Neutrino Properties and Astrophysics€¦ · Neutrino Properties and Astrophysics Wick Haxton, ... y f orbid den: neutrino, antineutrino or thog onal WW e e e-e-W n p n p decay forbidden:

Neutrino Propertiesand Astrophysics

Wick Haxton, INT Summer School on Nuclear & Particle Astrophysics June/July, 2009

Monday, July 6, 2009

The plan:

• the early history that led to the Standard Model

• lepton number

• Dirac and Majorana masses

• neutrino oscillations

• the MSW mechanism


• Experiments on radioactive nuclei had, by the mid-1920s, demonstrated that the positrons emitted in beta decay carried off only about half of the energy expected to be released in the nuclear decay

• Speculations included Niels Bohr’s suggestion that mass/energy equivalence might not hold in the new “quantum mechanics;” and Chadwick’s suggestion that perhaps some unobserved and unmeasured radiation accompanied the positron

• In 1930 Pauli hypothesized that an unobserved neutral, spin-1/2 “neutron” accounted for the apparent anomaly -- a new particle with mass < 1% that of the proton, the ν

Liebe Radioaktive Damen and Herren.....“... a genius, comparableperhaps only to Einsteinhimself ” N. Bohr

“I have done a terrible thing. I have postulateda particle that cannotbe detected.”


• Pauli viewed the ν as an atomic constituent -- knocked out in the β decay process

• Chadwick’s 1932 discovery of (today’s) neutron

• prompted Fermi to propose (1934)

!

p

e

e

p

p

n e+

!e

electromagneticanalog

current-currentbut no counterpart

to electric field

1933 7th Solvay Conference: Pauli’s first public presentation of the neutrino

Fermi


We can look at this from a slightly more modern view: introduce isospin to distinguish otherwise nearly identical p,n

so e-neutron or e-proton interaction vs. weak interaction

E&M: ρS + ρV(0) weak ρV(±)

makes sense: Fermi used the “missing” components of isovector charge


Fermi recognized that Lorentz invariance meant that this relationmust extend to currents. So again from a more modern perspective

so weak interaction modeled as current-current four-fermion interaction:electromagnetism and the weak interaction made use of all the isospin components of the vector hadronic current: a step toward unification!

Then:


Fermi’s β-decay ↔ electromagnetism analogy ↔ vector weak current ⇒

JVµ (x) 1 !p/M

µ = 0 µ = 1, 2, 3

⇒ selection rules for “allowed” decays of

ΔJ = 0 Δπ = 0, e.g., 0+→ 0+ decays with relativistic corrections ΔJ = 0, ±1 (but no 0→0) Δπ = 1, e.g., 1−→ 0+ decays: suppressed by (v/c)2 in transition probabilities

Fermi’s relativistic correction, noted

by G and T


GT added an axial contribution to Fermi’s interaction

!p/M

So that one could obtain in lowest order (allowed) Fermi: ΔJ = 0 Δπ = 0, e.g., 0+→ 0+ decays and Gamow-Teller: ΔJ = 0, ±1 (but no 0→0) Δπ = 0, e.g., 1+→ 0+

“Either the matrix element M1 or the matrix element M2 or finally a linear combination of M1 and M2 will have to be used to calculate theprobabilities of the β-disintegrations. If the third possibility is the correctone, and the two coefficients in the linear combination have the same order of magnitude, then all transitions [satisfying the selection rules] would now [be strong allowed ones]”

gA!" · !p/M

JVµ (x) 1

µ = 0 µ = 1, 2, 3

JAµ (x) gA!"


• This implied the correct allowed rate in the absence of polarization

• They chose to generalize Fermi’s interaction into a sum of current- current four-fermion interactions

• This was quite close to an alternative generalization

giving the same β-decay formula, and - would have given the neutrino a definite helicity - and the form itself leaves the question: why is there no role for the third isospin component of the axial current? could have posed these questions 35 years before the SM and the neutral weak current

! ! |"1#|2 + g2A|""##|2


Today:

• We have the standard model

• A generalization of Fermi’s theory is an appropriate first-order ET

• The interactions are universal

• The currents are V-A

• There is favor mixing:

• And there is a neutral current - a sum of the electromagetic current and the (missing) third component of the isovector axial current


Beta decay and lepton number:CPT guarantees that each particle has an antiparticle --this operation reverses “charges,” the additively conserved q. nos.

clearly particle and antiparticle are distinct

but what about the neutrino? is the antiparticle distinct from particle?

so we do an experiment:

!+sourcee+ e!!e !e

target

this defines the which is then found to produce:!e e!


target

this defines the which is then found to produce:

and a second one:

!!source

!̄e

e! e+

e+

• with these definitions of the and , they appear operationally distinct, producing different final states

• introduce a “charge” to distinguish the neutrino states and to define the allowed reactions, le , which we require to be additively conserved

!e

!

in

le =!

out

le


lepton lee! +1e+ !1!e +1!̄e !1

• so this would

• can generalize for νμ and ντ: conservation of separate lepton number

• or can consider a weaker conservation law of total lepton number


These experiments are done virtually in neutrinoless decay!!

parent nucleus (A,Z) (A,Z+1) daughter (A,Z+2)

W

• only SM fermion where this question of identity under particle- antiparticle conjugation arises: other fermions carry charges

• but our conclusion is wrong: we have ignored the neutrino helicity

WW

ee

e-

e-

WX

n p

n p

decay

forbidden:

e ,anti-

eorthogonal

neu

trinoless !

! -d

ecay forb

idden

: neu

trino, an

tineu

trino o

rthogo

nal

WW

ee

e-e-

WX

np

np

decayforbidden:

e,anti-eorthogonal

neu

trin

ole

ss !!

-dec

ay forb

idden

: neu

trin

o, a

ntineu

trin

o o

rthogo

nal

W Wee

e-

e-

W

n

p

n

p

decay forbidden: e, anti- e orthogonal

neutrinoless !! -decay forbidden: neutrino, antineutrino orthogonal

e! e!

W

!̄e !e

forbidden byassumption ofl conservation

in accord withexperiment


If the weak interaction produces left-handed νs and right-handed νs,let’s re-examine in view of GGS

WW

ee

e-

e-

WX

n p

n p

decay

forbidden:

e ,anti-

eorthogonal

neu

trinoless !

! -d

ecay forb

idden

: neu

trino, an

tineu

trino o

rthogo

nal

WW

ee

e-e-

WX

np

np

decayforbidden:

e,anti-eorthogonal

neu

trin

ole

ss !!

-dec

ay forb

idden

: neu

trin

o, a

ntineu

trin

o o

rthogo

nal

W Wee

e-

e-

W

n

p

n

p



e! e!

W

!̄e !e

Wforbidden by lepton numberconservation


Remove the restriction of an additively conserved lepton number

WW

ee

e-

e-

WX

n p

n p

decay

forbidden:

e ,anti-

eorthogonal

neu

trinoless !

! -d

ecay forb

idden

: neu

trino, an

tineu

trino o

rthogo

nal

WW

ee

e-e-

WX

np

np

decayforbidden:

e,anti-eorthogonal

neu

trin

ole

ss !!

-dec

ay forb

idden

: neu

trin

o, a

ntineu

trin

o o

rthogo

nal

W Wee

e-

e-

W

n

p

n

p



e! e!

W

!e

W

!e

allowed, with a rateproportional to GF4

This would produce neutrinoless ββ decay rates much larger than experimental limits -- so this can’t be correct


But one can account for suppressed rates by the nearly exact handedness --if the neutrino mass is not too large

WW

ee

e-

e-

WX

n p

n p

decay

forbidden:

e ,anti-

eorthogonal

neu

trinoless !

! -d

ecay forb

idden

: neu

trino, an

tineu

trino o

rthogo

nal

WW

ee

e-e-

WX

np

np

decayforbidden:

e,anti-eorthogonal

neu

trin

ole

ss !!

-dec

ay forb

idden

: neu

trin

o, a

ntineu

trin

o o

rthogo

nal

W Wee

e-

e-

W

n

p

n

p



e! e!

W

!e

W

!e RH LH

allowed, but suppressed with a rate proportional to GF4

(mν/Eν)2

the helicity suppression not exact if the ν has a mass as the “RH-ed” ν statewith then contain a small piece of LH-ed helicity proportional to mν/Eν

where Eν ∼ 1/Rnuclear

more important, we have found that, because of PNC, there is no need for an additively conserved quantum number constraining descriptions of theneutrino, unlike the case for other SM fermions


Two massive neutrino descriptions

νLH νRH

boost

CPT

Majorana:boost

νLH

νRH

Dirac:

boosts

CPTCPT

νLH νLH νRHνRH

Lorentz invariance

or some linear combinations

of the two


Deconstructing the Dirac equation: Dirac and Majorana masses

Allow for flavor mixing

To give the mass 4n by 4n matrix

(!̄cL, !̄R, !̄L, !̄c

R)

!

