Neutrinos and the stars Georg Raffelt, MPI for Physics Lectures at the Topical Seminar Neutrino Physics & Astrophysics 17-21 Sept 2008, Beijing, China

Where do Neutrinos Appear in Nature? Earth Crust (Natural Radioactivity)  Sun  Nuclear Reactors  Supernovae (Stellar Collapse) SN 1987A  Particle Accelerators  Cosmic Big Bang (Today 330 n/cm3) Indirect Evidence Earth Atmosphere (Cosmic Rays)  Astrophysical Accelerators Soon ?

Where do Neutrinos Appear in Nature? Neutrinos from nuclear reactions: Energies 1-20 MeV Quasi thermal sources Supernova: T ~ few MeV Big-Bang Neutrinos: Very small energies today (cosmic red shift) Like matter today “Beam dump neutrinos” High-energy protons hit matter or photons Produce secondary p Neutrinos from pion decay p  m + nm m  e + nm + ne Energies ≫ GeV

Where do Neutrinos Appear in Nature? Low-energy neutrino astronomy (including geo-neutrinos) Energies ~ 1-50 MeV Long-baseline neutrino oscillation experiments with Reactor neutrinos Neutrino beams from accelerators Precision cosmology & limit on neutrino mass Big-bang nucleosynthesis Leptogenesis High-energy neutrino astronomy Closely related to cosmic-ray physics

Neutrinos from the Sun Helium Solar radiation: 98 % light Hans Bethe (1906-2005, Nobel prize 1967) Thermonuclear reaction chains (1938) Helium Reaction- chains Energy 26.7 MeV Solar radiation: 98 % light 2 % neutrinos At Earth 66 billion neutrinos/cm2 sec

Bethe’s Classic Paper on Nuclear Reactions in Stars No neutrinos from nuclear reactions in 1938 …

Gamow & Schoenberg, Phys. Rev. 58:1117 (1940)

Gamow & Schoenberg 2

Sun Glasses for Neutrinos? 8.3 light minutes Several light years of lead needed to shield solar neutrinos Bethe & Peierls 1934: “… this evidently means that one will never be able to observe a neutrino.”

First Detection (1954 - 1956) g p n Cd e+ e- Clyde Cowan (1919 – 1974) Fred Reines (1918 – 1998) Nobel prize 1995 Detector prototype Anti-Electron Neutrinos from Hanford Nuclear Reactor 3 Gammas in coincidence p n Cd e+ e- g

First Measurement of Solar Neutrinos Inverse beta decay of chlorine 600 tons of Perchloroethylene Homestake solar neutrino observatory (1967-2002)

Neutrinos from the Sun Solar Neutrinos

Hydrogen burning: Proton-Proton Chains < 0.420 MeV 1.442 MeV 100% 0.24% 15% 85% PP-I < 18.8 MeV hep 90% 10% 0.02% 0.862 MeV 0.384 MeV < 15 MeV PP-II PP-III

Solar Neutrino Spectrum

Hydrogen Burning: CNO Cycle (p,g) (p,a) (p,g) (p,a)

Missing Neutrinos from the Sun Homestake Chlorine 7Be 8B CNO Measurement (1970 – 1995) Calculation of expected experimental counting rate from various source reactions John Bahcall 1934 - 2005 Raymond Davis Jr. 1914 - 2006

Results of Chlorine Experiment Average Rate Average (1970-1994) 2.56  0.16stat  0.16sys SNU (SNU = Solar Neutrino Unit = 1 Absorption / sec / 1036 Atoms) Theoretical Prediction 6-9 SNU “Solar Neutrino Problem” since 1968

Neutrino Flavor Oscillations Two-flavor mixing Each mass eigenstate propagates as with Phase difference implies flavor oscillations Probability ne  nm sin2(2q) Bruno Pontecorvo (1913 – 1993) Invented nu oscillations z Oscillation Length

