Regular Series


Vol. 37 (2006), No. 3, pp. 543 – 1006


Einstein’s Revolutionary Light–Quantum Hypothesis

abstract

Albert Einstein’s light-quantum paper was the only one of his great papers of 1905 that he himself called “very revolutionary”. I sketch his arguments for light quanta, his analysis of the photoelectric effect, and his introduction of the wave-particle duality into physics in 1909. I show that Robert Andrews Millikan, in common with almost all physicists at the time, rejected Einstein’s light-quantum hypothesis as an interpretation of his photoelectric-effect experiments of 1915. I then trace the complex experimental and theoretical route that Arthur Holly Compton followed between 1916 and 1922 that led to his discovery of the Compton effect, a discovery that Peter Debye also made virtually simultaneously and independently. Compton’s discovery, however, was challenged on experimental grounds by William Duane and on theoretical grounds by Niels Bohr in the Bohr–Kramers–Slater theory of 1924, and only after that theory was disproved experimentally the following year by Walther Bothe and Hans Geiger in Berlin and by Compton and Alfred W. Simon in Chicago was Einstein’s light-quantum hypothesis generally accepted by physicists.


Let There Be Light: Cosmic Photons Prior to the Microwave Background

abstract

Cosmological photons as relics from the decoupling era in the childhood of the Universe were predicted in 1948 and detected in 1965. However, light has played a role in the history of cosmology at a much earlier date, first in a speculative sense and later in a more scientific context. The paper offers an incomplete survey of some of these early attempts to integrate light into cosmology. Of particular interest is a paper of 1945, written by J.B.S. Haldane, which includes what is probably the first suggestion of a radiation-dominated early Universe.


Photon: History, Mass, Charge

abstract

The talk consists of three parts. “History” briefly describes the emergence and evolution of the concept of photon during the first two decades of the 20th century. “Mass” gives a short review of the literature on the upper limit of the photon’s mass. “Charge” is a critical discussion of the existing interpretation of searches for photon charge. Schemes, in which all photons are charged, are grossly inconsistent. A model with three kinds of photons (positive, negative and neutral) seems at first sight to be more consistent, but turns out to have its own serious problems.


Gauge Principle and QED

abstract

One of the major developments of twentieth century physics has been the gradual recognition that a common feature of the known fundamental interactions is their gauge structure. In this talk the early history of gauge theory is reviewed, emphasising especially Weyl’s seminal contributions of 1918 and 1929.


Vector Meson Dominance

abstract

Historically vector meson physics arose along two different paths to be reviewed in Sections 1 and 2. In Section 3, the phenomenological consequences will be discussed with an emphasis on those aspects of the subject matter relevant in present-day discussions on deep inelastic scattering in the diffraction region of low values of the Bjorken variable.


Photon Structure Functions: 1978 and 2005

abstract

I describe the early days of the photon structure functions. In particular I discuss the parton model result of Walsh and Zerwas (1973), leading order QCD calculation of Witten (1976) and next-to-leading QCD calculation of Bardeen and myself (1978). A very brief summary of the progress made from 1978 til 2005 is also given.


Photon–Photon Collisions — Past and Future

abstract

I give a brief review of the history of photon–photon physics and a survey of its potential at future electron–positron colliders. Exclusive hadron production processes in photon–photon and electron–photon collisions provide important tests of QCD at the amplitude level, particularly as measures of hadron distribution amplitudes. There are also important high energy \(\gamma \gamma \) and \(e \gamma \) tests of quantum chromodynamics, including the production of jets in photon–photon collisions, deeply virtual Compton scattering on a photon target, and leading-twist single-spin asymmetries for a photon polarized normal to a production plane. Since photons couple directly to all fundamental fields carrying the electromagnetic current including leptons, quarks, \(W's,\) and supersymmetric particles, high energy \(\gamma \gamma \) collisions will provide a comprehensive laboratory for Higgs production and exploring virtually every aspect of the Standard Model and its extensions. High energy back-scattered laser beams will thus greatly extend the range of physics of the International Linear Collider.


