-Dubna-Munich-SaclayCollaboration NA4, CERN/SPSC/74-79, P19 (1974). [2] E. Derman, Phys. Rev. D7 (1973) 2755; S.M. Bilenky and S.T. Petcov, JINR, E2-10809 (1977); M. Gourdin, Paris, LPTHE 77/08 (1977), and references therein.
82
8 May 1978
[3] S. M. Berman and J.R. Primack, Phys. Rev. D9 (1974) 2171. [4] For recent neutrino and atomic physics results see: P. Musset, CERN/EP/PHYS 77-48, Invited Talk at the Lepton-Photon Symp. (Hamburg, 1977). [5] D.Yu. Bardin and N.M. Shumeiko, JINR, P2-10873 (1977). [6] R. Mohapatra and D. Sidhu, Phys. Rev. Lett. 35 (1977) 667. [7] A.De Rfijula, H. Georgi and S. Glashow, Ann. Phys. 109 (1977) 242. [8] Meeting of the NA4 Collaboration (Dubna, 1977) unpublished. [9] K. Winter, Phys. Lett. 67B (1977) 236. [10] R.N. Cahn and F.J. Gilman, SLAC-PUB-2002(1977), submitted to Phys. Rev.
PHYSICS LETTERS
8 May 1978
DEEP INELASTIC MUON SCATTERING AS A TEST OF GAUGE THEORIES M. KLEIN and T. RIEMANN 1 Joint Institute for Nuclear Research, High Energy Laboratory, Dubna, USSR
Received 14 February 1978
Different asymmetries in polarized lepton scattering are shown to be remarkably dependent on the valence quark and lepton multiplet structure in currently discussed gauge theories. Therefore deep inelastic muon experiments at SPS energies can contribute significantly to the investigation of neutral currents.
In the near future high energy deep inelastic muon experiments will be performed probing the nucleon structure at m o m e n t u m transfers, Q 2 of a few hundreds (GeV/c) 2 [1]. For muons and electrons both having electromagnetic and weak interactions, neutral current effects are expected to be of the order of K = a 2 G / ( v ~ . 2 r r o O ~ 1.8 X 10-4Q 2 ,
atomic experiments could require to extend the gauge group. As corresponding examples, we consider SU(2)L X SU(2)R X U(1) theories which predict the absence [6] *2 or a reduced size [7] of parity violation in atoms although having a rich V, A structure. The weak current coupling to the Z-field is given by
(1)
resulting from the interference of the one-photon exchange with the Z-boson exchange [2,3]. A measurement of these effects yields new and independent information on the structure of neutral currents which is very desirable considering the rather ambiguous experimental situation [4]. Therefore we perform a comprehensive quark parton model evaluation of different cross section asymmetries in polarized ~+- scattering for various gauge theories * 1. The main question involved concerns the extent to which the predictions of currently discussed gauge models differ from one another. Assuming natural flavour conservation, any neutral current process in the valence quark approximation is sensitive only to the £, u, d sector of corresponding models. Based on SU(2) × U(1) invariance, there are eight possibilities to arrange ~, u, d in righthanded (r.h.) singlets or doublets, respectively, which are included in the following discussion. The contradiction between neutral current results from neutrino and ,1 On leave of absence from: Institut ftir Hochenergiephysik tier Akademie der Wissenschaften der DDR, Berlin-Zeuthen. ,1 See ref. [5] for a recent investigation of the influence of electromagnetic corrections.
i2gz~'I'm(vff - a ~ ' ~ s ) ~ Z m .
(2)
Here ff is ta(e), u or d and gz is the coupling constant. In the SU(2) X U(1) theories under consideration one has for the conventional Higgs structure g2 = 2 M 2 G / v~and %=I L+I R-2Qsin20,
aqj = I L - I R,
(3)
where 1LfR) denotes the third component of the weak SU(2) in the corresponding 1.h. (r.h.) doublet, Q is the electric charge and sin20 the unification angle. Using the above definitions, we can calculate d ~ , the deep inelastic cross section of scattering leptons with charge -v, and an averaged beam helicity ~ off nucleons. Normalizing to the one-photon exchange cross section do 0, one has for any SU(2) X U(1) theory do~/do0 = 1 - K [uu V(x) T- a u A ( x ) g ( y )
(4)
+ ~ ( ~ a V(x) + u A ( x ) g ( y ) ) ] ,
with g(y) = y ( 2 - y ) / ( 1 + (1 ._y)2). Here V(x) and +2 Note some printing errors in ref. [6]. 79
Volume 76B, n u m b e r 1
PHYSICS LETTERS
A ( x ) are ratios of structure functions defined as in ref.
