P. Ratcliffe. International School for Advanced Studies, 1-34100 Trieste, Italy. Received 17 August 1982. Abstract. We suggest that since the coefficient of the.
Partides and Fields
Br Physik C
Z. Phys. C - Particles and Fields 17, 43-45 (1983)
@ Springer-Verlag 1983
A Simple Method for Isolating Order and 2 Corrections From Polarized Deep-Inelastic Scattering Data N.S. Craigie International Centre for Theoretical Physics, 1-34100 Trieste, Italy, and Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, 1-34100 Trieste, Italy
P. Ratcliffe International School for Advanced Studies, 1-34100 Trieste, Italy Received 17 August 1982
Abstract. We suggest that since the coefficient of the order ~ corrections to the ratic G,/F 2 is scheme independent, one can check in a sensitive way, in deep-inelastic polarization data, if the order e~2 corrections are significant in the MS or M O M subtraction schemes. One can also get direct evidence of the importance of higher twist.
In deep inelastic scattering with polarized beams and targets we have, in addition to the usual structure functions F~ and F2, two more structure functions G~ and G 2. The structure functions are related to the Fourier transform of the commutator of electromagnetic current JU(x) evaluated between nucleon states of definite spin s u and momentum pU:
S d4 x elq X5 GeV 2. One then compares (7) with the data to extract the value of A. If this value, Aexpt., is found to be n-independent and close to the MS or M O M value we have some evidence that the order e2 and higher twist contributions are small. In Fig. 1 we give curves for the first three moments, where we have subtracted the value of lnR at Q2= 10GeV 2 for each curve to remove the unknown constant in (7). One notices the sensitivity to the value of A and n for small n. Another quantity that could be plotted experimentally is
In
{G(~)]e 2 {G~)] \F(fl)! - l n \F(fl)]le?,
cq(Q z) 4 (2+
47z
2
3 \n ~ !
6 =
This directly measures the importance of order ~ and higher power corrections.
N.S. Craigie and P. Ratcliffe: A Simple Method for Isolating Order % and c~ Corrections
Whether the suggestions in this note will be of practical use will depend on the amount of data obtained for G(~"). An accuracy of better than 1 ~ for n = 1, 2 will need of the order of 10,000 events. In an ideal situation the polarized measurements are a valuable tool for examining order cd effects, as well as detecting higher twist contributions. As a final comment, if one finds that in the order e~ fit with the data the value of A obtained is independent of n, then this will be the value of A in Stevenson's optimized scheme [8] for this process. It would be interesting to see if in fact it is universal and for example close to Ags, etc. Notice however that there could still be large order ~ 2 effects in G 1 and F 2 separately that cancel in the ratio. This is not likely to be true on the other hand for higher twist contributions since they tend to have quite different helicity dependence than the leading twist.
45
References 1. M.A. Ahmed, G.G. Ross: Phys. Letters B56, 385 (1975); Nucl. Phys. B i l l , 441 (1976); H. Ito: Progr. Theoret. Phys. (Kyoto) 54, 555 (1975); K. Sasaki: Progr. Theoret. Phys. (Kyoto) 54, 1816 (1975) 2. E.G. Floratos, D.A. Ross, C.T. Sachrajda: Nucl. Phys. B129, 66 (1977); B139, 545 (1978); Phys. Lett. 80B, 269 (1979); W.A. Bardeen, A.J. Buras, D.W. Duke, T. Muta: Phys. Rev. D18, 3998 (1978) 3. T. Kodaira, S. Matsuda, K. Sasaki, T. Uematsu: Nucl. Phys. B159, 99 (1979); Phys. Rev. D20, 627 (1979) 4. A.J. Buras, E.G. Floratos, D.A. Ross, C.T. Sachrajda: Nucl. Phys. B131, 308 (1977) 5. For a proof of this see for example D. Gross in: Methods in field theory. Les Houches 1975, Eds. R. Balian, J. Zinn-Justin, Chap. 4. Amsterdam: North-Holland 6. For the % corrections to F 2 see also for example G. Altarelli, R.K. Ellis, G. Martinelli: NucI. Phys. B157, 461 (1979) 7. For the ~s corrections to G 1 see also P. Ratcliffe: SISSA preprint 24/82/E.P. 8. P.M. Stevenson: Phys. Rev. D23, 2916 (1981)
