Right-handed weak currents in neutrino scattering

Volume 59B, number 1

PHYSICS LETTERS

13 October 1975

R I G H T - H A N D E D W E A K C U R R E N T S IN N E U T R I N O S C A T T E R I N G ¢r v. BARGER and T. WEILER Department o f Physics, University o f Wisconsin, Madison, Wisconsin 537, USA

R.J.N. PHILLIPS Rutherford Laboratory, Chilton, Didcot, Oxon, UK Received 26 August 1975 We investigate transition strengths of right-handed weak charged currents in deep inelastic neutrino scattering, exploiting the dominance of p, n valence quarks in the nucleon. The energy dependences of a t and the average quantities
Recently a great deal of speculation [1-10] has centered on the possible existence of right-handed V + A terms in the weak current, in addition to the usual left-handed V - A terms. These V + A currents couple the p, n quarks to quarks with new quantum numbers, and become effective in neutrino reactions only at energies above threshold for weak production of the new quarks. In particular, they allow new particle production from valence quarks in the nucleon target. Such V + A interactions also carry important implications for the weak decays of hadrons with new quark constituents. A variety of weak current models involving V + A currents can be constructed. Here we pursue a model independent determination of right-handed weak current transition strengths from neutrino data. This information can be used to restrict the various theoretical possibilities for models of the weak current. Our method is based on the quark parton model (QPM) for deep inelastic neutrino scattering, with dominance of p and n valence quarks in the nucleon. The neglect of possible contributions from a quarkantiquark sea has been a popular simplifying theoretical assumption [1], which is well supported by the neutrino scattering data both from the CERN GargaSupported in part by the University of Wisconsin Research Committee with funds granted by the Wisconsin Alumni Research Foundation, and in part by the Energy Research and Development Administration under contract E(11-1) -881, C00-466.

56

melle experiment [11] and from the Harvard-PennWisconsin-Fermilab (HPWF) experiment [ 12, 13], at least for x > 0.1-0.2. For x < 0.2 the CERN results suggest a sea contribution, but the latest Fermilab resuits [13] are consistent with no antiparton contribution at all. For the present analysis we proceed on the assumption that right-handed transitions come dominantly from valence quarks through new V + A currents. Antiquarks if present can also give right-handed transitions through conventional V - A interactions; since we neglect these contributions, our estimates of V + A couplings can be read as upper bounds. The differential cross-sections o(x, y) = d2o(x, y)/dxdy in the deep inelastic scaling region may be written in the form

o(x, y)VN = G2ME x [FIN(x) + (1 --y)2F~N(x)] 1"(

(1)

o(x, y)~N _ G2ME x [F~ N (x) + (1 -y)2F-~N(x)] 7r

where the L, R subscripts denote structure functions associated with left- or right-handed quarks, respectively. FL, R are related to the more conventional F1, 3 by EL, R = (F 1 ~ F3)/2

(2)

where we assume the Callan-Gross relation xF 1 = F 2. In eq. (1) x and y are the usual scaling variables

Volume 59B, number 1

x = Q2/(2Mv),

PHYSICS LETrERS

y = vIE

(3)

and N denotes an average nucleon target N = ~(n + p). Below the threshold Wth for excitation of the new hadronic states, the conventional V - A currents give the structure functions FEN(x) = FIN(x) = p(x)

+ n (x)

(4a)

~N _ t,N F R (x) - F ~ (x) = 0

(4b)

13 October 1975

where ct and 13are sums of squares o f V + A weak current transition couplings from valence quarks to new quarks. We assume immediate rescaling above an effective threshold Wth , as indicated by the theta function in eq. (I0). At very high energies, where W > Wth for most of the range of x and y, the predictions of eqs. ( 5 ) - ( 9 ) are modified to

