# Presentation: 858644

## Searching for the Neutrino Magnetic Moment

-   e cross section
-  Čerenkov Radiation
-  Transition Radiation
-  Time-varying Fields
-  Stimulated Emission
-  Phase rotation

- Traditional:

- Non-Traditional:

- John Krane
- Iowa State University
- NuFACT’00

## Origin of the Magnetic Moment

-  Actually, the “effective moment”		  μeff = (μ2+d2)1/2
- also R-parity violating SUSY
- limited to <10-10 μB but SM expects more than109 smaller yet
- If neutrinos are massive, then to first order, SM says μ linearly dependent on neutrino mass

- c.f.: Lee and Shrock,PRD 16 1444 (1977)or                                        Marciano and Sanda,Phys Lett 67B 303 (1977)

## Traditional Method:measure the  e cross section

- Traditional approach followed by NuMu, HELLAZ, etc.  SM:  EM:
**For a NuFACT, there is no sig. E-dependence or charge-dependence. **

- c.f.: Miranda, Segura, Semikoz, and Valle,
- hep-ph/9906328

## Calculation of  e cross section

- High neutrino E does not help
- Quadratic dependence on mag moment
- Need a dedicated detector...yet can’t do much better than others

- To make a point, these plots were made with
- 10 MeV neutrinos; use
- 10 GeV and you won’t see a difference.

## Non-Traditional Methods

- The usual limitations might vanish
- Otherwise infinitesimal rates might become significant

- Because a NuFACT would give us unprecedented intensity and energy

## Čerenkov Radiation

- Consider a 1 km long water tank...
- With ultrarelativistic ’s, no E-dependence
- Quadratic in μ
- Numerical calculation for 2E20 ’s per year: 0.00033 photons per year...

- c.f. Grimus and Neufeld,Phys Lett B315 129 (1993)

## Transition Radiation

- From solar neutrino calculationsc.f. Grimus and Neufeld hep-ph 9410245
- Still quadratic in μ...
- Numerically integrating over  (for 2E20, 1E6 foils):4.5E-8 keV collected per year (X-rays are keV)

## TR: Small Adjustments, big gains?

- Lowering x-ray detection threshold from 20 keV to 5 keV gives you a factor of 100...but low efficiency in real detectors
- Increase p for big gains?
- Originally I was looking at a big reactor...2 meters away     ...I still am

## Resonant Cavity    for stimulated  conversion

- Essentially a low-energy photon target
- Stimulate (inverse-)radiative decays
- The fraction of converted neutrinos       ~ *quality*power*μ2
- No E-dependence as long as transition energy is much smaller

- C.f.: Vannucci, hep-ex 9911025

## ResCav:  No real limits for mm

- To get to a competitive limit, you need to notice a lack of 1 part in 1E17...
- The result could be framed in terms of  lifetime if you are interested
- Limits can improve for transition moments

- I assumed Q=1E9, 100 Watts

## Phase Rotation

- Decompose helicity and  into “left and right” components
- A transverse B-field can split these states
- While in the field, the  rotates from active to sterile and back (Dirac case)
- How long can we keep it in the B-field?

- Fritz DeJongh’s idea

## How Many Phase Rotations?

- Good news: depends on the product of B, t, and 
- Bad news: we can’t build a 1000 km magnetic field
- There is another way to do this...

- About 2 degrees of rotation...

- 1000 km

- Not !

## The One-way B-Gradient

-  enters the B field, experiences the gradient, energy states split, phase rotations begin
- B field goes to zero homogeneously in space; i.e., we turn it off (alternately, the cavity finishes its cycle)
- Because there is no spatial “return” gradient, the states never come back together and the phase rotations continue

- Silly mechanical example

## Now you don’t need      a huge field region

- A 400 MHz field needs a 0.75 m long homogeneous region
- Can put several fields in series
- Can raise B above 1 Tesla?

- About 2 degrees of rotation...

- 1000 km to detector

## A Notable Reference

- “Decelerating Neutral Dipolar Molecules,” Bethlem, Berden, and Meijer, Univ. of Nijmegen, PRL 83, 1558, 23 Aug. 1999.

- They changed the kinetic energy of CO molecules withelectric field stages. We propose splitting quantum states withmagnetic field stages.

- More info: One might also search SPIRES for (resonant) spin-flavor precession

## The Phase Rotation Experiment

- Find a “host” long-baseline experiment
- Generate a time-varying B at beam source,run with B for half the time,compare event rates with and without B
- Look for CC deficitor wrong-sign, wrong flavor neutrinos

- Dirac

- Majorana

## Sensitivity Estimate 1

- Dirac  case, where rotated  are sterile
- Assume 25% duty cyclefor the B field
- Compare CC cross section with and without field
- Normalized to 5000 events per year (50 ktons at 2800 km, 20 GeV muons)

## Sensitivity Estimate 2

- Majorana  case, where rotated  become ’
- Assume 25% duty cyclefor the B field
- Compare CC cross section with and without field
- Normalized to 5000 events per year (50 ktons at 2800 km, 20 GeV muons)

## I should say...

- Left to itself, the muon beam debunches.  We need bunches for the phase rotation scheme.
- Unless the muon beam is polarized, we won’t see Majorana neutrinos.  (Exception if we are very good at finding .)

## Summary

- Traditional search not viable at NuFact
- Čerenkov, TR fail
- Stimulated emission only competitive for  lifetime...interest?
- Phase Rotation is as good   as your B field