Heavy Quark Physics

We sum up the next-to-leading logarithmic corrections to the heavy-quarkonium hyperfine splitting using the nonrelativistic renormalization group. On the basis of this result, we predict the mass of the η b meson to be M (η b) = 9419 ± 11 (th) +9 −8 (δαs) MeV. The experimental measurement of M (η b) with a few MeV error would be sufficient to determine αs(MZ) with an accuracy of ±0.003. The use of the nonrelativistic renormalization group is mandatory to reproduce the experimental value of the hyperfine splitting in charmonium.

Inclusive D^{*+-} production in two-photon collisions is studied with the L3 detector at LEP, using 683 pb^{-1} of data collected at centre-of-mass energies from 183 to 208 GeV. Differential cross sections are determined as functions of the transverse momentum and pseudorapidity of the D^{*+-} mesons in the kinematic region 1 GeV P_T 12 GeV and |eta| 1.4. The cross sections sigma(e^+e^- ---> e^+e^-D^{*+-}X)$ in this kinematical region is measured and the sigma(e^+e^- ---> e^+e^- cc{bar}X) cross section is derived. The measurements are compared with next-to-leading order perturbative QCD calculations.

We present a new model based on the SU (3) ⊗ SU (2) ⊗ U (1) symmetry, in which there is a new consistent set of chiral fermion fields that renders the model free from anomalies. The new fermions do not share the usual family structure of the Standard Model and some of them have exotic electric charges, as the quarks X and Y with electric charge 5/3 and −4/3, respectively. Interestingly, the model contains a new heavy neutral lepton which may be a dark matter candidate. Two Higgs doublets are present in our construction, so that two CP even scalars are present in the model particle spectrum. One of them is similar to the Standard Model Higgs boson, while the other one couples mainly with the new exotic fermions. We performed a discovery analysis showing that the 8 TeV LHC can find the Y quark from single and pair production with masses from 300 GeV up to ∼ 750 GeV. We also show that the new spectrum does not contribute significantly to the oblique EW parameters, and that dangerous flavor changing neutral currents are suppressed. Characteristic signatures from the other new fermions in the model are also commented.

We compute the leading-order low-energy constants of the DeltaS=1 effective weak Hamiltonian in the quenched approximation of QCD with up, down, strange, and charm quarks degenerate and light (GIM limit). The low-energy constants are extracted by comparing the predictions of finite volume chiral perturbation theory with lattice QCD computations of suitable correlation functions carried out with quark masses ranging from

The vacuum polarization of a quark, when considered in terms of the external momentum q 2 , is a function of the Stieltjes type. Consequently, the mathematical theory of Pade Approximants assures that the full function, at any finite value of q 2 away from the physical cut, can be reconstructed from its low-energy power expansion around q 2 = 0. We illustrate this point by applying this theory to the vacuum polarization of a heavy quark and obtain the value of the constant K (2) governing the threshold expansion at order O(α 2 s).

The deviations with respect to the Standard Model that are currently observed in b → s transitions, or B anomalies, can be interpreted in terms of different New Physics (NP) scenarios within a model-independent effective approach. We identify a set of internal tensions of the fit that require further attention and whose theoretical or experimental nature could be determined with more data. In this landscape of NP, we discuss possible ways to discriminate among favoured NP hypotheses in the short term thanks to current and forthcoming observables. While an update of R K should help to disentangle the type of NP we may be observing (Lepton-Flavour Universality Violating and/or Lepton Flavour Universal), additional observables, in particular Q 5 , turn out to be central to determine which NP hypothesis should be preferred. We also analyse the preferences shown by the current global fit concerning various NP hypotheses, using two different tools: the behaviour of the pulls of individual observables under NP scenarios and the directions favoured by approximate quadratic parametrisations of the observables in terms of Wilson coefficients.

Using the new non-analytic reconstruction method obtained from Mellin-Barnes properties, one can extract the value m c (MS) = 1.12 ± 0.08 GeV from experimental data of the radiationcorrected measured hadronic cross section to the calculated lowest-order cross section for muon pair production in the heavy-quark approximation.

Inclusive non-diffractive photoproduction of (770) 0 , K (892) 0 and (1020) mesons is investigated with the H1 detector in ep collisions at HERA. The corresponding average p centre-of-mass energy is 210 GeV. The mesons are measured in the transverse momentum range 0: 5 < p T < 7 GeV and the rapidity range j y lab j < 1. Differential cross sections are presented as a function of transverse momentum and rapidity, and are compared to the predictions of hadroproduction models.