Photon Colliders: The First 25 Years

abstract

In this invited talk at the “historical” session of PHOTON2005, I was asked to recount the history and the development, from its earliest days to the present, of the idea of photon colliders based on conversion of high energy electrons to high-energy photons at a future high-energy linear \(e^+e^{-}\) collider. Described in this talk are the general features and schemes of a photon collider, the evolution in understanding of what the parameters of a realistic photon collider are, possible solutions of various technical problems, the physics motivation, and the present status of photon collider development. For a more detailed description of the photon collider at the ILC and a discussion of the associated technical issues, please refer to my talks at PLC2005, the conference that immediately followed PHOTON2005 (to be published in Acta Phys. Pol. B as well).


About Earlier History of Two-Photon Physics

abstract

The earlier history of two-photon physics is reviewed.


New Parametrizations for the Photon Structure Function

abstract

In the last year four new parametrizations of the Hadronic Photon Structure Function at Next to Leading Order have appeared. In this talk, I briefly review the main features of the three of them: the FFNS\(_{\rm CJK}\), CJK and AFG.


NLO Parametrization of Photon Parton Distributions Using \(ee\) and \(ep\) Data

abstract

An NLO photon parton parametrization is presented based on the existing \(F_2^\gamma \) measurements from \(e^+e^-\) data and the low-\(x\) proton structure function from \(ep\) interactions. Also included in the extraction of the NLO parton distribution functions are the dijets data coming from \(\gamma p \to j_1 + j_2 +X\). The new parametrization is compared to other available NLO parametrizations.


Photon Structure Function from L3 Data

abstract

With the reaction \({e^+ e^-}\rightarrow {e^+ e^-} \gamma ^*\gamma \rightarrow {e^+ e^-} {hadrons}\), the L3 experiment at LEP has measured the hadronic photon structure function \(F^\gamma _2\) in a wide \(Q^2\) and \(x\) range. The data are compared to other LEP experiments. Despite the high statistics and the small background contamination, the measurements are dominated by systematic uncertainties, mainly due poor agreement between the Monte Carlo models and the two-photon events.


Photon–Parton Splitting Functions at the Next-to-Next-to-Leading Order of QCD

abstract

We have calculated the splitting functions governing the evolution of the unpolarized parton distributions of the photon at the next-to-next-to-leading order (NNLO) of massless perturbative QCD. The results, presented here mainly in terms of compact and accurate parametrizations, are consistent with our previous approximations based on the lowest six even-integer Mellin moments. Consequently the NNLO corrections are small in both the \(\overline {\textrm {MS}}\) and the \(\textrm {DIS}_\gamma \) factorization schemes at momentum fractions \(x \gtrsim 0.1\).


Resolved Photon and Multi-Component Model for \(\gamma ^*p\) and \(\gamma ^* \gamma ^*\) Total Cross Section

abstract

We generalize our previous model for \(\gamma ^* p\) scattering to \(\gamma \gamma \) scattering. Performing a new simultaneous fit to \(\gamma ^* p\) and \(\gamma \gamma \) total cross section we find an optimal set of parameters to describe both processes. We propose new measures of factorization-breaking for \(\gamma ^* \gamma ^*\) collisions and present results for our new model.


Spin Degree of Freedom in the Nucleon

abstract

The short review of the spin structure of the nucleon (longitudinal) is given and some new experimental results are presented.


Inclusive Exploration of Proton Structure and QCD Dynamics at HERA

abstract

This report highlights most recent results on the quark-gluon structure of the proton obtained in inclusive deep inelastic ep scattering with the collider experiments H1 and ZEUS at HERA.


