QCD Predictions for the Transverse Energy Flow in Deep-Inelastic Scattering in the Small x HERA Regime

The distribution of transverse energy, $E_T$, which accompanies deep-inelastic electron-proton scattering at small $x$, is predicted in the central region away from the current jet and proton remnants. We use BFKL dynamics, which arises from the summation of multiple gluon emissions at small $x$, to derive an analytic expression for the $E_T$ flow. One interesting feature is an $x^{-\epsilon}$ increase of the $E_T$ distribution with decreasing $x$, where $\epsilon = (3\alpha_s/\pi)2\log 2$. We perform a numerical study to examine the possibility of using characteristics of the $E_T$ distribution as a means of identifying BFKL dynamics at HERA.Comment: 16 pages, REVTEX 3.0, no figures. (Hardcopies of figures available on request from Professor A.D. Martin, Department of Physics, University of Durham, DH1 3LE, England.) Durham preprint : DTP/94/0

Properties of the BFKL equation and structure function predictions for HERA

The general properties of the Lipatov or BFKL equation are reviewed. Modifications to the infrared region are proposed. Numerical predictions for the deep-inelastic electron-proton structure functions at small $x$ are presented and confronted with recent HERA measurements.Comment: 21 pages, 11 figures, Latex file, Durham preprint DTP 92/2

BFKL versus HERA

The BFKL equation and the kT-factorization theorem are used to obtain predictions for F2 in the small Bjorken-x region over a wide range of Q**2. The dependence on the parameters, especially on those concerning the infrared region, is discussed. After a background fit to recent experimental data obtained at HERA and at Fermilab (E665 experiment), we find that the predicted, almost Q**2 independent BFKL slope lambda >= 0.5 appears to be too steep at lower Q**2 values. Thus there seems to be a chance that future HERA data can distinguish between pure BFKL and conventional field theoretic renormalization group approaches.Comment: 26 pages, 6 eps figures, LaTeX2e using epsfig.sty and amssymb.st

The description of F2 at small x incorporating angular ordering

We study the perturbative QCD description of the HERA measurements of $F_2 (x, Q^2)$ using a gluon distribution that is obtained from an evolution incorporating angular ordering of the gluon emissions, and which embodies both GLAP and BFKL dynamics. We compare the predictions with recent HERA data for $F_2$. We present estimates of the charm component $F_2^c (x, Q^2)$ and of $F_L (x, Q^2)$.Comment: 8 LaTeX pages + 4 uuencoded figure

Constraints on gluon evolution at small x

The BFKL and the unified angular-ordered equations are solved to determine the gluon distribution at small $x$. The impact of kinematic constraints is investigated. Predictions are made for observables sensitive to the gluon at small $x$. In particular comparison is made with measurements at the HERA electron-proton collider of the proton structure function $F_2 (x, Q^2)$ as a function of $\ln Q^2$, the charm component, $F_2^c(x,Q^2)$ and diffractive $J/\psi$ photoproduction.Comment: 17 LaTeX pages and 9 postscript figure

A unified BFKL and GLAP description of F2F_2 data

We argue that the use of the universal unintegrated gluon distribution and the $k_T$ (or high energy) factorization theorem provides the natural framework for describing observables at small x. We introduce a coupled pair of evolution equations for the unintegrated gluon distribution and the sea quark distribution which incorporate both the resummed leading $ln (1/x)$ BFKL contributions and the resummed leading $ln (Q^2)$ GLAP contributions. We solve these unified equations in the perturbative QCD domain using simple parametic forms of the nonperturbative part of the integrated distributions. With only two (physically motivated) input parameters we find that this $k_T$ factorization approach gives an excellent description of the measurements of $F_2 (x,Q^2)$ at HERA. In this way the unified evolution equations allow us to determine the gluon and sea quark distributions and, moreover, to see the x domain where the resummed $ln (1/x)$ effects become significant. We use $k_T$ factorization to predict the longitudinal structure function $F_L (x,Q^2)$ and the charm component of $F_2 (x,Q^2)$.Comment: 25 pages, LaTeX, 9 figure

THE GLUON DISTRIBUTION AT SMALL x OBTAINED FROM A UNIFIED EVOLUTION EQUATION.

We solve a unified integral equation to obtain the $x, Q_T$ and $Q$ dependence of the gluon distribution of a proton in the small $x$ regime; where $x$ and $Q_T$ are the longitudinal momentum fraction and the transverse momentum of the gluon probed at a scale $Q$. The equation generates a gluon with a steep $x^{- \lambda}$ behaviour, with $\lambda \sim 0.5$, and a $Q_T$ distribution which broadens as $x$ decreases. We compare our solutions with, on the one hand, those that we obtain using the double-leading-logarithm approximation to Altarelli-Parisi evolution and, on the other hand, to those that we determine from the BFKL equation.Comment: LaTeX file with 10 postscript figures (uuencoded

Cardiorespiratory Fitness Modulates The Acute Flow-Mediated Dilation Response Following High-Intensity But Not Moderate-Intensity Exercise In Elderly Men.

Impaired endothelial function is observed with ageing and with low cardiorespiratory fitness (VO2peak) whilst improvements in both are suggested to be reliant on higher-intensity exercise in the elderly. This may be due to the flow-mediated dilation (FMD) response to acute exercise of varying intensity. We examined the hypothesis that exercise-intensity alters the FMD response in healthy elderly adults, and would be modulated by VO2peak Forty-seven elderly men were stratified into lower- (VO2peak = 24.3±2.9 ml.kg(-1)min(-1), n=27) and higher-fit groups (VO2peak = 35.4±5.5 ml.kg(-1)min(-1), n=20) after a test of cycling peak power output (PPO). In randomised order, participants undertook 27 min moderate-intensity continuous (MICE; 40% PPO) or high-intensity interval cycling exercise (HIIE; 70% PPO), or no-exercise control. Brachial FMD was assessed at rest, 10 and 60 min after exercise. In control, FMD reduced in both groups (P=0.05). FMD increased after MICE in both groups [increase of 0.86 % (95% CI, 0.17 to 1.56), P=0.01], and normalised after 60 min. In the lower-fit, FMD reduced after HIIE [reduction of 0.85 % (95% CI, 0.12 to 1.58), P=0.02), and remained decreased at 60 min (P=0.05). In the higher-fit FMD was unchanged immediately after HIIE and increased after 60 min [increase of 1.52 % (95% CI, 0.41 to 2.62), P<0.01], which was correlated with VO2peak (r =0.41; P<0.01). Exercise-intensity alters the FMD response in elderly adults, and VO2peak modulates the FMD response following HIIE, but not MICE. The sustained decrease in FMD in the lower-fit may represent a signal for vascular adaptation or endothelial fatigue

Deep inelastic events containing a forward photon as a probe of small xx dynamics

We calculate the rate of producing deep inelastic events containing an energetic isolated forward photon at HERA. We quantify the enhancement arising from the leading $\log 1/x$ gluon emissions with a view to using such events to identify the underlying dynamics.Comment: 11 pages, Latex, 7 ps figure