1. Optimization of a neutrino factory oscillation experiment 3 rd ISS Meeting Rutherford Appleton Laboratory, UK April 25-27, 2006 Walter Winter Institute for Advanced Study, Princeton

2. April 25, 2006ISS RAL NuFact - Walter Winter2 Contents Introduction Introduction Optimization summary: L-E  Optimization summary: L-E  Improved detector summary Improved detector summary Channel requirements Channel requirements –Some phenomenology: Why are other channels useful? –Platinum –Silver Where to concentrate the efforts? Synergies? How does the optimal neutrino factory look like? Where to concentrate the efforts? Synergies? How does the optimal neutrino factory look like? Comparison to beta beams Comparison to beta beams Summary Summary See my talk(s) at KEK and Patrick’s talk in Boston

3. April 25, 2006ISS RAL NuFact - Walter Winter3 Appearance channels  Complicated, but all interesting information there:  13,  CP, mass hierarchy (via A) (Cervera et al. 2000; Freund, Huber, Lindner, 2000; Freund, 2001)

4. April 25, 2006ISS RAL NuFact - Walter Winter4 Correlations and degeneracies Connected (green) or disconnected (yellow) degenerate solutions (at a chosen CL) in parameter space Connected (green) or disconnected (yellow) degenerate solutions (at a chosen CL) in parameter space Affect performance of appearance measurements. For example,  13 sensitivity Affect performance of appearance measurements. For example,  13 sensitivity (Huber, Lindner, Winter, 2002) Discrete degeneracies: (also: Barger, Marfatia, Whisnant, 2001) Intrinsic ( ,  13 )-degeneracy (Burguet-Castell et al, 2001) sgn-degeneracy (Minakata, Nunokawa, 2001) (  23,  /2-  23 )-degeneracy (Fogli, Lisi, 1996) Discrete degeneracies: (also: Barger, Marfatia, Whisnant, 2001) Intrinsic ( ,  13 )-degeneracy (Burguet-Castell et al, 2001) sgn-degeneracy (Minakata, Nunokawa, 2001) (  23,  /2-  23 )-degeneracy (Fogli, Lisi, 1996)

5. April 25, 2006ISS RAL NuFact - Walter Winter5 Combine with “silver channels” e ->  (Donini, Meloni, Migliozzi, 2002; Autiero et al, 2004) Combine with “silver channels” e ->  (Donini, Meloni, Migliozzi, 2002; Autiero et al, 2004) Combine with “platinum channels”  -> e ( sin 2 2  13 > 10 -3 ? Depends on BG-level!) (Boston workshop: Patrick’s talk) Combine with “platinum channels”  -> e ( sin 2 2  13 > 10 -3 ? Depends on BG-level!) (Boston workshop: Patrick’s talk) Better detectors: Higher energy resolution, higher efficiencies at low energies (CID!) (discussed at KEK, Boston) Better detectors: Higher energy resolution, higher efficiencies at low energies (CID!) (discussed at KEK, Boston) Second NF baseline: “Magic baseline” ( sin 2 2  13 > 10 -4 ) (Lipari, 2000; Burguet-Castell et al, 2001; Barger, Mafatia, Whisnant, 2002; Huber, Winter, 2003; others) Second NF baseline: “Magic baseline” ( sin 2 2  13 > 10 -4 ) (Lipari, 2000; Burguet-Castell et al, 2001; Barger, Mafatia, Whisnant, 2002; Huber, Winter, 2003; others) Other possibilities? Other possibilities? NF-Strategies to resolve degeneracies How much does what help? Where to concentrate the efforts?

6. Optimization of a neutrino factory 4 yr x 1.06 10 21  + decays + 4 yr x 1.06 10 21  - decays Detector: 50 kt magnetized iron calorimeter ISS-values? 100 kt, 5+5 years running time = factor 2.36 luminosity increase for 10 21 useful decays/year Most of the following work is done in collaboration with P. Huber M. Lindner M. Rolinec

7. April 25, 2006ISS RAL NuFact - Walter Winter7 Optimization summary: L-E  Example:  13 sensitivity relative to minimum in each plot (5  – new!) Example:  13 sensitivity relative to minimum in each plot (5  – new!) “Magic baseline” good degeneracy resolver “Magic baseline” good degeneracy resolver L ~ 2000 – 4000 km good for statistics L ~ 2000 – 4000 km good for statistics E  > 40 GeV E  > 40 GeV At 5  very robust to At 5  very robust to –Threshold effects –  m 31 2 larger –Luminosity (Huber, Lindner, Rolinec, Winter, to appear)

