# Presentation: 448065

## neutrino fluxes 

**neutrino fluxes**** **
**can be determined to ****+- ****10****-3 **
**at a ****Neutrino Factory?**

- source: M. Apollonio et al,
**OSCILLATION PHYSICS WITH A NEUTRINO FACTORY**
- arXiv:hep-ph/0210192 v1 13 Oct 2002

**Flux Control and Resulting Constraints on the Decay Ring Design**

## -- Neutrino Factory – CERN layout

**************e****+**** ********e**************

**_**

**interacts**
** ****giving **********

**oscillates ********e**********************
**interacts giving**************
**WRONG SIGN MUON**

**10****16****p/s**

**1.2 10****14 ********s =1.2 10****21 ********yr**

**3 10****20 ********e********yr**
**3 10****20 ****************yr**

**0.9 10****21 ********yr**

## why? 

- In the high intensity scenario
- the event rates in the far detector are above 10**9**./yr/Mton
- precision measurement of the mixing angle and mass differences.
- 2. the event rates in the near detectors are  at the level of 10**8**/yr/kg
- precision measurements of total cross-sections
- structure functions
-  SM tests etc...

## Detector

- Iron calorimeter
- Magnetized
- Charge discrimination
- B = 1 T
- R = 10 m, L = 20 m
- Fiducial mass = 40 kT

**Baseline**

**3500 Km**

**732 Km**

- 3.5 x 107

- 1.2 x 106

- 5.9 x 107

- 2.4 x 106

- 1.1 x 105

- 1.0 x 105

********** ****CC**

******e**** CC**

********  **signal ****(sin****2**** ********13****=0.01)**

- Events for 1 year

**Also: L Arg detector: magnetized ICARUS **
**Wrong sign muons, electrons,**** taus**** and NC evts      *->**

## Neutrino fluxes    + -> e+ e 

**********/******** e ****ratio reversed by switching ******************
******e************ spectra are different **
**No high energy tail. **
**Very well known flux (aim is 10****-3****)**
**- absolute flux measured from muon current **
** ****or by ************e******** -> ************ ********e ****in near expt.**** **
**-- in ****triangle ring****, **
**muon polarization precesses and averages out **
**(****preferred****, -> calib of energy, energy spread)**
**-- E&************ calibration from muon spin precession**
**-- angular divergence: small effect if ********< 0.2/******
**can be monitored**
**-- in ****Bow-tie ring,**** **
**muon polarization stays constant, no precession**
**       ****20% easy -> 40% hard**
**  ****Must be measured!!!! (precision?)**

****** ****polarization controls ********e**** flux: **
******+ ****-X> ********e****  ****in forward direction**

- Main parameters to MONITOR
-    1. Total number of muons circulating in the ring,
-    2. muon beam polarisation,
-    3. muon beam energy and energy spread,
-    4. muon beam angle and angular divergence.
-    5. Theory of decay, including radiative effects
- Beam shape parameters are crucial for:
-                            the measurement of oscillation length (i.e.m2 )
- Absolute normalisation is essential for
-  		   the measurement of the mixing angles.
- The relative normalisation of the two muon charges crucial for:
-                              CP asymmetries.

-  System where one stores a beam of decaying particles
- Neutrino Factory, (and Beta Beam?)
- potential for excellent neutrino flux control

## alternative: count the electrons at the exist of a straight. 

- Total beam current:  Beam Current Transformer
-        -- difficulties:
-            1. presence of decay electrons in the ring?
-            *Keil * *CERN-NUFACT Note 54 (2000), **showed that the electrons are swept in the arcs and destroyed. Since the lifetime is 200 turns, the maximum fraction of electrons is 0.3/200 = 1.6 10**-3** at the ****end ****of a straight section, much less at the entrance of it. *
-         Monitor should be placed at entrance of straight section.
-            2. absolute calibration? 10-3 difficult, not impossible.
-            3. the most practical way to cross-normalize vsfluxes
- alternative: count the electrons at the exist of a straight.
-            this has a nice feature of counting the decays!
-            the acceptance of the monitor (see polarimeter later) is tricky

## -- better: e- e in a dedicated near detector.

- -- Near detector will measure product of flux X cross-section
- -- better: **************e****-**** ********************e **in a dedicated near detector.
**type of detector: **
**ring imagind water cerenkov, **
**LA detector, **
**pressurized gas detector.  **
- small mass is enough as rates are high but cross-section is quite small.  (104 ev/kg/yr. need 100 kg.)
- Main problem is determination of fiducial mass.
- This provides an absolute normalization of the flux in the same way as bhabha scattering in e+e- colliders.
- Limitations: threshold (11 GeV) & only for stored beam
-         alternative is ******x****e****-**** ****************x********e****- **  (assumes SM)

## + -X> e  in forward direction

**Has a huge effect on the flux! **
******e ****flux varies by 100% **
**when P goes from –1 to +1**

****** ****polarization controls ********e**** flux: **
******+ ****-X> ********e****  ****in forward direction**

**Muon polarization **

## Muon Polarization

**muons are born longitudinally polarized in pion decay (~18%) **
**depolarization  is small ****(Fernow &Gallardo)****  **
**effects in electric and magnetic fields is (mostly) described by spin tune:**

- which is small: at each kick of a 200 MeV/c muon the polarization
- is kicked by 
- in the high energy storage ring polarization precesses. Interestingly
- for a beam energy of 45.3112 GeV: at that energy it flips at
- each turn.

