### Abstract

We visualize the fundamental property of pQCD: the smaller is the size of the colorless quark-gluon configuration, more rapid is the increase of its interaction with energy. Within the frame of the dipole model we use the k_{t} factorization theorem to generalize the DGLAP approximation and/or leading ln (x_{0} / x) approximation and evaluate the interaction of the quark dipole with a target. In the limit of fixed Q^{2} and x → 0 we find the increase with energy of transverse momenta of quark (antiquark) within the q over(q, ̄) pair produced by the strongly virtual photon. The average p_{t}^{2} is evaluated analytically within the double logarithmic approximation. We demonstrate that the invariant mass^{2} of the q over(q, ̄) pair increases with the energy as 0.7 Q^{2} (10^{- 2} / x)^{0.4 αs Nc / π}, for transverse photons, and ∼ 0.7 Q^{2} exp 0.36 [(α_{s} N_{c} / π) log (10^{- 2} / x)]^{1 / 2} for longitudinal photons. We found similar pattern of the energy dependence of M^{2} in the LO DGLAP approximation generalized to account for the k_{t} factorization. We discuss the impact of the found phenomenon on the dependence of the coherence length on the collision energy and demonstrate that in the regime of complete absorption effective shape of the sufficiently energetic hadron (nucleus) has the biconcave form instead of the pancake. We explain that the different representations of chiral symmetry for the central and peripheral collisions would be characteristic property of hadron (nucleus) nucleus collisions at large energies. Some implications of the found phenomena for pp collisions are discussed.

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

Pages (from-to) | 122-129 |

Number of pages | 8 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 679 |

Issue number | 2 |

DOIs | |

State | Published - Aug 17 2009 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*,

*679*(2), 122-129. https://doi.org/10.1016/j.physletb.2009.07.015

}

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*, vol. 679, no. 2, pp. 122-129. https://doi.org/10.1016/j.physletb.2009.07.015

**On the shape of a rapid hadron in QCD.** / Blok, B.; Frankfurt, L.; Strikman, Mark.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the shape of a rapid hadron in QCD

AU - Blok, B.

AU - Frankfurt, L.

AU - Strikman, Mark

PY - 2009/8/17

Y1 - 2009/8/17

N2 - We visualize the fundamental property of pQCD: the smaller is the size of the colorless quark-gluon configuration, more rapid is the increase of its interaction with energy. Within the frame of the dipole model we use the kt factorization theorem to generalize the DGLAP approximation and/or leading ln (x0 / x) approximation and evaluate the interaction of the quark dipole with a target. In the limit of fixed Q2 and x → 0 we find the increase with energy of transverse momenta of quark (antiquark) within the q over(q, ̄) pair produced by the strongly virtual photon. The average pt2 is evaluated analytically within the double logarithmic approximation. We demonstrate that the invariant mass2 of the q over(q, ̄) pair increases with the energy as 0.7 Q2 (10- 2 / x)0.4 αs Nc / π, for transverse photons, and ∼ 0.7 Q2 exp 0.36 [(αs Nc / π) log (10- 2 / x)]1 / 2 for longitudinal photons. We found similar pattern of the energy dependence of M2 in the LO DGLAP approximation generalized to account for the kt factorization. We discuss the impact of the found phenomenon on the dependence of the coherence length on the collision energy and demonstrate that in the regime of complete absorption effective shape of the sufficiently energetic hadron (nucleus) has the biconcave form instead of the pancake. We explain that the different representations of chiral symmetry for the central and peripheral collisions would be characteristic property of hadron (nucleus) nucleus collisions at large energies. Some implications of the found phenomena for pp collisions are discussed.

AB - We visualize the fundamental property of pQCD: the smaller is the size of the colorless quark-gluon configuration, more rapid is the increase of its interaction with energy. Within the frame of the dipole model we use the kt factorization theorem to generalize the DGLAP approximation and/or leading ln (x0 / x) approximation and evaluate the interaction of the quark dipole with a target. In the limit of fixed Q2 and x → 0 we find the increase with energy of transverse momenta of quark (antiquark) within the q over(q, ̄) pair produced by the strongly virtual photon. The average pt2 is evaluated analytically within the double logarithmic approximation. We demonstrate that the invariant mass2 of the q over(q, ̄) pair increases with the energy as 0.7 Q2 (10- 2 / x)0.4 αs Nc / π, for transverse photons, and ∼ 0.7 Q2 exp 0.36 [(αs Nc / π) log (10- 2 / x)]1 / 2 for longitudinal photons. We found similar pattern of the energy dependence of M2 in the LO DGLAP approximation generalized to account for the kt factorization. We discuss the impact of the found phenomenon on the dependence of the coherence length on the collision energy and demonstrate that in the regime of complete absorption effective shape of the sufficiently energetic hadron (nucleus) has the biconcave form instead of the pancake. We explain that the different representations of chiral symmetry for the central and peripheral collisions would be characteristic property of hadron (nucleus) nucleus collisions at large energies. Some implications of the found phenomena for pp collisions are discussed.

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U2 - 10.1016/j.physletb.2009.07.015

DO - 10.1016/j.physletb.2009.07.015

M3 - Article

AN - SCOPUS:68249098934

VL - 679

SP - 122

EP - 129

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 2

ER -