[3], which are independent o f x for an isoscalar target V=(2vu - v d ) . 6 / 5 ,
A=(a d-2au).6/5.
(5)
According to eq. (4) several asymmetry parameters can be measured: (i) parity violation asymmetries varying only the helicity: A ~ - do~(~>0) - da*(~<0) da~(~ > 0 ) + da~(~ < 0 )
(6)
= _• I~l(;-aV+v~zag(.y)) ;
(ii) a "beam conjugation" asymmetry varying both the beam charge and the helicity: a - da+(~ > 0 ) - d a - ( ~ < 0 ) do+(~ > 0) + d a - ( ~ < 0 )
(7)
= _ ~(a u + [ ~ [ o u ) A g ( y ) ;
(iii) charge asymmetries varying only the beam charge: D = .d°+(~) - do- (~) _
K a u ( A g ( y ) + ~V) ,
do+(~) + do-(G)
(8)
c= D(~=O). Note that certain ratios of asymmetries measure purely leptonic or purely hadronic couplings, i.e. C/B=au/(a
+ I~lvu),
C/O=Zg(y)/(Zg(y)+~V).
(9)
The SU(2)L × SU(2)R × U(1) model of Mohapatra and Sidhu (MS) [6] having two Z-bosons predicts A + = A - = 0 and B = C = D = - a ( 1 ) A ( 1 ) g ( y ) • 2~/(1 + e) #
(10)
a~(1) = _ 1/2,A (1) = - 9 / 5 , e m 0.1) because Z 1 has only axial couplings and Z2 only vector couplings to massive particles. In the model of De ROjula, Georgi and Glashow (DGG) [7], Z 1 corresponds to the neutral gauge boson in the Salam-Weinberg]GIM-theory (SW) and Z 2 has again only vector couplings. Asymmetries arise in DGG which are about one half of those predicted by SW. Deep inelastic muon experiments at the CERN SPS
80
8 May 1978
will reach a Q2 of about 200 (GeV/c)2 with an accuracy of 1% for the asymmetries using a 50 m carbon target [1,8]. Adopting this Q2 as a reasonable value for illustration, we study A - D as functions of the relative energy transfer y, the helicity ~ and the unification angle sin20. In fig. 1 the y-dependence ofA - D is shown at sin20 = 1/4 +3 and ~ = 1 for the gauge models considered disregarding the pure vector model where all asymmetries are zero. As can be seen, different models yield remarkably different predictions all being only weakly dependent on y. The strongest differences are revealed by the parity violation asymmetry A + and the beam charge asymmetry D. Evidently, experinaental errors smaller or about 1%, i.e. (5 × 10-3Q2)%, are necessary to decide whether the lepton is in a r.h. doublet or not. If ~ occurs only in l.h. doublets (solid curves), the quark couplings can be determined from the asymmetry D. On the other hand, one easily realizes that an improved accuracy of at least 1/2% is required to resolve the quark coupling structure if there is a r.h. lepton doublet (dashed curves). The behaviour of the SU(2) L X SU(2)R X U(1) models considered is shared by none of the SU(2) X U(1) models. Note the particularly large charge asymmetry in MS. Additional informations arise from the helicity dependence ofA - D . The slopes and intercepts of the straight lines a +b~ can be determined by varying ~, i.e. varying the momentum of the n,K parent beam and keeping the muon momentum fixed [9]. The asymmetries depend linearly on sin20. Therefore in fig. 2, the angular dependence of A - D is given for y = 3/4 and ~ = 1. One can distinguish three groups of asymmetry parameters. The information being extractable from A - is nearly independent of sin20. For A+ and B the mean spacing between different predictions decreases with increasing sin20. Note, however, that even the exotic value of sin20 ~ 0.5 would allow one to determine the coupling of the muon in SU(2) X U(1) models from A +. Finally, the usefulness of C and D is the same for any sin20 fixed. Thus, if nature prefers another unification angle than 1/4 analogous conclusions can be drawn. *3 Taken seriously, the value of sin20 = 1/4 [4] implies v• = 0 in the standard model (eq. (3)). T h u s in the f r a m e w o r k of SU(2) X U(1) invariance, the recent CDHS neutrino experiment is most contradictory to atomic parity experiments indicating a~ = 0,
Volume 76B, n u m b e r 1
PHYSICS LETTERS
A-
A-"
B
*/* 4
(u~d)
2
d
I
-
C
S W
.