Elastic scattering or CC reaction Cherenkov Effect Cherenkov Ring Elastic scattering or CC reaction Light Electron or Muon (Charged Particle) Neutrino Water

Super-Kamiokande Neutrino Detector

Super-Kamiokande: Sun in the Light of Neutrinos

2002 Physics Nobel Prize for Neutrino Astronomy Ray Davis Jr. (1914 - 2006) Masatoshi Koshiba (*1926) “for pioneering contributions to astrophysics, in particular for the detection of cosmic neutrinos”

Solar Neutrino Spectrum 7-Be line measured by Borexino (since 2007)

Solar Neutrino Spectroscopy with BOREXINO Neutrino electron scattering Liquid scintillator technology (~ 300 tons) Low energy threshold (~ 60 keV) Online since 16 May 2007 Expected without flavor oscillations 75 ± 4 counts/100t/d Expected with oscillations 49 ± 4 counts/100t/d BOREXINO result (May 2008) 49 ± 3stat ± 4sys cnts/100t/d arXiv:0805.3843 (25 May 2008)

Next Steps in Borexino Collect more statistics of Beryllium line Seasonal variation of rate (Earth orbit eccentricity) Measure neutrinos from the CNO reaction chain Information about solar metal abundance Measure geo-neutrinos (from natural radioactivity in the Earth crust) Approx. 7-17 events/year Main background: Reactors ~ 20 events/year

Geo Neutrinos: Why and What? We know surprisingly little about the interior of the Earth: Deepest bore hole ~ 12 km Samples from the crust are available for chemical analysis (e.g. vulcanoes) Seismology reconstructs density profile throughout the Earth Heat flow from measured temperature gradients 30-44 TW (BSE canonical model, based on cosmo-chemical arguments, predicts ~ 19 TW from crust and mantle, none from core) Neutrinos escape freely Carry information about chemical composition, radioactive heat production, or even a putative natural reactor at the core

Expected Geo Neutrino Fluxes S. Dye, Talk 5/25/2006 Baltimore

Geo Neutrinos Predicted geo neutrino flux KamLAND scintillator detector (1 kton) Reactor background

Kamland Observation of Geoneutrinos First tentative observation of geoneutrinos at Kamland in 2005 (~ 2 sigma effect) Very difficult because of large background of reactor neutrinos (is main purpose for neutrino oscillations)

Neutrinos from the Sun Solar Models

Equations of Stellar Structure Assume spherical symmetry and static structure (neglect kinetic energy) Excludes: Rotation, convection, magnetic fields, supernova-dynamics, … Hydrostatic equilibrium r P GN Mr Lr e Radius from center Pressure Newton’s constant Mass density Integrated mass up to r Luminosity (energy flux) Local rate of energy generation [erg/g/s] Opacity Radiative opacity Electron conduction Energy conservation Energy transfer Literature Clayton: Principles of stellar evolution and nucleosynthesis (Univ. Chicago Press 1968) Kippenhahn & Weigert: Stellar structure and evolution (Springer 1990)

Convection in Main-Sequence Stars Sun Kippenhahn & Weigert, Stellar Structure and Evolution

Virial Theorem and Hydrostatic Equilibrium Integrate both sides L.h.s. partial integration with P = 0 at surface R Classical monatomic gas: (U density of internal energy) Average energy of single “atoms” of the gas Virial Theorem Most important tool to understand self-gravitating systems

Virial Theorem Applied to the Sun Approximate Sun as a homogeneous sphere with Mass Radius Gravitational potential energy of a proton near center of the sphere Thermal velocity distribution Estimated temperature T = 1.1 keV Central temperature from standard solar models

Constructing a Solar Model: Fixed Inputs Solve stellar structure equations with good microphysics, starting from a zero-age main-sequence model (chemically homogeneous star) to present age Fixed quantities Solar mass M⊙ = 1.989  1033 g 0.1% Kepler’s 3rd law Solar age t⊙ = 4.57  109 yrs 0.5% Meteorites Quantities to match Solar luminosity L⊙ = 3.842  1033 erg s-1 0.4% Solar constant Solar radius R⊙ = 6.9598  1010 cm 0.1% Angular diameter Solar metals/hydrogen ratio (Z/X)⊙ = 0.0229 Photosphere and meteorites Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006

