Electroweak Processes in External Active Media

279 Pages·2013·3.757 MB·English

by  Alexander Kuznetsov, Nickolay Mikheev (auth.)

Springer Tracts in Modern Physics 252
Alexander Kuznetsov
Nickolay Mikheev
Electroweak
Processes in
External Active
Media
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Alexander Kuznetsov Nickolay Mikheev
•
Electroweak Processes
in External Active Media
123
Alexander Kuznetsov
Nickolay Mikheev
Theoretical Physics Department
Yaroslavl StateP.G. DemidovUniversity
Yaroslavl
Russia
ISSN 0081-3869 ISSN 1615-0430 (electronic)
ISBN 978-3-642-36225-5 ISBN 978-3-642-36226-2 (eBook)
DOI 10.1007/978-3-642-36226-2
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Preface
Inthelatetwentiethandtheearlytwenty-firstcenturies,themostintensiveprogress
wasobservedinthesciences,thatdevelopatthejunctionoftwosciences.Themost
interesting among them, seem to be those that combine the branches most distant
fromeachother.Ifso,thenitiseasytoidentifytheleaderofsuchsciences.Itisone
thatconnectsthesmallestobjectsavailableforresearch,elementaryparticles,and
these giant objects like stars, and has the name of Particle Astrophysics. It is not
difficulttoidentifythemajormilestonesinthelifeofthisrelativelyyoung,butvery
rapidlydevelopingscience.Thebirthismostlikelytobedatedtothebeginningof
the 1930s. Just then, after the discovery of a neutron by J. Chadwick in 1932, the
concept of a neutron star was proposed by L. D. Landau, and independently by
W.BaadeandF.Zwicky.Thestartofthematurationofthissciencecanbemoreor
lessconfidentlydatedto1987whenextragalacticneutrinoswereregisteredforthe
firsttimefromthesupernovaSN1987AexplosionintheLargeMagellanicCloud,a
satellite galaxy of our Milky Way. For the date of the endpoint of the maturation
period for particle astrophysics, one can propose 2001 when the solar-neutrino
puzzle was solved in a unique experiment at the heavy-water detector installed at
theSudburyNeutrinoObservatory.ThisexperimentconfirmedB.Pontecorvo’skey
idea concerning neutrino oscillations and, along with experiments that studied
atmospheric and reactor neutrinos, thereby proved the existence of a nonzero
neutrinomassandtheexistenceofmixingintheleptonsector.TheSunappearedin
this case asa natural laboratory for investigationsof neutrino properties.
Thereexistsomebooksonthetopicwherethebasicsofthisnewsciencecanbe
studied. However, new facts and ideas appear so fast that it is necessary for
specialists to follow not only journal papers but also electronic preprints, in order
to keep abreast of the latest developments.
Apageofthisnewscience,whichontheonehandisratherdifficultandonthe
other hand is not covered enough by books or reviews, deals with the particle
processes under the extreme conditions of the stellar interior—hot dense plasma
and strong electromagnetic fields. This discipline, which can be called Quantum
Field Theory in an External Active Media, was founded in the 1970s, and now it
continues in motion. As an attempt to set some milestone, the objective of our
previous monograph [1] was to give a systematic description of the methods of
calculation of the quantum processes, both at the tree and loop levels, in external
v
vi Preface
electromagnetic fields. The aim of the present monograph is to consider the
quantum processes under an influence of, along with a magnetic field, one more
external active media which is hot dense plasma.
The review is based in part on the special lecture course given to the second-
yearmaster-coursestudentsstudyingattheTheoreticalPhysicsDepartmentofthe
Yaroslavl State University, Yaroslavl, Russia. It can be used by graduate and
postgraduate students specializing in theoretical physics and being familiar with
the basics of the Quantum Field Theory and the Standard Model of the Electro-
weak Interactions. The authors make a great effort to give all the details that will
makethisbookavaluabletextforstudents.Themonographcanbealsousefulfor
specialistsintheQuantumFieldTheoryandparticlephysics,whoareinterestedin
the problems of physics of quantum phenomena in external active media.
We have obtained a part of the results presented in this monograph in
co-authorshipwithourcolleaguesandwithourgraduateandpostgraduatestudents
attheDepartmentofTheoreticalPhysicsofYaroslavlStateUniversity.We thank
L. A. Vassilevskaya, A. A. Gvozdev, A. Ya. Parkhomenko, M. V. Chistyakov,
I. S. Ognev, E. N. Narynskaya, D. A. Rumyantsev, A. A. Okrugin, R. A. Anikin,
A. M. Shitova, and M. S. Radchenko for collaboration and helpful discussions.
We are grateful to S.I. Blinnikov, V.A. Rubakov, V.B. Semikoz, and M.I.