H1 and Zeus Results on \(F_2^{c\bar {c}}\) and \(F_2^{b\bar {b}}\)

abstract

Recent results from the H1 and ZEUS collaborations on the contribution of heavy quarks to the inclusive proton structure function are presented. Measurements of the charm structure function \(F_2^{c\bar {c}}\) are made mainly by explicit reconstruction of a \(D\) meson. The measurement of the inclusive beauty structure function \(F_2^{b\bar {b}}\), and also \(F_2^{c\bar {c}}\), is made using precise information from silicon vertex detectors in order to reconstruct the impact parameter of tracks from the decay of the heavy hadron. The results are compared with the predictions of calculations based on perturbative QCD.


Structure Function Measurements at LHC

abstract

Since the current uncertainty on the structure of the proton affects the new physics discovery potential of LHC, the ATLAS collaboration is investigating methods to constrain this uncertainty over the whole LHC kinematic regime. The Standard Model processes such as direct \(\gamma \), \(Z\), \(W\) and inclusive jet productions are optimal candidates for this purpose.


Recent Results in Prompt Photon Production

abstract

An introduction is given to recent results in prompt photon production in different reactions.


Deeply Virtual Compton Scattering and Prompt Photon Production at ZEUS and H1 Experiments

abstract

Recent results on prompt photon production and Deeply Virtual Compton Scattering (DVCS) from ZEUS and H1 experiments are presented.


High-\(p_{\rm T}\) Direct-Photon Results from PHENIX

abstract

Direct-photon measurements in \(p+p\) and Au+Au collisions at \(\sqrt {s_{\mathrm {NN}}} = 200\) GeV from the PHENIX experiment are presented. The \(p+p\) results are found to be in good agreement with next-to-leading-order (NLO) perturbative QCD calculations. Direct-photon yields in Au+Au collisions scale with the number of inelastic nucleon–nucleon collisions and do not exhibit the strong suppression observed for charged hadrons and neutral pions. This observation is consistent with models which attribute the suppression of high-\(p_{\mathrm {T}}\) hadrons to energy loss of quarks and gluons in the hot and dense medium produced in Au+Au collisions at RHIC.


Prompt Photon Production at the Tevatron

abstract

The DØ and CDF experiments have measured prompt photon production using Run II data taken at a centre-of-mass energy \(\sqrt {s}\) of 1.96 TeV. The results are compared to different types of perturbative CD calculations.


Jet and Inclusive Particle Production in Photon Induced Collisions

abstract

Recent progress in application of higher order QCD calculations to jet and inclusive particle production in photon induced collisions is reviewed. Attention is paid to theoretical uncertainties of such calculations, particularly those coming from the choice of renormalization and factorization scales.


Jets in \(ep\) and \(\gamma p\) Scattering at HERA

abstract

Recent jet physics results from \(ep\) and \(\gamma p\) scattering at HERA will be reviewed covering cross-section measurements, the extraction of QCD parameters, the transition region from photoproduction to deep-inelastic scattering and the question of parton evolution in the proton.


High Momentum Particle and Jet Production in Photon–Photon Collisions

abstract

Jet and particle production have been studied in collisions of quasi-real photons collected during the LEP2 program. OPAL and DELPHI report good agreement of NLO perturbative QCD with the measured differential di-jet cross sections, which reach a mean transverse energy of the di-jet system of 25 GeV. L3, on the other hand, finds drastic disagreement of the same calculation with single jet production for transverse jet momenta larger than about 25 GeV. L3 observes similar disagreement between data and NLO QCD in their measurements of charged and neutral particle production at high transverse momenta of the particles. A recent measurement performed by DELPHI of the same quantities does not confirm this observation.


Heavy Quark Production Overview

abstract

An overview of the physics of heavy quark production at collider experiments is presented. Recent measurements of open charm and beauty production and of charmonium at HERA, LEP and the Tevatron are reported. The data are compared with each other and with predictions from perturbative QCD calculations. The main results from charmonium measurements at the \(B\)-factories are discussed and some of the recently discovered new resonance states are presented.


