PRODUCTION OF FAST NEUTRINO BEAMS

V. S. B a r a s h e n k o v a n d H s i e n T i n g - c h ' a n g

Translated from Atomnaya Energiya, Vol. 9, No. 6, pp. 489-490, December, 1960 Original article submitted June 22, 1960

The attention of many physicists has recently been turned to experiments with high-energy neutrinos [1]. These experiments give considerable possibility for investigations of many important characteristics of weak interactions. In particular, it is possible to check whether weak interactions actually become strong at high energies [2].

An intense beam of high-energy neutrinos can be obtained from large proton accelerators, such as the proton synchrotron at Dubna and the 30-Bey accelerator at Geneva. In this case, the neutrino is produced as the result of the decay of charged lr mesons generated in collisions of fast nucleons (Fig. 1). The energy spectrum and angular distri- bution of such neutrinos can be calculated if the spectrum and angular distribution of the ~r mesons produced in NN collisions are known. In the general case, this is a very complicated problem, especially if the finite size of the neu- trino detector is taken into account [3]. However, the calculations are considerably simplified if only fast neutrinos emitted at small angles to the primary proton beam direction are considered. In this case, the angle of emission of the neutrino Ou differs very little from the angle at which the decaying lr meson moves: Ou "~ O (see Fig. 1).

Y

Fig. 1. Neutrino beam produced by the decay of ~r + mesons generated by fast protons.

Let us consider a neutrino of energy E > 1 Bev and angles Ou of the order of a few degrees. Since in the planned experiments the neutrino detector with a transverse cross section SD ~ 1 m z is to be placed at distances of several tern of meters from the target,* such an approximation is quite satisfactory.

If W~r (p; O) is the momentum distribution of the charged ~r mesons emitted at an angle O to the primary proton beam, the cor- responding energy spectrum of the neutrinos at a distance L from the target in which the ~r mesons are produced has the form

Wv(E; | L)=a f ]'Irz(p; O) :< >ctE/m

Here, a = mZ/(m2-~t2); m is the rr-meson mass, and /J is the /~-meson mass. If L is given in meters, then l = r c . 10"z= = 7.68 (r is the lifetime of a charged Ir meson).

This expression differs from the corresponding expression for ~ quanta produced in the decay of lr ~ mesons [4, 5] only in the exponential term and the value of the coefficient a .

Figure 2 shows the calculated neutrino spectra for the angle O = 00.

The calculat iom indicate that the spectra of neutrinos emitted at small angles depends very weakly on the angle. For example, the number of neutrinos of given energy emitted at an angle O = 3 ~ is only g% less than the number of neutrinos emit ted at the same energy at an angle of O = 0 ~ This is also illustrated in Fig. 3, in which the values of the entire neutrino flux of energy E > 1 Bev and E > 2 Bey are shown for the angles O = 0 ~ and O = 30:

W(vi)(O;L)~ f Wv(E; O; L) dE; W~)(O;L): f Wv(E;O;L) dE" E~I E~>2

*We recall that, owing to the relativistic time dilatation, the ~r mesons decay only at large distances from the target.

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The spectra Wv (E) and the functions W v (i) (L) shown in Figs. 2 and 3 are normal ized to a single inelas t ic NN coll is ion in the target and to a unit soild angle:

f Wv (E; 6); L) d,Q dE=n,

where n = 2, 3 is the mean number of charged Ir mesons produced in a single NN coll is ion at an energy of 10 Bey [5, 6]. As in [5], the values of the function Wlr (p; O) was ca lcu la ted from the s ta t is t ica l theory of mul t ip le production.

/

/O-I

/O-Z

~J

XXX\,

g e ~ l I E l

0,~

O, 3 . ..

/ o,2 , �9 t /

'/j //

/

2

/0 lO0 L, m

Fig. 2. Neutrino energy

distribution at various

distances from the target L at an angle O = 0 ~ to the pr imary proton beam in the laboratory system.

Fig. 3. Dependence of the neutrino flux of energy E > > 1 Bey (1) and E > 2 Bey (2) on the distance L to the target at neutrino angles of flight G = 0 ~ (solid curve)

and O = 3~ curve) wi threspect to the primary pro- ton beam in the laboratory system. The fluxes Wy are normal ized to a unit solid angle.

The neutrino flux per unit solid angle Wu(1) (O; L) increases rapidly with the distance from the target . l imi t ing values of the flux for L = co are

o w~ ~)(e, ~ ) w(,, z) (e, ~)

0 ~ t ,5 0,18 3* 1,4 O, t6

The

With an increase in L, however, the solid angle of the neutrino f~D = SD/L~ decreases rapidly; and,therefore, the num- ber of neutrinos recorded by the detector decreases with an increase in the distance between the de tec tor and the tar- get . Thus, at a distance of L = 30 m, 1.1 • 10 "s neutrinos pass through 1 cm 2 of detector area (per single inelas t ic NN coll is ion) , and at distances of L equal to 50 and 100 m, the values are 0.6 x 10 "s and 0.27 • 10 "s, respect ively . These values are very useful for various es t imates in planning neutrino exper iments .

In conclusion, the authors express their deep apprec ia t ion to M. A. Markov for many discussions and valuable advice , and to R. Asanov and I. Polubarinov for discussions and valuable c r i t i ca l remarks.

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LITERATURE CITED

i. M. Markov, Hyperonen und K-mesonen (Berlin, Verlag der Wissenschaften, 1960); T. Lee and C. Yang, Theo- retical Discussions on Possible High-Energy Neutrino Experiments, Preprint, 1960; N. Cabibbo and IL Gatto, Nuovo Cimento i_55,304 (1960); B. M. Pontecorvo, Report at the Ninth Annum Conference on High-Energy Phys- ics, Kiev, 1959 [in Russian].

2. D.I. Blokhintsev, Zhur. Eksp. i Teor. Fiz. 3__58, 257 (1958); Uspekhi Fiz. Nauk 62, 381 (1957); H. Nagai and D. Ito, Anomalous Creation of /~ Mesons Originating in the Weak Interactions, Preprint, Physics Institute, Hokkaido University, 1960.

3. I .V. Polubarinov, Interactions of Neutrinos Produced in a Parallel Monochromatic ~r-Meson Beam, Joint Insti- tute for Nuclear Studies, Preprint D-57V, 1960.

4. R. Sternheimer, Phys. Rev. 99, 277 (1955). 5. V.S. Barashenkov and Hsien Ting-ch'ang, Joint Institute for Nuclear Studies, Preprint D-577, 1960. 6. V.S. Barashenkov, Nuovo Cimento 14, 656 (1959).

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