""#

0 0 ML MTD

0 0 MD M†R

M†L M†

D 0 0M!

D MR 0 0

$

%%&

!

""#

!cL

!R

!L

!cR

$

%%&

Lm(x) ! mD!̄(x)!(x)"MD!̄(x)!(x)

C !R/L C!1 = !cR/L!R/L = 1

2 (1± "5)!]

!L !

!

"!e

L!µ

L!!

L

#

$


Observe that the handedness allows an additional generalization

(!̄cL, !̄R, !̄L, !̄c

R)

!

""#

0 0 ML MTD

0 0 MD M†R

M†L M†

D 0 0M!

D MR 0 0

$

%%&

!

""#

!cL

!R

!L

!cR

$

%%&

to give the more general matrix

which has a number of interesting properties

• the eigenvectors are two-component Majorana spinors: 2n of these

• the introduction of breaks the global invariance associated with a conserved lepton number

ML, MR !! ei!!

Lm(x)!MD!̄(x)!(x) + (!̄cL(x)ML!L(x) + !̄c

R(x)MR!R(x) + h.c.)


• the removal of makes the eigenvalues pairwise degenerate: two two-component spinors of opposite CP can be patched together to form one four-component Dirac spinor -- so one gets n of these

• the mass that appears in double beta decay is , where is the ith’s neutrino CP eigenvalue and the coupling probability to the electron: this vanishes when

• the MSM has no RHed neutrino field; can be constructed, but does not appear in the MSM because it is not renormalizable

it is the only such dimension-five operator in the SM, and thus a likely source of the new physics that would show the MSM is breaking down

• ββ decay constrains the LHed Majorana mass to be below about an eV

• removal of yields two sets of n decoupled LHed/RHed Majorana νs

ML, MR

!2ni=1 U2

ei!imi

!i U2ei

ML, MR ! 0

ML

ML ! !!"2Mnew

MD


Missing solar neutrinos were traced to the phenomenon of

neutrino oscillations: Neutrinos spontaneous change from one type (electron) to another (muon) before they

arrive on earth.

This phenomenon requires neutrinos to have a mass,

though our “standard model” of particle physics says neutrinos

must be massless.

The mass requires either the existence of new neutrino states or new interactions.

p h y s i c s w e b . o r gP H Y S I C S W O R L D M A Y 2 0 0 2 37

rinos. These neutrinos interact with atomic nuclei in thewater to produce electrons, muons or tau leptons that travelfaster than the speed of light in water to produce a shock waveof light called Cerenkov radiation. This radiation can bedetected by sensitive photomultiplier tubes surrounding thewater tank.

From these signals, the SuperKamiokande team could alsodetermine the directions from which the neutrinos came.Since the Earth is essentially transparent to neutrinos, thoseproduced high in the atmosphere on the opposite side of theplanet can reach the detector without any problems. Theteam discovered that about half of the atmospheric neutrinosfrom the other side of the Earth were lost, while those fromabove were not. The most likely interpretation of this result isthat the muon neutrinos converted or “oscillated” to tau neut-rinos as they passed through the Earth. SuperKamiokande isunable to identify tau neutrinos. The particles coming fromthe other side of the Earth have more opportunity to oscillatethan those coming from above. Moreover, if neutrinos con-vert to something else by their own accord, we conclude thatthey must be travelling slower than the speed of light andtherefore must have a mass.

SuperKamiokande was also used to monitor solar neut-rinos. The fusion reactions that take place in the Sun onlyproduce electron neutrinos, but these can subsequently oscil-late into both muon and tau neutrinos. Though the experi-ment was able to detect the solar neutrinos, it was unable to distinguish between the different neutrino types. In con-trast, the Sudbury Neutrino Observatory (SNO) in Canadacan identify the electron neutrinos because it is filled with“heavy water”, which contains hydrogen nuclei with an extraneutron. Small numbers of electron neutrinos react with theheavy-hydrogen nuclei to produce fast electrons that createCerenkov radiation (figure 1).

By combining the data from SuperKamiokande and its ownexperiment, the SNO collaboration determined how manymuon neutrinos or tau neutrinos were incident at the Japan-ese detector. The SNO results also provided further evidencefor neutrino mass and confirmed that the total number ofneutrinos from the Sun agreed with theoretical calculations.