We present a personal account of the development of research groups in high energy physics and of the Division of Particles and Fields of the Mexican Physical Society. We conclude that this area qualifies as a seriously cultivated scientific speciality, with several research groups active in both theoretical and experimental high energy physics.

Factorization scheme analysis of $F_2^{\gamma}(x,Q^2)$ in the next-to-leading order QCD is revisited. It is emphasized that the presence of the inhomogeneous term in the evolution equations for quark distribution functions of the photon implies subtle but important difference in the way factorization mechanism works in photon-hadron and photon-photon collisions as compared to the hadronic ones. It is argued that none of the existing NLO analyses of $F_2^{\gamma}(x,Q^2)$ takes this difference properly into account. The source of the ensuing incompleteness is traced back to the misinterpretation of the behaviour of $q^{\gamma}(x,M)$ as a function of $\alpha_s(M)$. Parton model interpretation of the so called ``constant terms'' in the LO photonic coefficient function $C_{\gamma}^{(0)}(x)$ is given and smooth transition between the properties of virtual and real photon analyzed. Finally phenomenological consequences of this analysis are discussed.

Cross sections of 7*7* collisions are presented and diffractive contributions axe studied. Interactions of quasi real and highly virtual photons axe considered. The Regge parameterization of Donnachie and Landshoff describes the cross section behavior of quasi real processes whereas BFKL Pomeron calculations axe not consistent with our data.

We reconsider the question of wave function renormalization in heavy fermion effective field theories. In particular, we work out a simple and efficient scheme to define the wave function renormalization with respect to the lowest order heavy fermion propagator. The method presented is free of a set of ambiguities which arise in heavy fermion effective field theories. In this context, we discuss the approaches used in the literature so far. We also calculate the fourth order pion mass contribution to the nucleon mass shift and discuss the tree and loop contributions to the electric Sachs form factor of the nucleon.

We present a new model based on the SU (3) ⊗ SU (2) ⊗ U (1) symmetry, in which there is a new consistent set of chiral fermion fields that renders the model free from anomalies. The new fermions do not share the usual family structure of the Standard Model and some of them have exotic electric charges, as the quarks X and Y with electric charge 5/3 and −4/3, respectively. Interestingly, the model contains a new heavy neutral lepton which may be a dark matter candidate. Two Higgs doublets are present in our construction, so that two CP even scalars are present in the model particle spectrum. One of them is similar to the Standard Model Higgs boson, while the other one couples mainly with the new exotic fermions. We performed a discovery analysis showing that the 8 TeV LHC can find the Y quark from single and pair production with masses from 300 GeV up to ∼ 750 GeV. We also show that the new spectrum does not contribute significantly to the oblique EW parameters, and that dangerous flavor changing neutral currents are suppressed. Characteristic signatures from the other new fermions in the model are also commented.

The next-to-next-to-next-to-leading order (N 3 LO) Hamiltonian of potential nonrelativistic QCD is derived. The complete matching of the Hamiltonian and the contribution from the ultrasoft dynamical gluons relevant for perturbative boundstate calculations is performed including one-, two-, and three-loop contributions. The threshold expansion is used to disentangle and match contributions of different scales in the effective-theory calculations. As a physical application, the heavyquarkonium spectrum is obtained at N 3 LO for the case of vanishing QCD beta function. Our results set the stage for a full N 3 LO analysis of the heavy-quarkonium system.

Inclusive production of D * ± mesons in two-photon collisions was measured by the L3 experiment at LEP. The data were collected at a centre-of-mass energy √ s = 189 GeV with an integrated luminosity of 176.4 pb −1. Differential cross sections of the process e + e − → e + e − D * ± X are determined as functions of the transverse momentum and pseudorapidity of the D * ± mesons in the kinematic region 1 GeV < p D * T < 5 GeV and |η D * | < 1.4. The cross section integrated over this phase space domain is measured to be 132±22(stat.)±26(syst.) pb. The differential cross sections are compared with next-to-leading order perturbative QCD calculations.

Inclusive charged hadron production, e + e − → e + e − h ± X, is studied using 414 pb −1 of data collected at LEP with the L3 detector at centre-of-mass energies between 189 and 202 GeV. Single particle inclusive differential cross sections are measured as a function of the particle transverse momentum, p t , and pseudo-rapidity, η. For p t ≤ 1.5 GeV, the data are well described by an exponential, typical of soft hadronic processes. For higher p t , the onset of perturbative QCD processes is observed. The π ± production cross section for p t > 5 GeV is much higher than the NLO QCD predictions.