O(X, y)~N/o(x, y)vN = [(1 _ y ) 2 + el/[1 + t~(1 _ y ) 2 ]

where p(x) and n(x) are the QPM quark distributions in the proton, in the excellent approximation of zero Cabibbo angle. Immediate consequences of only left-hand currents which follow from eq. (1) are

o t N / o t N = (1/3)(1 +3c0/(1 +/3/3)

(12)

(y)~N = (1/4)(1 + 6a)/(1 + 3a)

(13)

o(x, y)~N/o(X, y)vN = (1 _ y ) 2

(5)

(y)UN = (1/2)(1 +/3/6)/(1 +/3/3)

(14)

o t N / o t N : 0.33

(6)

(Q2)-ffN/(Q2)VN = (y)-~N /(y)VN .

(15)

(y)~-N = 0.25

(7)

(y)vN = 0.5

(8)

(Q2)~N/(Q2)VN = 0.5

(9)

where ( ) is used to denote an average quantity at a given energy E. Eqs. ( 5 ) - ( 9 ) hold for any fixed x, or integrals over any range ofx. The data from the HPWF experiment [12, 13] are compatible with eqs. ( 5 ) - ( 9 ) for E < 30 GeV. The excellent agreement of the data with eqs. (6) and (7), integrating over all x, supports our neglect of the quark-antiquark sea. The ratio of (Q2) in eq. (9) is in general not sensitive to assumptions about the sea, since Q2 = 2MExy and the sea at most contributes only at small x. At energies above 30 GeV appreciable deviations of the data from eqs. (5) and (7) have been reported [ 12, 13 ]. We consider the consequences of ascribing these deviations to new particle production via V + A interactions with a high threshold. Above this threshold, the left-handed structure functions are still given by eq. (4a) while the right-handed structure functions become

FEN(x) = U [p(x) + n(x)] O(W-

Wth) (10)

F~N(x) = ~ [p(x) + n(x)l O(W- Wth)

(11)

These high energy limits are quite sensitive to the value for the b-N right-handed parameter a, but are fairly insensitive to the vN parameter/3. To illustrate the dependence on ct, we give the results of eqs. ( 1 2 ) - ( 1 5 ) below for two cases: (~=1/2,~3=1)

(a=l,/3=l)

otN/ot N

0.63

1

(y)~N

0.40

0.44

(y)VN

0.44

0,44

(Q2)~N/(Q2)VN

0.91

1

With even a small value of a, the values of o~N/o~ N, (y)~N, and (Q2)~N/(Q2)VN are significantly increased from the sub-threshold values in eqs. (6)-(9). Thus the energy dependences of these quantities provide a very sensitive measure of t~, as well as the threshold energy at which the new hadronic states are produced [14]. The behavior above threshold (Q2)pN/(Q2)VN is very different for fight-hand currents involving valence partons, than in models where the right-hand currents in v-N come solely from the sea (e.g. the ;k ~ c quark transition in conventional charm model [15] calculations [16]). When new quarks are produced in v-N scat57

Volume 59B, number 1

PHYSICS LETTERS

tering from sea quarks [4, 6, 15, 16] we predict very little change in (Q2>-aN/(Q2>VN in crossing the new quark p r o d u c t i o n threshold, because the sea contrib u t i o n s are at small x and therefore suppressed. Thus data on VN/(Q2>VN as a f u n c t i o n o f E can help distinguish b e t w e e n these two general classes o f models for V + A currents. We also emphasize that v a l e n c e - ( V + A ) effects are present at all x, so that another clear way to separate them from possible a n t i q u a r k - ( V - A ) effects would be to select data with x > 0.1 or 0.2. Ideally we would prefer to work with at, (y> and evaluated for x > 0.1, b u t such data are n o t presently available; it would be helpful if these values could be extracted, as functions o f energy. Meanwhile we have to accept also the x < 0.1 events, with the possibility o f some antiquark effects. A caveat must be added here. Although the valencequark effects in eqs. ( 5 ) - ( 9 ) and ( 1 1 ) - ( 1 5 ) are formally i n d e p e n d e n t of x, in the regions below and above threshold, the relative weights o f these two regions are x - d e p e n d e n t in any given e x p e r i m e n t (since W2 ,~ 2MEy(1 - x ) ) . Small-x bins c o n t a i n a higher p r o p o r t i o n of above-threshold effects than large-x bins: new c o n t r i b u t i o n s appear more strongly at smaller x. In order to make our analysis more quantitative, we make a valence QPM parametrization for p(x) + n(x), (see for example ref. [17]), fitted to the vN and u-N x-distributions [13] t b r E < 30 GeV, and normalized to the QPM sum rule constraint

