1. Physics with a very long neutrino factory baseline IDS Meeting CERN March 30, 2007 Walter Winter Universität Würzburg

2. March 30, 2007IDS CERN - Walter Winter2 Contents Introduction: Magic baseline Introduction: Magic baseline Open questions Open questions A more realistic density model A more realistic density model Answers: e.g.: which detector locations? Answers: e.g.: which detector locations? More physics applications: More physics applications: – Matter density measurement –  13 precision measurement – Octant degeneracy – MSW effect sensitivity Physics case for a very long baseline Physics case for a very long baseline (mainly based on: Gandhi, Winter: “Physics with a very long neutrino factory baseline”, Phys. Rev. D75 (2007) 053002, hep-ph/0612158)

3. March 30, 2007IDS CERN - Walter Winter3 Appearance channels:  e  Information:  13,  CP, mass hierarchy (via A) (Cervera et al. 2000; Freund, Huber, Lindner, 2000; Akhmedov et al, 2004) Expansion in small sin 2  13 and  :

4. March 30, 2007IDS CERN - Walter Winter4 Idea of the “Magic baseline” Idea: Yellow term = 0 independent of E, oscillation parameters Idea: Yellow term = 0 independent of E, oscillation parameters Purpose: “Clean” measurement of  13 and mass hierarchy Purpose: “Clean” measurement of  13 and mass hierarchy No dependence on E, osc. parameters No dependence on E, osc. parameters Drawback: No  CP measurement at magic baseline Drawback: No  CP measurement at magic baseline  combine with shorter baseline, such as L=3 000 km

5. March 30, 2007IDS CERN - Walter Winter5 Magic baseline: Quantified Use two-baseline space (L 1,L 2 ) with (25kt, 25kt) and compute  13 reach including correlations and degeneracies: Animation in  13 -  CP -space: (Huber, Winter, 2003) sin 2 2  13  CP (3  ; red: measure for risk – in this case  m 21 2 )

6. March 30, 2007IDS CERN - Walter Winter6 Open questions Which density for condition ? Not exactly known from geophysics! Which density for condition ? Not exactly known from geophysics! Is the constant density approximation sufficient? Is the constant density approximation sufficient? Is the expansion in  and  13 accurate enough? Is the expansion in  and  13 accurate enough? What happens if my preferred detector location is not exactly on the “magic baseline”? What happens if my preferred detector location is not exactly on the “magic baseline”? Is there a preferred detector site from geophysics? Is there a preferred detector site from geophysics? Matter density uncertainties in 3D models ~ 5% (http://cfauvcs5.harvard.edu/lana/rem/mapview.htm)

7. March 30, 2007IDS CERN - Walter Winter7 A more realistic density profile model PREM profile approximated by 7 profile steps between L~6000 km and 9000 km „Profile 7 “ PREM profile approximated by 7 profile steps between L~6000 km and 9000 km „Profile 7 “  Efficient for computation  More realistic for model Dashed: Often used baseline-averaged density Dashed: Often used baseline-averaged density (Gandhi, Winter, 2006)

8. March 30, 2007IDS CERN - Walter Winter8 Constant reference density  Ref Idea: Find constant dens. which best matches Profile 7 :  Ref Idea: Find constant dens. which best matches Profile 7 :  Ref Method: Minimize total  2 from all channels between Profile 7 and  Ref (simulate Profile 7 and fit  Ref for same osc. Params) Method: Minimize total  2 from all channels between Profile 7 and  Ref (simulate Profile 7 and fit  Ref for same osc. Params)  Least contribution of profile effect to statistical analysis (Gandhi, Winter, 2006)

9. March 30, 2007IDS CERN - Walter Winter9 Constant reference density  Ref = Mean density? Answer: ~ 5% off Reason: long constant density layer dominates  Ref = Mean density? Answer: ~ 5% off Reason: long constant density layer dominates Parameter dependence (  13,  ) strongest for small  13, but there  2 function shallow (last slide) Parameter dependence (  13,  ) strongest for small  13, but there  2 function shallow (last slide) (Gandhi, Winter, 2006) (see e.g. Akhmedov, 2000)