The implications of neutrino mass are so great that it is not surprising that particle physicists had been searching for direct evidence of its existence for over four decades. Inretrospect, it is easy to understand why these searches wereunsuccessful (figure 3). Since neutrinos travel at relativisticspeeds, the effect of their mass is so tiny that it cannot bedetermined kinematically. Rather than search for neutrinomass directly, experiments such as SuperKamiokande andSNO have searched for effects that depend on the difference inmass between one type of neutrino and another.

In some respects these experiments are analogous to inter-ferometers, which are sensitive to tiny differences in frequencybetween two interfering waves. Since a quantum particle canbe thought of as a wave with a frequency given by its energydivided by Planck’s constant, interferometry can detect tinymass differences because the energy and frequency of theparticles depend on their mass.

Interferometry works in the case of neutrinos thanks to thefact that the neutrinos created in nuclear reactions are actu-ally mixtures of two different “mass eigenstates”. This means,for example, that electron neutrinos slowly transform into tau neutrinos and back again. The amount of this “mixing” is

quantified by a mixing angle, !. We can only detect interfer-ence between two eigenstates with small mass differences ifthe mixing angle is large enough. Although current experi-ments have been unable to pin down the mass difference andmixing angle, they have narrowed down the range of possi-bilities (figure 4).

Implications of neutrino massNow that neutrinos do appear to have mass, we have to solvetwo problems. The first is to overcome the contradiction be-tween left-handedness and mass. The second is to understandwhy the neutrino mass is so small compared with other parti-cle masses – indeed, direct measurements indicate that elec-trons are at least 500 000 times more massive than neutrinos.When we thought that neutrinos did not have mass, theseproblems were not an issue. But the tiny mass is a puzzle, andthere must be some deep reason why this is the case.

Basically, there are two ways to extend the Standard Modelin order to make neutrinos massive. One approach involvesnew particles called Dirac neutrinos, while the other ap-proach involves a completely different type of particle calledthe Majorana neutrino.

The Dirac neutrino is a simple idea with a serious flaw. Ac-cording to this approach, the reason that right-handed neut-rinos have escaped detection so far is that their interactions areat least 26 orders of magnitude weaker than ordinary neut-

2 Neutrinos meet the Higgs boson

µ

e

"

t

##L

$ $$$ $$$

tR

tL

tR

tL

µL

µR

µLµR$

$$

$ $

$

µR

µL

$$

$eL

eR eL

eR

$$

$$

#

#

#L #R #L

#L#L

1/M

(a) According to the Higgs mechanism in the Standard Model, particles in thevacuum acquire mass as they collide with the Higgs boson. Photons (") aremassless because they do not interact with the Higgs boson. All particles,including electrons (e), muons (µ) and top quarks (t), change handednesswhen they collide with the Higgs boson; left-handed particles become right-handed and vice versa. Experiments have shown that neutrinos (#) arealways left-handed. Since right-handed neutrinos do not exist in the StandardModel, the theory predicts that neutrinos can never acquire mass. (b) In oneextension to the Standard Model, left- and right-handed neutrinos exist.These Dirac neutrinos acquire mass via the Higgs mechanism but right-handed neutrinos interact much more weakly than any other particles.(c) According to another extension of the Standard Model, extremely heavyright-handed neutrinos are created for a brief moment before they collide withthe Higgs boson to produce light left-handed Majorana neutrinos.

a

b

c

p h y s i c s w e b . o r gP H Y S I C S W O R L D M A Y 2 0 0 2 37

rinos. These neutrinos interact with atomic nuclei in thewater to produce electrons, muons or tau leptons that travelfaster than the speed of light in water to produce a shock waveof light called Cerenkov radiation. This radiation can bedetected by sensitive photomultiplier tubes surrounding thewater tank.

From these signals, the SuperKamiokande team could alsodetermine the directions from which the neutrinos came.Since the Earth is essentially transparent to neutrinos, thoseproduced high in the atmosphere on the opposite side of theplanet can reach the detector without any problems. Theteam discovered that about half of the atmospheric neutrinosfrom the other side of the Earth were lost, while those fromabove were not. The most likely interpretation of this result isthat the muon neutrinos converted or “oscillated” to tau neut-rinos as they passed through the Earth. SuperKamiokande isunable to identify tau neutrinos. The particles coming fromthe other side of the Earth have more opportunity to oscillatethan those coming from above. Moreover, if neutrinos con-vert to something else by their own accord, we conclude thatthey must be travelling slower than the speed of light andtherefore must have a mass.