Beauty Production in Two-Photon Reactions at LEP

abstract

The cross section for open beauty production in photon–photon collisions is measured using the L3 detector at LEP using a data sample of 627 pb\(^{-1}\) collected at a \(e^+e^-\) center-of-mass energy \(\sqrt {s}=189\)–209 GeV. The \( e^+e^-\rightarrow e^+e^-b \bar b X\) cross section is measured within our fiducial volume and then extrapolated to the full phase space. These results are found to be in significant excess with respect to Monte Carlo predictions and next-to-leading order QCD calculations before and after extrapolation.


Beauty Production at HERA

abstract

An overview of new measurements of beauty production in \(ep\) collisions done by the H1 and ZEUS experiments at HERA is presented. Various techniques are used to efficiently tag the beauty flavour in the events, thereby exploring different regions of phase space. Differential cross sections are measured both in photoproduction and in deep inelastic scattering. The measured data are found to be somewhat higher then perturbative QCD calculations done at next-to-leading order.


Charm Production at HERA

abstract

Measurements of charm production in \(ep\) collisions at a centre of mass energy of \(\sqrt {s}=318\) GeV performed by the ZEUS and H1 experiments at HERA are presented. Final states containing \(D\) mesons are used to identify charm production. Measurements cover both the photoproduction (\(\gamma p\)), i.e. \(Q^2\sim 0\), and deep inelastic scattering (DIS), i.e. large \(Q^2\), kinematic regimes. Experimental results are compared to QCD predictions.


Heavy Flavor Production in CDF

abstract

This paper summarizes results on heavy flavor production at CDF. Heavy flavor production is classified in low and high \(p_{\rm t}\). While at low \(p_{\rm t}\) it is possible to perform exclusive reconstruction of the final state, at higher \(p_{\rm t}\) heavy flavors are identified from jets coming from a secondary vertex.


Heavy Quark Photoproduction from \(k_{\rm t}\)-Factorisation

abstract

The \(k_t\)-factorisation approach to production of heavy quarks at HERA and at LEP is shortly reviewed.


Introduction to Small-\(x\) and Diffraction

abstract

This talk describes the measurement of \(F_2\) and inclusive and exclusive diffractive cross-sections in the low-\(x\) region by HERA experiments. The abundance of diffractive reactions observed at HERA indicates the presence of perturbative multi-ladder exchanges. The exclusive diffractive vector-meson and diffractive dijet production are discussed in terms of dipole models which connect the measurement of \(F_2\) with diffractive processess and in which multiple exchanges and saturation processes are natural. The diffractive dijets are also discussed within the diffractive parton density approach. Good description of diffractive dijets in the dipole picture and in the diffractive parton density approach indicates that these two seemingly different views on diffraction are not really distinct.


Diffractive Interactions in \(ep\) Collisions

abstract

The H1 and ZEUS experiments are measuring diffractive interactions in \(ep\) collisions at HERA. Performing QCD fits of these data with NLO DGLAP, diffractive parton distribution functions can be calculated. These diffractive PDFs can be used to test QCD factorization with dijet and charm data.


Jet Production in \(\gamma \gamma \) Collisions

abstract

The production of two high \(p_{\rm T}\) jets in the interactions of quasi-real photons is studied with DELPHI (LEP, CERN) data. The differential di-jet cross-section is measured as a function of mean jets momentum \(\overline {p_{\rm T}}\) and is compared to the perturbative QCD calculations.


Measurement of \(\gamma ^*\gamma ^*\) Cross-Section

abstract

Double-tagged interactions of photons with virtualities \(Q^2\) between 10 GeV\(^2\) and 200 GeV\(^2\) are studied. The cross-section of the reaction \(\gamma ^*\gamma ^* \rightarrow \) hadrons is measured and compared to the LO and NLO BFKL calculations.


Non-Forward BFKL Kernel at NLO

abstract

The kernel of the BFKL equation at next-to-leading order is presented and discussed in general case of non-zero momentum transfer \(t\) and any possible \(t\)-channel colour state.


