Particle Physics Particle Physics Theory Sub-Group Theory Sub-Group

PresentationPresentation

Benedict AllbrookeBenedict AllbrookePaul ClarksonPaul ClarksonLauren LewisLauren Lewis

Jennifer WallaceJennifer Wallace

2 Generation Case2 Generation Case

• In some cases is a good approximation – eg. For In some cases is a good approximation – eg. For solar neutrinos.solar neutrinos.

• Mixing matrix relates the weak and mass Mixing matrix relates the weak and mass eigenstates.eigenstates.

• Propagates as a QM wave function.Propagates as a QM wave function.• Probability is proportional to the amplitude of the Probability is proportional to the amplitude of the

QM wave function squared at a position.QM wave function squared at a position.

2

1

cossin

sincos

e

2 Generation Case continued...2 Generation Case continued...

• Probability of oscillation.Probability of oscillation.

• Where Where θθ is the mixing angle, is the mixing angle, ΔΔMM22 is the difference between mass eigenstates squared in eV2, L is the baseline in km, and E is the energy of the neutrino in GeV.

E

LMP

222 27.1

sin2sin

3 Generation Case3 Generation Case

• 3 generation case relates the three known 3 generation case relates the three known mass eigenstates to the three known weak mass eigenstates to the three known weak eigenstates.eigenstates.

• This case can become a combination of 2 This case can become a combination of 2 generation cases.generation cases.

• Maki-Nakagawa-Sakata (MNS) matrix.Maki-Nakagawa-Sakata (MNS) matrix.• Analogous to CKM matrix for quarks.Analogous to CKM matrix for quarks.

3 generation case continued...3 generation case continued...

• Maki-Nakagawa-Sakata (MNS) matrixMaki-Nakagawa-Sakata (MNS) matrix

• αα is the Majorana phase is the Majorana phase• δδ is the CP violating phase is the CP violating phase

ijij

ijij

s

c

sin

cos

MNS ExplainedMNS Explained

• If sterile neutrinos are inferred, then the If sterile neutrinos are inferred, then the matrix MNS becomes 4x4.matrix MNS becomes 4x4.

• If neutrinos are Majorana, the matrix is not If neutrinos are Majorana, the matrix is not orthogonal.orthogonal.

• The matrix is unitary, therefore if all known The matrix is unitary, therefore if all known parameters are found and it is not, new parameters are found and it is not, new physics must be present.physics must be present.

3 generation probability equations3 generation probability equations

E

LmP

E

LmP

E

LmP

e

e

2322

232

134

2322

132

232

2322

132

232

267.1sin2sincos)(

267.1sin2sincos)(

267.1sin2sinsin)(

• These are the probabilities ignoring CP violation and considering neutrinos as Dirac particles.

• Ref: Neutrino Factories: Physics, Steve Geer, FNAL, 2008.

CP violation CP violation

• P – parity, C - charge conjugation.P – parity, C - charge conjugation.• The weak force does not conserve either, The weak force does not conserve either,

therefore both are violated.therefore both are violated.• However, together, CP restores However, together, CP restores

invariance.invariance.• If CP is violated, particles and antiparticles If CP is violated, particles and antiparticles

have different oscillation probabilities.have different oscillation probabilities.

CP Violation continued...CP Violation continued...

• Neutrinos and antineutrinos have Neutrinos and antineutrinos have different chiralities, left and right different chiralities, left and right handed respectively.handed respectively.

• The weak force coupling depends on The weak force coupling depends on handedness.handedness.

• The CP violating phase The CP violating phase δδ is inferred is inferred by the unitarity of the MNS matrix.by the unitarity of the MNS matrix.

Majorana or Dirac?Majorana or Dirac?

• Majorana particles are the same as their Majorana particles are the same as their antiparticles, therefore can only be antiparticles, therefore can only be electrically neutral fermions.electrically neutral fermions.

• Dirac particles are not the same as their Dirac particles are not the same as their antiparticle.antiparticle.

• In the MNS matrix, if neutrinos are Dirac, In the MNS matrix, if neutrinos are Dirac, αα is zero.is zero.

• If Majorana, If Majorana, αα is the angle between is the angle between neutrino and antineutrino.neutrino and antineutrino.

Majorana or Dirac continued...Majorana or Dirac continued...

• Majorana neutrinos violate lepton number.Majorana neutrinos violate lepton number.• Can only be determined through neutrino-Can only be determined through neutrino-

less double beta decay.less double beta decay.• The see-saw mechanism is a theory that The see-saw mechanism is a theory that

combines both Dirac and Majorana mass combines both Dirac and Majorana mass terms.terms.

See-Saw MechanismSee-Saw Mechanism

• Way to explain small mass of neutrino by Way to explain small mass of neutrino by implying corresponding heavy neutrinos.implying corresponding heavy neutrinos.

