Neutrino data, right-handed currents and number of quark flavors

Volume 64B, number 1

PHYSICS LETTERS

NEUTRINO

DATA, RIGHT-HANDED

30 August 1976

CURRENTS

A N D N U M B E R O F Q U A R K F L A V O R S ~* S. NANDI t Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, US.~ Received 26 May 1976 Models with various numbers of quark flavors and various structures of weak currents are critically examined in the light of current high-energy v, F-data. A model with 8 quark flavors and right-handed currents is proposed which gives a reasonable agreement with all aspects of the data. Within the context o f an SU(2)× U(1 )gauge theory of weak and EM interactions and within the framework of quark-patton model, we show that the current high energy v, ~ data [ 1 ] do not support, at all, the conventional 4-quark model with charm [2] or Han-Nambu [3] model with color, or any other model [4, 5] with only left-handed weak currents. There is a considerable evidence in the data for the presence o f a righthanded part in the structure of weak currents. Vectorlike 6-quark model [6, 7], though favored by some qualitative aspects o f the data (like ( y ~ , R = ovC-/oC), can not explain some others (like single muon y distribution, dou[dy; Ocuu)7-~ 0.3 (xu~)v where (xuu)represent average x for dimuon events) and its overall quantitative agreement with data is rather poor. We propose here, a model with 8-quark flavor and righthanded current which gives a reasonable agreement with all aspects o f the data. The crucial pieces of the data (on the isoscalar target of ref. [1]) that we concentrate on are: i) Threshold behavior o f mean y, (Y~v in ~-scattering (fig. 1); ii) y-distribution of the ~-induced single/a-events, doF/dy (fig. 2); and also dov/dy; iii) Energy dependence o f the ratio, R = oe/o c (fig. 3); iv) Average x, (xu~)vi ~ i n v and ~-induced dimuon events; in particular the fact'that (xuu>vi ~ ~ 0.22-+0.04 whereas Ocu~>vis. 0.06-+0.02. ¢~Work supported in part by the National Science Foundation, Grant Number PHYS74-08833; and the Louis Block Fund, University of Chicago. * A preliminary version of this was circulated in January, 1976 under the title "High-y Anomaly and Eight Quark Model with Right-Handed Currents". 1 Address after Sept. 1: Physikalisches lnstitut der Universit~t, Nussallee 12, D-53 Bonn 1, West-Germany.

We calculate the above quantities using quark-parton model descriptions. ~Vhenever a heavy quark o f mass m is excited, we use the slow rescaling [8] variable z i = x + m 2 / 2 M E v y as suggested by simple parton model consideration. For the parton distribution function, we have used O(x) = x -1/2 [0.25(1 - x 2 ) 3 + 1.35(1 - x 2 ) 9 ] , where

O(x) + ~( x ) - ½ to(x) + n (x)l, and ~(X)--fi(X) -- -n(X)--X(X) =--K(X) = h x - 1 (1 - x ) 11 , with h = 0.17 (corresponds to 7% sea). This gives a very good agreement with the F~D(x) data of the/aproduction experiment [9] at Fermilab. Let us now consider the predictions o f various models for the above mentioned data, namely i), ii), iii) and iv). Model A. Conventional 4-quark model with charm: In this model, ( y ~ = [ ~ + Z. ½1/[] + z l where Z represent the percentage of the sea contribution. Now ( y ~ ~ 0.375 (value around E ~ 60 GeV, see fig. 1) corresponds to Z - 0.34 i.e., one needs about 34% sea contribution. However, in this energy range,/a-production experiment [9] in Fermi.lab shows no evidence o f such a large sea. There the sea contribution is ~7%, certainly < 12%. Also, if this threshold effect in ( y ~ around E F ~ 50 GeV is due to some new sea component which is being excited, then one should see similar threshold effects in the structure function in tz-production experiment in this energy range. Such effect has not been seen. Assuming'the charm quark mass, m e = 1.5 GeV, 81

Volume 64B, number 1

PHYSICS LETTERS

30 August 1976

1

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energy dependence of (y)~- and R is shown in fig. 1 and 3. The general qualitative train does not, at all, support this model. Changing h to 0.07 (4% sea) and 0.29 (12% sea) does not affect our conclusion.

