Strong fields and neutral particle magnetic moment dynamics
Martin Formanek, Stefan Evans, Johann Rafelski, Andrew Steinmetz, Cheng-Tao Yang
aa r X i v : . [ h e p - ph ] M a y Strong fields and neutral particle magnetic momentdynamics
Martin Formanek, Stefan Evans, Johann Rafelski,Andrew Steinmetz, and Cheng-Tao Yang,
Department of Physics, The University of Arizona, Tucson, AZ 85721, USA
Abstract.
Interaction of magnetic moment of point particles with externalelectromagnetic fields experiences unresolved theoretical and experimentaldiscrepancies. In this work we point out several issues within the relativisticquantum mechanics and the QED and we describe effects related to a newcovariant classical model of magnetic moment dynamics. Using this frameworkwe explore the invariant acceleration experienced by neutral particles coupled toan external plane wave field through the magnetic moment: we study the case ofultra relativistic Dirac neutrinos with magnetic moment in the range of 10 − to10 − µ B ; and we address the case of slowly moving neutrons. We explore howcritical accelerations for neutrinos can be experimentally achieved in laser-pulseinteractions. The radiation of accelerated neutrinos can serve as an importanttest distinguishing between Majorana and Dirac nature of neutrinos.PACS numbers: 13.40.Em,06.30.Ka,41.75.Jv Keywords : magnetic moment, laser-driven acceleration, neutrino, neutron
Submitted to:
Plasma Phys. Control. Fusion
Accepted April 26, 2018 trong fields and neutral particle magnetic moment dynamics
1. Introduction
The general consensus in theoretical physics is thatthe final word on classical Electrodynamics has notyet been said. More than a hundred and fiftyyears have passed since its original inception byFaraday, Maxwell and many others in the 19th century,and we still face unsolved conceptual problems of afundamental nature. One of the most prominent issuesof classical Electrodynamics is the problem of radiationreaction [1, 2, 3].Of comparable relevance is the incomplete under-standing of the magnetic (Stern-Gerlach type) force,i.e. the interaction of the magnetic moment of a pointparticle with an external electro-magnetic (EM) fieldin both classical and quantum mechanics [4, 5]. A re-lated experimental discrepancy exists: as of July 2017there is a 3.5 standard deviations difference betweenthe calculated magnetic moment of the muon basedon Standard Model QFT corrections and experimentalmeasurements [6].We report on the recent progress in understandingthe magnetic moment dynamics [7]. Here we areinterested in the dynamics of a neutral particle withnon-zero magnetic moment placed in an external EMfield. Any new magnetic moment physics is in thissituation a first order effect. As an application ofthese considerations we describe how Dirac neutrinoscould be studied experimentally, by exploiting theirinteraction with intense laser fields. We note anothereffort to improve understanding of particle interactionwith strong laser fields [8]. Our work can alsocontribute to the study of plasma behavior influencedby external non-homogeneous fields.Before addressing the primary contents of thisreport we will first consider briefly the quantum physicsof the magnetic moment in section 2, clarifying how theclassical and quantum physics relate. We summarizethe insights of Ref. [7] in section 3, and we obtainthe invariant acceleration acting on any particle in theplane wave field in section 4, before describing thephysics of ultrarelativistic neutrinos in interaction withthe plane wave field in section 5.