We compute on the lattice the "bag" parameters of the five ∆B = 2 operators of the supersymmetric basis, by combining their values determined in full QCD and in the static limit of HQET. The extrapolation of the QCD results from the accessible heavy-light meson masses to the B-meson mass is constrained by the static result. The matching of the corresponding results in HQET and in QCD is for the first time made at NLO accuracy in the MS(NDR) renormalization scheme. All results are obtained in the quenched approximation.

A determination of the hadronic fragmentation functions of the Z ° boson is presented from a study of the inclusive hadron production with the DELPHI detector at LEP. These fragmentation functions were compared with the ones at lower energies, thus covering data in a large kinematic range: 196 ~ Q2 ~< 8312 GeV 2 and x (= Ph/Ebeam) > 0.08. A large scaling violation was observed, which was used to extract the strong coupling constant in second order QCD: ~s (Mz) = 0.118 ± 0.005. The corresponding QCD scale for five quark flavours is: A ~5) = 230 ± 60 MeV.

The production of multihadronic states in collisions at LEP has been studied with the DELPHI detector. The analyzed data correspond to an integrated luminosity of about 32 pb 1 , collected in the LEP runs of 1990-1992. Minimum bias data and a sample of events with jets at high p T have been selected under the requirement that no scattered electron or positron is observed. The two data sets have been compared to Monte Carlo predictions. The non-perturbative contribution described by the Vector Meson Dominance Model and direct q q production from pointlike photons described by the Quark Parton Model were found to be insucient to reproduce the data. It has been necessary to include a third interaction component, which is due to perturbative hard scattering of the partonic constituents of the photon. Several parametrizations of the quark and gluon densities of the photon have been tested. The interplay with the cut in jet transverse momentum, which i s necessary for the separation of the perturbative and non-perturbative regions, is discussed. The data favour parametrizations with rather soft partonic content of the photon.

We study the dynamics of heavy quarks in a thermalized quark-gluon plasma with a time-correlated thermal noise, η. In this case, it is said that η has memory. We use an integro-differential Langevin equation in which the memory enters via the thermal noise and the dissipative force. We assume that the time correlations of the noise decay exponentially on a timescale, τ, which we treat as a free parameter. We compute the effects of τ ≠ 0 on the thermalization time of the heavy quarks, on their momentum broadening, and on the nuclear modification factor. We find that overall memory slows down the momentum evolution of heavy quarks: In fact, transverse momentum broadening and the formation of R AA are slowed down by memory and the thermalization time of the heavy quarks become larger. The potential impact on other observables is discussed briefly.

This paper presents measurements of D * ± production in deep inelastic scattering from collisions between 27.5 GeV positrons and 820 GeV protons. The data have been taken with the ZEUS detector at HERA. The decay channel D * + → (D 0 → K − π +)π + (+ c.c.) has been used in the study. The e + p cross section for inclusive D * ± production with 5 < Q 2 < 100 GeV 2 and y < 0.7 is 5.3 ± 1.0 ± 0.8 nb in the kinematic region 1.3 < p T (D * ±) < 9.0 GeV and | η(D * ±) | < 1.5. Differential cross sections as functions of p T (D * ±), η(D * ±), W and Q 2 are compared with next-to-leading order QCD calculations based on the photon-gluon fusion production mechanism. After an extrapolation of the cross section to the full kinematic region in p T (D * ±) and η(D * ±), the charm contribution F cc 2 (x, Q 2) to the proton structure function is determined for Bjorken x between 2 • 10 −4 and 5 • 10 −3 .

Double vector meson photoproduction, p(γ, G → V V)p, mediated by a scalar glueball G is investigated. Using vector meson dominance (VMD) and Regge/pomeron phenomenology, a measureable glueball enhancement is predicted in the invariant V V = ρρ and ωω mass spectra. The scalar glueball is assumed to be the lightest physical state on the daughter pomeron trajectory governing diffractive vector meson photoproduction. In addition to cross sections, calculations for hadronic and electromagnetic glueball decays, G → V V ′ (V, V ′ = ρ, ω, φ, γ), and γvV → G transition form factors are presented based upon flavor universality, VMD and phenomenological couplings from φ photoproduction analyses. The predicted glueball decay widths are similar to an independent theoretical study. A novel signature for glueball detection is also discussed.