The Energy Dependence of the Saturation Scale

abstract

At low \(x \cong Q^2\)/\(W^{~2} \ll 1\), in deep inelastic scattering, the photon fluctuates into a \(q \bar q\) vector state that interacts via two gluons with the proton. The energy dependence is determined by the saturation scale, in our approach given by \({\mit \Lambda }^2_{\rm sat} (W^{~2}) \sim (W^{~2})^{C_{2}}\). Imposing DGLAP evolution, we find \(C_{2}^{\rm theory} = 0.27\) in agreement with the model-independent analysis of the HERA data. Different values of the exponent \(C_{2}\) are correlated with different ratios of the longitudinal to transverse structure function. This stresses the need for experiments to separate longitudinal and transverse contributions in deep inelastic scattering.


How to Measure Pomeron Phase and Discover Odderon at HERA and RHIC

abstract

We suggest to measure the Pomeron phase and discover odderon via the measurement of charge asymmetry of pions in the diffractive processes \(ep\to e\pi ^+\pi ^- p\), \(eA\to e\pi ^+\pi ^- A\) and in the processes \(AA\to AA\pi ^+\pi ^-\) with two rapidity gaps.


Hard Pomeron in Exclusive Meson Production at ILC

abstract

We calculate the exclusive process \(\gamma ^*_{\rm L} (Q_1^2)\gamma ^*_{\rm L}(Q_2^2) \to \rho ^0_{\rm L} \rho ^0_{\rm L},\) at high energy. The Born level estimate and the leading (LLA) and next to leading order (NLLA) BFKL resummation effects show the feasibility of experimental detection in a quite large range of \(Q^2\) values at future high energy \(e^+e^-\) linear colliders ILC.


Sum Rules for Parity Violating Compton Amplitudes

abstract

After discussion of legitimacy of the dispersive approach in the Standard Model sum rules (s.r.) for parity violating (p.v.) amplitudes are presented. These are s.r. for polarizabilities and p.v. analogue of the Gerasimov–Drell–Hearn sum rule. Phenomenological implications are reviewed.


Exclusively Exclusive Final States in Two Photon Collisions

abstract

The study of exclusive final states in two photon collisions is motivated by the range of physics that can be explored from chiral dynamics, to resonance physics to quark dynamics, all within a few GeV of threshold.


Phenomenological Test of the Large \(N_{\rm c}\) ChPT Predictions for the Pseudoscalar Mixing Parameters

abstract

A phenomenological analysis of various decay processes is performed in order to test the large \(N_{\rm c}\) Chiral Perturbation Theory predictions for the octet and singlet pseudoscalar decay constants and mixing angles. The results obtained hint at a disagreement with the expectations of this theoretical framework although the statistical significance is still limited.


Exclusive \(\rho \rho \) Production in \(\gamma \gamma \) Interaction at LEP

abstract

Exclusive \(\rho \rho \) production in two-photon collisions is studied at LEP for quasi-real photons (\(\gamma \gamma \), centre-of-mass energies 161 GeV \(\le \sqrt {s} \le 209\) GeV, total integrated luminosity \(L=698\,{\rm pb}^{-1}\)) and one virtual photon (\(\gamma \gamma ^*\), 89 GeV \(\le \sqrt {s} \le 209\) GeV \(L=855\,{\rm pb}^{-1}\)). The cross sections of the \(\rho \rho \) production processes are determined as a function of the photon virtuality, \(Q^{~2}\), and the two-photon centre-of-mass energy, \(W_{\gamma \gamma }\), in the kinematic region: \(Q^{~2} \le 30\) GeV\(^2\) and 1 GeV \(\le W_{\gamma \gamma } \le 3\) GeV.