2. Relativistic Quantum Mechanics
Every quantum particle should be described usingthree free parameters: its mass, its electric chargeand its magnetic moment. However, the Diracequation reduces the number of parameters to two, bypredicting the magnetic moment µ = ge ~ / m with thegyromagnetic ration g = 2. In reality, the effective g -factor is never exactly equal to two and in oureffort to understand the dynamics of realistic particles we need to generalize our expressions to account foran anomalous magnetic moment with a = g/ − a = 0 in the format( γ µ ( i ~ ∂ µ − eA µ ) − mc ) ψ = a e ~ mc σ µν F µν ψ . (1)The main problem with this approach is that themodified Dirac equation cannot be used to computevirtual processes, since the additional so called Pauliterm diverges and requires counter terms.An alternative theoretical description of magneticmoment first “squares” the Dirac equation, resulting ina second order formulation similar to the Klein-Gordon(KG) equation for spin 0 particles supplemented withthe Pauli term (cid:18) ( i ~ ∂ µ − eA µ ) − ge ~ σ µν F µν − m c (cid:19) ψ = 0 , (2)where σ µν = i [ γ µ , γ ν ]. A solution of the Diracequation is also a solution of this KG-Pauli Eq. (2) once g = 2 is chosen. The problem with KG-Pauli is thatone must carefully analyze and understand the set ofsolutions of the higher order equation.The advantage of KG-Pauli Eq. (2), compared toDirac-Pauli Eq. (1) is that we can choose an arbitraryvalue of the gyromagnetic factor g ; if value g = 2‘works’ so will an arbitrary value. We emphasize thatthese two quantum equations, the Dirac-Pauli Eq. (1)and the KG-Pauli Eq. (2), are not equivalent and resultin different physical behavior. Thus experiment willdetermine which form corresponds to the quantumphysics of e.g. bound states in hydrogen-like Coulombpotential. We will return to this matter under seperatecover. In principle quantum electrodynamics is formulatedaround a Dirac particle with g = 2 with modificationsarising in the context of a perturbative expansionleading to the evaluation of the actual magneticmoment, i.e. g = 2 of the electron in perturbativeseries that today requires in precision study alsothe consideration of strong interactions and vacuumstructure. This approach masks the opportunity touse the actual particle magnetic moment for particlesresponsible for the vacuum properties such as invacuum polarization.The study of the vacuum response to externalfields has a long and distinguished history that spans trong fields and neutral particle magnetic moment dynamics g = 2.When g = 2 is introduced, a modification of theanalytical form of the effective EH action is discov-ered [12, 13] and further non-trivial modifications inthe vacuum structure arise [14, 15]. A solution tothe previously divergent result for effective action with | g | > π ( q ) = − e π (cid:18) g − (cid:18) − m q (cid:19)(cid:19) × h
13 + Z dx ln (cid:16) − q m x (1 − x ) (cid:17)i . (3)The coefficient in Eq. (3) shows explicitly all threeparameters of a particle: its magnetic moment in formof g , its charge e and its mass m . One can easilyrecombine terms to show dependence on the magneticanomaly a = g/ −
1. This form demonstrates thatin perturbative QED expansion, the magnetic momentdependence arises from the higher order QED vacuumpolarization tensor (the photon line crossing the loop)contributing. This format hides the appearance ofthe actual particle magnetic moment in the vacuumpolarization as is seen in Eq. (3). We will return to thequestion how magnetic moment is renormalized underseparate cover.Once we recognize the dependence of vacuumpolarization on magnetic moment and the dependenceof EH effective action on magnetic moment onemust further revisit Schwinger‘s proof of vacuumtransparency to a single plane wave for g = 2.
3. Magnetic moment in classical theory