Dark photons are hypothetical massive vector particles that could mix with ordinary photons. The simplest theoretical model is fully characterised by only two parameters: the mass of the dark photon m$$_{\gamma ^{\mathrm {D}}}$$ γ D and its mixing parameter with the photon, $$\varepsilon $$ ε . The sensitivity of the SHiP detector is reviewed for dark photons in the mass range between 0.002 and 10 GeV. Different production mechanisms are simulated, with the dark photons decaying to pairs of visible fermions, including both leptons and quarks. Exclusion contours are presented and compared with those of past experiments. The SHiP detector is expected to have a unique sensitivity for m$$_{\gamma ^{\mathrm {D}}}$$ γ D ranging between 0.8 and 3.3$$^{+0.2}_{-0.5}$$ - 0.5 + 0.2  GeV, and $$\varepsilon ^2$$ ε 2 ranging between $$10^{-11}$$ 10 - 11 and $$10^{-17}$$ 10 - 17 .

final states are studied with the L3 detector at LEP using data collected at centre-of-mass energies from 183 GeV up to 202 GeV. The mass spectrum of the K 0 S K ± π ∓ final state shows an enhancement around 1470 MeV, which is identified with the pseudoscalar meson η (1440). This state is observed in γγ collisions for the first time and its two-photon width is measured to be Γ γγ η (1440) × BR η (1440) → KKπ = 212 ± 50 (stat.) ± 23 (sys.) eV. Clear evidence is also obtained for the formation of the axial vector mesons f 1 (1420) and f 1 (1285). In the η π + π − channel the f 1 (1285) is observed, and upper limits for the formation of η (1440) and η (1295) are obtained.

Cross sections of 7*7* collisions are presented and diffractive contributions axe studied. Interactions of quasi real and highly virtual photons axe considered. The Regge parameterization of Donnachie and Landshoff describes the cross section behavior of quasi real processes whereas BFKL Pomeron calculations axe not consistent with our data.

We study the dynamics of heavy quarks in a thermalized quark-gluon plasma with a time-correlated thermal noise, η. In this case, it is said that η has memory. We use an integro-differential Langevin equation in which the memory enters via the thermal noise and the dissipative force. We assume that the time correlations of the noise decay exponentially on a timescale, τ, which we treat as a free parameter. We compute the effects of τ ≠ 0 on the thermalization time of the heavy quarks, on their momentum broadening, and on the nuclear modification factor. We find that overall memory slows down the momentum evolution of heavy quarks: In fact, transverse momentum broadening and the formation of R AA are slowed down by memory and the thermalization time of the heavy quarks become larger. The potential impact on other observables is discussed briefly.

The impact of momentum anisotropy on the heavy quark transport coefficients due to collisional and
radiative processes in the QCD medium has been studied within the ambit of kinetic theory. Anisotropic
aspects (momentum) are incorporated into the heavy quark dynamics through the nonequilibrium
momentum distribution function of quarks, antiquarks, and gluons. These nonequilibrium distribution
functions that encode the physics of momentum anisotropy and turbulent chromo-fields are obtained by
solving the ensemble-averaged diffusive Vlasov-Boltzmann equation. The momentum dependence of
heavy quark transport coefficients in the medium is seen to be sensitive to the strength of the anisotropy for
both collisional and radiative processes. In addition, the collisional and radiative energy loss of the heavy
quark in the anisotropic hot QCD medium is analyzed. The effects of anisotropy on the drag and diffusion
coefficients are observed to have a visible impact on the nuclear suppression factor both at the RHIC
and LHC.

We study the dynamics of heavy quarks in a thermalized quark-gluon plasma with a time-correlated thermal noise, η. In this case, it is said that η has memory. We use an integro-differential Langevin equation in which the memory enters via the thermal noise and the dissipative force. We assume that the time correlations of the noise decay exponentially on a timescale, τ, which we treat as a free parameter. We compute the effects of τ ≠ 0 on the thermalization time of the heavy quarks, on their momentum broadening, and on the nuclear modification factor. We find that overall memory slows down the momentum evolution of heavy quarks: In fact, transverse momentum broadening and the formation of R AA are slowed down by memory and the thermalization time of the heavy quarks become larger. The potential impact on other observables is discussed briefly.

