Enzymatic Primer-Extension with Glycerol-Nucleoside Triphosphates on DNA Templates

selection. Template-dependent GNA synthesis is essential to any GNA-based selection system.In this study, we investigated the ability of various DNA polymerases to use glycerol-nucleoside triphosphates (gNTPs) as substrates for GNA synthesis on DNA templates. Therminator DNA polymerase catalyzes quantitative primer-extension by the incorporation of two glyceronucleotides, with much less efficient extension up to five glyceronucleotides. Steady-state kinetic experiments suggested that GNA synthesis by Therminator was affected by both decreased catalytic rates and weakened substrate binding, especially for pyrimidines. In an attempt to improve pyrimidine incorporation by providing additional stacking interactions, we synthesized two new gNTP analogs with 5-propynyl substituted pyrimidine nucleobases. This led to more efficient incorporation of gC, but not gT.We suggest that directed evolution of Therminator might lead to mutants with improved substrate binding and catalytic efficiency

A Measurement of Rb using a Double Tagging Method

The fraction of Z to bbbar events in hadronic Z decays has been measured by the OPAL experiment using the data collected at LEP between 1992 and 1995. The Z to bbbar decays were tagged using displaced secondary vertices, and high momentum electrons and muons. Systematic uncertainties were reduced by measuring the b-tagging efficiency using a double tagging technique. Efficiency correlations between opposite hemispheres of an event are small, and are well understood through comparisons between real and simulated data samples. A value of Rb = 0.2178 +- 0.0011 +- 0.0013 was obtained, where the first error is statistical and the second systematic. The uncertainty on Rc, the fraction of Z to ccbar events in hadronic Z decays, is not included in the errors. The dependence on Rc is Delta(Rb)/Rb = -0.056*Delta(Rc)/Rc where Delta(Rc) is the deviation of Rc from the value 0.172 predicted by the Standard Model. The result for Rb agrees with the value of 0.2155 +- 0.0003 predicted by the Standard Model.Comment: 42 pages, LaTeX, 14 eps figures included, submitted to European Physical Journal

Measurement of the B+ and B-0 lifetimes and search for CP(T) violation using reconstructed secondary vertices

The lifetimes of the B+ and B-0 mesons, and their ratio, have been measured in the OPAL experiment using 2.4 million hadronic Z(0) decays recorded at LEP. Z(0) --> b (b) over bar decays were tagged using displaced secondary vertices and high momentum electrons and muons. The lifetimes were then measured using well-reconstructed charged and neutral secondary vertices selected in this tagged data sample. The results aretau(B+) = 1.643 +/- 0.037 +/- 0.025 pstau(Bo) = 1.523 +/- 0.057 +/- 0.053 pstau(B+)/tau(Bo) = 1.079 +/- 0.064 +/- 0.041,where in each case the first error is statistical and the second systematic.A larger data sample of 3.1 million hadronic Z(o) decays has been used to search for CP and CPT violating effects by comparison of inclusive b and (b) over bar hadron decays, No evidence fur such effects is seen. The CP violation parameter Re(epsilon(B)) is measured to be Re(epsilon(B)) = 0.001 +/- 0.014 +/- 0.003and the fractional difference between b and (b) over bar hadron lifetimes is measured to(Delta tau/tau)(b) = tau(b hadron) - tau((b) over bar hadron)/tau(average) = -0.001 +/- 0.012 +/- 0.008

Deep-Inelastic Inclusive ep Scattering at Low x and a Determination of alpha_s

A precise measurement of the inclusive deep-inelastic e^+p scattering cross section is reported in the kinematic range 1.5<= Q^2 <=150 GeV^2 and 3*10^(-5)<= x <=0.2. The data were recorded with the H1 detector at HERA in 1996 and 1997, and correspond to an integrated luminosity of 20 pb^(-1). The double differential cross section, from which the proton structure function F_2(x,Q^2) and the longitudinal structure function F_L(x,Q^2) are extracted, is measured with typically 1% statistical and 3% systematic uncertainties. The measured partial derivative (dF_2(x,Q^2)/dln Q^2)_x is observed to rise continuously towards small x for fixed Q^2. The cross section data are combined with published H1 measurements at high Q^2 for a next-to-leading order DGLAP QCD analysis.The H1 data determine the gluon momentum distribution in the range 3*10^(-4)<= x <=0.1 to within an experimental accuracy of about 3% for Q^2 =20 GeV^2. A fit of the H1 measurements and the mu p data of the BCDMS collaboration allows the strong coupling constant alpha_s and the gluon distribution to be simultaneously determined. A value of alpha _s(M_Z^2)=0.1150+-0.0017 (exp) +0.0009-0.0005 (model) is obtained in NLO, with an additional theoretical uncertainty of about +-0.005, mainly due to the uncertainty of the renormalisation scale.Comment: 68 pages, 24 figures and 18 table