## Muon Polarization

- muon polarization is too small to be very useful for physics
- (AB, Campanelli) but it must be monitored.
- In addition it is precious for energy calibration  (Raja&Tollestrup, AB)

- a muon polarimeter would perform the momentum analysis of the
- decay electrons at the end of a straight section.
- Because of parity violation in muon decay the ratio of high energy
- to low energy electrons is a good polarization monitor.

## # positons with E in [0.6-0.8] E

- here is the ratio of
- # positons with E in [0.6-0.8] E****
- to number of muons in the ring.
-  There is no RF in the ring.
- spin precession and
- depolarization are clearly visible
- This is the Fourier Transform
- of the muon energy spectrum
- (AB)
- amplitude=> polarization
- frequency => energy
- decay => energy spread.

-  E/E and E/E to 10-6
- polarization to a few percent.

## If there is RF in the storage 

- If there is RF in the storage
- ring to keep the muons
- bunched, depolarization
- is suppressed.
- (synchrotron oscillations)

- Even in this case,
- the muon polarization,
- averaged over ~500 turns
- is very small
- (<<0.18/500 = 410-4)
- and will be monitored.

##                  end of the bow tie.   

- This was true for a race track or triangle decay ring,
- in which polarization precesses.
- A bow-tie has been suggested to avoid this spin precession and
- depolarization (net bend is zero, so muon polarization does
- not precess either)
- This has several inconvenients:
- -- P is different for the two straights (who shall be pleased?)
- -- P cannot be reversed
- -- E and  E) can no longer be measured
- -- in  order to know the flux to 0.1% on must know P to 0.1% and
- this is hard!
-                  **end of the bow tie.   **

## CERN baseline scenario

**CERN baseline scenario**

## this corresponds to  = 0.5 m /E

- If the muons have transverse momentum comparable to that of
- muon decay (50 MeV) the neutrino beam will  be seriously degraded
- this corresponds to  = 0.5 m****** **/E********

- in order for the effect of beam divergence to affect the flux by less than
- a few 10-3 beam divergence must be very small.

- I. Papadopoulos has calculated the effect.

## Slide 17

## Divergence MUST be measured. 

**divergence of 0.1/******** keeps 95% of the original flux. **
**Straight section with this property were designed for the US Study II and by ****Keil**
- Divergence MUST be measured.
- A gas Cerenkov device to measure the beam emittance was devised by Piteira.
- Various efects were considered (optical aberrations, heating of gas, multiple scattering,
- etc...and concluded that the divergence is easier to measure the bigger it is
- so that this should not be a problem)

## Schematic of a muon beam divergence measurement device. A low-pressure He gas volume is contained by windows (one of which must be transparent) within a straight section of the the muon decay ring. The Cerenkov light is collected by a parallel to point optics in the direction of interest, so as to provide an image of the angular distribution of particles in the focal plane.

## Radiative effects

- Ratio of 1st/0th order neutrino flux

- by Broncano & Mena

- Dominated by the presence of a photon in the final state, which
- reduces the energy of the neutrino and thus the flux in forward direction.
*(the total number of neutrinos emitted is constant of course) *
- Effect is –0.4% with a slight distortion of the end-point.
- Error is small fraction thereof.

##                           Main parameters to MONITOR

-    1. Total number of muons circulating in the ring,
-                     BCT, near detector for purely leptonic processes
-    2. muon beam polarisation,
-                     polarimeter
-    3. muon beam energy and energy spread,
-                     race-track or triangle. NO BOW-TIE!
-                     +polarimeter
-    4. muon beam angle and angular divergence.
-                     straight section design
-                     +beam divergence monitors e.g. Cerenkov
-    5. Theory of decay, including radiative effects
-                     OK
- Yes, we believe that the neutrino flux can be monitored to 10-3 IF
-      + design of accelerator foresees sufficient diagnostics.
-      + quite a lot of work to do to design and simulate these diagnostics.

-  Conclusions I

## Main parameters to MONITOR

-    1. Total number of ions circulating in the ring,
-                 BCT, near detector for purely leptonic processes
-    2. ion beam polarisation, NO they are spin 0! no problem
-    3. ion beam energy and energy spread,
-               no polarization -- need magnetic field measurement.
-               precision required a few 10-4 (evt. rate goes like E3)
-    4. ion beam angle and angular divergence.
-                     beam divergence monitor e.g. Cerenkov
-    5. Theory of ion decay, including radiative effects
-                     To be done
-  neutrino flux can probably be monitored to 10-3
-          – somewhat more difficult than for muons, but not impossible.
- provided:
-      + design of accelerator foresees sufficient diagnostics.
-      + quite a lot of work to do to design and simulate these diagnostics.

-  Conclusions II: and the Beta-beam?

## CONCLUSIONS

- the configuration of a storage ring as neutrino source provides
- as expected, extrememly high precision on the absolute flux.
- The neutrino factory is extremely favourable in this respect, thanks
- in part to beam polarization. Triangle or racetrack are preferred.
- The basic elements of beam monitoring have been identified.
- Beta beams have similar qualities although somewhat less easily
- achieved. The event rates are lower because of the lesser energy.
- Storage ring source = Precision neutrino physics!