Squark contributions to photon structure functions and positivity constraints

Abstract

Photon structure functions in supersymmetric QCD are investigated in terms of the parton model where squark contributions are evaluated. We calculate the eight virtual photon structure functions by taking the discontinuity of the squark massive one-loop diagrams of the photon-photon forward amplitude. The model-independent positivity constraints derived from the Cauchy-Schwarz inequalities are satisfied by the squark parton model calculation and actually the two equality relations hold for the squark contribution. We also show that our polarized photon structure function g γ 1 for the real photon leads to the vanishing 1st moment sum rule, and the constraint |g γ 1 | ≤ F γ 1 is satisfied by the real photon. We also discuss a squark signature in the structure function W τ T T .

Photon Structure in Supersymmetric QCD

“…There is no significant difference in the small-x region between QCD and SQCD, while at large x, it turns out that there exists a sizable difference between the massive QCD and SQCD. When compared to the squark contribution to F γ 2 in the parton model calculation [15], the squark component in the SQCD is suppressed at large x due to the radiative correction. We expect that the future linear collider would enable such an analysis to be carried out on photon structure functions.…”

“…where T i 's are the projection operators given in the Appendix of ref. [15], and these eight structure functions are simply related to the s-channel helicity amplitudes as discussed in ref. [11].…”

“…The graphs show that all the structure functions tend to vanish as x → x max which is the kinematical constraint. The positivity constraints derived from the general Cauchy-Schwarz inequalities [14] in fact lead to the following equalities for the squark contributions [15]:…”

Photon structure function in supersymmetric QCD revisited

“…3, there is no significant difference in the small-x region between QCD and SQCD, while at large x, it turns out that there exists a sizable difference between the massive QCD and SQCD. When compared to the squark contribution to F γ 2 in the parton model calculation [30], the squark component in the SQCD is suppressed at large x due to the radiative correction. We expect that the future linear collider would enable such an analysis to be carried out on photon structure functions.…”

Photon structure functions with heavy particle mass effects

“…We have also applied our formalism for the photon structure functions in supersymmetric QCD (SQCD) where there exist squarks and gluinos in addition to the quarks and gluons. The squark contribution in the parton model was studied in [17]. For the SQCD radiative corrections, we based our argument on the parton distribution functions (PDF's) which satisfy the DGLAPtype evolution equation.…”