Benutzer:Mschuma3/Spielwiese

http://physik2.uni-goettingen.de/research/former-research-groups-1/6_schum

Delbrück-Streuung

Abschnitt

• Addendum:

Diese Messung wurde am DESY (Hamburg) ausgeführt. Sie entspricht dem Fall der extremen Vorwärtsstreuung bei dem nur der Imaginärteil der Streuamplitude einen Beitrag liefert (Schattenstreuung). Die Rechnung von Cheng und Wu<ref name=ref4> entspricht einer Näherung, die später von Milstein und Strakhovenko$^{[8]}$ verifiziert wurde. Diese Autoren$^{[8]}$ gehen von einem quasiklassischen Ansatz aus, der sich erheblich von dem von Cheng und Wu$^{[4][5]}$ unterscheidet. Es konnte aber gezeigt werden, dass beide Ansätze äquivalent sind und zu demselben numerischen Resultat führen. Der endgültige Nachweis der Delbrück-Streuung erfolgte 1975 in Göttingen bei einer Energie von 2.754 MeV$^{[9]}$. Bei dieser Energie wird der differentielle Wirkungsquerschnitt vom Realteil der Delbrück-Streuamplitude dominiert, der mit kleineren Beiträgen der atomaren und nuklearen Rayleigh-Streuung interferiert. In diesem Experiment wurde erstmalig die exakte auf dem Feynman-Graphen basierende Rechnung verifiziert. Die dabei erzielte hohe Präzision sowohl der theoretischen Vorhersage als auch des Experimentes ermöglichte den Nachweis, dass neben der niedrigsten Ordnung (siehe den abgebildeten Feynman-Graphen) auch ein kleinerer Betrag der nächst höheren Ordnung vorhanden ist. Eine umfassende Darstellung des gegenwärtigen Standes der Erforschung der Delbrück-Streuung befindet sich in$^{[10][11]}$. Gegenwärtig finden präzise Untersuchungen zur hochenergetischen Delbrück-Streuung im Budger-Institut in Novosibirsk (Russland) statt$^{[12]}$. Hier wurde auch erstmalig die Photon-Spaltung nachgewiesen, bei der eines der beiden bei der Delbrück-Streuung mit dem Kern ausgetauschten virtuellen Photonen als reelles Photon emittiert wird$^{[13][14]}$.

8. A.I. Milstein, V.M. Strakhovenko, Phys. Lett. a 95 (1983) 135; Sov. Phys. - JETP 58 (1983) 8.

9. M. Schumacher, et. al., Phys. Lett. 58 B (1975) 134.

10. A.I. Milstein, M. Schumacher, Phys. Rep. 234 (1994) 183.

11. M. Schumacher, Rad. Phys. Chem. 56 (1999) 101.

12. S.Z. Akhmadalev, et al., Phys. Rev. C 58 (1998) 2844.

Structure of scalar mesons and the Higgs sector of strong interaction[1]

The scalar mesons $\sigma (600)$, $\kappa (800)$, $f_{0}(980)$ and $a_{0}(980)$ together with the pseudo Goldstone bosons $\pi$, $K$ and $\eta$ may be considered as the Higgs sector of strong interaction. After a long time of uncertainty about the internal structure of the scalar mesons there now seems to be consistency which is in line with the major parts of experimental observations. Great progress has been made by introducing the unified model of Close and Törnqvist [2]. This model states that scalar mesons below 1 GeV may be understood as $q^{2}{\overline {q}}^{2}$ in S-wave with some $q{\overline {q}}$ in P-wave. Further out they rearrange as meson-meson states. We show that the P-wave component inherent in the structure of the neutral scalar mesons can be understood as doorway state for the formation of the scalar meson via two-photon fusion, whereas in nucleon Compton scattering these P-wave components serve as intermediate states of the scattering process [3,4]. Explicit expressions for the flavour structure of the $q{\overline {q}}$ states are derived and it is shown that these flavour structures are consistent with the two-photon widths of the scalar mesons. The masses of the scalar mesons are predicted in terms of spontaneous and explicit symmetry breaking. Spontaneous symmetry breaking leads to the same mass for all scalar mesons being 652 MeV. Explicit symmetry breaking increases the masses of the scalar mesons by an amount which depends on the fraction of strange and/or anti-strange quarks in the scalar meson. The Goldstone bosons showing up as part of the spontaneous symmetry-breaking process as mass-less particles acquire mass due to explicit symmetry breaking. This mass is absorbed into the mass of the scalar meson and in this way contributes to explicit symmetry breaking of the scalar meson. Good agreement is obtained between the experimental and predicted masses of the scalar mesons. A comparison between spontaneous symmetry breaking in strong and EW interaction is given.

