Neutrino-Quark Scattering in Java

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12.8 Neutrino-Quark Scattering
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EXERCISE 12.18 Show that deep inelastic electron electromagnetic scattering on an isoscalar target gives
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2 '1Ta 2 [ 2] 5 - x s 1 +(1 - y) -18 [Q(x) + Q (x)] Q4
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(12.78)
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per nucleon, see Exercise 9.5. Note that, in contrast to vN -+ /LX, (12.78) embodies parity conservation so Q and Q appear symmetrically.
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If there were just three valence quarks in a nucleon, Q = 0, the vN -+ /L -X and vN -+ /L+X data would exhibit the dramatic V-A properties of the weak interac-
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tion exactly. That is,
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da(v)
= c,
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da(v) 2 dy = c(1 - y) ,
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(12.79)
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where c can be found from (12.76); and for the integrated cross sections, a(v) 1
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Fig. 12.14 Quark and antiquark momentum distributions in a nucleon as measured at CERN and the Fermi laboratory. The experiments reveal that only about half the proton's momentum is carried by quarks. We have associated the remainder with the gluon constituents (see Section 9.4).
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Weak Interactions
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The data approximately reproduce these expectations. In fact, (12.76) and (12.77) allow a determination of Q(x) and Q(x). An example is shown in Fig. 12.14. There is about a 5% Qcomponent in a proton.
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EXERCISE 12.19 If a(v)/a(p) = R, show that
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fXQ(x)dx fXQ(x) dx
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Detailed analyses show that the functions u(x), d(x), . .. , are indeed the same whether one extracts them from electroproduction or neutrino experiments. This is a definitive success of the parton model: the u(x), d(x), describe the intrinsic structure of the hadronic target and are the same whatever experimental probe is used to determine them.
12.9 First Observation of Weak Neutral Currents The detection in 1973 of neutrino events of the type (12.80)
N -+ X}
p"N -+ P"X
(12.81)
heralded a new chapter in particle physics. These events are evidence of a weak neutral current. Until then, no weak neutral current effects had been observed, and indeed very stringent limits had been set on the (strangeness changing) neutral current by the absence of decay modes such as
K -+J.L+J.L-,
K+-+ 7T+e+e-, K+-+ 7T+PV. Induced weak neutral current effects are expected to occur by the combined action of the (neutral) electromagnetic and the (charged) weak current (for example, K +-+ 7T+e+e- can proceed via a virtual photon: K +-+ 7T+Y with y -+ e+e-), but these effects are very small. The rate, compared to the corresponding allowed weak decay, is of the order
----'---------!.... -
r(K+-+ 7T+e+e-) r(K+-+ 7Toe+Pe )
(aG)2
(12.82)
in agreement with the data. (Here, the 1/q2 behavior of the propagator of the virtual photon is canceled by the helicity suppression of the 0--+ o-y coupling.)
12.10 Neutral Current Neutrino-Quark Scattering
However, reactions (12.80) and (12.81) were found to occur at rates very similar to those of other weak scattering processes.
12.10 Neutral Current Neutrino-Quark Scattering
A quantitative comparison of the strength of neutral current (NC) to charged current (CC) weak processes has been obtained, for example, by scattering neutrinos off an iron target. The present experimental values are
Rv =
_ aNC(v) _ a(v"N -+ v"X) cc = ( _ ) = 0.31 0.01, a (v) a v" N -+ J.L X
(12.83)
_ aNC(v) _ a(v"N -+ v"X) Rji = cc = ( ) = 0.38 0.02. a (v) a v"N-+J.L+X
The vN -+ vX data can be explained in terms of neutral current-current vq interactions, see Fig. 12.15, with amplitudes
N 0lL- G
[u y(l _ -" v
5 Y)U v ] [UqY,,(C q v
q 5 CAY)U q
(12.84)
where q = u, d, ... are the quarks in the target. A priori, there is no reason why the neutral weak interaction should have the four-vector current-current form of (12.84). It is decided by experiment, for instance, by the observed y distribution (see Exercise 12.20). It is appropriate at this stage to introduce the conventional normalization of c . The invariant amplitude for an arbitrary neutral the weak neutral currents, current process is written
(12.85)
compare (12.13) for a charged current process. The vq
vq amplitude of (12.84)
J:;clql
Fig. 12.15 Neutral current Pq
Pq scattering.
Weak Interactions
is of this form; the customary definition of the neutral currents is
J:C(v) =
t(u y"Hl v
y5)u v ),
(12.86) (12.87)
J:C(q) = (uqy"Hc~ - c~y5)Uq).
In general, the J:c , unlike the charged current J", are not pure V-A currents (c v '* cA ); they have right-handed components. However, the neutrino is lefthanded; and so, c~ = c~ == in (12.86). The parameter p in (12.85) determines the relative strength of the neutral and charged current processes. In the standard theoretical model all the c~, c~ (with i = v, e, u ... ) are given in terms of one parameter, and p = 1 (see s 13 and 15). In other words, if the model is successful, all neutral current phenomena will be described by a common parameter. In fact, the present experiments give p = 1 to within small errors. However, for the moment let us leave c~, c~ and p as free parameters to be determined by experiment. Upon inserting the currents (12.86) and (12.87) into (12.85), we obtain the vq -+ vq amplitude of (12.84) with
GN = pG( = G).
(12.88)
We now return to our interpretation of the vN -+ vX data. The calculation of the vq -+ vq cross sections proceeds exactly as that for the charged current processes vq -+ /Lq'. For example, using the results (12.73) and (12.74),
da(vLd L -+ /L u ) = G 2 xs --, dy 1T da(vLu R -+ /L d ) = G 2xs (1 _ y)2, dy 1T (12.89)