8. April 25, 2006ISS RAL NuFact - Walter Winter8 CP violation and mass hierarchy L ~ 3000 – 5000 km good for CP violation (large  13 : 1500 – 6000) L ~ 3000 – 5000 km good for CP violation (large  13 : 1500 – 6000) L > 6000 km necessary for mass hierarchy (if small  13 ) L > 6000 km necessary for mass hierarchy (if small  13 ) Use 4000 and 7500 km (“magic baseline”) as standard baselines Use 4000 and 7500 km (“magic baseline”) as standard baselines CP violationMass hier.

9. April 25, 2006ISS RAL NuFact - Walter Winter9 Improved (golden) detector summary Better energy resolution? Was: 0.15 x E (approximation) Improve to: ? Better energy resolution? Was: 0.15 x E (approximation) Improve to: ? Lower appearance threshold? Was: 4 GeV, linearly climbing to maximum at 20 GeV Improve to: Max. already at 1 GeV? Lower appearance threshold? Was: 4 GeV, linearly climbing to maximum at 20 GeV Improve to: Max. already at 1 GeV? CC/NC Backgrounds: Assume BG fraction  x E -2 such that ~ 5 x 10 -6 integrated over spectrum (  ~ 10 -3 ) CC/NC Backgrounds: Assume BG fraction  x E -2 such that ~ 5 x 10 -6 integrated over spectrum (  ~ 10 -3 )  Background increases at low energies  Even if CID improved, NC background limits performance! (Fig. from Huber, Lindner, Winter, 2002; Gray curve from Cervera et al, 2000) (Cervera et al, 2000)

10. April 25, 2006ISS RAL NuFact - Walter Winter10 Improved detector: MH and CP violation Improved detector would be excellent degeneracy resolver! Improved detector would be excellent degeneracy resolver! Also: E  = 20 GeV possible (while 50 GeV do not harm) Also: E  = 20 GeV possible (while 50 GeV do not harm) Blue shading: Optimization potential: Golden*

11. April 25, 2006ISS RAL NuFact - Walter Winter11 Improved detector: Systematics CP violation measurement very robust with respect to systematics (signal normalization error) and BG level as long as  10 -2 CP violation measurement very robust with respect to systematics (signal normalization error) and BG level as long as  10 -2 Note that 20% BG uncertainty assumed Note that 20% BG uncertainty assumed Standard “improved” detector

12. April 25, 2006ISS RAL NuFact - Walter Winter12 Systematics: Leading atm. parameters For Dm312 systematics somewhat important For Dm312 systematics somewhat important Dashed: 10% error on solar params Energy resolution important for leading atm. parameters Energy resolution important for leading atm. parameters Systematics somewhat important for  m 31 2, but impact of solar input much larger Systematics somewhat important for  m 31 2, but impact of solar input much larger

13. April 25, 2006ISS RAL NuFact - Walter Winter13 Channel requirements: Phenomenology (Akhmedov, Johansson, Lindner, Ohlsson, Schwetz, 2004) Antineutrinos: Antineutrinos: Magic baseline: Magic baseline: Silver: Silver: Platinum: Platinum: Assume specific hierarchy

14. April 25, 2006ISS RAL NuFact - Walter Winter14 Platinum channel Changes sign of CP-odd term Changes sign of CP-odd term Compare to antineutrinos: Compare to antineutrinos:  Antineutrino channel without matter effect suppression/enhancement (dep. on hierarchy)  Support information on  CP for large  13 ?

15. April 25, 2006ISS RAL NuFact - Walter Winter15 Platinum channel: Assumptions Electron detection properties are MINOS-like (NuMI note NuMI-L-714) Electron detection properties are MINOS-like (NuMI note NuMI-L-714) 2.5 GeV threshold 2.5 GeV threshold 40% efficiency 40% efficiency Energy resolution 0.15 x E Energy resolution 0.15 x E 1% BG from all neutral current events 1% BG from all neutral current events 1% BG from charge identification 1% BG from charge identification Fiducial detector mass: same as “golden” mass Fiducial detector mass: same as “golden” mass Matter density uncertainty: Correlated with golden channel Matter density uncertainty: Correlated with golden channel If platinum is possible, use it in all “golden” detectors, such as for NuFact+NuFact@MB at both places! If platinum is possible, use it in all “golden” detectors, such as for NuFact+NuFact@MB at both places! Limits the  13 for which this channel is useful!