Jet energy measurement with the ATLAS detector in proton-proton collisions at root s=7 TeV

The jet energy scale and its systematic uncertainty are determined for jets measured with the ATLAS detector at the LHC in proton-proton collision data at a centre-of-mass energy of √s = 7TeV corresponding to an integrated luminosity of 38 pb-1. Jets are reconstructed with the anti-kt algorithm with distance parameters R=0. 4 or R=0. 6. Jet energy and angle corrections are determined from Monte Carlo simulations to calibrate jets with transverse momenta pT≥20 GeV and pseudorapidities {pipe}η{pipe}<4. 5. The jet energy systematic uncertainty is estimated using the single isolated hadron response measured in situ and in test-beams, exploiting the transverse momentum balance between central and forward jets in events with dijet topologies and studying systematic variations in Monte Carlo simulations. The jet energy uncertainty is less than 2. 5 % in the central calorimeter region ({pipe}η{pipe}<0. 8) for jets with 60≤pT<800 GeV, and is maximally 14 % for pT<30 GeV in the most forward region 3. 2≤{pipe}η{pipe}<4. 5. The jet energy is validated for jet transverse momenta up to 1 TeV to the level of a few percent using several in situ techniques by comparing a well-known reference such as the recoiling photon pT, the sum of the transverse momenta of tracks associated to the jet, or a system of low-pT jets recoiling against a high-pT jet. More sophisticated jet calibration schemes are presented based on calorimeter cell energy density weighting or hadronic properties of jets, aiming for an improved jet energy resolution and a reduced flavour dependence of the jet response. The systematic uncertainty of the jet energy determined from a combination of in situ techniques is consistent with the one derived from single hadron response measurements over a wide kinematic range. The nominal corrections and uncertainties are derived for isolated jets in an inclusive sample of high-pT jets. Special cases such as event topologies with close-by jets, or selections of samples with an enhanced content of jets originating from light quarks, heavy quarks or gluons are also discussed and the corresponding uncertainties are determined. © 2013 CERN for the benefit of the ATLAS collaboration

Measurement of the W+W−γW^{+}W^{-} \gamma Cross-section and First direct Limits on Anomalous Electroweak Quartic Gauge Couplings