Model B: Han-Nambu model with color gluon excitation: In certain unified gauge models [10], the intermediate vector bosons may mix with color gluons and thus the sea of color gluons inside the nucleon may be excited in v, ~-scattering. Since the contribution of color gluons to do/dy is proportional to (1 - y ) , in this case, ( y ~ = [ ~ + 2 X 0 . 0 7 X ½ + Z . ~ I / [ ½ + 2 X 0 . 0 7 + Z. ~ ], where Z is the percentage of the color gluon contributions and a 7% contribution for each sea has been assumed. Note that even a 100% color gluon contribution can raise (y)~ to only up to ~0.32.

Model C." 6 or &quark model [4, 5] with only lefthanded currents: Such models are not favored, because the increase in ( y ~ has to come from the sea contributions of the extra heavy quarks introduced; and consequently such a large sea has to be observed in the/aproduction experiment [9] in Fermilab which is not the case. Model D: Vector like 6-quark model: Here, the left and right-handed doublets [6] are:

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nology. Note, in R, b can not mix with n or X because of the absence of right-handed currents in neutron or lambda/3-decay. Here, above threshold, b could be excited off the valence p-quark in V-scattering giving a fiat y distribution. We have calculated (y)-ff, dou/dy , R, douu/dy, douu/dx, (xuu) using mass of the b-quark = 4, 5, 6 GeV and mass of the t-quark = 2,4, 5 and - . Considering all aspects of the data, closest agreement is obtained with m b = 5 GeV and m t = --. To agree with d%/dy for single /a-events, one needs a large t-quark mass (at least m t > 5 GeV). Also, a small t-quark mass (m t < 5 GeV) worsen the agreement with R. In calculating do/dy for single g-events, average has been taken over the incident v ~ ) spectrum. Results for (y~, do-ff/dy and R are shown in fig. 1,2 and 3. Though predictions agree with the qualitative feature of the data, quantitative agreement is poor. Also, we shall see later, that in the case of dimuon events, even there is qualitative disagreement of this model with the data. Observe that the main difficulty with model D is that the transition (p ~ bR) is giving too much contribution to ( y ~ , doF/dy and (xuu) ~ (to be discussed later). The only way to suppress this is to mix b R with some other quark of the same charge and to assume that this other quark has not been excited in Fermilab energy. So we are forced to introduce another doublet, (~',) and to go to the eight quark model.

Eight-quark model with both left and right-handed currents: The assignment of the doublets we choose ate:

Volume 64B, n u m b e r 1

PHYSICS LE'I'rERS

L:(p c t t') n c k c b b' '

R:

p bsina+b'cosa

30 August 1976

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Here, we assume that b is excited in ~-scattering around E ~ 50 GeV and t may or may not have been excited; and b' and t' has not been excited in Fermilab. We take c to be the usual charmed quark responsible for the J/~O-states observed. With this assumption, the assignment of the right-handed doublets is more or less unique. The only other inequivalent assignment is c ~ t' in R. So far as v, F-scattering is concerned, the two schemes differ only by small sea contributions. We have, again, calculated y, dOu/dY, R, douu/dY, douu/dx, (xuu) using the mass of the b-quark = 3,4, 5, 6 GeV and the mass of the t-quark = 2, 4, 5 and oo and for various values of sin 2. The best overall agreement of our model with the data obtained for rn b = 4 GeV and m t = oo and sin2a = 0.4 and is shown in fig. 1,2 and 3. Agreement of (y)7 and doT/dy with data is excellent and of R is reasonable. The agreement for dov/dy (not shown) is also good. Dimuon and dilepton events: [lb]. In all these' models, the second muon (or the electron) are assumed to come from the production of a hadron containing c or b-quark and its subsequent semileptonic decay. By determining Bi, i = c-quark or b-quark (where B i is the semileptonic branching ratio of the hadron produced containing the ith quark) to fit the observed magnitude of dimuon events [lb], we have calculated the x andy-distribution for the dimuon events, averaged over the incident u (~) spectrum* i. For conventional 4-quark model, we get
0

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disagrees with experimental value [lb], ~ 0.3 vi~. This has been raised as a serious problem [12], with the quark-parton model description of the v, ~-data. In our model, though both v and P-induced dimuon events come from both valence and sea contributions; in the case o f F , coupling of the valence p-quark to b is suppressed by the sin2a (=0.4) factor and consequently in the case of F, sea contribution to the dimuons dominate the valence contribution. For rob= 4, m r = 0% and sin2a = 0.4, we get, (xuu)u-~O.16, (xuu) v ~ 0.09 which is in good agreement with data and thus solves the problem raised in ref. [ 12]. Details o f x and y distribution of the dimuon events in our model is in agreement with the data.