We measure the particle-level forward-backward production asymmetry in bb pairs with masses (m bb) larger than 150 GeV/c 2 , using events with hadronic jets and employing jet charge to distinguish b fromb. The measurement uses 9.5 fb −1 of pp collisions at a center of mass energy of 1.96 TeV recorded by the CDF II detector. The asymmetry as a function of m bb is consistent with zero, as well as with the predictions of the standard model. The measurement disfavors a simple model including an axigluon with a mass of 200 GeV/c 2 whereas a model containing a heavier 345 GeV/c 2 axigluon is not excluded.

Spherical fuzzy set (SFS) is also one of the fundamental concepts for address more uncertainties in decision problems than the existing structures of fuzzy sets, and thus its implementation was more substantial. The well-known sine trigonometric function maintains the periodicity and symmetry of the origin in nature and thus satisfies the expectations of the experts over the multi parameters. Taking this feature and the significance of the SFSs into the consideration, the main objective of the article is to describe some reliable sine trigonometric laws $\left( STL\right) $ for SFSs. Associated with these laws, we develop new average and geometric aggregation operators to aggregate the Spherical fuzzy numbers (SFNs). Then, we presented a group decision- making (DM) strategy to address the multi-attribute group decision making (MAGDM)\ problem using the developed aggregation operators. In order to verify the value of the defined operators, a MAGDM strategy is provided along with an a...

We present preliminary results of the non-perturbative renormalization group (RG) running of the flavor non-singlet tensor operator. We employ the SF scheme for = 3 QCD using ensembles generated by the ALPHA collaboration for the computation of the quark mass running. The SF property of automatic () improvement prevents the () mixing of the correlation functions.

We present the current status of a revised strategy to compute the running of renormalized quark masses in QCD with three flavours of massless O(a) improved Wilson quarks. The strategy employed uses the standard finite-size scaling method in the Schrödinger functional and accommodates for the non-perturbative scheme-switch which becomes necessary at intermediate renormalized couplings as discussed in [9].

Inclusive charged hadron production, e + e − → e + e − h ± X, is studied using 414 pb −1 of data collected at LEP with the L3 detector at centre-of-mass energies between 189 and 202 GeV. Single particle inclusive differential cross sections are measured as a function of the particle transverse momentum, p t , and pseudo-rapidity, η. For p t ≤ 1.5 GeV, the data are well described by an exponential, typical of soft hadronic processes. For higher p t , the onset of perturbative QCD processes is observed. The π ± production cross section for p t > 5 GeV is much higher than the NLO QCD predictions.

We establish in this manuscript a new model complex picture fuzzy N-soft sets (CPFN-SSs) which is the fusion of complex picture fuzzy sets (CPFSs) along with N-soft sets (N-SSs) and a novel definition of CPFSs which is a mixture of complex fuzzy sets (CFSs) and picture fuzzy sets (PFSs). In CPFN-SS notions of N-SSs, fuzzy N-SSs (FN-SSs), intuitionistic FN-SSs (IFN-SSs), picture FN-SSs (PFN-SSs) complex FN-SSs (CFN-SS), complex IFN-SSs (CIFN-SSs) are generalized. We also talk about few basic operations on CPFN-SSs with the assistance of examples. Additionally, we establish two kinds of union (extended and restricted) and intersection (extended and restricted) of CPFN-SSs and illustrate them through examples. We also establish a complement of CPFN-SSs along with an example. Furthermore, we define an algorithm to solve the data in the environment of CPFN-SSs, and then we represent two real-world applications (performance assessment of e-waste recycling program and predication about the...

The K 0 S K ± π ∓ final state in two-photon collisions is studied with the L3 detector at LEP at e + e − centre-of-mass energies from 183 to 209 GeV with an integrated luminosity of 664.6 pb −1. The η (1475) and f 1 (1420) mesons are observed and their contribution is separated by measuring the formation rates as a function of the photon virtuality Q 2. The η (1475) is found to be dominant for Q 2 ≤ 0.01 GeV 2 and its two-photon width is measured to be 0.23±0.05 (stat.)±0.05 (sys.) keV. At higher Q 2 , the f 1 (1420) is formed and decays to K * (892)K. The γγ coupling and form factor parameters of this state are measured to be Γ γγ = 3.2 ± 0.6 (stat.) ± 0.7 (sys.) keV and Λ 1 = 926 ± 72 (stat.) ± 32 (sys.) MeV, respectively.