13 October 1975

RIGHT-HANDED CURRENT THRESHOLD E F F E C T S

U3

0.6 ¢ ",-

~ •

¢

."

-

.................. .q=! ]" ................. ..I. ....

z

_

_

_,

_

v

o.:f 0

5

'o

t 0'0

150 ,

Fig. 1. Threshold behavior of average-y in ~-N scattering. The curves illustrate effects of right-handed weak transitions above a threshold Wth. Results for a = 1/2, Wth = 7.5 GeV (solid curve), ~ = 1/2, Wth = 4 GeV (dashed curve), and a = 1, Wth = 7.5 GeV (dotted curve) are shown. Here c~is the ratio E~N/F~N of right-to left-handed structure functions. HPWF data from ref. [13].

THRESHOLD EFFECTS OF RIGHT-HANDED CURRENT

1.0

~L!.:.p..~.! .......... tO I,z ,1 .c

0.8

.-'"

...""

¢

1 f [p(x) + n ( x ) ] dx = 3. 0

(16)

The description o f all data for E > 30 GeV is then specified by three parameters: Wth, c~, and/3. The results are not very sensitive to/3. We illustrate the case/3 = I, but/5 = 0 would be equally satisfactory. The curves in figs. 1 and 2 represent the cases

z

z I~.,,.,,

ii 0.6

,

I

a = 1 / 2 , ,o=1 .

a = 1/2, /3 = 1

Wth = 7.5 GeV (solid curve)

a = 1/2, /3 = 1

Wth = 4

ot = 1,

Wth = 7.5 GeV ( d o t t e d curve).

/3 = l

GeV (dashed curve)

F r o m comparing with the data [12, 13, 18] on (y>~N and cr~N/o~ N in figs. 1 and 2, we deduce that parameter values approximately

.

.

.

.

.

.

0.4

0.2

,

,

0

58

200

E (GEM)

100

150

E (GeV)

Fig. 2. Energy dependence of thegN to vN total cross section ratio, for right-handed weak transitions above a threshold Wth. Results for a = 1/2, # = 1, Wth = 7.5 GeV (solid curve), a = 1/2, ~ = 1, Wth = 4 GeV (dashed curve), a = 1, # = 1, Wth = 7.5 GeV (dotted curve) are shown, where a = F~N/F(N and f3= F~N[F~N. The curves are relatively insensitive to the value of/3. HPWF data from ref. [ 13 ] ; CITF data from ref. [ 18 ].

Volume 59B, number 1 Wth ~ 7.5 GeV,

PHYSICS LETTERS (17)

a ~ 1/2

are needed in a (V + A)-current interpretation. The threshold in (y)VN should become evident at similar energies in o~-N/o~N ; present m e a s u r e m e n t s on the total cross-section ratio are n o t sufficiently precise to check the expected threshold behavior. The spectrum averaged y-distributions from this right-handed current parametrization are compared with the HPWF energy averaged data in fig. 3. Right-handed currents involving valence quarks m o d i f y the Adler and Gross-Llewellyn-Smith sum rules above threshold [2]. Specifically, the sum rules become

13 October 1975 V+A couplings

Model

v--N

vN

Conventional charm [ 15 ]

~=0

/3 = 0

New charm current [3, 4]

a =0

/3 = 1

Model C of ref. [81 and a =1 Models of refs. 191 and [10]

/3 = 1

Model D of ref. [8]

c~ = sin 7 •

_ ~..