A study of W+W- events accompanied by hard photon radiation produced in e+e- collisions at LEP is presented. Events consistent with two on-shell W-bosons and an isolated photon are selected from 183pb^-1 of data recorded at root{s}=189GeV. From these data, 17 W+W-gamma candidates are selected with photon energy greater than 10GeV, consistent with the Standard Model expectation. These events are used to measure the e+e- to W+W-gamma cross-section within a set of geometric and kinematic cuts; sigma{W+W-gamma} = 136+-37+-8 fb, where the first error is statistical and the second systematic. The photon energy spectrum is used to set the first direct, albeit weak, limits on possible anomalous contributions to the {W+ W- gamma gamma} and {W+ W- gamma Z0} vertices: -0.070GeV^{-2} < a_0/Lambda^2 < 0.070GeV^{-2}, -0.13GeV^{-2} < a_c/Lambda^2 < 0.19GeV^{-2}, -0.61GeV^{-2} < a_n/Lambda^2 < 0.57GeV^{-2}, where Lambda represents the energy scale for new physics.A study of W+W- events accompanied by hard photon radiation produced in e+e- collisions at LEP is presented. Events consistent with two on-shell W-bosons and an isolated photon are selected from 183pb^-1 of data recorded at root{s}=189GeV. From these data, 17 W+W-gamma candidates are selected with photon energy greater than 10GeV, consistent with the Standard Model expectation. These events are used to measure the e+e- to W+W-gamma cross-section within a set of geometric and kinematic cuts; sigma{W+W-gamma} = 136+-37+-8 fb, where the first error is statistical and the second systematic. The photon energy spectrum is used to set the first direct, albeit weak, limits on possible anomalous contributions to the {W+ W- gamma gamma} and {W+ W- gamma Z0} vertices: -0.070GeV^{-2} < a_0/Lambda^2 < 0.070GeV^{-2}, -0.13GeV^{-2} < a_c/Lambda^2 < 0.19GeV^{-2}, -0.61GeV^{-2} < a_n/Lambda^2 < 0.57GeV^{-2}, where Lambda represents the energy scale for new physics.A study of W+W- events accompanied by hard photon radiation produced in e+e- collisions at LEP is presented. Events consistent with two on-shell W-bosons and an isolated photon are selected from 183pb^-1 of data recorded at root{s}=189GeV. From these data, 17 W+W-gamma candidates are selected with photon energy greater than 10GeV, consistent with the Standard Model expectation. These events are used to measure the e+e- to W+W-gamma cross-section within a set of geometric and kinematic cuts; sigma{W+W-gamma} = 136+-37+-8 fb, where the first error is statistical and the second systematic. The photon energy spectrum is used to set the first direct, albeit weak, limits on possible anomalous contributions to the {W+ W- gamma gamma} and {W+ W- gamma Z0} vertices: -0.070GeV^{-2} < a_0/Lambda^2 < 0.070GeV^{-2}, -0.13GeV^{-2} < a_c/Lambda^2 < 0.19GeV^{-2}, -0.61GeV^{-2} < a_n/Lambda^2 < 0.57GeV^{-2}, where Lambda represents the energy scale for new physics.A study of W+W- events accompanied by hard photon radiation produced in e+e- collisions at LEP is presented. Events consistent with two on-shell W-bosons and an isolated photon are selected from 183pb^-1 of data recorded at root{s}=189GeV. From these data, 17 W+W-gamma candidates are selected with photon energy greater than 10GeV, consistent with the Standard Model expectation. These events are used to measure the e+e- to W+W-gamma cross-section within a set of geometric and kinematic cuts; sigma{W+W-gamma} = 136+-37+-8 fb, where the first error is statistical and the second systematic. The photon energy spectrum is used to set the first direct, albeit weak, limits on possible anomalous contributions to the {W+ W- gamma gamma} and {W+ W- gamma Z0} vertices: -0.070GeV^{-2} < a_0/Lambda^2 < 0.070GeV^{-2}, -0.13GeV^{-2} < a_c/Lambda^2 < 0.19GeV^{-2}, -0.61GeV^{-2} < a_n/Lambda^2 < 0.57GeV^{-2}, where Lambda represents the energy scale for new physics.A study of W+W- events accompanied by hard photon radiation produced in e+e- collisions at LEP is presented. Events consistent with two on-shell W-bosons and an isolated photon are selected from 183pb^-1 of data recorded at root{s}=189GeV. From these data, 17 W+W-gamma candidates are selected with photon energy greater than 10GeV, consistent with the Standard Model expectation. These events are used to measure the e+e- to W+W-gamma cross-section within a set of geometric and kinematic cuts; sigma{W+W-gamma} = 136+-37+-8 fb, where the first error is statistical and the second systematic. The photon energy spectrum is used to set the first direct, albeit weak, limits on possible anomalous contributions to the {W+ W- gamma gamma} and {W+ W- gamma Z0} vertices: -0.070GeV^{-2} < a_0/Lambda^2 < 0.070GeV^{-2}, -0.13GeV^{-2} < a_c/Lambda^2 < 0.19GeV^{-2}, -0.61GeV^{-2} < a_n/Lambda^2 < 0.57GeV^{-2}, where Lambda represents the energy scale for new physics.A study of W+W- events accompanied by hard photon radiation produced in e+e- collisions at LEP is presented. Events consistent with two on-shell W-bosons and an isolated photon are selected from 183pb^-1 of data recorded at root{s}=189GeV. From these data, 17 W+W-gamma candidates are selected with photon energy greater than 10GeV, consistent with the Standard Model expectation. These events are used to measure the e+e- to W+W-gamma cross-section within a set of geometric and kinematic cuts; sigma{W+W-gamma} = 136+-37+-8 fb, where the first error is statistical and the second systematic. The photon energy spectrum is used to set the first direct, albeit weak, limits on possible anomalous contributions to the {W+ W- gamma gamma} and {W+ W- gamma Z0} vertices: -0.070GeV^{-2} < a_0/Lambda^2 < 0.070GeV^{-2}, -0.13GeV^{-2} < a_c/Lambda^2 < 0.19GeV^{-2}, -0.61GeV^{-2} < a_n/Lambda^2 < 0.57GeV^{-2}, where Lambda represents the energy scale for new physics.A study of W+W- events accompanied by hard photon radiation produced in e+e- collisions at LEP is presented. Events consistent with two on-shell W-bosons and an isolated photon are selected from 183pb^-1 of data recorded at root{s}=189GeV. From these data, 17 W+W-gamma candidates are selected with photon energy greater than 10GeV, consistent with the Standard Model expectation. These events are used to measure the e+e- to W+W-gamma cross-section within a set of geometric and kinematic cuts; sigma{W+W-gamma} = 136+-37+-8 fb, where the first error is statistical and the second systematic. The photon energy spectrum is used to set the first direct, albeit weak, limits on possible anomalous contributions to the {W+ W- gamma gamma} and {W+ W- gamma Z0} vertices: -0.070GeV^{-2} < a_0/Lambda^2 < 0.070GeV^{-2}, -0.13GeV^{-2} < a_c/Lambda^2 < 0.19GeV^{-2}, -0.61GeV^{-2} < a_n/Lambda^2 < 0.57GeV^{-2}, where Lambda represents the energy scale for new physics.A study of W+W- events accompanied by hard photon radiation produced in e+e- collisions at LEP is presented. Events consistent with two on-shell W-bosons and an isolated photon are selected from 183pb^-1 of data recorded at root{s}=189GeV. From these data, 17 W+W-gamma candidates are selected with photon energy greater than 10GeV, consistent with the Standard Model expectation. These events are used to measure the e+e- to W+W-gamma cross-section within a set of geometric and kinematic cuts; sigma{W+W-gamma} = 136+-37+-8 fb, where the first error is statistical and the second systematic. The photon energy spectrum is used to set the first direct, albeit weak, limits on possible anomalous contributions to the {W+ W- gamma gamma} and {W+ W- gamma Z0} vertices: -0.070GeV^{-2} < a_0/Lambda^2 < 0.070GeV^{-2}, -0.13GeV^{-2} < a_c/Lambda^2 < 0.19GeV^{-2}, -0.61GeV^{-2} < a_n/Lambda^2 < 0.57GeV^{-2}, where Lambda represents the energy scale for new physics.A study of W + W − events accompanied by hard photon radiation produced in e + e − collisions at LEP is presented. Events consistent with two on-shell W-bosons and an isolated photon are selected from 183 pb −1 of data recorded at s =189 GeV. From these data, 17 W + W − γ candidates are selected with photon energy greater than 10 GeV, consistent with the Standard Model expectation. These events are used to measure the e + e − →W + W − γ cross-section within a set of geometric and kinematic cuts, σ ̂ WW γ =136±37±8 fb, where the first error is statistical and the second systematic. The photon energy spectrum is used to set the first direct, albeit weak, limits on possible anomalous contributions to the W + W − γγ and W + W − γ Z 0 vertices: −0.070 GeV −