SuperKamiokande was also used to monitor solar neut-rinos. The fusion reactions that take place in the Sun onlyproduce electron neutrinos, but these can subsequently oscil-late into both muon and tau neutrinos. Though the experi-ment was able to detect the solar neutrinos, it was unable to distinguish between the different neutrino types. In con-trast, the Sudbury Neutrino Observatory (SNO) in Canadacan identify the electron neutrinos because it is filled with“heavy water”, which contains hydrogen nuclei with an extraneutron. Small numbers of electron neutrinos react with theheavy-hydrogen nuclei to produce fast electrons that createCerenkov radiation (figure 1).

By combining the data from SuperKamiokande and its ownexperiment, the SNO collaboration determined how manymuon neutrinos or tau neutrinos were incident at the Japan-ese detector. The SNO results also provided further evidencefor neutrino mass and confirmed that the total number ofneutrinos from the Sun agreed with theoretical calculations.

The implications of neutrino mass are so great that it is not surprising that particle physicists had been searching for direct evidence of its existence for over four decades. Inretrospect, it is easy to understand why these searches wereunsuccessful (figure 3). Since neutrinos travel at relativisticspeeds, the effect of their mass is so tiny that it cannot bedetermined kinematically. Rather than search for neutrinomass directly, experiments such as SuperKamiokande andSNO have searched for effects that depend on the difference inmass between one type of neutrino and another.

In some respects these experiments are analogous to inter-ferometers, which are sensitive to tiny differences in frequencybetween two interfering waves. Since a quantum particle canbe thought of as a wave with a frequency given by its energydivided by Planck’s constant, interferometry can detect tinymass differences because the energy and frequency of theparticles depend on their mass.

Interferometry works in the case of neutrinos thanks to thefact that the neutrinos created in nuclear reactions are actu-ally mixtures of two different “mass eigenstates”. This means,for example, that electron neutrinos slowly transform into tau neutrinos and back again. The amount of this “mixing” is

quantified by a mixing angle, !. We can only detect interfer-ence between two eigenstates with small mass differences ifthe mixing angle is large enough. Although current experi-ments have been unable to pin down the mass difference andmixing angle, they have narrowed down the range of possi-bilities (figure 4).

Implications of neutrino massNow that neutrinos do appear to have mass, we have to solvetwo problems. The first is to overcome the contradiction be-tween left-handedness and mass. The second is to understandwhy the neutrino mass is so small compared with other parti-cle masses – indeed, direct measurements indicate that elec-trons are at least 500 000 times more massive than neutrinos.When we thought that neutrinos did not have mass, theseproblems were not an issue. But the tiny mass is a puzzle, andthere must be some deep reason why this is the case.

Basically, there are two ways to extend the Standard Modelin order to make neutrinos massive. One approach involvesnew particles called Dirac neutrinos, while the other ap-proach involves a completely different type of particle calledthe Majorana neutrino.

The Dirac neutrino is a simple idea with a serious flaw. Ac-cording to this approach, the reason that right-handed neut-rinos have escaped detection so far is that their interactions areat least 26 orders of magnitude weaker than ordinary neut-

2 Neutrinos meet the Higgs boson

µ

e

"

t

##L

$ $$$ $$$

tR

tL

tR

tL

µL

µR

µLµR$

$$

$ $

$

µR

µL

$$

$eL

eR eL

eR

$$

$$

#

#

#L #R #L

#L#L

1/M

(a) According to the Higgs mechanism in the Standard Model, particles in thevacuum acquire mass as they collide with the Higgs boson. Photons (") aremassless because they do not interact with the Higgs boson. All particles,including electrons (e), muons (µ) and top quarks (t), change handednesswhen they collide with the Higgs boson; left-handed particles become right-handed and vice versa. Experiments have shown that neutrinos (#) arealways left-handed. Since right-handed neutrinos do not exist in the StandardModel, the theory predicts that neutrinos can never acquire mass. (b) In oneextension to the Standard Model, left- and right-handed neutrinos exist.These Dirac neutrinos acquire mass via the Higgs mechanism but right-handed neutrinos interact much more weakly than any other particles.(c) According to another extension of the Standard Model, extremely heavyright-handed neutrinos are created for a brief moment before they collide withthe Higgs boson to produce light left-handed Majorana neutrinos.

a

b

c

P H Y S I C S W O R L D M A Y 2 0 0 2p h y s i c s w e b . o r g38

rinos. The idea of the Dirac neutrino works in the sense thatwe can generate neutrino masses via the Higgs mechanism(figure 2b). However, it also suggests that neutrinos should havesimilar masses to the other particles in the Standard Model. Toavoid this problem, we have to make the strength of neutrinointeractions with the Higgs boson at least 1012 times weakerthan that of the top quark. Few physicists accept such a tinynumber as a fundamental constant of nature.

