Abstract
We calculate a class of polarized fermion string scattering amplitudes (PFSSA) at arbitrary mass levels. We discover that, in the hard scattering limit, the functional forms of the non-vanishing PFSSA at each fixed mass level are independent of the choices of spin polarizations. This result agrees with Gross conjecture on high energy string scattering amplitudes extended to the fermionic sector. In addition, this peculiar property of hard PFSSA is to be compared with the usual spin polarization dependence of the hard polarized fermion field theory scatterings.
Highlights
We calculate a class of polarized fermion string scattering amplitudes (PFSSA) at arbitrary mass levels
Since Gross conjecture was shown to be valid for both GSO even and odd states in the NS sector [10], for simplicity in this paper, we are going to ignore the GSO projection, and the other three string states in the SSA will be chosen to be one massless fermion and two tachyon states (GSO odd)
It was remarkable to discover that all the hard bosonic SSA at each fixed mass level share the same functional forms with the following ratios [8, 9]
Summary
It was shown for the bosonic SSA that at each fixed mass level M2 = 2(N − 1) only tensor states of the following form [8, 9]. Are of leading order in energy in the hard scattering limit. It was remarkable to discover that all the hard bosonic SSA at each fixed mass level share the same functional forms with the following ratios [8, 9]. There is only one hard SSA T (N,0,0) at each fixed mass level. For the leading hard SSA of the Regge trajectory states, one can choose to put all the tensor polarizations ǫm1 = · · · = ǫmn = ǫT. Where zij = zi − zj, Γμ are 10D Dirac matrices calculated in Eq(3.33) and C matrix calculated in Eq(3.36)
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