TY - JOUR

T1 - Anomalous cross section for photon-photon scattering in gauge theories

AU - Witten, Edward

N1 - Funding Information:
The short distance analysis of deep inelastic scattering \[1\]m akes the following predictions: The scaling behavior of the structure functions, for any hadron target, differs from that of free field theory by known logarithmic factors; the actual shape of the structure functions is not determined. Here we consider the corresponding problem with a photon ~.~r~et, in other words, we are considering the total cross section for 7 + 7 -~ hadrons, with one photon on or near mass shell while the other photon has a large Euclidean momentum. It has been suggested \[2\]t hat this cross section could be measured by studying e±e ± -~ e±e -+ + hadrons in colliding beams. We find the following, somewhat anomalous results: The scaling behavior is that of the free quark model; the magnitude and shape of the structure functions are completely determined, but do not agree with the free quark model. Technically, these results arise as follows. Because the photon is an elementary particle, there are new "contact" terms in the short distance analysis. Because the photon interacts weakly, the new terms can be explicitly evaluated. Moreover, they turn out to be the dominant terms for large Q2. If there are other weakly interacting * Work supported in part by the National Science Foundation under grant no. MPS75-22514. ** Current address: Lyman Laboratories, Harvard University, Cambridge Mass. 02138.

PY - 1977/3/14

Y1 - 1977/3/14

N2 - We consider the deep inelastic structure functions of the photon in an asymptotically free gauge theory. In contrast to the case of a hadronic target, we find that the shortdistance analysis determines the shape and magnitude and not merely the Q2 dependence of the structure functions. The structure functions of the free quark theory are renormalized by finite, calculable factors. For example, at x = 0.1, we find that F2 will, at large Q2, exceed the free quark result by a factor 1.751, while for x = 0.5, F2 is suppressed asymptotically, relative to the free quark theory, by a factor 0.964, and at x = 0.8, by a factor 0.611.

AB - We consider the deep inelastic structure functions of the photon in an asymptotically free gauge theory. In contrast to the case of a hadronic target, we find that the shortdistance analysis determines the shape and magnitude and not merely the Q2 dependence of the structure functions. The structure functions of the free quark theory are renormalized by finite, calculable factors. For example, at x = 0.1, we find that F2 will, at large Q2, exceed the free quark result by a factor 1.751, while for x = 0.5, F2 is suppressed asymptotically, relative to the free quark theory, by a factor 0.964, and at x = 0.8, by a factor 0.611.

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U2 - 10.1016/0550-3213(77)90038-4

DO - 10.1016/0550-3213(77)90038-4

M3 - Article

AN - SCOPUS:24544451965

SN - 0550-3213

VL - 120

SP - 189

EP - 202

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 2

ER -