Monochromatic beam - (NBB) – WBBMonochromatic beam - (NBB) – WBBSome (purely speculative) thoughtsSome (purely speculative) thoughts

Golden 07Golden 07IFIC, ValenciaIFIC, Valencia

June 28, 2007June 28, 2007

Walter WinterWalter WinterUniversität WürzburgUniversität Würzburg

June 28, 2007 Mono vs WBB - Walter Winter 2

ContentsContents How many measurements?How many measurements? ““Good” detector versus “good” beam?Good” detector versus “good” beam? StatisticsStatistics SystematicsSystematics DiscussionDiscussion

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Appearance channels: Appearance channels: ee

Complicated, but all interesting information there: Complicated, but all interesting information there: 1313, , CPCP, mass hierarchy (via A), mass hierarchy (via A)

(Cervera et al. 2000; Freund, Huber, Lindner, 2000; Freund, 2001)

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How much tells us one number?How much tells us one number?

Suppose we measure PSuppose we measure Pappapp(L(L11,E,E11))+ fix + fix 1212, , 2323, , mm2121

22, , mm313122, ,

Obtain curve f(Obtain curve f(1313,,)=const.)=const. Need second measurement, Need second measurement,

e. g. anti-e. g. anti-Obtain curve g(Obtain curve g(1313,,)=const.)=const.

Still remaining discrete degeneracies, e.g. intrinsic Still remaining discrete degeneracies, e.g. intrinsic degeneracy degeneracy (Burguet-Castell et al, 2001)(Burguet-Castell et al, 2001)

Need (at least) a third complementary Need (at least) a third complementary measurement: e.g. at Emeasurement: e.g. at E22, L, L22 etc. etc.

Best-fit

f

g

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The straightforward choice: EThe straightforward choice: E In general: N In general: N

sufficiently indep./sufficiently indep./uncorrelated (high uncorrelated (high statistics) statistics) measurements to measurements to measure N parametersmeasure N parameters

Use different neutrino Use different neutrino energies at the same Lenergies at the same L

Distentangle solutionsDistentangle solutions

(Minakata, Nunokawa, 2001)

sin2213=0.05

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„„Good“ detector vs. „good“ beamGood“ detector vs. „good“ beam

Use Use wide-band beamwide-band beam Detector needs to separate Detector needs to separate

events from different events from different neutrino energiesneutrino energies

Examples: Examples: NF@MIDNF@MIDBB@WC (QE events)BB@WC (QE events)WBB@WC (QE events)WBB@WC (QE events)

Energy binning!Energy binning!

Use Use monochromatic beammonochromatic beam Detector does not need to Detector does not need to

seperate events from seperate events from different energiesdifferent energies

Example: Example: Electron capture Electron capture beam@WC beam@WC (QE & (QE & non-QE events?non-QE events?))

Time binning!Time binning!

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Example: Beta beamsExample: Beta beams

Energy binning vs. time binningEnergy binning vs. time binning

Wide-band beam:Wide-band beam:Split into two energy Split into two energy binsbins

Monochromatic beam:Monochromatic beam:Split into to „time“ Split into to „time“ bins with different bins with different

Assume fixed total number N of useful ion decays at source, two bins

E1 E2 1 2tE

Note that in both cases: N Note that in both cases: N n n11+n+n22 (modulo E-dep.) (modulo E-dep.)

But: Energy resolution mixes up energy bins; bad!?But: Energy resolution mixes up energy bins; bad!?

n1 n2 n1 n2

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Statistics (beta beams)Statistics (beta beams) Is statistics really the main issue for a monochromatic Is statistics really the main issue for a monochromatic

versus wide-band beta beam?versus wide-band beta beam? For isotopes similarly difficult to produce: For isotopes similarly difficult to produce:

probably no! (modulo endpoint energy) probably no! (modulo endpoint energy) Does the statistics issue reduce to the simple Does the statistics issue reduce to the simple

comparison of isotopes (end point energy andcomparison of isotopes (end point energy andeffort to produce a certain number ions) for BBs?effort to produce a certain number ions) for BBs?

‘‘s have to be chosen physics-wise, not „event“-wise s have to be chosen physics-wise, not „event“-wise (=as high as possible) for a monochromatic beta beam (=as high as possible) for a monochromatic beta beam (cf., neutrino factory: advantage for precision (cf., neutrino factory: advantage for precision instrument, problem for a discovery machine?)instrument, problem for a discovery machine?)

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The use of more binsThe use of more bins(overconstraining the measurement)(overconstraining the measurement)

Usually: use WBB and N >> 2 binsUsually: use WBB and N >> 2 bins Advantages:Advantages:

– Little technical effort for N >> 2 compared to N=2Little technical effort for N >> 2 compared to N=2ButBut: N >> 2 required if more than just : N >> 2 required if more than just 1313 and and CPCP to measure!to measure!

– Most systematical errors are somehow correlated Most systematical errors are somehow correlated among the bins; e.g. flux normalization, time-dep. among the bins; e.g. flux normalization, time-dep. effectseffects

Monochromatic beam: very likely uncorrelated Monochromatic beam: very likely uncorrelated errors between the bins! How large?errors between the bins! How large?

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Example: NBB versus WBBExample: NBB versus WBB

Compare e.g. Compare e.g. – T2KK: NBB with two different L‘s T2KK: NBB with two different L‘s

(similar to two (similar to two ‘s?), WC detectors („large detectors“)‘s?), WC detectors („large detectors“)– WBB-120: WB-SB at one baseline, liquid argon TPC („good detector“)WBB-120: WB-SB at one baseline, liquid argon TPC („good detector“)

WBB is more robust with respect to systematics and WBB is more robust with respect to systematics and mm313122

Similar conclusions likely for WBB versus monochromatic Similar conclusions likely for WBB versus monochromatic beam?beam?

(Barger et al., hep-ph/0703029)

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DiscussionDiscussion How many How many different measurementsdifferent measurements (such as (such as

energies) does one want/need? What about energies) does one want/need? What about antineutrino running?antineutrino running?

Machine+statistics:Machine+statistics:Does the whole statistics discussion reduce to the Does the whole statistics discussion reduce to the question what the simplest method is toquestion what the simplest method is to obtain 10obtain 101818 useful ion decays leading to a certain spectrum? useful ion decays leading to a certain spectrum? How much effort is it to adjust the How much effort is it to adjust the ??

SystematicsSystematics @ any monochromatic beam:@ any monochromatic beam:blessing or curse?blessing or curse?