• Heavy neutrinos must be Majorana.Heavy neutrinos must be Majorana.• The observable neutrinos are the small The observable neutrinos are the small

neutrinos.neutrinos.

Mass HierarchyMass Hierarchy

• 2 possible schemes for mass eigenstates.2 possible schemes for mass eigenstates.

Matter EffectsMatter Effects

• Can be used to determine mass hierarchy.Can be used to determine mass hierarchy.

• A=2(√2)GA=2(√2)GFFYYeeρρEEVV

Matter Effects Continued...Matter Effects Continued...

• Oscillation probabilities different in a vacuum Oscillation probabilities different in a vacuum than in matter.than in matter.

• For normal hierarchy, it enhances the For normal hierarchy, it enhances the probability for neutrino oscillation, and suppress probability for neutrino oscillation, and suppress the probability for antineutrino oscillation, and the probability for antineutrino oscillation, and vice-versa for inverted hierarchy.vice-versa for inverted hierarchy.

• To investigate, need to run for half of the time To investigate, need to run for half of the time with with ννe e & anti-& anti-ννμμ and half the time withand half the time with anti-anti-ννe e && ννμμ..

Proposal – Detector 1Proposal – Detector 1

• Neutrino source energy of 15GeV to Neutrino source energy of 15GeV to increase sensitivity to increase sensitivity to θθ13 13 measurements.measurements.

• Baseline of 7300km to minimise CP Baseline of 7300km to minimise CP violating phase.violating phase.

• Beam would go through mantle, increasing Beam would go through mantle, increasing matter effects.matter effects.

Proposal – Detector 2Proposal – Detector 2

• Off axis detector with a baseline of Off axis detector with a baseline of 3000km, enhances CP violation. 3000km, enhances CP violation.

• Neutrino energy of 6GeV.Neutrino energy of 6GeV.• Only goes through crust and not mantle, Only goes through crust and not mantle,

still has matter effects.still has matter effects.

Matter Effects and CP ViolationMatter Effects and CP Violation

• Ref: Neutrino Factories: Physics, Steve Geer, FNAL, 2008.

Muon Storage RingMuon Storage Ring

• This shows the inclination of the beams needed This shows the inclination of the beams needed for baselines 7300km and 3000km.for baselines 7300km and 3000km.

• This diagram assumes an equilateral triangle.This diagram assumes an equilateral triangle.

Possible Locations for Detectors

Physics with a very long neutrino factory baseline; Raj Gandhi, Walter Winter

Running TimeRunning Time

• Run the experiment for half of the time Run the experiment for half of the time with with ννe e & anti-& anti-ννμμ (from (from μμ+ decays) and half + decays) and half

the time withthe time with anti-anti-ννe e && ννμμ (from (from μμ- decays).- decays).

• Run for two and a half years both ways (if Run for two and a half years both ways (if can only run for five years).can only run for five years).

What we can measure and howWhat we can measure and how

• ΘΘ1313 can be measured by looking at can be measured by looking at ννee ννμμ and and

ν‾ν‾ee νν‾‾μμ in appearance mode.in appearance mode.

• This is also true for the reverse channels.This is also true for the reverse channels.• Sensitivity for this should be down to the order of Sensitivity for this should be down to the order of

1010-4-4 . .• Mass hierarchy and the CP violating phase can Mass hierarchy and the CP violating phase can

be evaluated by looking at the difference be evaluated by looking at the difference between appearances of neutrinos and between appearances of neutrinos and antineutrinos.antineutrinos.

What we can measure and how What we can measure and how continued...continued...

• ΔΔmm2232 32 can be measured from the dip in can be measured from the dip in ννμμ and and

ν‾ν‾μμ..

• Matter effects will enhance or suppress the dip Matter effects will enhance or suppress the dip depending upon it being inverted or normal.depending upon it being inverted or normal.

• The disappearance of The disappearance of ννμμ will give a greater will give a greater

measurement of measurement of ΔΔmm2221 21 and and θθ12 12 ..

• If there is an excess of If there is an excess of ννee, sterile neutrinos can , sterile neutrinos can

be inferred.be inferred.

What we can not measureWhat we can not measure

• If If θθ1313 is too small then it will only be possible is too small then it will only be possible

to set an upper limit on the parameter.to set an upper limit on the parameter.

• If If θθ1313 is too small then it will not be possible is too small then it will not be possible

to measure the CP violating phase. to measure the CP violating phase. • We will not be able to quantify the Majorana We will not be able to quantify the Majorana

phase though may find hints that neutrinos phase though may find hints that neutrinos are Majorana.are Majorana.

Flux incident on detectorFlux incident on detector

• Opening angle of neutrino factory, Opening angle of neutrino factory, θθ=0.1/=0.1/γγμμ..

