### Abstract

We use QCD to compute the cross section for high-energy coherent production of a dijet (treated as a qq̄ moving at high relative transverse momentum, κ_{t}) from a nucleon and a nuclear target. The direct evaluation of the relevant Feynman diagrams shows that, in the target rest frame, the space-time evolution of this reaction is dominated by the process in which the high κ_{t} qq̄ component (point-like configuration) of the pion wave function is formed before reaching the target. This point-like configuration then interacts through a two-gluon exchange with the target. In the approximation of keeping the leading order in powers of α_{s} and in the leading logarithmic approximation in α_{s}ln(κ_{t}^{2}/ Λ_{QCD}^{2}), the amplitudes for other processes are shown to be smaller by at least a power of α_{s} and/or the powers of Sudakov-type form factors and the small probability, w_{2}, to find a qq̄ pair with no gluons at an average separation between constituents. Thus the high κ_{t}t component of the pion wave function, including the contribution of Gegenbauer polynomials of rank n>0, can be measured in principle at sufficiently large values of κ_{t}^{2}. At large values of κ_{t}^{2}, the resulting dominant amplitude is proportional to z(1 - z)α_{s}(k_{t}^{2}) κ_{t}^{-4}[ln(κ_{t}^{2}/ Λ^{2})]^{CF/β} [z is the fraction light cone (+) momentum carried by the quark in the final state, β is the coefficient in the running coupling constant] times the skewed gluon distribution of the target. For pion scattering by a nuclear target, this means that at fixed χ_{N}=2κ_{t}^{2}/s (but κ_{t}^{2}→∞) the nuclear process in which there is only a single interaction is the most important one to contribute to the reaction. Thus in this limit color transparency phenomena should occur-initial and final state interaction effects are absent for sufficiently large values of κ_{t}. These findings are in accord with the recent experiment performed at Fermilab. We also reexamine a potentially important nuclear multiple scattering correction which is positive and varies as the length of the nucleus divided by an extra factor of 1/κ_{t}^{4}. The meaning of the signal obtained from the experimental measurement of pion diffraction into two jets is also critically examined and significant corrections are identified. We show also that for values of κ_{t} achieved at fixed target energies, dijet production by the electromagnetic field of the nucleus leads to an insignificant correction which gets more important as κ_{t} increases. We explain also that the same regularities are valid for photoproduction of forward light quark dijets.

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

Article number | 094015 |

Pages (from-to) | 940151-9401527 |

Number of pages | 8461377 |

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

Volume | 65 |

Issue number | 9A |

DOIs | |

State | Published - May 1 2002 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*65*(9A), 940151-9401527. [094015]. https://doi.org/10.1103/PhysRevD.65.094015

}

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 65, no. 9A, 094015, pp. 940151-9401527. https://doi.org/10.1103/PhysRevD.65.094015

**Coherent QCD phenomena in the coherent pion-nucleon and pion-nucleus production of two jets at high relative momenta.** / Frankfurt, L.; Miller, G. A.; Strikman, Mark.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Coherent QCD phenomena in the coherent pion-nucleon and pion-nucleus production of two jets at high relative momenta

AU - Frankfurt, L.

AU - Miller, G. A.

AU - Strikman, Mark

PY - 2002/5/1

Y1 - 2002/5/1

N2 - We use QCD to compute the cross section for high-energy coherent production of a dijet (treated as a qq̄ moving at high relative transverse momentum, κt) from a nucleon and a nuclear target. The direct evaluation of the relevant Feynman diagrams shows that, in the target rest frame, the space-time evolution of this reaction is dominated by the process in which the high κt qq̄ component (point-like configuration) of the pion wave function is formed before reaching the target. This point-like configuration then interacts through a two-gluon exchange with the target. In the approximation of keeping the leading order in powers of αs and in the leading logarithmic approximation in αsln(κt2/ ΛQCD2), the amplitudes for other processes are shown to be smaller by at least a power of αs and/or the powers of Sudakov-type form factors and the small probability, w2, to find a qq̄ pair with no gluons at an average separation between constituents. Thus the high κtt component of the pion wave function, including the contribution of Gegenbauer polynomials of rank n>0, can be measured in principle at sufficiently large values of κt2. At large values of κt2, the resulting dominant amplitude is proportional to z(1 - z)αs(kt2) κt-4[ln(κt2/ Λ2)]CF/β [z is the fraction light cone (+) momentum carried by the quark in the final state, β is the coefficient in the running coupling constant] times the skewed gluon distribution of the target. For pion scattering by a nuclear target, this means that at fixed χN=2κt2/s (but κt2→∞) the nuclear process in which there is only a single interaction is the most important one to contribute to the reaction. Thus in this limit color transparency phenomena should occur-initial and final state interaction effects are absent for sufficiently large values of κt. These findings are in accord with the recent experiment performed at Fermilab. We also reexamine a potentially important nuclear multiple scattering correction which is positive and varies as the length of the nucleus divided by an extra factor of 1/κt4. The meaning of the signal obtained from the experimental measurement of pion diffraction into two jets is also critically examined and significant corrections are identified. We show also that for values of κt achieved at fixed target energies, dijet production by the electromagnetic field of the nucleus leads to an insignificant correction which gets more important as κt increases. We explain also that the same regularities are valid for photoproduction of forward light quark dijets.

AB - We use QCD to compute the cross section for high-energy coherent production of a dijet (treated as a qq̄ moving at high relative transverse momentum, κt) from a nucleon and a nuclear target. The direct evaluation of the relevant Feynman diagrams shows that, in the target rest frame, the space-time evolution of this reaction is dominated by the process in which the high κt qq̄ component (point-like configuration) of the pion wave function is formed before reaching the target. This point-like configuration then interacts through a two-gluon exchange with the target. In the approximation of keeping the leading order in powers of αs and in the leading logarithmic approximation in αsln(κt2/ ΛQCD2), the amplitudes for other processes are shown to be smaller by at least a power of αs and/or the powers of Sudakov-type form factors and the small probability, w2, to find a qq̄ pair with no gluons at an average separation between constituents. Thus the high κtt component of the pion wave function, including the contribution of Gegenbauer polynomials of rank n>0, can be measured in principle at sufficiently large values of κt2. At large values of κt2, the resulting dominant amplitude is proportional to z(1 - z)αs(kt2) κt-4[ln(κt2/ Λ2)]CF/β [z is the fraction light cone (+) momentum carried by the quark in the final state, β is the coefficient in the running coupling constant] times the skewed gluon distribution of the target. For pion scattering by a nuclear target, this means that at fixed χN=2κt2/s (but κt2→∞) the nuclear process in which there is only a single interaction is the most important one to contribute to the reaction. Thus in this limit color transparency phenomena should occur-initial and final state interaction effects are absent for sufficiently large values of κt. These findings are in accord with the recent experiment performed at Fermilab. We also reexamine a potentially important nuclear multiple scattering correction which is positive and varies as the length of the nucleus divided by an extra factor of 1/κt4. The meaning of the signal obtained from the experimental measurement of pion diffraction into two jets is also critically examined and significant corrections are identified. We show also that for values of κt achieved at fixed target energies, dijet production by the electromagnetic field of the nucleus leads to an insignificant correction which gets more important as κt increases. We explain also that the same regularities are valid for photoproduction of forward light quark dijets.

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U2 - 10.1103/PhysRevD.65.094015

DO - 10.1103/PhysRevD.65.094015

M3 - Article

VL - 65

SP - 940151

EP - 9401527

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 0556-2821

IS - 9A

M1 - 094015

ER -