Constructing a Solar Model: Free Parameters Convection theory has 1 free parameter: Mixing length parameter aMLT determines the temperature stratification where convection is not adiabatic (upper layers of solar envelope) 2 of the 3 quantities determining the initial composition: Xini, Yini, Zini (linked by Xini + Yini + Zini = 1). Individual elements grouped in Zini have relative abundances given by solar abundance measurements (e.g. GS98, AGS05) Construct a 1 M⊙ initial model with Xini, Zini, (Yini = 1 -–Xini - Zini) and aMLT evolve it for the solar age t⊙ match (Z/X)⊙, L⊙ and R⊙ to better than one part in 105 Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006

Standard Solar Model Output Information Eight neutrino fluxes: production profiles and integrated values. Only 8B flux directly measured (SNO) so far Chemical profiles X(r), Y(r), Zi(r) electron and neutron density profiles (needed for matter effects in neutrino studies) Thermodynamic quantities as a function of radius: T, P, density (r), sound speed (c) Surface helium abundance Ysurf (Z/X and 1 = X + Y + Z leave 1 degree of freedom) Depth of the convective envelope, RCZ Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006

Standard Solar Model: Internal Structure Temperature Density

Helioseismology and the New Opacity Problem Neutrinos from the Sun Helioseismology and the New Opacity Problem

Helioseismology: Sun as a Pulsating Star Discovery of oscillations: Leighton et al. (1962) Sun oscillates in > 105 eigenmodes Frequencies of order mHz (5-min oscillations) Individual modes characterized by radial n, angular l and longitudinal m numbers Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006

Helioseismology: p-Modes Solar oscillations are acoustic waves (p-modes, pressure is the restoring force) stochastically excited by convective motions Outer turning-point located close to temperature inversion layer Inner turning-point varies, strongly depends on l (centrifugal barrier) Credit: Jørgen Christensen-Dalsgaard

Examples for Solar Oscillations + + = http://astro.phys.au.dk/helio_outreach/english/

Helioseismology: Observations Doppler observations of spectral lines measure velocities of a few cm/s Differences in the frequencies of order mHz Very long observations needed. BiSON network (low-l modes) has data for  5000 days Relative accuracy in frequencies 10-5 Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006

Helioseismology: Comparison with Solar Models Oscillation frequencies depend on r, P, g, c Inversion problem: From measured frequencies and from a reference solar model determine solar structure Output of inversion procedure: dc2(r), dr(r), RCZ, YSURF Relative sound-speed difference between helioseismological model and standard solar model

New Solar Opacities (Asplund, Grevesse & Sauval 2005) Large change in solar composition: Mostly reduction in C, N, O, Ne Results presented in many papers by the “Asplund group” Summarized in Asplund, Grevesse & Sauval (2005) Authors (Z/X)⊙ Main changes (dex) Grevesse 1984 0.0277 Anders & Grevesse 1989 0.0267 DC = -0.1, DN = +0.06 Grevesse & Noels 1993 0.0245 Grevesse & Sauval 1998 0.0229 DC = -0.04, DN = -0.07, DO = -0.1 Asplund, Grevesse & Sauval 2005 0.0165 DC = -0.13, DN = -0.14, DO = -0.17 DNe = -0.24, DSi = -0.05 (affects meteoritic abundances) Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006

Origin of Changes Improved modeling 3D model atmospheres Spectral lines from solar photosphere and corona Improved modeling 3D model atmospheres MHD equations solved NLTE effects accounted for in most cases Improved data Better selection of spectral lines Previous sets had blended lines (e.g. oxygen line blended with nickel line) Meteorites Volatile elements do not aggregate easily into solid bodies e.g. C, N, O, Ne, Ar only in solar spectrum Refractory elements, e.g. Mg, Si, S, Fe, Ni both in solar spectrum and meteorites meteoritic measurements more robust