Other consequences: a) According to our interpretation that the so called high-), anomaly is not due to any sea effect, but due to the excitation of b-quark out of valence p-quark by right-handed charged current; there is no reason why the anomaly should remain only at small x. If the experiment could be done with a narrow band F-beam (as in Caltech-fermilab group), we predict a drastic increase in the anomaly range o f x as we go from E 70 GeV to say, E ~ 120 or 130 GeV. b) No threshold effect should be observed in ( y ~ N N or R = oir/o v in neutral current events which is the case experimentally [13]; c ) No threshold effect in the structure function in /a-production experiment which is also the case experimentally [9]. d) We should see if-like narrow states (bb) in SLAC around 8 - 1 0 GeV. So our conclusion is: 1) conventional 4-quark model with charm is not, at all, supported by v, ~-data. It can 83

Volume 64B, number 1

PHYSICS LETTERS

not explain the rise of ( y ~ and R with energy; 2) vector-like 6-quark model successfully explain R; but in poor quantitative agreement with ( y ~ and do-f[dy and fails to explain dimuon distributions; especially the fact that Ocvu)~s" ~ 0.3 Ocvu~vis,;3) our proposed 8quark model gives a reasonable agreement with all aspect of the data; and thus there is no problem (as raised in ref. [ 1 2 ] ) w i t h the quark-parton model description of the high-energy v, ~-data. Let us compare our work with ref. [14]. In ref. [14] do/dy for the single/a-events (especially do-a/dy, fig. 2) and the experimental fact Ocuu)~s"~ 0.3 Ocuu)~i~ has not been discussed which is the main area o f disagreement of the data with the vector-like 6-quark model. Our model also naturally explains the problem raised in ref. [12]. Finally, one should notice that our model need not be vector-like. The left-handed doublets (~ t ' ) and the right-handed doublet (t) does not play any role in our analysis and can be taken off without any change in our conclusion. In that case, any anomaly in the hadronic sector can be cancelled by introducing one or more heavy leptons in the leptonic sector. Value of R in SLAC energy range can also be explained using heavy leptons in the leptonic sector. Other detailed applications of our model like wrong sign dimuons, trimuons, leptonic sectors, etc., will be discussed elsewhere. I thank Y. Nambu and T. Eguchi for discussions and encouragement, and T.-Y. Ling of the HPWP group for many discussions on their data, and S.K. Datta for help in numerical computation. After the completion of this paper, we received the preprint of ref. [12] which discusses the 4 and 6-quark part of our paper with similar conclusion.

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30 August 1976

References [1] A. Benvenuti et al., Further data on the high-), anomaly and inelastic F-scattering, to be published in Phys. Rev. Letters; A measurement of the ratio ac(~/~+ N --*/~++X)/oc(u+N -~/J-+ X) at high energy, Wisconsin preprint (1975). [lb] A. Benvenuti et al., Phys. Rev. Lett. 35 (1975) 1199, 1203, 1249; J. Von Krogh et al., Phys. Rev. Lett. 36 (1976) 710, H. Blietschan et al., Phys. Lett. 60B (1976) 207. [2] S.L. Glashow, J. Itiopoulos and L. Maiani, Phys. Rev. D2 (1970) 1285. [3] M-.Y. Han and Y. Nambu, Phys. Rev. B139 (1965) 1006. [4] M. Suzuki, Phys. Rev. Lett. 35 (1975) 1553. [5] R.M. Barnett. Phys. Rev. Lett. 34 (1975) 41. [6] H. Fritzsch, M. Gell-Mann and P. Minkowski, Phys. Lett. 59B (1975) 256. [7] A. De Rujuia, H. Georgi and S.L Glashow: Harvard preprint, 1975. [8] H. Georgi and D. Politzer: Harvard preprint (1975). [9] H.L. Anderson et al., Measurement of nucleon structure function at muon scattering at 147 GeV/c, ChicagoHarvard-Illinois-Oxford preprint, to be published in Phys. Rev. Lett. [10] J.C. Pati and A. Salam, Phys. Rev. Lett. 36 (1976) 11; G. Rajasekharan and P. Roy: Phys. Rev. Lett. 36 (1976) 355. [11] E. Golowich and B.R. Holstein, Phys. Rev. Lett. 35 (1975) 831. [12] V. Barger, T. Weiler and R.J.N. Phillips, A problem with the patton model descriptions of neutrino data: Wisconsin preprint, April, 1976. [13] P. Wanderer: Madison Conf. report (April 1976). [14] R. Barnett, Evidence in neutrino scattering for right-handed currents associated with heavy quarks, Harvard preprint (1976).