[1] M. Schumacher, Abstract submitted to "Hadron 2011, München 13 - 17 June", arXiv:1107.4226 [hep-ph]

[2] F.E. Close and N.A. Törnqvist, J. Phys. G: Nucl. Part. Phys. 28 R249 (2002), arXiv:hep-ph/0204205

[3] M. Schumacher, Eur. Phys. J. C 67, 283 (2010), arXiv:1001.0500 [hep-ph].

[4] M. Schumacher, Journal of Physics G: Particle and Nuclear Physics 38 (2011) 083001, arXiv:1106.1015 [hep-ph].

Scalar mesons as a prototype of the Higgs boson

The scalar meson below 1 GeV as there are the $\sigma (600)$, the $\kappa (800)$, and the $a_{0}(980)$ and $f_{0}(980)$ may be considered as tetraquarks as their main structure component. There are many proposals for an explanation of the different masses. The first was given by the diquark model where special forces were assumed to exist between two quarks and two antiquarks. Other models make use of dimeson structures or special dynamics of the tetraquark configuration. We have made essential progress by showing that all the scalar meson have the same mass of 652 MeV for the hypothetical case that the EW Higgs field is turned off. This result is obtained via spontaneous symmetry breaking for the case that the current quarks are massless. Turning the EW Higgs field on leads to nonzero current-quark masses and thus to an increase of the masses of the scalar mesons. The size of the mass increase depends on the fraction $f_{s}$ of strange and/or antistrange quarks in the tetraquarks which is $f_{s}=0$ for the $\sigma$ meson, $f_{s}=1/4$ for the $\kappa$ mesons and $f_{s}=1/2$ for the $a_{0}$ and $f_{0}$ mesons. The masses of the scalar mesons consist of two components which are added in quadrature. The first component is equal to twice the constituent-quark mass including the effects of explicit symmetry breaking and the second component equal to the mass of the accompanying pseudo Goldstone boson. Though there are apparent similarities between strong and EW symmetry breaking there is a pronounced difference as far as the mases of the pseudo Goldstone bosons is concerned. In case of strong symmetry breaking these masses are absorbed into the masses of the scalar mesons whereas in EW symmetry breaking the Goldstone boson mases are absorbed into the longitudinal components of EW gauge bosons $Z$ and $W^{\pm }$.

Higgs Boson and sigma Meson

Preface: If the Higgs bosons is the God Particle then the sigma meson may be the Holy Spirit or Paradise Particle

Jokes normally are forbidden in serious physics articles but they help to make serious physics popular. This has been shown by Leon Lederman who wrote a popular book about different aspects of particle physics and named it God Particle [1]. In this book the topic God Particle is only of minor importance and only a very short section is devoted to it. But nevertheless this title had an enormous impact on the present discussion of the goals of high-energy physics research. The Large Hadron Collider at CERN in Geneva is a several billion dollar project aimed to find the Higgs boson, or in the words of Leon Lederman, the God Particle. The Higgs boson is the last missing particle of the standard model of particle physics, introduced into this theory to give all the existing particles including itself a mass. In this sense the Higgs boson is some kind of a creator which may lead physicist to the joke that it is the God Particle. On the other hand this name of the Higgs boson may serve as a tool to explain to the general public the reason why several billion dollars invested into the CERN-LHC project are well spent. When going from jokes to serious physics one first has to translate the name of the space where the physics is going on. This translation is possible by identifying heaven, the space of God into electroweak vacuum, the space of the Higgs boson.