Vysotsky for many fruitful discussions and to G.G. Raffelt for collaboration in
obtaining the results, concerning the self-energy neutrino operator in a magnetic
field.WearethankfultoH.-T.JankaandB.Müllerforprovidinguswithdetailed
data on radial distributions and time evolution of physical parameters in the
supernovacore,obtainedintheirmodeloftheSNexplosion.Withawarmfeeling
wewanttomentionthemanylivelydiscussionswithK.A.Ter-Martirosian,whose
strong support in the 1990s proved to be crucial for our research group.
A part of the results presented in this monograph was obtained in the study
performed within the State Assignment for Yaroslavl University (Project #
2.7508.2013),andsupportedbytheRussianFoundationforBasicResearch(Project
# 11-02-00394-a).
Yaroslavl, March 2013 Alexander Kuznetsov
Nickolay Mikheev
Reference
1. A.V. Kuznetsov, N.V. Mikheev, Electroweak Processes in External Electro-
magnetic Fields (Springer, New York, 2003)
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Solutions of the Dirac Equation in an External
Electromagnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 The Ground Landau Level . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Crossed Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4 Density Matrix of the Plasma Electron in a Magnetic Field
with the Fixed Number of a Landau Level. . . . . . . . . . . . . . . . 22
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3 Propagators of Charged Particles in External Active Media . . . . . 25
3.1 Propagators of Charged Particles in a Magnetic Field . . . . . . . . 25
3.1.1 Propagators in the Fock Proper-Time Presentation . . . . . 26
3.1.2 A Note on the Noninvariant Phase . . . . . . . . . . . . . . . . 29
3.1.3 Propagators in the Weak-Field Expansion . . . . . . . . . . . 30
3.1.4 Propagators in an Expansion over Landau Levels. . . . . . 31
3.1.5 Electron Propagator in a Strong Magnetic Field . . . . . . . 37
3.2 Propagators of Charged Particles in a Crossed Field . . . . . . . . . 38
3.3 Direct Derivation of the Electron Propagator in a Magnetic
Field as the Sum over Landau Levels on a Basis
of the Dirac Equation Exact Solutions. . . . . . . . . . . . . . . . . . . 39
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4 Particle Dispersion in External Active Media . . . . . . . . . . . . . . . . 45
4.1 Dispersion in Media: Main Definitions. . . . . . . . . . . . . . . . . . . 45
4.2 Photon Polarization Operator in an External Magnetic Field. . . . 48
4.3 Generalized Two-Point Loop Amplitude j!f(cid:2)f !j0
in an External Electromagnetic Field. . . . . . . . . . . . . . . . . . . . 52
4.3.1 Magnetic Field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.3.2 Crossed Field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.4 Photon Polarization Operator in Plasma. . . . . . . . . . . . . . . . . . 60
vii
viii Contents
4.5 Neutrino Self-energy Operator in Plasma . . . . . . . . . . . . . . . . . 66
4.5.1 Defnition of the Operator R(p) in Plasma . . . . . . . . . . . 68
4.5.2 Neutrino Additional Energy in Hot Dense Plasma. . . . . . 68
4.5.3 On the Neutrino Radiative Decay in Plasma. . . . . . . . . . 73
4.5.4 Ultra-High Energy Neutrino Dispersion in Plazma . . . . . 78
4.6 Neutrino Self-energy Operator in an External Magnetic Field. . . 89
4.6.1 Defnition of the Operator R(p) in a Magnetic Field . . . . 89
4.6.2 Low Landau Level Contribution
into the Operator R(p). . . . . . . . . . . . . . . . . . . . . . . . . 93
4.6.3 Calculation of the Operator R(p) in a ‘‘Weak’’ Field. . . . 96
4.6.4 The Case of a Moderately Strong Field. . . . . . . . . . . . . 100
4.6.5 The Neutrino Operator R(p) in a Crossed Field . . . . . . . 106
4.6.6 Field-Induced Neutrino Magnetic Moment. . . . . . . . . . . 109
4.7 Neutrino Self-energy Operator in Magnetized Plasma . . . . . . . . 109
4.7.1 Neutrino Scattering on Magnetized Plasma . . . . . . . . . . 110
4.7.2 Neutrino Additional Energy in Magnetized Plasma. . . . . 114
4.7.3 Asymptotic Expressions for the Neutrino Additional
Energy in Magnetized Plasma . . . . . . . . . . . . . . . . . . . 117
4.7.4 Induced Neutrino Magnetic Moment
in Magnetized Plasma . . . . . . . . . . . . . . . . . . . . . . . . . 119