.
.
t
-
lu,d) .
D (%d)
MS 0
8 May 1978
(u,)u~qd~L);)I/.ilU/J)
.
,,-
4 5 J(u,d) 0.5
\.
\
"..MMSj 0.75
1 0.5
0.75
0.5
0.75
1 0.5
0.75
~.MS 0.5
0.75
1
Y Fig. 1. A s y m m e t r i e s (cqs. ( 6 ) - ( 8 ) ) as functions o f y at sin20 = 1/4, Q2 = 200 (GeV/c) ~ and ~ = 1 for various gauge theories. The SU(2) X U(1) curves are denoted by the particles occuring in r.h. doublets. SW is Salam-Weinberg/GIM, MS is ref. [6]. DGG [7] n o t shown here yields about one half o f SW.
It is evident that the complete set of asymmetries can be studied only for muons, where positively and negatively charged polarized beams are available. Deep inelastic electron experiments measure only A - (eq. (6)) and must be combined with other reaction channels as the elastic one to draw definite conclusions on the weak couplings [10].
A-
A "+
To summarize, deep inelastic polarized muon experiments reaching momentum transfers, Q2, of sever. al hundred (GeV/c) 2 can be considered as a new and independent source of information on the isospin structure of weak neutral currents of leptons and of hadrons. They are expected to be able to distinguish between currently discussed classes of gauge theories
B
C
_10
0.1
D
iu,~),~,~.);~, ;Cu,d) /
0.3
0.5
0.1
0.3
0.5
0.1
0.3
0.5
0.1
0.3
0.5
~,~"~.~,~;
0.1
0.3
0.5
sin2 e
Fig. 2. A s y m m e t r i e s (eqs. ( 6 ) - ( 8 ) ) as functions of sin20 at y = 3]4, Q2 = 200 (GeV/c) 2 and ~ = 1 for various gauge theories. The SU(2) X U(1) curves are denoted b y the particles occuring in r.h. doublets. SW is Salam-Weinberg/GIM, MS is ref. [6]. DGG [7] n o t shown here yields about one half of SW.
81
Volume 76B, number 1
PHYSICS LETTERS
provided the experimental accuracy for corresponding observables is smaller than (5 × 10-3Q2)% which appears to be reachable at the CERN SPS. We are indebted to D. Yu. Bardin, S. M. Bilenky, A. De Rfijula, W. -D. Nowak, I. A. Savin, and N. M. Shumeiko for valuable discussions and suggestions.
References [1 ] CERN-Dubna-Munich-SaclayCollaboration NA4, CERN/SPSC/74-79, P19 (1974). [2] E. Derman, Phys. Rev. D7 (1973) 2755; S.M. Bilenky and S.T. Petcov, JINR, E2-10809 (1977); M. Gourdin, Paris, LPTHE 77/08 (1977), and references therein.
82
8 May 1978
[3] S. M. Berman and J.R. Primack, Phys. Rev. D9 (1974) 2171. [4] For recent neutrino and atomic physics results see: P. Musset, CERN/EP/PHYS 77-48, Invited Talk at the Lepton-Photon Symp. (Hamburg, 1977). [5] D.Yu. Bardin and N.M. Shumeiko, JINR, P2-10873 (1977). [6] R. Mohapatra and D. Sidhu, Phys. Rev. Lett. 35 (1977) 667. [7] A.De Rfijula, H. Georgi and S. Glashow, Ann. Phys. 109 (1977) 242. [8] Meeting of the NA4 Collaboration (Dubna, 1977) unpublished. [9] K. Winter, Phys. Lett. 67B (1977) 236. [10] R.N. Cahn and F.J. Gilman, SLAC-PUB-2002(1977), submitted to Phys. Rev.