In the present article we are interested in the sigma meson which is the counterpart of the Higgs boson in the strong interaction sector. Instead of the electroweak vacuum we now have to consider the QCD vacuum. In more popular terms we may replace the heaven by the paradise which is some intermediate state between heaven and the earth of our daily life. In this sense the sigma meson may be named the paradise particle. The sigma meson is predicted to supplement on the mass generation of light quarks which remain too light by a factor of about 40 after the action of the Higgs boson alone. Up to recently it was uncertain whether or not the sigma meson exists, because the experimental signals pointing into this direction were very weak. However, this has changed drastically in the last ten years and to a large extent the progress was due to a somewhat unfamiliar type of reaction. This unfamiliar reaction is Compton scattering by the nucleon through which the sigma meson became visible as part of the structure of the constituent quark. In this location the sigma meson is supposed to interact with the QCD vacuum and in this way provides mass to the constituent quark and to itself. An overview of the present status of research has been published in a recent topical review [2]. The purpose of the present article is to explain the content of this topical review to the non-specialist physicist or general reader.

1 Introduction

In 1957 Julian Schwinger [3] wrote a seminal paper entitled "A Theory of the Fundamental Interactions". The abstract consists of a citation of A. Einstein saying "The axiomatic basis of theoretical physics cannot be extracted from experiment but must be freely invented." In this work Schwinger laid the groundwork for what eventually became the theory of strong and electroweak spontaneous symmetry breaking and of the electroweak synthesis [3]. The sigma meson was introduced as a scalar-isoscalar partner of the pseudoscalar-isovctor pi meson and it was postulated that spontaneous symmetry breaking leads to a nonzero vacuum expectation value of the sigma field and through this to the mass of particles. After this idea was outlined, spontaneous symmetry breaking in a different domain was investigated in this work, viz. in the domain of the photon and charged vector bosons. But these were not the only outstanding achievements in [3]. The list of successes in this paper is summarized in [4] as follows: VA weak interaction theory, two neutrinos, charged intermediate vector bosons, dynamical unification of weak and electromagnetic interactions, scale invariance, chiral transformations, mass generation through vacuum expectation value of scalar field. Due to this and other work, Schwinger's name is associated with many ideas and techniques in physics.

Despite this impressive list of path-breaking achievements, Schwinger suffered few major near misses. By 1957, he had almost all the ingredients to construct the SU(2)xU(1) electroweak theory. Yet he failed to follow up on his own idea of electroweak unifcation. Fortunately for physics, he suggested the problem to Sheldon Glashow for further investigation. This led directly to the work of Shelden Glashow [5] six years before that of Steven Weinberg [6]. Glashow, Weinberg and Abdus Salam [7] shared the Nobel Prize (1979) for the unification of weak interactions with electromagnetism.

Nowadays the origin of the theory of spontaneous symmetry breaking is most frequently attributed to the work of Peter Higgs [8-10]. But as Peter Higgs himself correctly noted [10], "That vacuum expectation values of scalar fields, or 'vacuons', might play a role in breaking of symmetries was first noted by Schwinger". This means that strong and electroweak symmetry breaking both can be traced back to the seminal work of Schwinger [3] and that the introduction of the sigma meson inspired the electroweak symmetry breaking, though these two processes take place at completely different scales. The interest in this interplay between the two sectors of symmetry breaking is of importance up to the present. to be continued

      References

[1] Leon Lederman , Dick Teresi, A MARINER BOOK, Houghton Mifflin Company,

     BOSTON, NEW York, 2006

[2] Martin Schumacher, Journal of Physics G: Nuclear and Particle Physics 38 (2011) 083001, arXiv:1106.1015 [hep-ph].

[3] J. Schwinger, Ann. Phys. (N.Y.) 2, 407 (1957).

