Making money with neutrinos...Neutrino and anti-neutrino fluxes in the absence of oscillation at L = 10 000 Km from a neutrino factory in wich 2x1021 muons have decayed in the beam

Making money withneutrinos …

Friday 20th July, INSS 2012 problem presentation

R. Castillo, M. Reeves, C. Sun, L. Yang

?

The question

● What kind of neutrino source would be viable?

● What kind of effects would the signal experience in transmission through the earth?

● How should the information be sent?

● What kind of detector should be used to receive the signal?

“Imagine you were trying to set up a fast communications link using neutrinos to do insider trading (see forbes article) What kind of neutrino detector and neutrino source would you need for this to work?”

Our approach

Show me the money!

“... High-frequency traders are notoriously secretive about divulging trading times even to colleagues within their own firms, since any such time-dependent trading edge can be fleeting. But many programmed trades are now known to take place within milliseconds or less.

“Thirty milliseconds is a lot of time in high-velocity trading,” said former J.P. Morgan Chase options trader Espen Gaarder Haug, an expert in automated high-frequency trading, and a professor of finance at the Norwegian University of Life Sciences near Oslo. ...” http://www.forbes.com/sites/brucedorminey/2012/04/30/neutrinos-to-give-high-frequency-traders-the-

millisecond-edge/2/

Neutrino Factory

FFAG 100 GeV

4

Composition and spectra of intense neutrino beams from muon storage ring

will be determined by the charge, momentum and polarization of stored

muons through decays.

Stored muons energy, Eµ = 100 GeV

>4billion dollars More varibles to use on the encoding message

Muon neutrino distribution energy and angles at muon rest frame:

Electron anti-neutrino distribution energy at muon rest frame:

Total neutrino and anti-neutrino interaction rates per muon decay:

Neutrino and anti-neutrino fluxes in the absence of oscillation at L = 10 000 Km from

a neutrino factory in wich 2x1021 muons have decayed in the beam.

Muon stored energy = 100 GeV -> neutrino flux= ~4x1011 m-2year-1 at L = 10 000 Km

Collimated with an aperture an aperture angle of 1/νμ ~0.00105

Muon gamma factor = 946

Long muon decay pipe needed.

Neutrino Oscilla/on in Vacuum

να = Uαk*

k∑ ν k

ν k (t) = e−iEkt ν k

Pνα→νβ(t) = Uαk

* UβkUα jk, j∑ Uβ j

* e−i(Ek−Ej )t

Ek −Ej ≅Δmkj

2

2E

Pνα→νβ(L,E) = sin2 2θ sin2(1.27Δm2 L

E)∝ L

E'

()

*

+,2

Neutrino Oscilla/on in Ma3er

Ma3er-‐induced poten/al of neutrinos With energy , the 1-‐2 mixing is strongly suppressed by ma3er. The problem is reduced to an effec/ve two-‐flavor one.

V (x) ≡ 2GFN e(x)Electron number density in ma3er N e(x)

E > Δm312 / 2V

Δm2 ≡ Δm312 ,θ ≡θ13


P2 ≡ P(νe ↔νa )νa = sinθ 23νµ + cosθ23ντP(νe ↔νµ ) = sin

2θ23P2P(νe ↔ντ ) = cos

2θ23P2

Transi/on Probability


P2 = (Δm2

4E)2 sin2 2θ dx

0

L

∫ e−i2φ (x )2

L is the neutrino path length in ma3er, Φ(x) is the phase acquired.


When neutrino don’t cross the Earth’s core( cosΘ>-‐0.837), Θ is the zenith angle of the neutrino trajectory, and so experience a slowly changing poten/al V(x), the accuracy of the approxima/on is very good even in the MSW resonance region E~5-‐8GeV. The ma3er density profile of the earth sa/sfies, , where V’ is the change of poten/al over the oscilla/on length for slowly changing density. And therefore for oscilla/on in the earth this approxima/on is expected to work well. This is fulfilled in the high energy limit.

V '/V ≤ 0.5


PRL 95, 211801 (2005)

Neutrino Interac/on in Ma3er

Eν =100GeVσ ~10−36cm2


The interac/on length of a neutrino The distance from New York to Tokyo

Lint =1

σρNA

~1015m

5.5×106m


Pb =zLint

~ 10−8 ~ 0

Conversion Probability

PhysRevLe3.88.161102

SignalRough estimation through an example

EncodingAnalogue to digitalA ’bit’ details regarding networkDecodingOscillation correctionBackground noiseExperiment

The signal is expressed by using eitherΦνe

Φνµ

orΦνµ

Φνe

, which makes

the communication more reliable by comparison with each other.For the first generation of this communication station, we are justconsidering some easy binary signal, 1 and 0. In the future it is alsopossible to make the transmission in other radix, like hexadecimal.

