QCD predictions for the distribution functions of the photon using Altarelli-Parisi type equations

In a leading approximation, the distribution functions of the photon are investigated using Altarelli-Parisi type equations including point-like and hadron-like components. Using a new method to make a Mellin transformation, the full inhomogeneous equation is solved numerically. The point-like and hadron-like parts of photon distribution function are discussed separately. The point-like part has a form $\text{?(x, t)}\text{In}\text{Q}{}^2$, where t = In Q². Analytic expressions for the photon distribution functions near x = 1 and x = 0 are also given. These results are compared with others which have been given using other methods.     

Extent of sensitivity of single photon production to parton distribution functions

We have studied the production of single isolated prompt photons in high-energy proton–proton collisions at the RHIC ( \(\sqrt {s}\) = 200 GeV) and the LHC ( \(\sqrt {s}\) = 7 TeV) energies within the framework of perturbative QCD upto next-to leading order of strong coupling (α _s). We have used five different parametrizations of parton distribution function (PDF) starting from the old CTEQ4M to the new CT10 distributions and compared our results with the recent single-prompt photon data from the PHENIX and the CMS Collaborations. The prompt photon cross-section is found to be described equally well by all the PDFs within the experimental errors at the RHIC and the LHC energies. The deviation in the single-prompt photon yield for different PDF sets is within ±20% when compared to CTEQ4M, indicating the upper bound of uncertainty in determining the gluon density. The diphoton measurement could be a potential candidate to constrain the gluon distribution inside the proton.     

Deep inelastic structure functions of the photon

Three independent structure functions of a real photon can be measured in photon-photon collisions in e^±e^? storage rings. These are M₁ and M_L (related to the usual structure functions W₁andνW₂, as defined for any target) and a third function M₃, which arises from the strong plane polarisation of the colliding photons. We show, using a dispersion relation in the photon mass, that M₃ and the longitudinal structure function M_L both scale and are independent of the vector-dominant hadronic structure of the real photon. Therefore in a parton model, or in the quark light-cone algebra, they are given by the bare quark box diagrams which also dominate when both photons have large q²; this uniquely predicts the behaviour , $\text{M}{}_3\text{= [(}\text{1}\text{2}\text{π)Σ e}{}_{\mathrm{i}}{}^4\text{](?x}{}^2\text{)}$ for the real photon structure functions in the Bjorken limit (q₂² → ?∞, q₁²=0, x=?q₂²/2q₁·q₂=constant).     

Solutions of the Maxwell equations and photon wave functions

Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including sources, is invariant under Lorentz transformations. Complete sets of eigenfunctions of the Hamiltonian for the electromagnetic fields, which may be interpreted as photon wave functions, are given both for plane waves and for angular-momentum eigenstates. Rotationally invariant projection operators are used to identify transverse or longitudinal electric and magnetic fields. For plane waves, the velocity transformed transverse wave functions are also transverse, and the velocity transformed longitudinal wave functions include both longitudinal and transverse components. A suitable sum over these eigenfunctions provides a Green function for the matrix Maxwell equation, which can be expressed in the same covariant form as the Green function for the Dirac equation. Radiation from a dipole source and from a Dirac atomic transition current are calculated to illustrate applications of the Maxwell Green function.     

Photon distribution functions of the fluorescence photons from a single nanoparticle in various photon counting methods

Simple expressions have been derived for three photon distribution functions w _N ^M (T), w _N ^Z (T), and w _N ^O (T) corresponding to three different methods for counting fluorescence photons from a single nanoparticle excited by continuous laser radiation. In contrast to the previously derived expressions represented in the form of N multiple integrals, the new expressions contain only single or double integrals of Poisson functions, which makes it possible to easily perform the numerical calculation of the photon distribution. The simplest photon counting method corresponds to the lengthiest function w _N ^M (T); on the contrary, the simplest function w _N ^O (T) corresponds to the most complex photon counting method. The functions w _N ^M (T), w _N ^Z (T), and w _N ^O (T) are noticeably different in short time intervals T; however, the distributions calculated using these functions are almost indistinguishable from each other in long T intervals. This circumstance makes it possible to use the simplest function w _N ^O (T) to consider the photon statistics measured by the simplest method. This possibility is particularly important for investigating the fluorescence photon statistics, where the intensity fluctuates.     