There are two models which describe the magneticmoment of a point particle. The ‘Amperian’ Modelapproximates the particle magnetic moment by acurrent loop which leads to a force F ASG = ∇ ( µ · B ) , (4)where µ is the magnetic moment of the particle and B is magnetic field. On the other hand the ‘Gilbertian’ Model creates a magnetic dipole, consisting of twohypothetical monopoles, and leads to a differentexpression F GSG = ( µ · ∇ ) B . (5)We expect that there should be a way to reconcile theseclassical models and to create a covariant description ofthe dynamics for both particle 4-velocity u µ and spin s µ , which would unite these two approaches. Therehave been efforts to do so - the first covariant modelwas created by Frenkel [4, 16]. This model is based onclassical arguments starting with the principle of leastaction and couples back the spin motion of the particlewith the particle motion.Another method of approach begins with rela-tivistic quantum Dirac theory which naturally incor-porates description of the spin behavior (although g =2 strictly) and finding an appropriate classical limitshould yield a full classical description of the particlebehavior. The most important example of such an ap-proach is the Foldy-Wouthuysen transformation [5]Both of these approaches predict different behav-ior in the external EM field and can be distinguishedexperimentally as was explored in the article [8]. Welearn from this work that ultra-intense laser pulses areespecially suitable for investigating the viability of suchmodels.As presented in the work [7], the spin ofa particle should not be its quantum propertybut rather a classical characteristic similar to theparticle‘s mass. Both of these are eigenvalues ofCasimir operators of the Poincar´e group of space-timesymmetry transformations, whose values describe arepresentation of this group for a given particle. Thisinsight allowed us to create a new covariant descriptionof the spin dynamics of particles [7] which has the form˙ u µ = 1 m ( qF µν − s · ∂F ∗ µν d ) u ν , (6)˙ s µ = 1 + e am qF µν − e b e a s · ∂F ∗ µν d ! s ν − e a u µ mc u · qF − e b e a s · ∂F ∗ d ! · s ! , (7)where e a and e b are arbitrary constants. We explicitlydistinguish between particle charge q and elementarymagnetic dipole charge d , which is used to convertthe spin of a particle s to the magnetic moment µ as c | s | d ≡ | µ | . Finally, the dual EM tensor reads F ∗ µν = ǫ µναβ F αβ /
2, with the fully antisymmetrictensor defined as ǫ ≡ +1 (beware of a sign ifcontravariant indices are used).We see that the equation of motion Eq. (14) ofthe particle depends explicitly on the spin dynamicsEq. (7) through the spin 4-vector s µ ( τ ), thus generating trong fields and neutral particle magnetic moment dynamics d = 0 these dynamical equationsreduce to Thomas-Bargmann-Michel-Telegdi (TBMT)equations [17, 18] with e a = a . TBMT equations arewidely used to model particle dynamics in externalfields and yet these do not contain coupling of the spinto the particle motion.On the other hand, we can also explore theother limit: the dynamics of neutral particles q =0 with magnetic moment d = 0 in external fields.Equations (14), (7) become only functions of parameter e b , which we will further explore in section 5.To conclude this short overview of the resultsobtained in Ref. [7] we note that the two forms of theforce, the Amperian and the Gilbertian, were shown tobe equivalent. Thus a consistent theoretical frameworknow exists for exploring the dynamics of a magneticmoment in external fields.
4. Dynamics of particles in a plane wave field
The generalized Lorentz force equation reads [7], seeEq. (14)˙ u µ = 1 m e F µν u ν , e F µν ≡ qF µν − s · ∂F ∗ µν d . (8)Imagine a point particle with both electric charge andmagnetic moment in the plane wave field given byexpression A µ ( ξ ) = A ε µ f ( ξ ) , ξ = k · x, k · ε = 0 , k = 0 , (9)where k µ is a wave vector of the plane wave; ε µ itspolarization; ξ phase; and A amplitude. f ( ξ ) isa function characterizing the laser pulse. Just theformula for the dynamics of the 4-velocity Eq. (8)alone is sufficient to obtain an expression for invariantacceleration in the plane wave field. In this case thegeneralized EM tensor reads e F µν = A q ( k µ ε ν − k ν ε µ ) f ′ ( ξ ) − A f ′′ ( ξ )( k · s ) ǫ µναβ k α ε β d , (10)where primes denote derivatives of the pulse function f ( ξ ) with respect to its phase. If we multiply thisexpression with k µ we get zero because of the identitiesin Eq. (9). Then Eq. (8) implies that k · ˙ u = 0 , ⇒ k · u = k · u (0) , (11)is an integral of motion. We can obtain the invariantacceleration by squaring the expression Eq. (8),which can be evaluated using Eq. (9), antisymmetricproperties of ǫ , our integral of motion Eq. (11), andcontraction identity ǫ µναβ ǫ µργδ = − δ ναβργδ , (12) which is a generalized Kronecker delta. The final resultis˙ u = − A m (cid:2) q f ′ ( ξ ) + ( k · s ) f ′′ ( ξ ) d (cid:3) ( k · u (0)) . (13)The cross term vanishes because the force due toparticle electric charge and magnetic moment areorthogonal for a plane wave field. The only unknownin this expression is the product ( k · s ( τ )), which is stilla function of proper time. As explained in the reference [7] the torque Eq. (7) isconstructed to be compatible with the force Eq. (8).For neutral particles we require in addition as didRef.