τ\tau decays with neutral kaons

The branching ratio of the tau lepton to a neutral K meson is measured from a sample of approximately 200,000 tau decays recorded by the OPAL detector at centre-of-mass energies near the Z0 resonance. The measurement is based on two samples which identify one-prong tau decays with KL and KS mesons. The combined branching ratios are measured to be B(tau- -->pi- K0bar nutau) = (9.33+-0.68+-0.49)x10^-3 B(tau- -->pi- K0bar [>=1pi0] nutau) = (3.24+-0.74+-0.66)x10^-3 B(tau- -->K- K0bar [>=0pi0] nutau) = (3.30+-0.55+-0.39)x10^-3 where the first error is statistical and the second systematic.The branching ratio of the tau lepton to a neutral K meson is measured from a sample of approximately 200,000 tau decays recorded by the OPAL detector at centre-of-mass energies near the Z0 resonance. The measurement is based on two samples which identify one-prong tau decays with KL and KS mesons. The combined branching ratios are measured to be B(tau- -->pi- K0bar nutau) = (9.33+-0.68+-0.49)x10^-3 B(tau- -->pi- K0bar [>=1pi0] nutau) = (3.24+-0.74+-0.66)x10^-3 B(tau- -->K- K0bar [>=0pi0] nutau) = (3.30+-0.55+-0.39)x10^-3 where the first error is statistical and the second systematic