[4] Y. Jack. Ng, in: Julian Schwinger, The Physicist, the Teacher, and the Man, World

    Scientific, Singapore 1997 p.VII. 10

[5] S. Glashow, Nucl. Phys. 22, 579 (1961).

[6] S. Weinberg, Phys. Rev. Lett. 19 (1967) 1264

[7] A. Salam, in Elementary Particle Theory, N. Svartholm, eds. Amqvist and Wiksells,

    Stockholm (1969) p. 376.

[8] P.W. Higgs, Phys. Lett. 12, 132 (1964).

[9] P.W. Higgs, Phys. Rev. Lett. 13, 508 (1964).

[10] P.W. Higgs, Phys. Rev. 145, 1156 (1966).

Polarizabilities of the nucleon

Preface:

The polarizabilities belong to the fundamental structure constants of the nucleon, in addition to the mass, the electric charge, the spin and the magnetic moment. The proposal to measure the polarizabilities dates back to the 1950th. Two experimental options were considered (i) Compton scattering by the proton and (ii) the scattering of slow neutrons in the Coulomb field of heavy nuclei. The idea was that the nucleon with its pion cloud obtains an electric dipole moment under the action of an electric field vector which is proportional to the electric polarizability. After the discovery of the photoexcitation of the $\Delta$ resonance it became obvious that the nucleon also should have a strong paramagnetic polarizabilty, because of a virtual spin-flip transition of one of the constituent quarks due to the magnetic field vector provided by a real photon in a Compton scattering experiment. However, experiments showed that this expected strong paramagnetism is not observed. Apparently a strong diamagnetism exists which compensates the expected strong paramagnetism. Though this explanation is straightforward, it remained unknown how it may be understood in terms of the structure of the nucleon. A solution of this problem was found very recently when it was shown that the diamagnetism is a property of the structure of the constituent quarks. In retrospect this is not a surprise, because constituent quarks generate their mass mainly through interactions with the QCD vacuum via the exchange of a $\sigma$ meson. This mechanims is predicted by the linear $\sigma$ model on the quark level (QLL$\sigma$M) which also predicts the mass of the $\sigma$ meson to be m$_{\sigma }$=666 MeV. The $\sigma$ meson has the capability of interacting with two photons being in parallel planes of linear polarization. We will show in the following that the $\sigma$ meson as part of the constituent quark structure, therefore, provides the largest part of the electric polarizability and the total diamagnetic polarizability.

Definition of electromagnetic polarizabilities

A nucleon in an electric field E and a magnetic field H obtains and electric dipole moment d and magnetic dipole moment m given by

${\mathbf {d} }\,\,=4\pi \,\alpha \,{\mathbf {E} }$

${\mathbf {m} }=4\pi \,\beta \,{\mathbf {H} }$

in a unit system where the electric charge $e$ is given by $e^{2}/4\pi =\alpha _{e}=1/137.04$. The proportionality constants $\alpha$ and $\beta$ are denoted as the electric and magnetic polarizabilities, respectively. These polarizabilities may be understood as a measure of the response of the nucleon structure to the fields provided by a real or virtual photon and it is evident that we need a second photon to measure the polarizabilities. This may be expressed through the relations

$\delta W=-{\frac {1}{2}}\,4\pi \,\alpha \,{\mathbf {E} }^{2}-{\frac {1}{2}}\,4\pi \,\beta \,{\mathbf {H} }^{2}$

where $\delta W$ is the energy change in the electromagnetic field due to the presence of the nucleon in the field. The definition implies that the polarizabilities are measured in units of a volume, i.e. in units of fm$^{3}$ (1 fm=$10^{-15}$ m).

Modes of two-photon reactions and experimental methods

Static electric fields of sufficient strength are provided by the Coulomb field of heavy nuclei. Therefore, the electric polarizability of the neutron can be measured by scattering slow neutrons in the electric field E of a Pb nucleus. The neutron has no electric charge. Therefore two simultaneously interacting electric field vectors (two virtual photons) are required to produce a deflection of the neutron. Then the electric polarizability can be obtained from the differential cross section measured at a small deflection angle. A further possibility is provided by Compton scattering of real photons by the nucleon, where during the scattering process two electric and two magnetic field vectors simultaneously interact with the nucleon.