16. April 25, 2006ISS RAL NuFact - Walter Winter16 Platinum channel: Results BG-dominated Golden Golden+Platinum Golden Good degeneracy resolver; especially for large  13 ! Good degeneracy resolver; especially for large  13 !

17. April 25, 2006ISS RAL NuFact - Walter Winter17 Silver channel Changes sign of CP-even and CP-odd terms Changes sign of CP-even and CP-odd terms Here: we only test maximal mixing Here: we only test maximal mixing Interesting for matter density correlation: 2 nd and 3 rd terms fully correlated/anticorrelated with matter density uncertainty from 1 st term (if same matter profile as golden channel) Interesting for matter density correlation: 2 nd and 3 rd terms fully correlated/anticorrelated with matter density uncertainty from 1 st term (if same matter profile as golden channel)

18. April 25, 2006ISS RAL NuFact - Walter Winter18 Silver channel: Assumptions Emulsion cloud chamber a la OPERA (Autiero et al, 2004) Emulsion cloud chamber a la OPERA (Autiero et al, 2004) Threshold starting at 2.5 GeV (Fig. 7, Autiero et al, 2004) Threshold starting at 2.5 GeV (Fig. 7, Autiero et al, 2004) Energy resolution 0.20 x E (optimistic?) Energy resolution 0.20 x E (optimistic?) 10 kt fiducial mass 10 kt fiducial mass Only neutrinos detected Only neutrinos detected Matter density uncertainty: Correlated with golden channel if at same baseline Matter density uncertainty: Correlated with golden channel if at same baseline Also: Test improved Silver* with 5 x Signal, 3 x BG (if all leptonic and hadronic  decay channels could be measured?) (Migliozzi, private communication) Also: Test improved Silver* with 5 x Signal, 3 x BG (if all leptonic and hadronic  decay channels could be measured?) (Migliozzi, private communication)

19. April 25, 2006ISS RAL NuFact - Walter Winter19 Silver channel: Options Which baseline? Which baseline? –Same as golden channel + correlated matter effect –Different from golden channel + uncorrelated matter effect (e.g., L=732 km) Main results (qualitatively): Main results (qualitatively): –Muon energies should probably not be too low (higher tau production threshold!) –Silver channel hardly affects golden channel opt. –Correlated matter effect helps and makes 4000 + 4000 km attractive

20. April 25, 2006ISS RAL NuFact - Walter Winter20 Silver channel: Results and comparison Matter density correlation helps Matter density correlation helps Silver without upgrades not competitive to platinum Silver without upgrades not competitive to platinum Silver* at “golden” baseline complementary to platinum Silver* at “golden” baseline complementary to platinum Effect of correlated matter effect

21. April 25, 2006ISS RAL NuFact - Walter Winter21 Better detector vs. new channels Better detector = increase reach by improved statistics/energy info Better detector = increase reach by improved statistics/energy info Different channel = resolve degs by complementary information Different channel = resolve degs by complementary information

22. April 25, 2006ISS RAL NuFact - Walter Winter22 Overall picture: Comparison matrix Baselines Detector effort One baseline Two baselines 1Golden (Golden) MB Beta beam (  =350, L=730 km) (Burguet-Castell et al, 2005) n/a 2 (Golden) 2L Golden*Golden+SilverGolden+Platinum Golden+(Golden) MB Golden+(Silver) 732 3Golden+Silver+Platinum Golden*+(Golden*) MB Golden+(Golden) MB +Platinum 4 Golden*+(Golden*) MB +Platinum

23. April 25, 2006ISS RAL NuFact - Walter Winter23 Accelerator degree of freedom Comparison matrix: Explanations Detector degree of freedom Synergies: Comparable statistics Direct comparison of options at same baseline Overall effort Optimized detector, additional channel, or increased luminosity increase “detector effort” by one Baseline: 4000 km, unless different one in index (MB=“Magic baseline”). Muon energy: 50 GeV Stars: Improved golden detector; in any star option the muon energy is 20 GeV