An alternative way to make right-handed neutrinos ex-tremely weakly interacting was proposed in 1998 by NimaArkani-Hamed at the Stanford Linear Accelerator Center,Savas Dimopoulous of Stanford University, Gia Dvali of theInternational Centre for Theoretical Physics in Trieste andJohn March-Russell of CERN. They exploited an idea fromsuperstring theory in which the three dimensions of spacewith which we are familiar are embedded in 10- or 11-dimen-sional space–time. Like us, all the particles of the StandardModel – electrons, quarks, left-handed neutrinos, the Higgsboson and so on – are stuck on a three-dimensional “sheet”called a three-brane.

One special property of right-handed neutrinos is that theydo not feel the electromagnetic force, or the strong and weakforces. Arkani-Hamed and collaborators argued that right-handed neutrinos are not trapped on the three-brane in thesame way that we are, rather they can move in the extradimensions. This mechanism explains why we have neverobserved a right-handed neutrino and why their interactionswith other particles in the Standard Model are extremelyweak. The upshot of this approach is that neutrino massescan be very small.

The second way to extend the Standard Model involvesparticles that are called Majorana neutrinos. One advantageof this approach is that we no longer have to invoke right-handed neutrinos with extremely weak interactions. How-ever, we do have to give up the fundamental distinctionbetween matter and antimatter. Although this sounds bizarre,neutrinos and antineutrinos can be identical because theyhave no electric charge.

Massive neutrinos sit naturally within this framework.Recall the observer travelling at the speed of light who over-takes a left-handed neutrino and sees a right-handed neut-rino. Earlier we argued that the absence of right-handedneutrinos means that neutrinos are massless. But if neutrinosand antineutrinos are the same particle, then we can arguethat the observer really sees a right-handed antineutrino andthat the massive-neutrino hypothesis is therefore sound.

So how is neutrino mass generated? In this scheme, it ispossible for right-handed neutrinos to have a mass of theirown without relying on the Higgs boson. Unlike other quarksand leptons, the mass of the right-handed neutrino, M, is nottied to the mass scale of the Higgs boson. Rather, it can bemuch heavier than other particles.

When a left-handed neutrino collides with the Higgs boson,it acquires a mass, m, which is comparable to the mass ofother quarks and leptons. At the same time it transforms intoa right-handed neutrino, which is much heavier than energyconservation would normally allow (figure 2c). However, theHeisenberg uncertainty principle allows this state to exist for ashort time interval, !t, given by !t ~ h!/Mc2, after which theparticle transforms back into a left-handed neutrino withmass m by colliding with the Higgs boson again. Put simply,we can think of the neutrino as having an average mass ofm2/M over time.

This so-called seesaw mechanism can naturally give rise tolight neutrinos with normal-strength interactions. Normallywe would worry that neutrinos with a mass, m, that is similarto the masses of quarks and leptons would be too heavy. How-ever, we can still obtain light neutrinos if M is much largerthan the typical masses of quarks and leptons. Right-handedneutrinos must therefore be very heavy, as predicted by grand-unified theories that aim to combine electromagnetism withthe strong and weak interactions.

Current experiments suggest that these forces were unifiedwhen the universe was about 10–32 m across. Due to the un-certainty principle, the particles that were produced in suchsmall confines had a high momentum and thus a large mass.It turns out that the distance scale of unification gives right-handed neutrinos sufficient mass to produce light neutrinosvia the seesaw mechanism. In this way, the light neutrinos thatwe observe in experiments can therefore probe new physics atextremely short distances. Among the physics that neutrinoscould put on a firm footing is the theory of supersymmetry,which theorists believe is needed to make unification happenand to make the Higgs mechanism consistent down to suchshort distance scales.

Why do we exist?Abandoning the fundamental distinction between matter andantimatter means that the two states can convert to eachother. It may also solve one of the biggest mysteries of our uni-verse: where has all the antimatter gone? After the Big Bang,the universe was filled with equal amounts of matter and anti-matter, which annihilated as the universe cooled. However,roughly one in every 10 billion particles of matter survivedand went on to create stars, galaxies and life on Earth. Whatcreated this tiny excess of matter over antimatter so that wecan exist?