Consequences of New Element Abundances What is good Much improved modeling Different lines of same element give same abundance (e.g. CO and CH lines) Sun has now similar composition to solar neighborhood New problems Agreement between helioseismology and SSM very much degraded Was previous agreement a coincidence? Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006

Standard Solar Model 2005: Old and New Opacity Sound Speed Density Old: BS05 (GS98) New: BS05 (ASG05) Helioseismology RCZ 0.713 0.728 0.713 ± 0.001 YSURF 0.243 0.229 0.2485 ± 0.0035 <dc> 0.001 0.005 --- <dr> 0.012 0.044 Adapted from A. Serenelli’s lectures at Scottish Universities Summer School in Physics 2006

Old and New Neutrino Fluxes Old: BS05 (GS98) New: BS05 (AGS05) Measurement (SNO) Flux cm-2 s-1 Error % pp 5.99  1010 0.9 6.06  1010 0.7 pep 1.42  108 1.5 1.45  108 1.1 hep 7.93  103 15.5 8.25  103 7Be 4.84  109 10.5 4.34  109 9.3 8B 5.69  106 +17 -15 4.51  106 +13 -11 4.99  106  6.6 13N 3.05  108 +36 -27 2.00  108 +15 -13 15O 2.31  108 +37 -27 1.44  108 +17 -14 17F 5.84  106 +72 -42 3.25  106 Cl (SNU) 8.12 6.6 Ga (SNU) 126.1 118.9 Bahcall, Serenelli & Basu (astro-ph/0412440 & astro-ph/0511337)

Very Low-Energy Solar Neutrinos Neutrinos from the Sun Very Low-Energy Solar Neutrinos

Neutrinos from Thermal Plasma Processes Photo (Compton) Plasmon decay Pair annihilation Bremsstrahlung These processes first discussed in 1961-63 after V-A theory

Solar Neutrinos from Compton Process Photo (Compton) Cross section (non-relativistic limit) Volume energy loss rate Energy loss rate per unit mass To be compared with nuclear energy generation rate in the Sun

Thermal vs. Nuclear Neutrinos from the Sun Haxton & Lin, The very low energy solar flux of electron and heavy-flavor neutrinos and anti-neutrinos, nucl-th/0006055

Search for Solar Axions Neutrinos from the Sun Search for Solar Axions

Search for Solar Axions Axion Helioscope (Sikivie 1983) g Magnet S N a Axion-Photon-Oscillation Primakoff production Axion flux a g Sun Tokyo Axion Helioscope (“Sumico”) (Results since 1998, up again 2008) CERN Axion Solar Telescope (CAST) (Data since 2003) Alternative technique: Bragg conversion in crystal Experimental limits on solar axion flux from dark-matter experiments (SOLAX, COSME, DAMA, ...)

Tokyo Axion Helioscope (“Sumico”) S.Moriyama, M.Minowa, T.Namba, Y.Inoue, Y.Takasu & A.Yamamoto, PLB 434 (1998) 147

LHC Magnet Mounted as a Telescope to Follow the Sun

CAST at CERN

Limits from CAST-I and CAST-II CAST-I results: PRL 94:121301 (2005) and JCAP 0704 (2007) 010 CAST-II results (He-4 filling): preliminary

High-Energy Neutrinos Neutrinos from the Sun High-Energy Neutrinos from the Sun

Search for WIMP Dark Matter Direct Method (Laboratory Experiments) Crystal Energy deposition Recoil energy (few keV) is measured by Ionisation Scintillation Cryogenic Galactic dark matter particle (e.g.neutralino) Indirect Method (Neutrino Telescopes) Sun Annihilation High-energy neutrinos (GeV-TeV) can be measured Galactic dark matter particles are accreted

