### Abstract

We calculate nonperturbatively and for small Q the cross section (Q) for a scattering process to occur with loss of four-momentum Q to unobserved photons, a quantity which may be measured by observing the net recoil to all other particles. The calculation proceeds by means of a threshold theorem which asserts that for small Q, (Q)0P(Q), where 0 is independent of Q, and P(Q) is the spectral of the coherent state of bremsstrahlung photons defined by a(k)=i(2)-32aua(ua)-1, where ak) is the annihilation operator for a photon of four-momentum k, and ea and ua are the charges and four-velocities of the scattered charged particles. Although is not in the Fock space, the evaluation of P(Q)=4(Q-Pop), where Pop is the operator of total electromagnetic four-momentum, is straightforward. The resulting function P(Q) simplifies if Q is near the light cone, where the bulk of the probability is in fact located, P(Q)(Q0)(Q2)[(1+B)]-1B(Q22)B-1I0 (Q)exp[F(Q)], where I0(Q)=-(2)-3[aeaua (uaQ)-1]2>0, B=dkI0(Q0=1, Qk), and F(Q) is given explicitly in the text, satisfies F(Q)=F(Q)-B ln, and is a smooth function as the light cone is approached. The spectral function exhibits two scaling laws, one governing the approach to the origin along a ray limQ)=0P(Q), the other governing the approach to the light cone at fixed energy Q0=E and angle k^ lim|Q|E[(E-|Q|)1-BP(E,Q]=const×[(1+B)]-1BEB-1I0(k)exp[F(k)], where k=(E,Ek). For e+-e- annihilation at 3 on 3 Gev, exp[F(k)]=E-Bexp[F(k)] produces a 30% angular modulation.

Original language | English (US) |
---|---|

Pages (from-to) | 2011-2026 |

Number of pages | 16 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 20 |

Issue number | 8 |

DOIs | |

State | Published - 1979 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

**Energy and momentum spectral function of coherent bremsstrahlung radiation.** / Zwanziger, Daniel.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 20, no. 8, pp. 2011-2026. https://doi.org/10.1103/PhysRevD.20.2011

}

TY - JOUR

T1 - Energy and momentum spectral function of coherent bremsstrahlung radiation

AU - Zwanziger, Daniel

PY - 1979

Y1 - 1979

N2 - We calculate nonperturbatively and for small Q the cross section (Q) for a scattering process to occur with loss of four-momentum Q to unobserved photons, a quantity which may be measured by observing the net recoil to all other particles. The calculation proceeds by means of a threshold theorem which asserts that for small Q, (Q)0P(Q), where 0 is independent of Q, and P(Q) is the spectral of the coherent state of bremsstrahlung photons defined by a(k)=i(2)-32aua(ua)-1, where ak) is the annihilation operator for a photon of four-momentum k, and ea and ua are the charges and four-velocities of the scattered charged particles. Although is not in the Fock space, the evaluation of P(Q)=4(Q-Pop), where Pop is the operator of total electromagnetic four-momentum, is straightforward. The resulting function P(Q) simplifies if Q is near the light cone, where the bulk of the probability is in fact located, P(Q)(Q0)(Q2)[(1+B)]-1B(Q22)B-1I0 (Q)exp[F(Q)], where I0(Q)=-(2)-3[aeaua (uaQ)-1]2>0, B=dkI0(Q0=1, Qk), and F(Q) is given explicitly in the text, satisfies F(Q)=F(Q)-B ln, and is a smooth function as the light cone is approached. The spectral function exhibits two scaling laws, one governing the approach to the origin along a ray limQ)=0P(Q), the other governing the approach to the light cone at fixed energy Q0=E and angle k^ lim|Q|E[(E-|Q|)1-BP(E,Q]=const×[(1+B)]-1BEB-1I0(k)exp[F(k)], where k=(E,Ek). For e+-e- annihilation at 3 on 3 Gev, exp[F(k)]=E-Bexp[F(k)] produces a 30% angular modulation.

AB - We calculate nonperturbatively and for small Q the cross section (Q) for a scattering process to occur with loss of four-momentum Q to unobserved photons, a quantity which may be measured by observing the net recoil to all other particles. The calculation proceeds by means of a threshold theorem which asserts that for small Q, (Q)0P(Q), where 0 is independent of Q, and P(Q) is the spectral of the coherent state of bremsstrahlung photons defined by a(k)=i(2)-32aua(ua)-1, where ak) is the annihilation operator for a photon of four-momentum k, and ea and ua are the charges and four-velocities of the scattered charged particles. Although is not in the Fock space, the evaluation of P(Q)=4(Q-Pop), where Pop is the operator of total electromagnetic four-momentum, is straightforward. The resulting function P(Q) simplifies if Q is near the light cone, where the bulk of the probability is in fact located, P(Q)(Q0)(Q2)[(1+B)]-1B(Q22)B-1I0 (Q)exp[F(Q)], where I0(Q)=-(2)-3[aeaua (uaQ)-1]2>0, B=dkI0(Q0=1, Qk), and F(Q) is given explicitly in the text, satisfies F(Q)=F(Q)-B ln, and is a smooth function as the light cone is approached. The spectral function exhibits two scaling laws, one governing the approach to the origin along a ray limQ)=0P(Q), the other governing the approach to the light cone at fixed energy Q0=E and angle k^ lim|Q|E[(E-|Q|)1-BP(E,Q]=const×[(1+B)]-1BEB-1I0(k)exp[F(k)], where k=(E,Ek). For e+-e- annihilation at 3 on 3 Gev, exp[F(k)]=E-Bexp[F(k)] produces a 30% angular modulation.

UR - http://www.scopus.com/inward/record.url?scp=35949042294&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevD.20.2011

DO - 10.1103/PhysRevD.20.2011

M3 - Article

VL - 20

SP - 2011

EP - 2026

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 8

ER -