With Majorana neutrinos it is possible to explain whatcaused the excess matter. The hot Big Bang produced heavyright-handed neutrinos that eventually decayed into theirlighter left-handed counterparts. As the universe cooled, therewas insufficient energy to produce further massive neutrinos.Being an antiparticle in its own right, these Majorana neut-rinos decayed into left-handed neutrinos or right-handedantineutrinos together with Higgs bosons, which underwentfurther decays into heavy quarks. Even slight differences in theprobabilities of the decays into matter and antimatter wouldhave left the universe with an excess of matter.

3 Fermions weigh in

"2"1 "3

d s b

u c t

e µ #

meVµeV eV keV MeV GeV TeV

fermion masses

A comparison of the masses of all the fundamental fermions, particles withspin h!/2. Other than the neutrino, the lightest fermion is the electron, with amass of 0.5 MeV c–2. Neutrino-oscillation experiments do not measure themass of neutrinos directly, rather the mass difference between the differenttypes of neutrino. But by assuming that neutrino masses are similar to thismass difference, we can place upper limits on the mass of a few hundredmillielectron-volts.

Murayama’s ν mass cartoon

standard model masses

LHed Majorana neutrino

light Dirac neutrino

← the anomalous ν mass scale


The ν’s handedness allows a more general mass ⇒ explanation ν mass scale

• give the ν an MD typical of other SM fermions

• take ML ∼ 0, in accord with ββ decay

• assume MR >> MD as we have not found new RHed physics at low E

• take mν ∼ √m223 ∼ 0.05 eV and mD ∼ mtop ∼ 180 GeV

⇒ mR ∼ 0.3 × 1015 GeV

this is a novel mass generation mechanism, not shared by other SM fermions; ν mass may originate from physics near the GUT scale

!0 mD

mD mR

"! mlight

! " mD

#mDmR

$


0.0 0.2 0.4 0.6 0.8 1.0!(7Be) / !(7Be)SSM

0.0

0.2

0.4

0.6

0.8

1.0

!(8 B)

/ !(

8 B)SS

M

Monte Carlo SSMsTC SSMLow ZLow OpacityWIMPsLarge S11Dar-Shaviv Model

SSM90% C.L.

90% C.L.95% C.L.99% C.L.

TC Power Law

Combined Fit

Learned that νs are massive from atmospheric and solar experiments:

oscillations


Thus

• Standard electroweak theory has massless neutrinos

but if extended to include RHed νs or if treated as an effective theory, Majorana and Dirac mass terms would arise

• masses lead to the phenomenon of ν oscillations

e.g., solar νes oscillated into νμs

• oscillations can be altered by matter (electrons, nucleons, νs)

the Mikeyev-Smirnov-Wolfenstein mechanism


Vacuum flavor oscillations: mass and weak eigenstates

|!e > ! |!L > mL

|!µ > |!H > mH

flavorstates

massstates

Noncoincident bases ⇒ oscillations down stream:

νμ appearance downstream ⇔ vacuum oscillations

(some cheating here: wave packets)

|ve > = cos !|"L > + sin !|"H >

|vµ > = ! sin !|"L > + cos !|"H >

|"ke > = |"k(x = 0, t = 0) > E2 = k2 + m2

i

|"k(x " ct, t) > = eikx!

e!iELt cos !|"L > +e!iEHt sin !|"H >"

| < "µ|"k(t) > |2 = sin2 2! sin2

#

#m2

4Et

$

, #m2 = m2

H ! m2

L


Can slightly generalize this

yielding

vacuum mν2 matrix


solar matter generates a flavor asymmetry

• modifies forward scattering amplitude

• explicitly dependent on solar electron density

• makes the electron neutrino heavier at high density

solar matter generates a flavor asymmetryddddddd• modifies forward scattering amplitude, and thus ! index of refraction• explicitly "e dependent

m2!e = 4E

!2GF"e(x)

• makes the electron neutrino heavier at high densities

17

Z0 W-

a) b)

e

e

e,N

e,N

e

e

e

e


inserting this into mass matrix generates the 2-flavor MSW equation

or equivalently

the mν2 matrix’s diagonal elements vanish at a critical density


Alternately this in terms of local mass eigenstates

observe:

• mass splittings small at ρc: avoided level crossing

• at high density

• if vacuum θ small, in vacuum

thus there is a local mixing angle θ(x) that rotates fromas


mi2

2E

(xc)0

| L> | > | L> | e>

| H> | e>(x) /2

| H> | >(x) v


• it must be that

• if derivative gentle (change in density small over one local oscillation length) we can ignore: matrix then diagonal, easy to integrate