24. April 25, 2006ISS RAL NuFact - Walter Winter24 “Simple” options No surprises: L=4000 km good for CP violation, L=7500 km good for mass hierarchy No surprises: L=4000 km good for CP violation, L=7500 km good for mass hierarchy Beta beam very good for CP violation, but cannot measure mass hierarchy for small  13 Beta beam very good for CP violation, but cannot measure mass hierarchy for small  13

25. April 25, 2006ISS RAL NuFact - Walter Winter25 Synergies for detector effort “two” Synergies and optimal performance in “competing regions” for Golden*, Golden+Platinum, Golden+(Golden) MB Synergies and optimal performance in “competing regions” for Golden*, Golden+Platinum, Golden+(Golden) MB NEW: Magic baseline helps for large  13 ! NEW: Magic baseline helps for large  13 ! Compare to (Golden) 2L : If better in some region, real synergy effect! Compare with each other: If similar impact, concentrate on better one? (Thick curves: two baselines)

26. April 25, 2006ISS RAL NuFact - Walter Winter26 Physics case: Large sin 2 2  13 For large  13, only CP violation an issue For large  13, only CP violation an issue Beta beam best option even after optimization Beta beam best option even after optimization CP violation (3  ) Mass hierarchy (3  ) sin 2 2  13 (5  ) Discovery reaches for:

27. April 25, 2006ISS RAL NuFact - Walter Winter27 Physics case: Interm. sin 2 2  13 “Typical” physics case for a neutrino factory!? “Typical” physics case for a neutrino factory!? Improved detector and magic baseline sufficient to make physics case against beta beam for any performance indicator used here Improved detector and magic baseline sufficient to make physics case against beta beam for any performance indicator used here

28. April 25, 2006ISS RAL NuFact - Walter Winter28 Physics case: Small sin 2 2  13 Clear physics case for neutrino factory even with “moderate” improvements Clear physics case for neutrino factory even with “moderate” improvements Optimal reach for improved detector and magic baseline Optimal reach for improved detector and magic baseline Beta beam cannot determine mass hierarchy Beta beam cannot determine mass hierarchy

29. April 25, 2006ISS RAL NuFact - Walter Winter29 Where to concentrate the efforts? Optimized NuFact: Measure mass hierarchy and CP violation almost down to sin 2 2  13 = 10 -5 ! (including all degeneracies, for maximal mixing, 3  ) Optimized NuFact: Measure mass hierarchy and CP violation almost down to sin 2 2  13 = 10 -5 ! (including all degeneracies, for maximal mixing, 3  )

30. April 25, 2006ISS RAL NuFact - Walter Winter30 Comparison to beta beams Assumptions: 2.9 10 18 6 He decays/year 1.1 10 18 18 Ne decays/year at simultaneous operation for eight years (or double ion decays/year) 2.9 10 18 6 He decays/year 1.1 10 18 18 Ne decays/year at simultaneous operation for eight years (or double ion decays/year)  =350, L=730 km, 500 kt WC Maximum at CERN? (Burguet-Castell et al, 2005)  =350, L=730 km, 500 kt WC Maximum at CERN? (Burguet-Castell et al, 2005)  =1000, L=1300 km, 50 kt TASD High end. Optimal for CP violation (Huber, Lindner, Rolinec, Winter, 2005)  =1000, L=1300 km, 50 kt TASD High end. Optimal for CP violation (Huber, Lindner, Rolinec, Winter, 2005)  =1000, L=2600 km, 50 kt TASD High end. Optimal for mass hierarchy (Huber, Lindner, Rolinec, Winter, 2005)  =1000, L=2600 km, 50 kt TASD High end. Optimal for mass hierarchy (Huber, Lindner, Rolinec, Winter, 2005)  =1000, L=1300 km + 2600 km Why not two baselines similar to NuFact?  =1000, L=1300 km + 2600 km Why not two baselines similar to NuFact?

31. April 25, 2006ISS RAL NuFact - Walter Winter31 Comparison to beta beams (2) NF good for  13 discovery, MH discovery and  CP for small  13 NF good for  13 discovery, MH discovery and  CP for small  13 Beta beam competitive for CP violation (large  13 ); But: Extreme effort to measure MH if  13 small could make physics case difficult! Beta beam competitive for CP violation (large  13 ); But: Extreme effort to measure MH if  13 small could make physics case difficult!