Ioffe-time distribution of quarks in the photon

We have analysed the Ioffe-time distribution of quarks in virtual photons using Operator Product Expansion of the correlation function that determines the matrix element of the corresponding quark string operator. The distribution for a transversally polarised photon admits a spectral representation which can be continued to the on-shell region p ² = 0. The resulting model Ioffe-time distribution turns out to be larger than parametrisations of the available F ₂ ^γ data, because its slope at the origin is unphysically large. We suggest that this problem is linked to the use of purely quark interpolating currents and it affects the calculation of Ioffe-time distribution of quarks for any hadronic state.     

Photon distribution functions of fluorescence photons from single nanoparticles: Three different photon counting methods

Mathematical expressions are derived for three photon distribution functions w _N ^M (T), w _N ^Z (T), and w _N ^O (T) corresponding to three different methods for counting fluorescence photons from a single nanoparticle excited by continuous laser radiation. Each of the three functions is expressed in terms of Poisson functions, which makes it possible to pass in the w _N ^M (T), w _N ^Z (T), and w _N ^O functions from N multiple integrals to single or double integrals. This not only eases the numerical calculation of the photon distribution, but it also makes it possible to find that, for each exponential process in the dynamics of a nanoparticle, there is a Poisson function in the photon distribution function. All three photon counting methods yield the same photon distribution for continuous fluorescence and different photon distributions for blinking fluorescence.     

Dead time correction of photon correlation functions

The dynamic range of single photon counting measurements in quasi elastic light scattering is restricted by detector and counter dead time effects. While distortions of single interval statistics have been treated at great length, only lowest order corrections or very special cases of dead time effects on temporal correlation functions were computed in the past.Dead times result in a direct distortion of correlograms on time scales comparable to the dead time. This effect exists even at low count-rates. It is independent of the count rate for paralyzable systems. Nonparalyzable systems show a count rate dependence with increasing correlation times at high count rates.Furthermore, counting saturation produces additional distortions extending to all lag times. These distortions are computed for the rather general case of -distributed intensities with arbitrary shape of the photon correlation function. Such signals are commonly found in multiparticle homodyne experiments with a finite size detector, i.e. arbitrary value of the intercept or contrast of the correlogram. Exact results are provided for the paralyzable system including the effect of fluctuating dead times. The latter case is then used to compute a useful approximation for nonparalyzable systems as well.     

Nonlocal quark condensate and photon distribution amplitude

The magnetic susceptibility of the quark condensate and the light-cone photon distribution amplitude of the leading twist is studied in the leading order of the perturbative expansion within the nonlocal condensates framework.     

Isolated photon plus jet photoproduction as a toolto constrain the gluon distribution in the proton and the photon

We analyse how the reaction can serve to constrain the gluon distributions. Our results are based on a code of partonic event generator type which includes full NLO corrections. We conclude that there are phase space domains in which either the gluon in the photon or the gluon in the proton give important contributions to the cross section, which should be observable in HERA experiments.Received: 8 December 2003, Revised: 19 January 2004, Published online: 12 March 2004     

Off-shell photon light-cone wave functions with odd chirality

Based on a more reasonable simulation method for dealing with the Λ-parameter characterizing the pole form for the form factor (the Fourier transform of the instanton zero mode), and a unified way for regularizing the integrals appearing in the expressions of the light-cone photon wave functions, the transverse photon wave function (u, P ²) at the leading twist with the on-shell or off-shell momentum have been re-examined in the effective low-energy theory derived from the instanton vacuum, and the twist-two parts of the other two photon wave functions, h ^{(s), twisttwo} _{γ ||} (u, P ²) and h ^{(t), twisttwo} _{γ ||} (u, P ²), with odd chirality are calculated based on the Wandzura-Wilczek-like relations as well. A brief discussion of the dependence of the coupling f _γ ^⊥(P ²) and the light-cone photon wave functions with respect to P² and the end-point behavior of the photon wave functions are given.     

On the weak decays of high-mass hadrons

Several arguments for the dominance of certain types of non-leptonic weak decays of strange particles are examined for their applicability to high-mass hadrons. Arguments based on asymptotic freedom, duality, current algebra and PCAC, and coloured fermion quarks are all found to be weaker than for strange decays. Specific calculations in the Glashow-Iliopoulos-Maiani charm scheme yield total semi-leptonic decay rates of 20% or more. Estimates of branching ratios for two-body decays of charmed mesons are given, and remarks are made about charmed baryon decays.     