∫dE Φµ+ ·

(dΓµ+→νµνee+

dE

)∫dE Φµ− ·

(dΓµ−→νµνee−

dE

) (1)

M. Reeves, L. Yang, C. Sun, R. Castillo Neutrino Fast Link Communication



After we set a certain gate of number of events, we can have adigital signal. (—resolution, hexadecimal)

1

0

1´107

2´107

3´107

4´107

5´107

6´107

un-normalized ð of events




ASCII (American Standard Code for Information Interchange)

I only use capital A (��01000001) to Z (��01011010)

I A (�01000001) to Z (�01011010) and 0 (�00110000) to 9(�00111001)

I the word ’INSS’ is coded as 20 bits ’001001/ 001110/010011/ 010011’ and being encapsulated as 84 with controlsequence






I A (�01000001) to Z (�01011010) and 0 (�00110000) to 9(�00111001)







I A (�01000001) to Z (�01011010) and 0 (�00110000) to 9(�00111001)





In this case, two-layer network model, physical layer(bit as unit)and data link (frame as unit)

Figure: Open Systems Interconnection (OSI) modelM. Reeves, L. Yang, C. Sun, R. Castillo Neutrino Fast Link Communication



logic network → network layer. extra data encryption/ compression→ presentation layer, etc. More control sequence → lowers speed

Figure: Open Systems Interconnection (OSI) modelM. Reeves, L. Yang, C. Sun, R. Castillo Neutrino Fast Link Communication



For the µ+ and µ− beam, we can either use ratio of producedneutrino∫

dE Φµ+ ·(dΓµ+→νµνee+

dE

)· σνee→νee(E ) ·��Ntargets∫

dE Φµ− ·(dΓµ−→νµνee−

dE

)· σνµe→νµe(E ) ·��Ntargets

(2)

or ratio of anti-neutrino events∫dE Φµ− ·


dE

)· σνee→νee ·��Ntargets∫

dE Φµ+ ·(dΓµ+→νµνee+

dE

)· σνµe→νµe ·��Ntargets

(3)




or the total,

∫dE Φµ− ·


dE

)·[σνee→νee(E ) + σνµe→νµe(E )

]∫dE Φµ+ ·

(dΓµ+→νµνee+

dE

)·[σνµe→νµe(E ) + σνee→νee(E )

] (4)




∫dE Φ

µ+

dΓµ+→νµνe e+

dE

[Pνe→νe

+ P(−)ν x→νe

]σνe e→νe e(E) + [Pνµ→νµ + P

(−)ν x→νµ

]σνµe→νµe (E)

∫

dE Φµ−

dΓµ−→νµνe e−

dE

[Pνe→νe + P

(−)ν x→νe

]σνe e→νe e (E) + [Pνµ→νµ+ P

(−)ν x→νµ

]σνµe→νµe (E)

(5)

where the P’s are the survival/ oscillation probability for (−)νe and (−)

ν µ

respectively.




The background affects the recognizability of the signal and theinformation density, thus the bandwidth. But as far as we still havethe peak, it is possible to send the message.

1

0

1´107

2´107

3´107

4´107

5´107

6´107





Experimentally, when we are encoding and decoding, we also needto consider the signal pattern and and signal analysis, which Ididn’t include much here..refer to ’Demonstration of Communication Using Neutrinos’,(arXiv: 1203.2847v2 [hep-ex]).on-off-keying(OOK), and short distance 1.035km



Based on The OscSNS White Paper, it uses the followingprocessed to produce neutrinos,

p + Hg →π−π+ (6)

π+ →µ+νµ (7)

µ+ →e+νeνµ (8)

It has a νe flux of 5.45 · 1013ν/year/cm2, and a 6 meter radiussphere target full of CH2. If we use the formula

5.45 · 1013ν/year/cm2 · σνee−→νee− · 8 · 3.35 · 1031e−targets (9)

it gives us a number of 1302 ± 14 mean events per year at thedetector (receiving station). Suppose we require a transmissionrate of at least 1 s−1, i.e. 60 · 60 · 24 · 365 = 3.1536 · 108 (y−1),which requires a 105 times lager target, i.e a spherical target withradius of 278 meters. Of course stronger flux also helps.



Future idea

0123456789ABCDEF

1 ´ 107

2 ´ 107

3 ´ 107

4 ´ 107

5 ´ 107

6 ´ 107


fine tuning LE to use oscillation to encode info–next gen of νphone


Detection● Detector situated on far side of planet close to financial centre,

maximise benefits of neutrino's shorter path length.

● Must be able to resolve neutrino detection in real time → Imaging detector

● Must be able to resolve differences between particle/antiparticle and νe / νμ

Expected events ...

http://cupp.oulu.fi/neutrino/nd-cross.html

These approximate results are also valid for muon and tau -neutrinos at high energies.

Detectors● Water Cherenkov – at 100 GeV ~ Assume

~100% PID efficiency

● Put B field across detector to distinguish lepton product of DIS interaction → full flux resolution

● 100m radius x 100 m depth ~ 1 Mton

● Ntarget ~ 3.3x1028 x Vol = 1.036x1035

● Nevents ~

● Nevents too low require an increase in detector size by a factor of 1x105 or an increase in flux by 1x105 or a combination of both

● S-K ~ $90 million scaling up … ~ a few billion

● Future Detector – more events, more/quicker information

● Large liquid Argon TPC

● If the same radius Argon:Water Cherenkov Nevents ~ 6:1

● Nevents ~

● Also too small, but only requires scaling of 1x104

Conclusions and the future ...● Currently to get a “useful” neutrino rate that could in any

way compete with current light based communication is impractical

● In the future if a sufficiently intense source/large detector be made then neutrino communication could become feasible

● Business person of the future needs a neutrino detector on the go …

● Size of a watch … 10 x10 x 10 cm

● Using orbital mobile neutrino factory

● Ntarget required 3.13 x 1039 in 10 cm3

● Using Av constant would produce 5.19x1015 moles of Hydrogen

● Giving approx density of 5.9 x 109 kg/m3

● A little bit over the density of a White Dwarf Star!

Documents

Making money with neutrinos...Neutrino and anti-neutrino fluxes in the absence of oscillation at L = 10 000 Km from a neutrino factory in wich 2x1021 muons have decayed in the beam