IceCube Neutrino Telescope at the South Pole 1 km3 antarctic ice, instrumented with 4800 photomultipliers 40 of 80 strings installed (2008) Completion until 2011 foreseen

Muon Flux from WIMP Annihilation in the Sun

High-Energy Neutrinos from the Sun Ingelman & Thunman, High Energy Neutrino Production by Cosmic Ray Interactions in the Sun [hep-ph/9604288]

Neutrinos (and other Particles) from the Sun Thermal plasma reactions E ~ 1 eV - 30 keV No apparent way to measure Nuclear burning reactions E ~ 0.1 - 18 MeV Routine detailed measurements Cosmic-ray interactions in the Sun E ~ 10 - 109 GeV Future high-E neutrino telescopes (?) Dark matter annihilation in the Sun E ~ GeV - TeV (?) Future high-E neutrino telescopes (?) New particles, notably axions Are searched with CAST & Sumico

Basics of Stellar Evolution

Equations of Stellar Structure Assume spherical symmetry and static structure (neglect kinetic energy) Excludes: Rotation, convection, magnetic fields, supernova-dynamics, … Hydrostatic equilibrium r P GN Mr Lr e Radius from center Pressure Newton’s constant Mass density Integrated mass up to r Luminosity (energy flux) Local rate of energy generation [erg/g/s] Opacity Radiative opacity Electron conduction Energy conservation Energy transfer Literature Clayton: Principles of stellar evolution and nucleosynthesis (Univ. Chicago Press 1968) Kippenhahn & Weigert: Stellar structure and evolution (Springer 1990)

Nuclear Binding Energy Mass Number Fe

Thermonuclear Reactions and Gamow Peak Coulomb repulsion prevents nuclear reactions, except for Gamow tunneling Tunneling probability With Sommerfeld parameter Parameterize cross section with astrophysical S-factor LUNA Collaboration, nucl-ex/9902004

Main Nuclear Burnings 12C + 12C  23Na + p or 20Ne + 4He etc Hydrogen burning 4p + 2e-  4He + 2ne Proceeds by pp chains and CNO cycle No higher elements are formed because no stable isotope with mass number 8 Neutrinos from p  n conversion Typical temperatures: 107 K (~1 keV) Each type of burning occurs at a very different T but a broad range of densities Never co-exist in the same location Helium burning 4He + 4He + 4He  8Be + 4He  12C “Triple alpha reaction” because 8Be unstable, builds up with concentration ~ 10-9 12C + 4He  16O 16O + 4He  20Ne Typical temperatures: 108 K (~10 keV) Carbon burning Many reactions, for example 12C + 12C  23Na + p or 20Ne + 4He etc Typical temperatures: 109 K (~100 keV)

Hydrogen Exhaustion in a Main-Sequence Star Hydrogen Burning Helium-burning star Helium Burning Hydrogen

Burning Phases of a 15 Solar-Mass Star Hydrogen 3 H  He - 2.1 5.9 1.2 107 Duration [years] Ln/Lg rc [g/cm3] Tc [keV] Dominant Process Burning Phase Lg [104 Lsun] Helium 14 He  C, O 1.7 10-5 6.0 1.3103 1.3 106 Carbon C  Ne, Mg 53 1.7105 8.6 1.0 6.3 103 Neon Ne  O, Mg 110 1.6107 9.6 1.8 103 7.0 Oxygen O  Si 160 9.7107 9.6 2.1 104 1.7 Silicon Si  Fe, Ni 270 2.3108 9.6 9.2 105 6 days

Neutrinos from Thermal Plasma Processes Photo (Compton) Plasmon decay Pair annihilation Bremsstrahlung These processes first discussed in 1961-63 after V-A theory

Neutrino Energy Loss Rates

Existence of Direct Neutrino-Electron Coupling

Self-Regulated Nuclear Burning Virial Theorem Main-Sequence Star Small Contraction  Heating  Increased nuclear burning  Increased pressure  Expansion Additional energy loss (“cooling”)  Loss of pressure  Contraction  Heating  Increased nuclear burning Hydrogen burning at a nearly fixed T  Gravitational potential nearly fixed: GNM/R ~ constant  R  M (More massive stars bigger)

