Monochromatic beam - (NBB) – WBB Some (purely speculative) thoughts

1. Monochromatic beam - (NBB) – WBBSome (purely speculative) thoughts Golden 07 IFIC, Valencia June 28, 2007Walter Winter Universität Würzburg

2. Contents • How many measurements? • “Good” detector versus “good” beam? • Statistics • Systematics • Discussion Mono vs WBB - Walter Winter

3. Appearance channels: nmne • Complicated, but all interesting information there: q13, dCP, mass hierarchy (via A) (Cervera et al. 2000; Freund, Huber, Lindner, 2000; Freund, 2001) Mono vs WBB - Walter Winter

4. How much tells us one number? f • Suppose we measure Papp(L1,E1)+ fix q12, q23, Dm212, Dm312, r • Obtain curve f(q13,d)=const. • Need second measurement, e. g. anti-n: • Obtain curve g(q13,d)=const. • Still remaining discrete degeneracies, e.g. intrinsic degeneracy (Burguet-Castell et al, 2001) • Need (at least) a third complementary measurement: e.g. at E2, L2 etc. g Best-fit Mono vs WBB - Walter Winter

5. The straightforward choice: En • In general: N sufficiently indep./uncorrelated (high statistics) measurements to measure N parameters • Use different neutrino energies at the same L • Distentangle solutions sin22q13=0.05 (Minakata, Nunokawa, 2001) Mono vs WBB - Walter Winter

6. Use wide-band beam Detector needs to separate events from different neutrino energies Examples: NF@MIDBB@WC (QE events)WBB@WC (QE events) Energy binning! Use monochromatic beam Detector does not need to seperate events from different energies Example: Electron capture beam@WC (QE & non-QE events?) Time binning! „Good“ detector vs. „good“ beam Mono vs WBB - Walter Winter

7. Wide-band beam:Split into two energy bins Monochromatic beam:Split into to „time“ bins with different g: Example: Beta beamsEnergy binning vs. time binning Assume fixed total number N of useful ion decays at source, two bins n1 n2 n1 n2 E1 E2 g1 g2 t E • Note that in both cases: N  n1+n2 (modulo E-dep.) • But: Energy resolution mixes up energy bins; bad!? Mono vs WBB - Walter Winter

8. Statistics (beta beams) • Is statistics really the main issue for a monochromatic versus wide-band beta beam? • For isotopes similarly difficult to produce: probably no! (modulo endpoint energy) • Does the statistics issue reduce to the simple comparison of isotopes (end point energy andeffort to produce a certain number ions) for BBs? • g‘s have to be chosen physics-wise, not „event“-wise (=as high as possible) for a monochromatic beta beam (cf., neutrino factory: advantage for precision instrument, problem for a discovery machine?) Mono vs WBB - Walter Winter

9. The use of more bins(overconstraining the measurement) • Usually: use WBB and N >> 2 bins • Advantages: • Little technical effort for N >> 2 compared to N=2But: N >> 2 required if more than just q13 and dCP to measure! • Most systematical errors are somehow correlated among the bins; e.g. flux normalization, time-dep. effects • Monochromatic beam: very likely uncorrelated errors between the bins! How large? Mono vs WBB - Walter Winter

10. Example: NBB versus WBB • Compare e.g. • T2KK: NBB with two different L‘s (similar to two g‘s?), WC detectors („large detectors“) • WBB-120: WB-SB at one baseline, liquid argon TPC („good detector“) • WBB is more robust with respect to systematics and Dm312 • Similar conclusions likely for WBB versus monochromatic beam? (Barger et al., hep-ph/0703029) Mono vs WBB - Walter Winter

11. Discussion • How many different measurements (such as energies) does one want/need? What about antineutrino running? • Machine+statistics:Does the whole statistics discussion reduce to the question what the simplest method is toobtain 1018 useful ion decays leading to a certain spectrum? How much effort is it to adjust the g? • Systematics@ any monochromatic beam:blessing or curse? Mono vs WBB - Walter Winter