Evidences for two scales in hadrons

Some unusual features observed in hadronic collisions at high energies can be understood assuming that gluons in hadrons are located within small spots occupying only about 10% of the hadrons’ area. Such a conjecture about the presence of two scales in hadrons helps to explain the following: why diffractive gluon radiation is so suppressed; why the triple-Pomeron coupling shows no $t$ dependence; why total hadronic cross sections rise so slowly with energy; why diffraction cones shrink so slowly, and why ${\alpha }_{\mathbb{P}}^{\prime }\ll {\alpha }_{\mathbb{R}}^{\prime }$; why the transition from hard to soft regimes in the structure functions occurs at rather large $Q^2$; why the observed Cronin effect at collider energies is so weak; why hard reactions sensitive to primordial parton motion (direct photon, Drell-Yan dileptons, heavy flavors, back-to-back dihadrons, seagull effect, etc.) demand such a large transverse momenta of the projectile partons, which is not explained by next-to-leading order calculations; why the onset of nuclear shadowing for gluons is so delayed compared to quarks; and why shadowing is so weak.

Figure 1

The cross section of diffractive excitation of a proton expressed in terms of the total Pomeron-proton cross section.

Figure 2

Pomeron-proton total cross sections ${\sigma }_{\mathrm{tot}}^{\mathbb{P}p}$ as a function of invariant mass squared, $s^{\prime }=M_X^2$, extracted from data on $pp\to pX$ [56].

Figure 3

The total Pomeron-Pomeron cross section measured in double diffractive processes [57]. Samples labeled “AND” and “OR” correspond to different criteria of event selection. The solid and dashed curves correspond to expectations based on Regge factorization [57].

Figure 4

Slope of elastic $pp$ and $\overline{p}p$ differential cross sections as functions of energy. The dashed and solid curves correspond to Eq. (11) with ${\alpha }_{\mathbb{P}}^{\prime }=0.25{\mathrm{GeV}}^{-2}$ and to the slope predicted in 17 including the effects of unitarity saturation, respectively. For references to the depicted experimental data see 17.

Figure 5

Data points are Fourier transformed data for the differential elastic cross section [17]. Solid curves show the unitarized elastic amplitude, including Gribov inelastic corrections [55]. Dashed curves correspond to the Reggeon contribution, corrected for absorption.

Figure 6

The effective Pomeron trajectory measured in elastic photoproduction $\gamma p\to J/\Psi p$ [22]. The slope of the trajectory is ${\alpha }_{\mathbb{P}}^{\prime }=0.115\pm 0.018{\mathrm{GeV}}^{-2}$.

Figure 7

The effective Pomeron trajectory measured in elastic photoproduction $\gamma p\to \rho p$ [30].

Figure 8

Logarithmic scale derivative of the structure function as a function of $Q^2$ and $x$.

Figure 9

${\lambda }_{\mathrm{eff}}=d\ln F_2/d\ln (1/x)$ as a function of $Q^2$, calculated in 58 by fitting $F_2=A{x}^{-{\lambda }_{\mathrm{eff}}}$ to ZEUS and E665 data with $x<0.01$. The DL and GRV94 calculations are from Ref. 59 and the GRV94 NLO fit [60], respectively.

Figure 10

Nucleus-to-proton cross section ratio for pion production, versus $p_T$. Dashed and solid curves correspond to calculations without or with gluon shadowing [8].

Figure 11

Nucleus-to-proton cross section ratio for gluon radiation as a function of $p_T$. The upper and lower curves correspond to mean gluon propagation distances 1 fm (long range) and 0.3 fm (small spots), respectively [14].

Figure 12

Top plot: the photon and ${\pi }^0$ production cross sections from the E706 experiment at $\sqrt{s}=31.6\mathrm{GeV}$, compared to $k_T$-corrected NLO calculations [44]. Bottom plot: the ratio (Data-Theory)/Theory for direct photon production. Theory corresponds to the NLO calculations with primordial parton momentum $⟨k_T⟩$.

Figure 13

Logarithmic scale derivative of the structure function as a function of $Q^2$ and $x$.

Figure 14

Bjorken $x$ dependence of the factor $P$ in Eq. (39) for quarks and longitudinal (two upper curves) and transverse (next couple of curves) photons. Solid and dashed curves are calculated [51] for $Q^2=4$ and $40{\mathrm{GeV}}^2$, respectively. The bottom curve represents $P$ for gluons.

Figure 15

Ratio of the gluon distribution functions in nuclei (carbon, copper, and lead) and nucleons versus Bjorken $x$ at $Q^2=4{\mathrm{GeV}}^2$ (solid curves) and $40{\mathrm{GeV}}^2$ (dashed curves).