Do L3 Data Indicate the Existence of an Isotensor Meson?

abstract

The QCD analysis of the hard exclusive production of \(\rho ^+\rho ^-\) and \(\rho ^0\rho ^0\) mesons in two photon collisions shows that the recent experimental data obtained by the L3 Collaboration at LEP can be understood as a signal for the existence of an exotic isotensor resonance with a mass around \(1.5\,{\rm GeV}\).


Measurements of \(\gamma \gamma \rightarrow K^0_{\rm S}K^0_{\rm S}\) and Charmonium Production at Belle

abstract

We use data samples collected with the Belle detector at the KEKB \(e^+e^-\) collider at 397 fb\(^{-1}\) integrated luminosity to measure the cross sections and angular distributions of \(K^0_{\rm S}K^0_{\rm S}\) production in two-photon collisions at the center-of-mass energy (\(W\)) and angle (\(\theta ^*\)) ranges, 2.4 GeV\(\lt W\lt 4.0\) GeV and \(|\cos \theta ^*|\lt 0.6\). A \(\sin ^{-4}\theta ^*\) behavior of the cross section in the region 2.4 GeV \(\lt W\lt 4.0\) GeV is observed. Signals of \(\chi _{c0}\) and \(\chi _{c2}\) are also observed. Furthermore, new resonance \(Z\)(3930) is observed in \(\gamma \gamma \rightarrow D\overline {D}\) process using data corresponding to 280 fb\(^{-1}\) integrated luminosity.


The QCD Analysis of Hadron–Antihadron \(\to \gamma ^* \gamma \) in the Forward Region and Related Processes

abstract

A QCD analysis of the reactions \(A B \to \gamma ^* \gamma \) and \(\gamma ^* \gamma \to AB\) in the forward region shows that they can be factorized in a way which is quite similar to the framework developped for deeply virtual Compton scattering. The generalized parton distributions (GPDs) related to this latter process are being replaced by new non perturbative hadronic matrix elements, the transition distribution amplitudes (TDAs).


Spectroscopy at HERA

abstract

Recent results on spectroscopy with special focus on searches for pentaquarks are presented from the H1 and ZEUS collaborations. Cross sections of observed states and upper limits on the production cross section of unobserved states are extracted in order to enable comparison between experiments. Measurements of the inclusive photoproduction of the neutral mesons \(\eta \), \(\rho ^0\), \(f_0(980)\) and \(f_2(1270)\) in \(ep\) interactions at HERA at an average \(\gamma {p}\) collision energy of 210 GeV are also presented.


Exclusive Two-Photon Processes in QCD

abstract

Hadron pair production from two-photon annihilation plays an important role in unraveling the perturbative and non-perturbative structure of QCD, first by testing the validity and empirical applicability of leading-twist factorization theorems, second by verifying the structure of the underlying perturbative QCD subprocesses, and third, through measurements of angular distributions and ratios which are sensitive to the shape of the distribution amplitudes. In effect, photon–photon collisions provide a microscope for testing fundamental scaling laws of PQCD and for measuring distribution amplitudes. The determination of the shape and normalization of the distribution amplitude is particularly important in view of their importance in the analysis of exclusive semi-leptonic and two-body hadronic \(B\)-decays. The data from the Belle and CLEO collaborations on single and double meson production are in excellent agreement with the QCD predictions. In contrast, the normalization of the nominal leading-order predictions of PQCD for proton pair production appears to be significantly below recent Belle measurements. I also review issues relating to renormalization scale setting.


all authors

M. Cwiok, H. Czyrkowski, R. Dabrowski, W. Dominik, G. Kasprowicz, K. Kwiecinska, K. Malek, L. Mankiewicz, M. Molak, J. Mrowca-Ciulacz, K. Nawrocki, L.W. Piotrowski, P. Sitek, M. Sokolowski, J. Uzycki, G. Wrochna

Search for Optical Counterparts of Gamma Ray Bursts

abstract

Observing prompt optical emission from Gamma Ray Bursts (GRB) sources is crucial to understand the processes involved. After brief review of the status of this domain we present “Pi of the Sky” project proposing new aproach to the problem. Algorithm for detection of optical flashes is described and the first results from the prototype apparatus are given.