32. April 25, 2006ISS RAL NuFact - Walter Winter32 Summary Physics case for neutrino factory for small/intermediate sin 2 2  13 established; no clear physics case for large  13 yet (baseline reopt. and reduced matter density uncertainties help somewhat …) Physics case for neutrino factory for small/intermediate sin 2 2  13 established; no clear physics case for large  13 yet (baseline reopt. and reduced matter density uncertainties help somewhat …) The optimal neutrino factory has (at least) The optimal neutrino factory has (at least) –Two baselines with golden channel detectors –A golden detector as optimized as possible –Electron neutrino detection in all golden detectors The silver channel could be interesting if The silver channel could be interesting if –Improved efficiencies (more tau decay channels) –Correlated matter effects (put detector to golden baseline) –Specific physics case (non-maximal mixing, unitarity test etc.)

33. April 25, 2006ISS RAL NuFact - Walter Winter33 (Our) plans Refine systematics/BG impact study Refine systematics/BG impact study Check what one has to do for improved leading atm. parameter measurements Check what one has to do for improved leading atm. parameter measurements Re-check silver channel baseline optimization: 732 km? Both at same baseline? Change of optimization? Muon energies? Re-check silver channel baseline optimization: 732 km? Both at same baseline? Change of optimization? Muon energies? Test impact of matter density uncertainties after (correlated) platinum/silver channels Test impact of matter density uncertainties after (correlated) platinum/silver channels Possibly some work on large  13 case Possibly some work on large  13 case Finish this analysis (writeup as paper) Finish this analysis (writeup as paper)

34. Additional slides

35. April 25, 2006ISS RAL NuFact - Walter Winter35 MINOS: Larger value of  m 31 2 ? No qualitative changes in L-E-optimization, but improved absolute reaches! No qualitative changes in L-E-optimization, but improved absolute reaches! Physics case for magic baseline even stronger Physics case for magic baseline even stronger Example: 0.003 eV 2 Example: 0.003 eV 2

36. April 25, 2006ISS RAL NuFact - Walter Winter36 Better detector:  13 sensitivity High CL chosen (4  ): avoid threshold effects (  13,  CP )-degeneracy affects sensitivity limit at L ~ 1500-5000 km High CL chosen (4  ): avoid threshold effects (  13,  CP )-degeneracy affects sensitivity limit at L ~ 1500-5000 km Better detector threshold: L=2000-3000 km most attractive  13 -baseline Better detector threshold: L=2000-3000 km most attractive  13 -baseline “Magic baseline”

37. April 25, 2006ISS RAL NuFact - Walter Winter37 Better detector: Large  13 Both better Eres and threshold useful Both better Eres and threshold useful Both better detector and smaller matter density uncertainty useful Both better detector and smaller matter density uncertainty useful Either or combination sufficient to compete with the superbeam upgrades (prel.) Either or combination sufficient to compete with the superbeam upgrades (prel.) Large  +better detector prefers shorter baselines (1000-2000km); E  small OK Large  +better detector prefers shorter baselines (1000-2000km); E  small OK No  CP at L magic !

38. April 25, 2006ISS RAL NuFact - Walter Winter38 Better detector in L-E-space:  13 sens. 3  sensitivity to sin 2 2  13 3  sensitivity to sin 2 2  13 Better EresBetter thresholdBetter Eres+thresh. (Huber, Lindner, Rolinec, Winter, to appear)

39. April 25, 2006ISS RAL NuFact - Walter Winter39 Better detector in L-E-space: Large  13 CP fraction for CP violation (3  “Standard” “Optimal appearance” L=1000 km/E  =20 GeV possible alternative? CP fraction for CP violation (3  “Standard” “Optimal appearance” L=1000 km/E  =20 GeV possible alternative? (Huber, Lindner, Rolinec, Winter, to appear)

40. April 25, 2006ISS RAL NuFact - Walter Winter40 Silver channel: Optimal baseline? Correlated matter effect with L ECC =4000 km better than any other baseline (except  13 sensitivity for L ~ 1500 km) Correlated matter effect with L ECC =4000 km better than any other baseline (except  13 sensitivity for L ~ 1500 km)