[19] that torque involves full magnetic moment;that is, for the particle at rest in the laboratoryframe we have the torque ∝ µ × B . Restating theforce equation for neutral particles the two dynamicalequations thus are˙ u µ = − s · ∂F ∗ µν u ν dm , (14)˙ s µ = cd (cid:18) F µν s ν − u µ c ( u · F · s ) (cid:19) − s · ∂F ∗ µν s ν dm . (15)The full analytical solution of these equations are inpreparation for publication under separate cover. Hereof importance is the solution for the projection of spinon the wave vector of the laser k · s ( τ ) = k · s (0) cos[ A d ( f ( ξ ( τ )) − f ( ξ ))] − Wc sin[ A d ( f ( ξ ( τ )) − f ( ξ ))] , (16)where W is determined by initial conditions W ≡ [( k · u (0))( ε · s (0)) − ( ε · u (0))( k · s (0))] . (17)It is very important to know k · s ( τ ) because theinvariant acceleration of the particle, obtained bysquaring Eq. (14), is˙ u ( τ ) = − ( k · s ( τ )) ( k · u (0)) f ′′ ( ξ ) A d m . (18)The invariant acceleration therefore depends on theproducts ( k · u (0)) and ( k · s ( τ )). The first one is aDoppler shifted laser frequency as seen by the particlebeing hit by the laser pulse. In the laboratory framewith u µ (0) = γ c (1 , β ) , k µ = ω (1 , ˆ k ) /c , ǫ µ = (0 , ˆ εεε ) , (19)we can write k · u (0) = γ (1 − ˆ k · β ) ω . (20)To evaluate Eq. (18) we further need ( k · s (0)), denotingthe initial alignment of the particle spin and the wavevector. Since u · s = 0, the initial spin 4-vector in thelaboratory frame reads s µL (0) = ( β · s L , s L ) , (21) trong fields and neutral particle magnetic moment dynamics s L = s + γ − β ( β · s ) β , (22)where s L is the Lorentz transform of the initial spinof the particle s given in its rest frame. Therefore cω k · s (0) = γ ( β · s ) − ( γ − β · s )( ˆ β · ˆ k ) − ˆ k · s . (23)For the particle beam pointing against the laser pulseˆ β · ˆ k = −
1, we pick up a factor of γ cω k · s (0) = γ ( β + 1)( ˆ β · s ) − ( ˆ β · s ) − ˆ k · s . (24) k · s (0) factor plays an important role in theultrarelativistic interactions discussed in the followingsection.Finally, the combination of the initial conditionsEq. (17) evaluated in the laboratory frame reads Wc = γ ωc (cid:2) − ˆ εεε · s + (cid:18) − γ (cid:19) ( ˆ β · s )( ˆ β · ˆ εεε )+ (ˆ k · β )(ˆ εεε · s ) − ( β · ˆ εεε )(ˆ k · s ) (cid:3) , (25)which is also proportional to only one (in general highlyrelativistic) γ factor.
5. Neutrino acceleration (ultrarelativistic limit)
As discussed in preceding sections we are especiallyinterested in the case of charge neutral particles inthe external EM fields. The most prominent examplesof such particles are neutrons and neutrinos. Inthe absence of the classical Lorentz force the particledynamics is governed by spin effects and can directlybe used to measure the related properties of particles.The interaction of neutrinos with a laser field wasstudied previously [20] as a higher order scatteringeffect, but in the framework we developed [7] neutrinoscouple with external fields via magnetic momentdirectly.We recall that by symmetry arguments only theDirac neutrino can have a magnetic moment: inessence this is because the Majorana neutrino is theantiparticle of itself and thus under EM interactionsmust be neutral in both charge and magnetic moment.A very significant effort is underway to discover thedouble beta-decay [21] that could demonstrate thatthe neutrino is of the Majorana type. However, onecan question if a nil result would mean that theneutrino is a Dirac neutrino [22]. We believe that themeasurement of neutrino interactions with an externalfield via its magnetic moment would demonstrate thatthe neutrino is of the Dirac type. Our objective inthe following is to show that we not only can expectobservable effects when relativistic neutrinos interactwith an intense EM plane wave pulse, but that ameasurement of the magnetic moment of the neutrinoshould be possible.