Transverse and Longitudinal Bose Einstein Correlations in hadronic Z0Z^0 Decays

Bose-Einstein correlations in pairs of identical charged pions produced in asample of 4.3 million Z0 hadronic decays are studied as a function of the threecomponents of the momentum difference, transverse ("out" and "side") andlongitudinal with respect to the thrust direction of the event. A significantdifference between the transverse, r_t_side, and longitudinal, r_l, dimensionsis observed, indicating that the emitting source of identical pions, asobserved in the Longitudinally CoMoving System, has an elongated shape. This isobserved with a variety of selection techniques. Specifically, the values ofthe parameters obtained by fitting the extended Goldhaber parametrisation tothe correlation function C'= C^{DATA}}/C^{MC} for two-jet events, selected withthe Durham algorithm and resolution parameter ycut=0.04, arer_t_out=(0.647+-0.011(stat})+0.022-0.124(syst)) fm,r_t_side=(0.809+-0.009(stat)+0.019-0.032}(syst)) fm, r_l=(0.989+-0.011(stat)+0.030-0.015(syst})) fm andr_l/r_t_side=1.222+- 0.027(stat})+0.075-0.012(syst). The results are discussedin the context of a recent model of Bose-Einstein correlations based on stringfragmentation.Bose-Einstein correlations in pairs of identical charged pions produced in a sample of 4.3 million Z0 hadronic decays are studied as a function of the three components of the momentum difference, transverse ("out" and "side") and longitudinal with respect to the thrust direction of the event. A significant difference between the transverse, r_t_side, and longitudinal, r_l, dimensions is observed, indicating that the emitting source of identical pions, as observed in the Longitudinally CoMoving System, has an elongated shape. This is observed with a variety of selection techniques. Specifically, the values of the parameters obtained by fitting the extended Goldhaber parametrisation to the correlation function C'= C^{DATA}}/C^{MC} for two-jet events, selected with the Durham algorithm and resolution parameter ycut=0.04, are r_t_out=(0.647+-0.011(stat})+0.022-0.124(syst)) fm, r_t_side=(0.809+-0.009(stat)+0.019-0.032}(syst)) fm, r_l=(0.989+-0.011(stat)+0.030-0.015(syst})) fm and r_l/r_t_side=1.222+-0.027(stat})+0.075-0.012(syst). The results are discussed in the context of a recent model of Bose-Einstein correlations based on string fragmentation