• Radius of beam at baseline L given by L Radius of beam at baseline L given by L tan(tan(θθ))

• Source distributed as a 2D Gaussian with Source distributed as a 2D Gaussian with normalised equation:normalised equation:

X is horizontal position, y is vertical position.σ is the standard deviation.

Flux incident on detector Flux incident on detector continued...continued...

• Model full beam width as 5Model full beam width as 5σσ. . • Gives Gives σσ=0.34km for 7300km baseline.=0.34km for 7300km baseline.

Flux incident on detector Flux incident on detector continued...continued...

For a square detector of side length 2a:

Probability for one neutrino passing through a certain area:

Predicted results

• Modelled vacuum oscillations in ROOT to determine probabilities of oscillation

• Introduced other oscillation mechanisms such as matter effects

• Consider experimental parameters such as detection rate, source flux and efficiency

• This gives predictions of detectable events to look at uncertainties on any measurements

Predicted results graphsEnhanced by Matter effects Suppressed by Matter effects

Implications for other physicsImplications for other physics

• Extra dimensionsExtra dimensions• See saw mechanismSee saw mechanism• SUSYSUSY• String theoryString theory• Dark matterDark matter• LeptogenesisLeptogenesis• Neutrino communicationsNeutrino communications

Thank you for listening.Thank you for listening.

Any questions?Any questions?

Neutrinoless Double Beta Decay (additional page)

Shows that neutrinos are majorana. Need a nuclei that is stable against other types of decay. Example 76Ge, τ~1028 years. Can also determine the mass of the neutrino.

eYX AZ

AZ 22

Leptogenesis(additional slide)

N may have energies up to the GUT scale.In the early universe N decays into leptons and Higgs bosons. If CP is violated then the rates of decay will be different. In SM no. of baryons minus no. of leptons conserved. Excess Lepton no. could convert to excess baryon no. Therefore, explaining the asymmetry in the universe.

H

HN

HNHN

Implications on other physics (additional slide)

Extra Dimensions and String Theory: Neutrinos can move through extra dimensions from the three brane we are familiar with. Explains tiny mass and weak interactions.

Neutrino Communications: SETI search for extra terrestrial communications. Could one day be used on earth similar to radio waves. Advantages is they can pass through matter and are very fast. Disadvantage is that they are hard to detect.

Dark Matter: Non-baryonic dark matter contains neutrinos. Made of sterile neutrinos?

See saw MechanismSee saw Mechanism

Introduces a heavy right handed neutrino Introduces a heavy right handed neutrino for each light left handed neutrino.for each light left handed neutrino.Acquire mass through Dirac mass term on Acquire mass through Dirac mass term on same order as electroweak scale ~ same order as electroweak scale ~ 101022GeV.GeV.Small masses of left-handed Majorana Small masses of left-handed Majorana neutrinos created through pushing mass of neutrinos created through pushing mass of right handed neutrino to super high enery right handed neutrino to super high enery scale.scale.

Sterile NeutrinosSterile Neutrinos

Hypothetical particles – postulated due to Hypothetical particles – postulated due to LSND.LSND.

LSND – had excess of vLSND – had excess of vee..

Sterile neutrino needed to oscillate very Sterile neutrino needed to oscillate very weakly into mainly vweakly into mainly vee..

Two different mass schemes for extra Two different mass schemes for extra ΔΔmm22..MiniBoone in general did not find excess MiniBoone in general did not find excess of vof vee..

7300km Baseline7300km Baseline

Appearance Appearance probability for probability for vve e →v→vµ µ in in

matter.matter.

WhereWhere

Ref: hep-ph/0301257, “Neutrino Factories and the “magic” baseline”

7300km Baseline continued…7300km Baseline continued…

When When ΔΔA=nA=nππ, only the first term remains , only the first term remains therefore CP violating term has no effect.therefore CP violating term has no effect.

11stst non-trivial solution is when (√2)G non-trivial solution is when (√2)GFFnneeL=2L=2ππ..

Gives magic baseline equation of:Gives magic baseline equation of:

Corresponds to 7300km between Fermilab Corresponds to 7300km between Fermilab and Gran Sasso.and Gran Sasso.

3000km Baseline3000km Baseline

Optimal for CP violating phase.Optimal for CP violating phase.

Can distinguish between Can distinguish between θθ1313 and and δδ by by

comparing wrong sign muons and binning comparing wrong sign muons and binning energy of signal.energy of signal.

Total Flux through detector

• For detector at 7300km, side length after dead zone taken off: 20m

• Fraction of Flux on target: 5.195 E-4• Yearly flux on target:

• 5.195E17 X Efficiency of vμ type

• 5.195E17 X Efficiency of ve type

• Efficiency =used side length of storage ring ÷ total circumference of storage ring