The dipole magnetic moment is a well studiedelectromagnetic property of the Dirac neutrino. Aminimal extension of the Standard Model with non-zero Dirac neutrino masses places a lower bound onthe magnetic moment of the neutrino mass eigenstate ν i proportional to its mass m i and reads [23] µ i = 3 G F m e m i √ π µ B = 3 . × − (cid:16) m i eV (cid:17) µ B , (26)where µ B = e ~ / m e is the Bohr magneton. This valueis several orders of magnitude smaller than the presentexperimental upper bound [24] µ ν < . × − µ B . (27) We consider a beam of neutrinos with E ν ≃ m ν = 0 . E γ = 1 eV. The de Broglie wavelengthfor such neutrinos compared to the wavelength of thelaser light is λ ν λ γ = E γ E ν ( kin ) ≈ E γ E ν ≈ × − , (28)where we neglected the mass of the neutrinos comparedto their energy. This justifies the classical treatmentbecause the wavelength of the 1 eV laser light is 11orders of magnitude larger than the wavelength ofthe 20 GeV neutrinos, therefore the quantum wavecharacter of neutrinos will be invisible. The amplitude A of the laser field vector potential can be expressedin terms of the dimensionless normalized amplitude a as A = m e ce a . (29)The current state of the art for laser systems is a ∼ . The elementary dipole charge of the neutrino canbe rewritten using the neutrino magnetic moment inunits of Bohr magneton as d = em e c µ [ µ B ] . (30)This makes the relevant product A d = a µ ν [ µ B ] ≈ − − − (31)for state of the art laser systems and possible rangeof values for neutrino magnetic moment Eqs. (26, 27).From the Eq. (25) we get ultrarelativistic limit for W/c term and using (Eq. (24)) ultrarelativistic limitfor product k · s (0) Wc ∼ γ ~ ωc , k · s (0) ∼ γ ~ ωc . (32) trong fields and neutral particle magnetic moment dynamics A d (Eq. (31))we can see from Eq. (16) that there is no (neutrino) spinprecession and k · s ( τ ) ≈ k · s (0) , (33)with a very high precision.Equation (18) allows us to evaluate the invariantacceleration which the 20 GeV neutrino experiences inthe external plane wave field √ ˙ u ≈ (cid:12)(cid:12)(cid:12)(cid:12) ( k · s (0))( k · u (0)) f ′′ ( ξ ) A dm ν (cid:12)(cid:12)(cid:12)(cid:12) . (34)We turn now to estimate individual terms:i) The Doppler shifted frequency ( k · u (0)) is given inthe laboratory frame by the formula (20) and for theultra relativistic neutrinos with velocity β orientedagainst the laser beam propagation direction ˆ k we canwrite k · u (0) = γ (1 − ˆ k · β ) ω ≈ γ ω ≈ E ν E γ m ν c ~ . (35)ii) The product k · s (0) (Eq. (24)) is in the ultrarela-tivistic case proportional to k · s (0) ≈ γ ~ ωc ≈ E ν m ν c E γ c . (36)iii) Finally, we want to write the result in the units ofcritical acceleration for the neutrino which is a c = m ν c ~ . (37)Substituting all terms in equations,(29-37) into (34)yields an expression for the acceleration √ ˙ u [ a c ] ≈ a f ′′ ( ξ ) ( E ν [ eV ]) ( E γ [ eV ]) ( m ν [ eV ]) µ ν [ µ B ] . (38)For our 20 GeV neutrinos we see that the criticalacceleration can be achieved in the whole range ofmagnetic moment that Dirac neutrinos could have µ ν ∈ (10 − − − ) µ B for corresponding laser pulseparameters in the range a f ′′ ( ξ ) ∈ (10 − − − ) . (39)The state of the art laser systems have dimensionlessnormalized amplitude a , Eq. (29) on the order of 10 .Even the second derivative of the laser pulse functioncan be high, because typically we get f ( ξ ) as a productof oscillating function sin( ξ ) and envelope g ( ξ ) whichhas a second derivative f ′′ ( ξ ) = (sin( ξ ) g ( ξ )) ′′ = − sin( ξ ) g ( ξ ) + 2 cos( ξ ) g ′ ( ξ ) + sin( ξ ) g ′′ ( ξ ) . (40)The dominant term that we can exploit is the firstderivative of the envelope function which can be veryhigh on the front of the pulses with high contrastratio. For example if the intensity of the light dropsby 99% from the maximum on the distance of halfwavelength (therefore field amplitude drops by 90% on the same distance) we get g ′ ( ξ ) = 0 . /π ∼ − . Thuswe believe that critical neutrino acceleration can beachieved for the whole range of permissible neutrinomagnetic moment with accessible laser systems.Relativistic high intensity neutrino beams areavailable, and continue to be developed, at particleaccelerators (CERN, Fermilab) for neutrino oscillationexperiments and related ‘intensity frontier’ research.The typical energy of a high intensity ν, ¯ ν -beam is at10-20 GeV level, but a beam-dump sourced beam atCERN-LHC would produce neutrinos with 100 timeshigher energy. This high-energy beam of neutrinosresponds by a factor γ in our favor. In comparisonto accelerator sourced neutrinos, the highest natural ν -flux on Earth is at 0.6–1 MeV from pp -solar fusionchains. Interactions with the laser light at this energywould be suppressed by a factor 10 compared tothe 10 GeV neutrino beam, but the solar source‘shines’ with 100% duty cycle tracking sky locationof the Sun also across the Earth. This shows thatbefore an experiment can be realized, prioritization andoptimization between the intensity of the laser light,the accessible energy of neutrinos, and the luminosityof the neutrino flux have to be studied in order to selectan optimal experimental environment There are multiple ways how an accelerated neutrinocan radiate. It certainly produces magnetic dipoleelectromagnetic radiation as discussed in Refs.