Experimental properties of gluon and quark jets from a point source

Gluon jets are identified in hadronic Z0 decays as all the particles in a hemisphere opposite to a hemisphere containing two tagged quark jets. Gluon jets defined in this manner are equivalent to gluon jets produced from a color singlet point source and thus correspond to the definition employed for most theoretical calculations. In a separate stage of the analysis, we select quark jets in a manner to correspond to calculations, as the particles in hemispheres of flavor tagged light quark (uds) events. We present the distributions of rapidity, scaled energy, the logarithm of the momentum, and transverse momentum with respect to the jet axes, for charged particles in these gluon and quark jets. We also examine the charged particle multiplicity distributions of the jets in restricted intervals of rapidity. For soft particles at large transverse momentum, we observe the charged particle multiplicity ratio of gluon to quark jets to be 2.29 +- 0.09 +- 0.15 in agreement with the prediction that this ratio should approximately equal the ratio of QCD color factors, CA/CF = 2.25. The intervals used to define soft particles and large transverse momentum for this result, p<4 GeV/c and 0.8<p_t<3.0 GeV/c, are motivated by the predictions of the Herwig Monte Carlo multihadronic event generator. Additionally, our gluon jet data allow a sensitive test of the phenomenon of non-leading QCD terms known as color reconnection. We test the model of color reconnection implemented in the Ariadne Monte Carlo multihadronic event generator and find it to be disfavored by our data.Gluon jets are identified in hadronic Z0 decays as all the particles in a hemisphere opposite to a hemisphere containing two tagged quark jets. Gluon jets defined in this manner are equivalent to gluon jets produced from a color singlet point source and thus correspond to the definition employed for most theoretical calculations. In a separate stage of the analysis, we select quark jets in a manner to correspond to calculations, as the particles in hemispheres of flavor tagged light quark (uds) events. We present the distributions of rapidity, scaled energy, the logarithm of the momentum, and transverse momentum with respect to the jet axes, for charged particles in these gluon and quark jets. We also examine the charged particle multiplicity distributions of the jets in restricted intervals of rapidity. For soft particles at large transverse momentum, we observe the charged particle multiplicity ratio of gluon to quark jets to be 2.29 +- 0.09 +- 0.15 in agreement with the prediction that this ratio should approximately equal the ratio of QCD color factors, CA/CF = 2.25. The intervals used to define soft particles and large transverse momentum for this result, p<4 GeV/c and 0.8<p_t<3.0 GeV/c, are motivated by the predictions of the Herwig Monte Carlo multihadronic event generator. Additionally, our gluon jet data allow a sensitive test of the phenomenon of non-leading QCD terms known as color reconnection. We test the model of color reconnection implemented in the Ariadne Monte Carlo multihadronic event generator and find it to be disfavored by our data.Gluon jets are identified in hadronic Z0 decays as all the particles in a hemisphere opposite to a hemisphere containing two tagged quark jets. Gluon jets defined in this manner are equivalent to gluon jets produced from a color singlet point source and thus correspond to the definition employed for most theoretical calculations. In a separate stage of the analysis, we select quark jets in a manner to correspond to calculations, as the particles in hemispheres of flavor tagged light quark (uds) events. We present the distributions of rapidity, scaled energy, the logarithm of the momentum, and transverse momentum with respect to the jet axes, for charged particles in these gluon and quark jets. We also examine the charged particle multiplicity distributions of the jets in restricted intervals of rapidity. For soft particles at large transverse momentum, we observe the charged particle multiplicity ratio of gluon to quark jets to be 2.29 +- 0.09 +- 0.15 in agreement with the prediction that this ratio should approximately equal the ratio of QCD color factors, CA/CF = 2.25. The intervals used to define soft particles and large transverse momentum for this result, p<4 GeV/c and 0.8<p_t<3.0 GeV/c, are motivated by the predictions of the Herwig Monte Carlo multihadronic event generator. Additionally, our gluon jet data allow a sensitive test of the phenomenon of non-leading QCD terms known as color reconnection. We test the model of color reconnection implemented in the Ariadne Monte Carlo multihadronic event generator and find it to be disfavored by our data.Gluon jets are identified in hadronic Z0 decays as all the particles in a hemisphere opposite to a hemisphere containing two tagged quark jets. Gluon jets defined in this manner are equivalent to gluon jets produced from a color singlet point source and thus correspond to the definition employed for most theoretical calculations. In a separate stage of the analysis, we select quark jets in a manner to correspond to calculations, as the particles in hemispheres of flavor tagged light quark (uds) events. We present the distributions of rapidity, scaled energy, the logarithm of the momentum, and transverse momentum with respect to the jet axes, for charged particles in these gluon and quark jets. We also examine the charged particle multiplicity distributions of the jets in restricted intervals of rapidity. For soft particles at large transverse momentum, we observe the charged particle multiplicity ratio of gluon to quark jets to be 2.29 +- 0.09 +- 0.15 in agreement with the prediction that this ratio should approximately equal the ratio of QCD color factors, CA/CF = 2.25. The intervals used to define soft particles and large transverse momentum for this result, p<4 GeV/c and 0.8<p_t<3.0 GeV/c, are motivated by the predictions of the Herwig Monte Carlo multihadronic event generator. Additionally, our gluon jet data allow a sensitive test of the phenomenon of non-leading QCD terms known as color reconnection. We test the model of color reconnection implemented in the Ariadne Monte Carlo multihadronic event generator and find it to be disfavored by our data

On the Rise of the Proton Structure Function F2_2 Towards Low x

A measurement of the derivative (d ln F_2 / d lnx)_(Q^2)= -lambda(x,Q^2) of the proton structure function F_2 is presented in the low x domain of deeply inelastic positron-proton scattering. For 5*10^(-5)=1.5 GeV^2, lambda(x,Q^2) is found to be independent of x and to increase linearly with ln(Q^2)