Anatomy of the soft photon approximation in hadron-hadron bremsstrahlung

Abstract

A modified Low procedure for constructing soft-photon amplitudes has been used to derive two general soft-photon amplitudes, a two-s -two-t special amplitude M"' " and a two-u -two-t special amplitude M"" ", where s, t, and u are the Mandelstam variables. M"' " depends only on the elastic T matrix evaluated at four sets of (s, t) fixed by the requirement that the amplitude be free of derivatives (BT/Bs and/or BT/Bt). Likewise M"""" depends only on the elastic T matrix evaluated at four sets of (u, t) also fixed by the requirement that the amplitude M"u "be free of derivatives (BT/Bu and/or AT/tjt). In -TsTts deriving these two amplitudes, we imposed the condition that M"' " and M " " reduce to M"and -Tu Tts~. . . . -Ts TtsM", respectively, their tree-level approximations. The amplitude M"represents photon emission from a sum of one-particle t-channel exchange diagrams and one-particle s-channel exchange dia--Tu Tts grams, while the amplitude M"represents photon emission from a sum of one-particle t-channel exchange diagrams and one-particle u-channel exchange diagrams. The precise expressions for M "' " and

Virtual-pion and two-photon production inppscattering

“…This particular SPM [18,19,25] will be referred to as Low-SPM hereafter. More recently SPM's were developed by Liou, Lin and Gibson [21], based on the explicit evaluation of the tree-level diagrams. The differences between the different versions lie in the particular choice of the on-shell kinematics at which the T-matrix is evaluated.…”

“…The differences between the different versions lie in the particular choice of the on-shell kinematics at which the T-matrix is evaluated. Of particular interest for the discussion in this section is the SPM where the t and u Mandelstam variables are selected to define the on-shell kinematics for the T-matrix [21,22,25], which will be referred to as the tu-SPM hereafter.…”

“…Following ref. [21] the pole contribution to the amplitude is constructed by adding the contributions from the four Feynman diagrams corresponding to emission from each of the external legs (see Fig. (1)),…”

“…This novel SPM, based on a power-series expansion of the T-matrix, combines ideas of the two SPM's which are frequently used for singlephoton bremsstrahlung in pp scattering: the original SPM [19,20], which is directly inspired by the derivation of the low-energy theorem for bremsstrahlung by Low [18], and a later one proposed in ref. [21], which has been very successful in reproducing the observed cross sections [22,23]. The important distinction of the new SPM from the existing two is that no explicit contact terms, or the so-called internal contributions, need to be introduced.…”

New approach to determine proton-nucleus interactions from experimental bremsstrahlung data

“…The cross sections of the emitted photons have been measured for a long time (see Refs. [1][2][3][4][5][6][7][8][9][10][11]), and different theoretical models and approaches were developed to estimate the emitted photons (for example, see [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]). In particular, the spectra of the emitted photons are dependent on dynamics of the scattering of the proton off the nucleus, which is determined by interactions between the proton and nucleus.…”