Fortschritte der Physik / Progress of Physics: Band 27, Heft 2/3 1979 [Reprint 2021 ed.] 9783112522646, 9783112522639

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FORTSCHRITTE DER PHYSIK H E R A U S G E G E B E N IM A U F T R A G E D E R P H Y S I K A L I S C H E N

GESELLSCHAFT

DER DEUTSCHEN DEMOKRATISCHEN

REPUBLIK

VON F. K A S C H L l i H N, V. L Ö S C H E . H. I U T S C H L U N D R. ROM PK

H E F T 2 / 3 . 1979 • B A N D 27

A K A D E M I E - V E R L A G EVP 2 0 , - M 31728

.

B E R L I N

BEZUGSMÖGLICHKEITEN Bestellungen sind zu richten — in der DDR an das Zeitungsvertriebsamt, an eine Buchhandlung oder an den AKADEMIE-VERLAG, DDR - 108 Berlin, Leipziger Straße 3—4 — im sozialistischen Ausland an eine Buchhandlung für fremdsprachige Literatur oder an den zuständigen Postzeitungsvertrieb — in der BRD und Westberlin an eine Buchhandlung oder an die Auslieferungsstelle KUNST U N D WISSEN, Erich Bieber, 7 Stuttgart 1, Wilhelmstraße 4—6 — in Österreich an den Globus-Buchvertrieb, 1201 Wien, Höchstädtplatz 3 — in den übrigen westeuropäischen Ländern an eine Buchhandlung oder an die Auslieferungsstelle KUNST UND WISSEN, Erich Bieber GmbH, CH - 8008 Zürich/Schweiz, Dufourstraße 51 — im übrigen Ausland an den Internationalen Buch- und Zeitschriftenhandel; den Buchexport, Volkseigener Außenhandelsbetrieb der Deutschen Demokratischen Republik, DDR - 701 Leipzig, Postfach 160, oder an den AKADEMIE-VERLAG, DDR - 108 Berlin, Leipziger Straße 3 - 4

/ \ =

with

^ L

0 ) | p, s)

(1.4)

If — u(k') y^l + ys) u(k) =

I f d2o

w

] =

-1,

m

[ ? / ] = [?„*] = 3, tii = 1,

(1.9)

[ f ] = [«] = [»] = 3/2, [W,v] = [ W , ] = [W^]

= 0,

[W2] = t = [W^] = -2. The assumption that with high energies and high momentum transfers the masses of the particles involved become unessential allows qualitative statements about the asymptotic behavior of structure functions to be made by the aid of the principle of scaling invariance [2—4]. According to this principle, the functions involved should be dependent upon dimensionless combinations of independent variables only. I n addition, the assumption is made t h a t because of the lack of dimensional quantities the dimensions (1.9) are expressed by an energy variable, e.g., variable v. Asymptotically, W1 should be dependent upon a dimensionless variables only, and it is appropriate t h a t os £ = - — v

(1.10)

be chosen for the latter ; on the other hand, W2 and W3 should behave as v~l. Therefore, asymptotically W 1 « JT 10 (f), W2 Ws ^

(1.11) v-W30(i).

Functions T7j0(£) are called scaling functions. For an experimental test of such an hypothesis it is appropriate to study deep inelastic scattering in the Bjorlcen region : v —> oo, q2^

—oo,

i =

-

v

fixed.

(1.12)

In fact, the experiments described in [12] are in approximate agreement with the theoretically predicted behavior (1.11); certain characteristic deviations will be discussed later. • 1.2. The parton model

[13-15]

The observation that a behavior corresponding to the asymptotic relations (1.11) is consistent with the free field approximation proved to be of great importance for the theoretical treatment . By free field approximation is understood a calculation of W ^ in

80

B . GEYER, D . ROBASCHIK, E . WIECZOREK

the lowest perturbation-theoretical order [4], with the currents and states being made up of free fields, e.g., ?'„em = Q-nw(i-i3) Holding in this approximation is (p', «'I h(0) \p, s) = QuAp') Y^Ap)

(1.14)

consequently, there will be obtained

=

{2n) 6(p +

= Q2Hq2 + 2pq) [p^f,

q

~

p , )

(p

+ qy) + p,^

's] j"{0)

+ q/À) -

ìp

''

s

'}

{p

''

s ] m

'

lp

's)

g^pq).

If follows that W1 = Q*(pq) ó(q2 + 2pq) = 1 Q*