Exclusive ρ + ρ − production in two-photon collisions between a quasi-real photon, γ, and a mid-virtuality photon, γ * , is studied with data collected at LEP at centreof-mass energies 183 GeV ≤ √ s ≤ 209 GeV with a total integrated luminosity of 684.8 pb −1. The cross section of the γγ * → ρ + ρ − process is determined as a function of the photon virtuality, Q 2 , and the two-photon centre-of-mass energy, W γγ , in the kinematic region: 0.2 GeV 2 ≤ Q 2 ≤ 0.85 GeV 2 and 1.1 GeV ≤ W γγ ≤ 3 GeV. These results, together with previous L3 measurements of ρ 0 ρ 0 and ρ + ρ − production, allow a study of the γγ * → ρρ process over the Q 2-region 0.2 GeV 2 ≤ Q 2 ≤ 30 GeV 2 .

The reaction γγ → J/ΨJ/Ψ is discussed assuming dominance of the QCD BFKL pomeron exchange. We give prediction for the cross-section of this process for LEP2 and TESLA energies. We solve the BFKL equation in the non-forward configuration taking into account dominant non-leading effects which come from the requirement that the virtuality of the exchanged gluons along the gluon ladder is controlled by their transverse momentum squared. We compare our results with those corresponding to the simple two gluon exchange mechanism and with the BFKL pomeron exchange in the leading logarithmic approximation. The BFKL effects are found to generate a steeper t-dependence than the two gluon exchange. The cross-section is found to increase with increasing CM energy W as (W 2) 2λ. The parameter λ is slowly varying with W and takes the values λ ∼ 0.23 − 0.28. The magnitude of the total cross-section for the process γγ → J/ΨJ/Ψ is found to increase from 4 to 26 pb within the energy range accessible at LEP2.

The heavy quark system is an excellent probe to learn about the QCD dynamics at finite density. First, we discuss the properties of the J/ψ and D meson at finite nucleon density. We discuss why their properties should change at finite density and then introduce an exact QCD relation among these hadron properties and the energy momentum tensor of the medium. Second, we discuss attempts to calculate charmonium-hadron total cross section using effective hadronic models and perturbative QCD. We emphasize a recent calculation, where the cross section is derived using QCD factorization theorem. We conclude by discussing some challenges for SIS 200.

In this work, we find the expressions of continuum HQET four-fermion operators in terms of lattice operators in perturbation theory. To do so, we calculate the one-loop continuum-lattice HQET matching for the complete basis of ∆B = 2 and ∆B = 0 operators (excluding penguin diagrams), extending and completing previous studies. We have also corrected some errors in previous evaluations of the matching for the operator O LL. Our results are relevant to the lattice computation of the values of unknown hadronic matrix elements which enter in many very important theoretical predictions in B-meson phenomenology: B 0-B 0 mixing, τ B and τ Bs lifetimes, SUSY effects in ∆B = 2 transitions and the B s width difference ∆Γ Bs. We have reanalyzed our lattice data for the B B parameter of the B 0-B 0 mixing on 600 lattices of size 24 3 × 40 at β = 6.0 computed with the SW-Clover and HQET lattice actions. We have used the correct lattice-continuum matching factors and boosted perturbation theory with tadpole improved heavy-light operators to reduce the systematic error in the evaluation of the renormalization constants. Our best estimate of the renormalization scale independent B-parameter isB B = 1.29 ± 0.08 ± 0.06, where the first error is statistical and the second is systematic coming from the uncertainty in the determination of the renormalization constants. Our result is in good agreement with previous results obtained by extrapolating Wilson data. As a byproduct, we also obtain the complete one-loop anomalous dimension matrix for four-fermion operators in the HQET.

Cross sections of 7*7* collisions are presented and diffractive contributions axe studied. Interactions of quasi real and highly virtual photons axe considered. The Regge parameterization of Donnachie and Landshoff describes the cross section behavior of quasi real processes whereas BFKL Pomeron calculations axe not consistent with our data.

We present measurements of the hadronic photon structure function F 2 (x), i n t w o Q 2 ranges with mean values of 5:9 GeV 2 and 14:7 GeV 2. The data were taken by the OPAL experiment at LEP, with p s close to the Z 0 mass and correspond to an integrated e + e luminosity of 44.8 pb 1. In the context of a QCD-based model we nd the quark transverse momentum cuto separating the vector meson dominance (VMD) and perturbative QCD regions to be 0:270:10 GeV. We conrm that there is a signicant pointlike component of the photon when the probe photon has Q 2 > 4 GeV 2. Our measurements extend to lower values of x than any previous experiment, and no increase of F 2 (x) is observed.