[19, 27].At 20 GeV energy it is even possible that theneutrino will emit (virtual) electro-weak bosons W ± and Z , which will decay into relatively high 10-GeVenergy scale, and thus more easily observable, eitherdilepton pairs, and/or hadronic showers (hadronicdecay of Z , W ± ). Thus with some probabilityshooting a laser pulse onto an incoming 20 GeVneutrino beam may catalyze GeV scale particleproduction, a process that would be hard to interpretotherwise.While experiments seeking double- β -decay ofMajorana neutrinos are underway, an experimentseeking evidence for Dirac neutrino has not beenavailable before. The possible ultra-intense laserpulse catalysis of radiation by an ultra-relativisticneutrino provides this opportunity for the first time.Therefore these processes will be subject to futurestudy. Aside demonstrating possible Dirac nature ofthe neutrino, such experiments would provide vitalinformation about the neutrino magnetic moment andmass. trong fields and neutral particle magnetic moment dynamics
6. Neutrons
Given that a neutron is about 5 × heavier comparedto a neutrino one cannot expect a Lorentz-factor γ = E n /m n c that is anywhere near to the value 10 that makes neutrino magnetic interactions with theexternal field strong. Even so, we note that iThembaLABS can produce neutrons with kinetic energy of 200MeV [26], which corresponds to E n ≈
960 MeV. Thisstill places their dynamics into a classical regime, since λ n /λ γ ≈ × − for 1 eV laser photons.Even though the magnitude of the magneticmoment for the neutron is several orders of magnitudelarger | µ n | = 1 × − µ B the neutrons are 10 timesheavier and in conclusion we would require the product a f ′′ ( ξ ) to be as high as 10 in order to achievecritical accelerations which is definitely not currentlyaccessible. On the other hand the neutron-externalmagnetic field interaction is appreciable and has beenused to keep a neutron beam in a storage ring [28]. TheEM plane wave interaction with neutrons introducesa novel method of neutron motion and spin motioncontrole. We need the neutrons to move slowly enough so that wecan consider the non-relativistic limit, but not so slowlythat we have to take into account quantum mechanicaleffects. For example, slow neutrons at 10 eV have β ∼ − and λ n /λ γ ∼ − for a 1 eV laser source,which still puts them well into the classical region.This time the product A d which governs the spinprecession is for the state of the art laser appreciable A d ≈ − which makes both terms in the spinprecession Eq. (16) relevant and spin of neutron indeedrotates in the external laser field.The estimate of the k · s (0) term (Eq. (24)) in thezeroth order of β is k · s (0) ≈ − ωc ˆ k · s , (41)and the term W/c (Eq. (25)) in the zeroth order of β reads Wc ≈ − ωc ˆ εεε · s . (42)This means that the spin precession equation, Eq. (16),reduces toˆ k · s ( t ) ≈ ˆ k · s cos[ A d ( f ( ξ ( t )) − f ( ξ ))] − ˆ εεε · s sin[ A d ( f ( ξ ( t )) − f ( ξ ))] . (43)We see in Eq. (43) that just as in the relativisticresult Eq. (16), in the non-relativistic limit thespin precesses with A df ( ξ ( t )). However, unlikefor neutrinos, given the large magnetic moment of neutrons, the spin precession can be significant. Thespin projection oscillates between initial alignmentswith direction of plane wave propagation and againstthe polarization vector (and vice-verse). This isin agreement with the expectation based on non-relativistic torque action, which we will further discusselsewhere. Closing the discussion of neutron dynamics we drawattention to the recent recognition that neutron decayanomaly, i.e. the lifespan inconsistency between ‘inbottle’, and ‘in flight’ measurements, could be relatedto an unknown dark matter decay of the neutron [29].We have explored the question if this inconsistencycould be due to the neutron lifespan being affectedby the strong field environment accompanying the‘in flight’ type measurement experiments [30]. Wewere considering the modification of the proper timeby the strong field. Since it is hard to accelerateneutrons using their magnetic moment we did notidentify an effect. However, this lifespan discrepancyand associated presence of strong fields remains a topicdeserving further theoretical and, in the context oflaser strong fields, novel experimental investigationemploying i.g. neutrons kept in a storage ring [28]accompanied by a EM plane wave.