Degenerate Stars (“White Dwarfs”) Assume T very small  No thermal pressure  Electron degeneracy is pressure source Inverse mass-radius relationship for degenerate stars: R  M-1/3 Pressure ~ Momentum density x Velocity Electron density Momentum pF (Fermi momentum) Velocity Pressure Density (Stellar mass M and radius R) (Ye electrons per nucleon) For sufficiently large mass, electrons become relativistic Velocity = speed of light Pressure No stable configuration Hydrostatic equilibrium With dP/dr ~ -P/R we have approximately Chandrasekhar mass limit

Degenerate Stars (“White Dwarfs”) Inverse mass-radius relationship for degenerate stars: R  M-1/3 Chandrasekhar mass limit

Stellar Collapse Onion structure Main-sequence star Hydrogen Burning Collapse (implosion) Helium-burning star Helium Burning Hydrogen Degenerate iron core: r  109 g cm-3 T  1010 K MFe  1.5 Msun RFe  8000 km

Evolution of Stars M < 0.08 Msun Never ignites hydrogen  cools (“hydrogen white dwarf”) Brown dwarf 0.08 < M ≲ 0.8 Msun Hydrogen burning not completed in Hubble time Low-mass main-squence star 0.8 ≲ M ≲ 2 Msun Degenerate helium core after hydrogen exhaustion Carbon-oxygen white dwarf Planetary nebula 2 ≲ M ≲ 5-8 Msun Helium ignition non-degenerate 6-8 Msun ≲ M < ??? All burning cycles Onion skin structure with degenerate iron core Core collapse supernova Neutron star (often pulsar) Sometimes black hole? Supernova remnant (SNR), e.g. crab nebula

Evolution of a Low-Mass Star H Main-Sequence MS Ged-Giant Branch H He RGB Horizontal Branch H He HB Asymptotic Giant Branch H He C O AGB

Planetary Nebulae Hour Glass Nebula Planetary Nebula IC 418 Eskimo Nebula NGC 3132

Globular Clusters of the Milky Way http://www.dartmouth.edu/~chaboyer/mwgc.html Globular clusters on top of the FIRAS 2.2 micron map of the Galaxy The galactic globular cluster M3

Color-Magnitude Diagram for Globular Clusters Mass Stars with M so large that they have burnt out in a Hubble time No new star formation in globular clusters H Main-Sequence Hot, blue cold, red Color-magnitude diagram synthesized from several low-metallicity globular clusters and compared with theoretical isochrones (W.Harris, 2000)

Color-Magnitude Diagram for Globular Clusters H He C O Asymptotic Giant H He Red Giant H He Horizontal Branch H Main-Sequence C O White Dwarfs Hot, blue cold, red Color-magnitude diagram synthesized from several low-metallicity globular clusters and compared with theoretical isochrones (W.Harris, 2000)

Basics of Stellar Evolution Bounds on Neutrino Properties

Basic Argument Star Flux of weakly interacting particles Low-mass weakly-interacting particles can be emitted from stars New energy-loss channel Back-reaction on stellar properties and evolution What are the emission processes? What are the observable consequences?

Bernstein et al.

Color-Magnitude Diagram for Globular Clusters H He C O Asymptotic Giant H He Red Giant Particle emission delays He ignition, i.e. core mass increased H He Horizontal Branch H Main-Sequence Particle emission reduces helium burning lifetime, i.e. number of HB stars C O White Dwarfs Hot, blue cold, red Color-magnitude diagram synthesized from several low-metallicity globular clusters and compared with theoretical isochrones (W.Harris, 2000)

Neutrinos from Thermal Plasma Processes Photo (Compton) Plasmon decay Plasmon decay Pair annihilation Bremsstrahlung