Dark Matter and the ILC

abstract

We discuss the solution to the Dark Matter problem provided by the lightest neutralino of the Minimal Supersymmetric Standard Model (MSSM) and highlight the role of the International Linear Collider (ILC) in determining its cosmological relic density.


Photon as a Quantum Particle

abstract

Our present understanding of the nature of photons significantly differs from what has been known years ago when the concept of a photon has only been emerging. Unfortunately, very little of this knowledge trickles to those students who do not specialize in theoretical physics. In this lecture, in addition to giving a historical perspective on the “problem of the photon”, I shall say something about the description of the photon as a quantum mechanical particle. In addition, I shall show how the quantum description merges with the classical description of the electromagnetic field.


Some New Developments in Nonlinear Optics

abstract

We review some new developments in modern nonlinear optics. They are related to optics with both photons and atoms. The goals of the presentation were to give a cursory review on contemporary challenges in nonlinear optics (focusing on problems that are of interest to the Warsaw nonlinear optics group) and to show how fruitful it can be to transfer ideas across the border between different fields.


Linearly and Circularly Polarized Photon Emission from an Individual Semiconductor Quantum Dot

abstract

Anisotropic electron–hole exchange in semiconductor quantum dots is discussed in the context of efforts to obtain generation of entangled photon pairs from a biexciton–exciton cascade in a semiconductor quantum dot. Recent studies of anisotropy in III–V and II–VI quantum dots are described, followed by a discussion of attempts to compensate its influence by application of an electric field. Both macroscopic field generated by a voltage applied to electrodes and microscopic local fluctuation field are considered.


Photons and Hadrons for Health

abstract

Photons and hadrons are at the basis of one hundred years of research in fundamental particle physics and play nowadays a fundamental role in modern medicine. In diagnostics, computer tomography and positron emission tomography allow to explore the inner parts of the body and to determine with high precision the location of pathologies such as tumours. In the developed countries every 10 million inhabitants about 20000 oncological patients are irradiated every year with high-energy photons produced by electron linacs installed in hospital based radiotherapy centres. Hadrontherapy is a novel technique of radiotherapy which employs beams of charged hadrons, protons and carbon ions in particular. Due to their physical and radio-biological properties, they allow to obtain a more conformal treatment, sparing better the surrounding healthy tissues with a subsequent larger control rate and quality of life after treatment. By now about 40000 patients have been treated worldwide with protons and 15 hospital based centres are either running or under construction. Carbon ion beams are characterised by a larger biological effectiveness and are particularly indicated for the treatment of specific radio-resistant tumours. The fundamental role of photons and hadrons in modern medical applications is proof of the importance that fundamental research has for society.


Muon Pair Production in Relativistic Nuclear Collisions

abstract

The exclusive production of one \(\mu ^+\mu ^-\) pair in collisions of two ultra-relativistic nuclei is considered. We present the simple method for calculation of the Born cross section for this process. Then we found that the Coulomb corrections to this cross section (which correspond to multi-photon exchange of the produced \(\mu ^{\pm }\) with nuclei) are small while the unitarity corrections are large. This is in sharp contrast to the exclusive \(e^+e^-\) pair production where the Coulomb corrections to the Born cross section are large while the unitarity corrections are small. We calculated also the cross section for the production of one \(\mu ^+\mu ^-\) pair and several \(e^+e^-\) pairs in the leading logarithmic approximation. Using this cross section we found that the inclusive production of \(\mu ^+\mu ^-\) pair coincides in this approximation with its Born value.


Curves and the Photon

abstract

The study of the number of photons leads to a new way of characterizing curves and to a novel integral invariant over curves.


Photon 2005: Photons in a Special Year

abstract

A brief historical introduction accompanies a review of the theoretical contributions presented at PHOTON2005 together with a short summary of the experimental presentations.


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