In the following we discuss the experimental options we have to measure the polarizabilities of the nucleon. As outlined above two photons are needed which simultaneously interact with the electrically charged parts of the nucleon. These photons may be in parallel or perpendicular planes of linear polarization and in these two modes measure the polarizabilities $\alpha$, $\beta$ or spinpolarizabilities $\gamma$, respectively. The spinpolarizability is nonzero only for particles having a spin.

In total the experimental options discussed above provide us with 6 combinations of two electric and magnetic field vectors. These are described in the following two equations.

• Photons in parallel planes of linear polarization

$({\text{case}}\,1)\,\,\alpha :\,\,\,\,{\mathbf {E} }\uparrow \uparrow {\mathbf {E} }'\quad \quad ({\text{case}}\,2)\,\,\beta :{\mathbf {H} }\rightarrow \rightarrow {\mathbf {H} }'\quad \,({\text{case}}\,\,3)\,\,-\beta :{\mathbf {H} }\rightarrow \leftarrow {\mathbf {H} }'$

• Photons in perpendicular planes of linear polarization

$({\text{case}}\,\,4)\,\,\gamma _{E}:{\mathbf {E} }\uparrow \rightarrow {\mathbf {E} }'\quad ({\text{case}}\,\,5)\,\,\gamma _{H}:{\mathbf {H} }\rightarrow \downarrow {\mathbf {H} }'\quad ({\text{case}}\,\,6)\,\,-\gamma _{H}:{\mathbf {H} }\rightarrow \uparrow {\mathbf {H} }'$

Case (1) corresponds to the measurement of the electric polarizability $\alpha$ via two parallel electric field vectors E. These parallel electric field vectors may either be provided as longitudinal photons by the Coulomb fiels of a heavy nucleus, or by Compton scattering in the forward direction or by reflecting the photon by 180°.

Calculation of polarizabilities

$\alpha +\beta ={\frac {1}{2\pi ^{2}}}\int _{\omega _{0}}^{\infty }{\frac {\sigma _{\rm {tot}}(\omega )}{\omega ^{2}}}d\omega$

$\alpha -\beta ={\frac {1}{2\pi ^{2}}}\int _{\omega _{0}}^{\infty }{\sqrt {1+{\frac {2\omega }{m}}}}\left[\sigma (\omega ,E1,M2,\cdots )-\sigma (\omega ,M1,E2,\cdots )\right]{\frac {d\omega }{\omega ^{2}}}+(\alpha -\beta )^{t}$

$\gamma _{0}=-{\frac {1}{4\pi ^{2}}}\int _{\omega _{0}}^{\infty }{\frac {\sigma _{3/2}(\omega )-\sigma _{1/2}(\omega )}{\omega ^{3}}}d\omega$

$\gamma _{\pi }={\frac {1}{4\pi ^{2}}}\int _{\omega _{0}}^{\infty }{\sqrt {1+{\frac {2\omega }{m}}}}\left(1+{\frac {\omega }{m}}\right)\sum _{n}P_{n}[\sigma _{3/2}^{n}(\omega )-\sigma _{1/2}^{n}(\omega )]{\frac {d\omega }{\omega ^{3}}}+\gamma _{\pi }^{t}$

$P_{n}=-1$ for $E1,M2,\cdots$ multipoles and $P_{n}=+1$ for $M1,E2,\cdots$ multipoles.

$(\alpha -\beta )^{t}={\frac {g_{\sigma NN}{M}(\sigma \to \gamma \gamma )}{2\pi m_{\sigma }^{2}}}+{\frac {g_{f_{0}NN}{M}(f_{0}\to \gamma \gamma )}{2\pi m_{f_{0}}^{2}}}+{\frac {g_{a_{0}NN}{M}(a_{0}\to \gamma \gamma )}{2\pi m_{a_{0}}^{2}}}$

$\gamma _{\pi }^{t}={\frac {1}{2\pi m}}$