Hadronic final states and jet structure

The measurements of the scaling violations of the structure function of the pomeron provide a method to determine the parton distributions of the pomeron. The question of whether such an approach is useful can be addressed by applying these parton distributions to calculations for other processes which are directly sensitive to this partonic structure.

Historically, the measurements of <p_T^*2>, the mean transverse momentum-squared of the outgoing hadrons, as a function of x_F = p_L/p_L^max, the scaled longitudinal momentum distribution, provided insight into the structure of the proton. Here, the variables are measured in the hadronic centre of mass frame and with respect to the virtual photon-proton axis which is equivalent to the virtual photon-pomeron axis for small values of t. In Fig. 27(a), the H1 $\gamma^*I\hspace{-0.2em}P$ data (full circles) are compared to the EMC $\gamma^* p$ data at similar $M_X\equiv W$ values. The data are also compared to the RAPGAP (RG) Monte Carlo predictions incorporating quarks and gluons (-QG) and quarks only (-Q) [31]. (MEPS) and (CDM) refer to the Matrix Elements plus Parton Showers and Colour Dipole Model fragmentation schemes, respectively. The H1 data are approximately symmetric about x_F = 0 with a relatively large <p_T^*2> peaking around 0.6 GeV². The symmetry and relatively large p_T^* values reflect the underlying boson-gluon fusion process where a ``leading" gluon from the pomeron interacts with the virtual photon. This behaviour is in contrast to the EMC $\gamma^* p$ data where QCD radiation is suppresed in the negative-x_F (proton remnant) region. Quantitatively the RAPGAP Monte Carlo which incorporates the pomeron parton densities (-QG) gives a good description of the data, provided that quarks and gluons are incorporated whereas a model with only quark (-Q) fails to describe the data. These conclusions are relatively independent of the fragmentation scheme, but the colour dipole model tends to give a better description of the data.

Similarly, event shape variables have been used at e⁺e^- colliders in order to establish the existence of gluon Bremsstrahlung radiation. In this case, the measurement of e.g. mean thrust (the mean value of the scaled longitudinal momentum with respect to the axis which maximises this value) is sensitive to the gluon-induced diagrams. A comparison of <thrust> with e⁺e^- annihilation experiments as a function of the reciprocal of hadronic centre of mass is shown in Fig. 27(b). The diffractive data exhibit lower thrust values compared to e⁺e^- data for all values of M_X. This additional broadening is due to the boson gluon fusion process which has no analogue in e⁺e^- annihilation continuum region.

  

Figure: H1 preliminary hadronic final state distributions. (a) <p_T^*2> versus x_F compared to EMC inclusive DIS data at similar W values and the RAPGAP Monte Carlo predictions discussed in the text. (b) $<{\rm thrust}>$ versus 1/M_X compared to e⁺e^- data at similar 1/W values.

The general increase in thrust with increasing M_X (decreasing 1/M_X) is indicative of jet production. The question of the constituent content of the pomeron can also be addressed via measurements of diffractively produced jets in the photoproduction data [32]. Jets are reconstructed at large W ( 134< W < 277 GeV) using the cone algorithm with unit cone radius and two jets with E_T^jet > 6 GeV. The diffractive contribution is identified as a tail in the $\eta _{max}$ distribution of these events above the PYTHIA 5.7 [33] Monte Carlo expectation. In Fig. 28 the measured cross-section is compared to various model predictions as a function of $\beta^{OBS}$, an estimator of the fraction of the pomeron momentum transferred to the dijet system.

  

Figure: ZEUS preliminary dijet cross-sections from large E_T^jet photoproduction data with a large rapidity gap for (a) the pomeron and (b) the photon. The shaded band represents the (correlated) energy scale uncertainty. The data are compared to various combinations of quark and gluon input distributions of the pomeron for the QCD fits discussed in the text.

The non-diffractive contribution estimated from PYTHIA (not shown) is significantly lower than the data. Here, standard photon and proton parton distributions are adopted and the overall scale, which agrees with the non-diffractive data normalisation, is set by E_T^jet. Also shown are the predicted diffractive cross-sections from the LO QCD calculation plus parton showers of POMPYT, using a hard (z(1-z)) quark combined with either a hard, soft ((1-z)⁵) or singular gluon where a Donnachie-Landshoff flux factor is adopted. Sampling low-energy (soft) gluons corresponds to a small cross-section and can be discounted, whereas high-energy (hard) gluons and/or quarks can account for the cross-section by changing the relative weights of each contribution. The shape of the $\beta^{OBS}$ distribution is clearly sensitive to the shape of the input gluon distribution.

The $x_\gamma^{OBS}$ distribution for these events, where $x_\gamma^{OBS}$ is the corresponding estimator of the fraction of the photon momentum transferred to the dijet system, is peaked around 1, indicating that at these E_T^jet values a significant fraction of events is due to direct processes where the whole photon interacts with the pomeron constituents.

So far we have only considered the case of small-t diffraction with respect to the outgoing proton. Further insight into the diffractive exchange process can be obtained by measurements of the rapidity gap between jets. Here, a class of events is observed with little hadronic activity between the jets [34]. The jets have E_T^jet > 6 GeV and are separated by a pseudorapidity interval ( $\Delta\eta$) of up to 4 units. The scale of the momentum transfer, t, is not precisely defined but is of order (E_T^jet)². A gap is defined as the absence of particles with transverse energy greater than 300 MeV between the jets. The fraction of events containing a gap is then measured as a function of $\Delta\eta$, as shown in Fig. 29. The fit indicates the sum of an exponential behaviour, as expected for non-diffractive processes and discussed in relation to the diffractive DIS data, and a flat distribution expected for diffractive processes. At values of $\Delta\eta \raisebox{-.6ex}{${\textstyle\stackrel{>}{\sim}}$ }3$, an excess is seen with a constant fraction over the expectation for non-diffractive exchange at $\simeq 0.07\pm 0.03$. This can be interpreted as evidence for large-t diffractive scattering. In fact, secondary interactions of the photon and proton remnant jets could fill in the gap and therefore the underlying process could play a more significant rôle. The size of this fraction is relatively large when compared to a similar analysis by DØ and CDF where a constant fraction at $\simeq 0.01$ is observed [36,37], as discussed below.

  

Figure: ZEUS gap-fraction, $f(\Delta \eta )$, as a function of the rapidity gap between the two jets compared with the result of a fit to an exponential plus a constant.