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5 Electromagnetic Interactions in External Active Media. . . . . . . . . 127
5.1 Photon Decay into an Electron–Positron Pair
in a Strong Magnetic Field. . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.1.1 Direct Calculation Based on the Solutions
of the Dirac Equation . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.1.2 Calculation Based on the Imaginary Part
of the Loop Amplitude . . . . . . . . . . . . . . . . . . . . . . . . 132
5.2 The c!e(cid:2)eþ Decay in a Crossed Field . . . . . . . . . . . . . . . . . 133
5.2.1 Direct Calculation Based on the Solutions
of the Dirac Equation . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.2.2 Calculation Based on the Imaginary Part
of the Loop Amplitude . . . . . . . . . . . . . . . . . . . . . . . . 139
5.3 Photon Emission by Electron in a Strong Magnetic Field. . . . . . 140
5.4 Electromagnetic Interactions of the Dirac Neutrino with
a Magnetic Moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.4.1 Magnetic Moment of the Dirac Neutrino
and its Astrophysical Manifestations . . . . . . . . . . . . . . . 143
5.4.2 Neutrino Interaction with Background. . . . . . . . . . . . . . 146
5.4.3 The Rate of Creation of the Right-Handed Neutrino. . . . 147
5.4.4 Contributions of Plasma Components
into the Neutrino Scattering Process . . . . . . . . . . . . . . . 152
5.4.5 Illustration: Completely Degenerate Plasma at T = 0. . . . 154
Contents ix
5.4.6 Uniform Ball Model for the Supernova Core . . . . . . . . . 157
5.4.7 Models of the Supernova Core with Radial
Distributions of Physical Parameters: Limits
on the Neutrino Magnetic Moment . . . . . . . . . . . . . . . . 159
5.4.8 Possible Effect of the Neutrino Magnetic Moment:
Shock-Wave Revival in a Supernova Explosion . . . . . . . 163
5.4.9 Possible Effect of the Neutrino Magnetic Moment:
Neutrino Pulsar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6 Neutrino-Electron Interactions in External Active Media . . . . . . . 175
6.1 The m!e(cid:2)Wþ Process in a Strong Magnetic Field . . . . . . . . . 175
6.2 The m!me(cid:2)eþ Process in a Strong Magnetic Field . . . . . . . . . 180
6.2.1 Calculation of the Differential Probability Based
on the Solutions of the Dirac Equation . . . . . . . . . . . . . 180
6.2.2 Calculation Based on the Imaginary Part
of the Loop Amplitude . . . . . . . . . . . . . . . . . . . . . . . . 182
6.2.3 The Total Process Probability. . . . . . . . . . . . . . . . . . . . 183
6.3 The m!me(cid:2)eþ Process in a Crossed Field. . . . . . . . . . . . . . . . 186
6.3.1 A Historical Overview. . . . . . . . . . . . . . . . . . . . . . . . . 186
6.3.2 Calculation of the Differential Probability Based
on the Imaginary Part of the Loop Amplitude . . . . . . . . 187
6.3.3 The Total Process Probability. . . . . . . . . . . . . . . . . . . . 189
6.4 Possible Astrophysical Manifestations of the m!me(cid:2)eþ
Process in an External Magnetic Field. . . . . . . . . . . . . . . . . . . 192
6.4.1 Mean Losses of the Neutrino Energy and Momentum. . . 192
6.4.2 Applicability of the Results Obtained in a Pure
Magnetic Field for the Plasma Environment. . . . . . . . . . 194
6.4.3 Possible Astrophysical Manifestations. . . . . . . . . . . . . . 196
6.5 Neutrino in Strongly Magnetized Electron–Positron Plasma . . . . 197
6.5.1 What Do We Mean Under Strongly Magnetized
e(cid:2)eþ Plasma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
6.5.2 Neutrino-Electron Processes in Strongly Magnetized
Plasma: A Kinematic Analysis . . . . . . . . . . . . . . . . . . . 199
6.5.3 The Probability of the Process m!me(cid:2)eþ. . . . . . . . . . . 201
6.5.4 The Total Probability of the Neutrino Interaction
with Magnetized Electron–Positron Plasma . . . . . . . . . . 205
6.5.5 Mean Losses of the Neutrino Energy and Momentum. . . 209
6.5.6 Integral Action of Neutrinos on a Magnetized Plasma. . . 212
6.5.7 Neutrino-Electron Processes Involving the Contributions
of the Excited Landau Levels. . . . . . . . . . . . . . . . . . . . 215
6.5.8 Pulsar Natal Kick Via Neutrino-Triggered
Magnetorotational Asymmetry . . . . . . . . . . . . . . . . . . . 220
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227