Plasmon Decay in Neutrinos Propagation in vacuum: Photon massless Can not decay into other particles, even if they themselves are massless Interaction in vacuum: Massless neutrinos do not couple to photons May have dipole moments or even “millicharges” Propagation in a medium: Photon acquires a “refractive index” In a non-relativistic plasma (e.g. Sun, white dwarfs, core of red giant before helium ignition, …) behaves like a massive particle: Plasma frequency (electron density ne) Degenerate helium core (r = 106 g/cm3, T = 8.6 keV) Interaction in a medium: Neutrinos interact coherently with the charged particles which themselves couple to photons Induces an “effective charge” In a degenerate plasma (electron Fermi energy EF and Fermi momentum pF) Degenerate helium core (and CV = 1)

Plasmon Decay vs. Cherenkov Effect Photon dispersion in a medium can be “Time-like” w2 - k2 > 0 “Space-like” w2 - k2 < 0 Refractive index n (k = n w) n < 1 n > 1 Example Ionized plasma Normal matter for large photon energies Water (n  1.3), air, glass for visible frequencies Allowed process in medium that is forbidden in vacuum Plasmon decay to neutrinos Cherenkov effect

Neutrino-Photon-Coupling in a Plasma Neutrino effective in-medium coupling For vector-current analogous to photon polarization tensor Usually negligible

Neutral-Current Couplings and Plasmon Decay Standard-model plasmon decay process produces almost exclusively A neutral-current process that was never useful for “neutrino counting” unlike big-bang nucleosynthesis (of course today Z0-decay width fixes Nn = 3) Neutrino Fermion CV CA Electron Proton Neutron

Neutrino Electromagnetic Form Factors Effective coupling of electromagnetic field to a neutral fermion Charge en = F1(0) = 0 Anapole moment G1(0) Magnetic dipole moment m = F2(0) Electric dipole moment e = G2(0) Charge form factor F1(q2) and anapole G1(q2) are short-range interactions if charge F1(0) = 0 Connect states of equal helicity In the standard model they represent radiative corrections to weak interaction Dipole moments connect states of opposite helicity Violation of individual flavor lepton numbers (neutrino mixing)  Magnetic or electric dipole moments can connect different flavors or different mass eigenstates (“Transition moments”) Usually measured in “Bohr magnetons” mB = e/2me

Standard Dipole Moments for Massive Neutrinos In standard electroweak model, neutrino dipole and transition moments are induced at higher order Massive neutrinos ni (i = 1,2,3), mixed to form weak eigenstates Explicit evaluation for Dirac neutrinos (Magnetic moments mij electric moments eij)

Standard Dipole Moments for Massive Neutrinos Diagonal case (Magnetic moments of Dirac neutrinos) Off-diagonal case (Transition moments) First term in f(mℓ/mW) does not contribute (“GIM cancellation”) Largest neutrino mass eigenstate 0.05 eV < m < 0.2 eV For Dirac neutrino expect

Consequences of Neutrino Dipole Moments Spin precession in external E or B fields Scattering T electron recoil energy Plasmon decay in stars Decay or Cherenkov effect

Plasmon Decay and Stellar Energy Loss Rates Assume photon dispersion relation like a massive particle (nonrelativistic plasma) Photon decay rate (transverse plasmon) with energy Eg Millicharge Dipole moment Standard model Energy-loss rate of stellar plasma (temperature T and plasma frequency wpl)

Globular Cluster Limits on Neutrino Dipole Moments Compare magnetic-dipole plasma emission with standard case For red-giant core before helium ignition wpl = 18 keV Require this to be < 1 Globular-cluster limit on neutrino dipole moment

Neutrino Radiative Lifetime Limits decay Plasmon decay For low-mass neutrinos, plasmon decay in globular cluster stars yields most restrictive limits

Limits on Milli-Charged Particles Davidson, Hannestad & Raffelt JHEP 5 (2000) 3 Globular cluster limit most restrictive for small masses