7. Conclusions
The novel domain of EM magnetic moment interac-tions in external fields which has been recently formu-lated also holds promise to enhance the understandingof physics of plasmas. In this paper we focused on thedynamics on neutral particles, namely neutrinos andneutrons. The purpose of this paper was to introducenew particle physics opportunities present in the ul-tra intense laser physics frontier. Among results wehave obtained is for example that (ultra-relativistic)neutrinos embedded in ultra-strong high contrast laserpulses are not subjected to any appreciable spin preces-sion unlike neutrons for which spin dynamics becomesimportant.The relevant Eq. (16) and, respectively, Eq. (43)depend alone on the behavior related to TBMT torquedynamics, section 3. However, a prior study ofcovariant neutron (spin) dynamics in the presence ofa EM plane wave is not known to us and we believethat these results are presented here for the first time.We have proposed exploration of laser pulseinteraction with ultrarelativistic neutrinos. As ourdiscussion shows the ultra large neutrino Lorentz- γ factor enhances the interaction strength with theexternal field opening opportunity to revolutionize thestudy of physical properties of the Dirac neutrinos as trong fields and neutral particle magnetic moment dynamics W, Z radiation decay channels.Here it is important to realize that only a positiveoutcome of the double- β decay experiment provesthat neutrino is a Majorana particle; in the absenceof a result a complementary experiment aiming torecognize Dirac neutrino magnetic moment would serveas an important test which could resolve the questionwhether the neutrino is a Dirac or a Majorana particle. References [1] Y. Hadad, L. Labun, J. Rafelski, N. Elkina, C. Klier andH. Ruhl, “Effects of Radiation-Reaction in RelativisticLaser Acceleration,” Phys. Rev. D , 096012 (2010)doi:10.1103/PhysRevD.82.096012 [arXiv:1005.3980 [hep-ph]].[2] S. E. Gralla, A. I. Harte and R. M. Wald, “A RigorousDerivation of Electromagnetic Self-force,” Phys. Rev.D , 024031 (2009) doi:10.1103/PhysRevD.80.024031[arXiv:0905.2391 [gr-qc]].[3] H. Spohn, “Dynamics of charged particles and theirradiation field,” Cambridge University press (2004),ISBN 9780521037075.[4] J. Frenkel, “Die Elektrodynamik des rotierenden Elek-trons,” Z. Phys. , 243 (1926). doi:10.1007/BF01397099[5] L. L. Foldy and S. A. Wouthuysen, “On the Dirac theoryof spin 1/2 particle and its nonrelativistic limit,” Phys.Rev. , 29 (1950). doi:10.1103/PhysRev.78.29[6] D. Giusti, V. Lubicz, G. Martinelli, F. Sanfilippo andS. Simula, “Strange and charm HVP contributionsto the muon ( g −
2) including QED correctionswith twisted-mass fermions,” JHEP , 157 (2017)doi:10.1007/JHEP10(2017)157 [arXiv:1707.03019 [hep-lat]].[7] J. Rafelski, M. Formanek and A. Steinmetz, “RelativisticDynamics of Point Magnetic Moment,”Eur. Phys. J. C , no. 1, 6 (2018) doi:10.1140/epjc/s10052-017-5493-2[arXiv:1712.01825 [physics.class-ph]].[8] M. Wen, C. H. Keitel and H. Bauke, “Spin-one-half particles in strong electromagnetic fields: Spineffects and radiation reaction,” Phys. Rev. A ,no. 4, 042102 (2017) doi:10.1103/PhysRevA.95.042102[arXiv:1610.08951 [physics.plasm-ph]].