Virtual photon exchange,intermolecular interactions and optical response functions

According to molecular quantum electrodynamics, coupling between material particles occurs due to an exchange of one or more virtual photons. In this work, the relationship between polarisability and hyperpolarisability tensors of atoms and molecules that feature in linear and nonlinear optical processes, and their analytically continued form in the complex frequency domain that appear in formulae describing fundamental inter-particle interactions, is studied. Examples involving a single virtual photon exchange, which are linearly proportional to electric dipole moments at each centre, include the electrostatic energy and the resonant transfer of excitation energy. The Casimir–Polder dispersion potential, and its discriminatory counterpart applicable to coupled chiral molecules, are used to illustrate response properties depending on the exchange of two virtual photons. Meanwhile, the energy shift between two hyperpolarisable species, a higher order discriminatory contribution to the dispersion potential, is employed to represent forces arising from the three virtual photon exchange. It is shown that for energy shifts that are quadratic or bilinear or cubic in the transition dipole moment, it is necessary to account for all two- and three-photon optical processes, such as absorption, emission and linear and nonlinear scattering of light in order to arrive at the correct form of the molecular response tensor.     

Measuring the photon distribution with ON/OFF photodetectors

Reconstruction of photon statistics of optical states provides fundamental information on the nature of any optical field and helps with various relevant applications. Nevertheless, no detector that can reliably discriminate the number of incident photons is available. On the other hand, the alternative of reconstructing the density matrix by quantum tomography leads to various technical difficulties that are particularly severe in the pulsed regime (where mode matching between a signal and local oscillator is very challenging). Even if on/off detectors, as usual avalanche photodiodes operating in Geiger mode, seem useless as photo-counters, it was recently shown how reconstruction of photon statistics is possible by considering a variable quantum efficiency. Here we present experimental reconstructions of photon number distributions of both continuous-wave and pulsed light beams in a scheme based on on/off avalanche photodetection assisted by maximum-likelihood estimation. Reconstructions of the distribution for both semiclassical and quantum states of light (as single photon, coherent, pseudothermal, and multithermal states) are reported for single-mode and multimode beams. The stability and good accuracy obtained in the reconstruction of these states clearly demonstrate the interesting potentialities of this simple technique.     

Quantum key distribution using quantum-correlated photon sources

Quantum key exchanges using weak coherent (Poissonian) single-photon sources are open to attack by a variety of eavesdropping techniques. Quantum-correlated photon sources provide a means of flagging potentially insecure multiple-photon emissions and thus extending the secure quantum key channel capacity and the secure key distribution range. We present indicative photon-counting statistics for a fully correlated Poissonian multibeam photon source in which the transmitted beam is conditioned by photon number measurements on the remaining beams with non-ideal multiphoton counters. We show that significant rejection of insecure photon pulses from a twin-beam source cannot be obtained with a detector having a realistic quantum efficiency. However quantum-correlated (quadruplet or octuplet) multiplet photon sources conditioned by high efficiency multiphoton counters could provide large improvements in the secure channel capacity and the secure distribution range of high loss systems such as those using the low earth orbit satellite links proposed for global quantum key distribution. Received 14 July and Received in final form 20 November 2001     

外场作用下BaF分子发射光子累积量及等待时间分布的研究

利用产生函数方法对BaF分子在激光场与射频场作用下发射光子的累积量及等待时间分布进行了研究. 累积量κ₁ 和κ₂ 表明在固有偶极和射频场的作用下, 系统表现出外场辅助吸收的现象, 即当Δ₁=nω_rf时, 系统存在吸收峰. 二阶、三阶等待时间分布呈现出明显的振荡现象.     

Manipulation of spatiotemporal photon distribution via chromatic aberration

We demonstrate a spatiotemporal laser-pulse-shaping scheme that exploits the chromatic aberration in a dispersive lens. This normally harmful effect transforms the phase modulation into a beam-size modulation at the focal plane. In combination with the intricate diffraction effect via beam apodization, this method provides a spatiotemporal control of photon distribution with an accuracy of diffraction limit on a time scale of femtoseconds.     

Parton distribution and decay functions

We define parton distribution and decay functions in QCD and prove some of their basic properties. These include renormalization, light-cone expansions and sum rules.