Explanation of experimental 112, 131 ~N anomaly sea quarks [161 sea quarks [61 valence quarks valence quarks (~ ~ O)

1 X

0

(19)

1

f [F~N(x)+F;N(x)] d x = - 6

+ 3(0,:+~).

X

0

For a =/3 = 1/2, which is consistent with the HPWF data in the scaling region, charge s y m m e t r y is preserved. It is of interest to compare our upper b o u n d of a ~ 1/2 with some proposed weak current models:

The investigation o f right-handed currents and new thresholds would be rather straightforward, if accurate x- and y-distributions were available at m a n y precise energies, b u t present statistics are m u c h too low for this. The essential point of the present work, however, is that the energy-dependences o f averaged quantities (y) and (Q2) are already quite well determined, and that these data provide sensitive measures o f righthanded current effects and new thresholds. Our quantitative b o u n d o f a ~ 1/2 depends on neglecting possible antiquark c o n t r i b u t i o n s . A still cleaner separation from antiquarks would be possible if (y) and (Q2) were available for the data subset x > 0.1.

References RIGHT HANDED TRANSITIONS FOR Wth =7.5 GeV WITH

g..~N / [~ ~N -R "-L - I/2

x>.l 1

8

ond

F g S / F L~,N =1

x<.l

6

15. od.

E

o

10.

0 "

2

5.

0

0

.2

.4

.6 Y

.8

.;

1. y

Fig. 3. Spectrum-averaged y-distributions for right-hand weak transitions (c~ = 1/2,/3 = 1) above a threshold Wth = 7.5 GeV, compared with HPWF data from ref. [13].

[1] A. De Rujula et al., Rev. Mod. Phys. 46 (1974) 391. [2] A. De Rujula and S.L. Glashow, Phys. Lett. 46B (1973) 377; Phys. Rev. 9D (1974) 180. [3] R. Mohapatra, Phys. Rev. D6 (1972) 2023. [4] A. De Rujula et al., Phys. Rev. Lett. 35 (1975) 69. [5] A. Love, D.V. Nanopoulos and G.G. Ross, Nucl. Phys. B55 (1973) 33. [6] V. Barger, T. Weiler and R.J.N. Phillips, U.W.-Madison report C00-459 (1975). [7] F. Wilczek, Princeton preprint (1975). 18] F. Wilczek, A. Zee, R. Kingsley and S. Treiman, Fermilab-Pub-75/44-THY. [9] S. Pakvasa, W.A. Simmons and S.F. Tuan, University of Hawaii Report 511-196-75. [10] H. Fritsch and P. Minkowski, Cal-Tech Report-68-503 (1975). [11] T. Eiehten et al., Phys. Lett. 46B (1973) 274; H. Deden et al., Nucl. Phys. B85 (1975) 269. [12] B. Aubert et al., Phys. Rev. Lett. 33 (1974) 984; A. Benvenuti et al., Phys. Rev. Lett. 34 (1975), 10,597. 59

Volume 59B, number 1

PHYSICS LETTERS

[13] D. Cline and C. Rubbia, invited talks at the Palermo Conference (1975); A. Mann, invited talk at the Washington APS meeting (1975). [14] W.J. Wilson, LBL preprint 3862 (1975). [15] S. Glashow, J. Iliopoulos and L. Maiani, Phys. Rev. D2 (1970) 1285.

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13 October 1975.

[16] v. Barger, T. Weiler and R.J.N. Phillips, U.W.-Madison report C00-441 (1975). [17] V. Barger and R.J.N. Phillips, Nuel. Phys. B73 (1974) 269. [18] B.C. Barish et al., Reports in the London Conference Proceedings (1974); Phys. Rev. Lett. 31 (1973) 565.