[9] E. A. Uehling, “Polarization effects in the positron theory,”Phys. Rev. (1935) 55. doi:10.1103/PhysRev.48.55[10] W. Heisenberg and H. Euler, “Consequences of Dirac’stheory of positrons,” Z. Phys. , 714 (1936)doi:10.1007/BF01343663 [physics/0605038].[11] J. S. Schwinger, “On gauge invariance and vac-uum polarization,” Phys. Rev. , 664 (1951).doi:10.1103/PhysRev.82.664[12] L. Labun and J. Rafelski, “Acceleration and VacuumTemperature,” Phys. Rev. D , 041701 (2012)doi:10.1103/PhysRevD.86.041701 [arXiv:1203.6148 [hep-ph]].[13] J. Rafelski and L. Labun, “A Cusp in QED atg=2,”[arXiv:1205.1835 [hep-ph]].[14] R. Angeles-Martinez and M. Napsuciale, “Renor-malization of the QED of second order spin1/2 fermions,” Phys. Rev. D , 076004 (2012)doi:10.1103/PhysRevD.85.076004 [arXiv:1112.1134[hep-ph]].[15] C. A. Vaquera-Araujo, M. Napsuciale and R. Angeles-Martinez, “Renormalization of the QED of Self-Interacting Second Order Spin 1/2 Fermions,” JHEP , 011 (2013) doi:10.1007/JHEP01(2013)011[arXiv:1205.1557 [hep-ph]].[16] J. Frenkel, “Spinning electrons,”Nature , 2949 (1926).[17] L. H. Thomas, “The motion of a spinning electron,” Nature , 514 (1926). doi:10.1038/117514a0[18] V. Bargmann, L. Michel and V. L. Telegdi, “Precession ofthe polarization of particles moving in a homogeneouselectromagnetic field,” Phys. Rev. Lett. , 435 (1959).doi:10.1103/PhysRevLett.2.435[19] P. D. Morley and D. J. Buettner, “Instantaneous Power Ra-diated from Magnetic Dipole Moments,”Astropart. Phys. , 7 (2015) doi:10.1016/j.astropartphys.2014.07.005[arXiv:1407.1274 [astro-ph.HE]].[20] S. Meuren, C. H. Keitel and A. Di Piazza, “Nonlinearneutrino-photon interactions inside strong laser pulses,”JHEP , 127 (2015) doi:10.1007/JHEP06(2015)127[arXiv:1504.02722 [hep-ph]].[21] C. Alduino et al. [CUORE Collaboration], “First Resultsfrom CUORE: A Search for Lepton Number Violationvia 0 νββ Decay of
Te,”Phys. Rev. Lett. , no.13, 132501 (2018) doi:10.1103/PhysRevLett.120.132501[arXiv:1710.07988 [nucl-ex]].[22] M. Hirsch, R. Srivastava and J. W. F. Valle, “Can one everprove that neutrinos are Dirac particles?,”Phys. Lett.B , 302 (2018) doi:10.1016/j.physletb.2018.03.073[arXiv:1711.06181 [hep-ph]].[23] K. Fujikawa and R. Shrock, “The Magnetic Mo-ment of a Massive Neutrino and Neutrino SpinRotation,” Phys. Rev. Lett. , 963 (1980).doi:10.1103/PhysRevLett.45.963[24] C. Patrignani et al. [Particle Data Group], “Review ofParticle Physics,” Chin. Phys. C , no. 10, 100001(2016). doi:10.1088/1674-1137/40/10/100001[25] D. Duchesneau [OPERA Collaboration], “Latest re-sults from the OPERA experiment,” J. Phys. Conf.Ser. , no. 1, 012004 (2017). doi:10.1088/1742-6596/888/1/012004[26] M. Mosconi, E. Musonza, A. Buffler, R. Nolte, S. R¨ottger,and F. D. Smit, “Characterisation of the high-energy neutron beam at iThemba LABS,” RadiationMeasurements , no. 10, 1342 (2010).[27] J.D. Jackson, “Classical Electrodynamics ”, 2nd Edition,Wiley, (1975).[28] W. Paul, F. Anton, W. Mampe, L. Paul and S. Paul,“Measurement of the Neutron Lifetime in a Mag-netic Storage Ring,” Z. Phys. C , 25 (1989).doi:10.1007/BF01556667[29] B. Fornal and B. Grinstein, “Dark Matter Interpretationof the Neutron Decay Anomaly,” arXiv:1801.01124 [hep-ph].[30] J. S. Nico et al. , “Measurement of the neutronlifetime by counting trapped protons in a coldneutron beam,”Phys. Rev. C71