• most adiabatic behavior is near the crossing point: small splitting ⇒ large local oscillation length ⇒ can “see” density gradient

• derivative at governs nonadiabatic behavior (Landau Zener)

so


0.32 0.34 0.36

0.05

0.06

0.07

0.08

rc

nonadiabatic

sin22 = 0.005

m2/E = 10

-6eV

2/MeV

r (units of r )

(r)/(0)

0.0

0.2

0.4

0.6

0.8

1.0(r)/(0)

0.0 0.2 0.4 0.6 0.8 1.0

rc

r (units of r )

we can do thisproblem

analytically


ϒc >> 1 ⇔ adiabatic, so strong flavor conversion

ϒc << 1 ⇔ nonadiabatic, little flavor conversion

so two conditions for strong flavor conversion: sufficient density to create a level crossing adiabatic crossing of that critical density

MSW mechanism is about passing through a level crossing


sin22 v

10-4

10-2

1

10-8

10-6

10-4

m /

E2

(eV

2

/MeV)

nonadiabatic

no level crossing

pp

7Be

8B

Flavorconversion

here

γ<<1

solving the solar neutrino problem


sin22 v

10-4

10-2

1

10-8

10-6

10-4

m /

E2

(eV

2

/MeV)

nonadiabatic

no level crossing

pp

7Be

8B

Lowsolution


sin22 v

10-4

10-2

1

10-8

10-6

10-4

m /

E2

(eV

2

/MeV)

nonadiabatic

no level crossingpp

7Be

8B

Small anglesolution


sin22 v

10-4

10-2

1

10-8

10-6

10-4

m /

E2

(eV

2

/MeV)

nonadiabatic

no level crossingpp

7Be

8B

Large anglesolution

this is thesolutionmatchingSNO andSuperKresults

+Ga/Cl/KII

tan2θv~0.40


5 10E (MeV)

0.0

0.2

0.4

0.6

0.8

1.0

P(E)

sin22 = 0.6

sin22 = 0.006

Borexino




0 1 2 3 4 5 60

1

2

3

4

5

6

7

8

)-1 s-2 cm6

(10e!

)-1

s-2

cm

6 (

10

"µ! SNO

NC!

SSM!

SNO

CC!SNO

ES!

Figure 2: Flux of 8B solar neutrinos is divided into !µ/!! and !e flavors bythe SNO analysis. The diagonal bands show the total 8B flux as predictedby the SSM (dashed lines) and that measured with the NC reaction in SNO(solid band). The widths of these bands represent the ±1" errors. Thebands intersect in a single region for #(!e) and #(!µ/!! ), indicating thatthe combined flux results are consistent with neutrino flavor transformationassuming no distortion in the 8B neutrino energy spectrum.

9


!22

sin0 0.2 0.4 0.6 0.8 1

)2

(eV

2m

"

10-6

10-5

10-4

10-3

Rate excludedRate+Shape allowed

LMAPalo Verde excludedChooz excluded

Figure 4: The 95% c.l. LMA allowed region of SNO and other solar neutrinoexperiments is shown in red. The regions marked “Rate and Shape allowed”show the 95% c.l. KamLAND allowed solutions. The thick dot indicatesthe best fit to the KamLAND data, corresponding to sin2 2!12 ! 1.0 and"m2

12 ! 6.9 " 10!5 eV2.

by solar neutrino mass di!erence "m212 ! 10!5 eV2.) However, as the sign of

"m223 is not known, it is also possible that m3 is the lightest neutrino, with

the nearly degenerate m1 and m2 heavier. Finally, the best direct laboratoryconstraint on absolute neutrino masses comes from studies of tritium betadecay, as described in I. Studies of the tritium spectrum near its endpointenergy places a bound of 2.2 eV [13] on the #̄e mass (or more properly, on theprincipal mass eigenstate contributing to the #̄e). Consequently, one can addan overall scale of up to 2.2 eV to the mass splittings described above. Thatis, no terrestrial measurement rules out three nearly degenerate neutrinos,each with a mass ! 2.2 eV, but split by requisite "m2

atmos and "m2solar.

As discussed in I, the absolute neutrino mass is crucial in cosmology,as a sea of neutrinos produced in the Big Bang pervades all of space. If

12

Results from the reactor

experimentKamLAND


Neutrino Properties and Astrophysics€¦ · Neutrino Properties and Astrophysics Wick Haxton, ... y f orbid den: neutrino, antineutrino or thog onal WW e e e-e-W n p n p decay forbidden:

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