10. March 30, 2007IDS CERN - Walter Winter10 How we address the main questions What if the detector location is off the MB? What if the detector location is off the MB?  Show sensitivity as a function of baseline Unknown matter density (geophysics): What if  Ref wrong by ~5%? Unknown matter density (geophysics): What if  Ref wrong by ~5%?  Show results for 0.95  Ref and 1.05  Ref Profile effects: How well does a constant density simulate the matter density profile? Is the actual sensitivity better or worse? Profile effects: How well does a constant density simulate the matter density profile? Is the actual sensitivity better or worse?  Show results for Profile 7 and  Ref

11. March 30, 2007IDS CERN - Walter Winter11  13 sensitivity Strong impact for one baseline only Strong impact for one baseline only Exact detector location not so important for combination with shorter baseline (L ~ 7000 – 9000 km) Exact detector location not so important for combination with shorter baseline (L ~ 7000 – 9000 km) (Gandhi, Winter, 2006)

12. March 30, 2007IDS CERN - Walter Winter12 CP violation measurement Very long baseline clearly helps Very long baseline clearly helps Optimal L ~ 7700 km +- 500 km Optimal L ~ 7700 km +- 500 km (Gandhi, Winter, 2006) Very long baseline helps for L ~ 7000 km to 9000 km, but small absolute impact Very long baseline helps for L ~ 7000 km to 9000 km, but small absolute impact Profile effect enhances perform. Profile effect enhances perform. No clear preference of a very long baseline (poor statistics dominated) No clear preference of a very long baseline (poor statistics dominated)

13. March 30, 2007IDS CERN - Walter Winter13 Consequences for detector locations Mass hier.: L ~ 6000 - 9000 km good for sin 2 2  13 > 10 -4 Mass hier.: L ~ 6000 - 9000 km good for sin 2 2  13 > 10 -4 Choose, e.g., L ~ 7000 – 9000 km: Choose, e.g., L ~ 7000 – 9000 km:

14. March 30, 2007IDS CERN - Walter Winter14 Some answers Magic baseline is a very accurate description for one baseline only Magic baseline is a very accurate description for one baseline only Very long baselines between ~ 7000 km and 9000 km OK if second detector at shorter L Very long baselines between ~ 7000 km and 9000 km OK if second detector at shorter L  In this case, little impact from profile effects and poor geophysics information Mean density is not a good choice for a constant reference density Mean density is not a good choice for a constant reference density  Use  Ref further on, which reproduces profile very well Profile effects improve absolute sensitivity somewhat compared to constant density Profile effects improve absolute sensitivity somewhat compared to constant density

15. Further applications of a very long neutrino factory baseline

16. March 30, 2007IDS CERN - Walter Winter16 Matter density measurement Idea: Treat  as yet another oscillation parameter to be measured; marginalize oscillation parameters! Idea: Treat  as yet another oscillation parameter to be measured; marginalize oscillation parameters! Comes „for free“ from very long baseline!? Comes „for free“ from very long baseline!? Two different models: Two different models: 1.Measure  Ref 2.Measure  LM (lower mantle density) (Winter, 2005; Minakata, Uchinami, 2006; Gandhi, Winter, 2006) Lower mantle density

17. March 30, 2007IDS CERN - Walter Winter17 Matter density: Geophysical use? Example: Plume hypothesis Example: Plume hypothesis A precision measurement << 1% could discriminate different geophysical models A precision measurement << 1% could discriminate different geophysical models  Possible selector of detector locations? (Courtillot et al., 2003; see talk from B. Romanowicz, Neutrino geophysics 2005)

18. March 30, 2007IDS CERN - Walter Winter18 Results for one-parameter measurement Assume that only one parameter measured Assume that only one parameter measured For large  13, < 1% precision at 3  For large  13, < 1% precision at 3  Indep. confirmed by Minakata, Uchinami (for one baseline) Indep. confirmed by Minakata, Uchinami (for one baseline) (Gandhi, Winter, 2006)

19. March 30, 2007IDS CERN - Walter Winter19 A more sophisticated model Assume that upper mantle density (  UM ) only known with certain precision: Assume that upper mantle density (  UM ) only known with certain precision: (Gandhi, Winter, 2006)

20. March 30, 2007IDS CERN - Walter Winter20 Reduction of matter density uncertainty Use of very long baseline reduces the impact of matter density uncertainties as well Use of very long baseline reduces the impact of matter density uncertainties as well  No need for extra geophysics effort if two baselines used (Huber, Lindner, Rolinec, Winter, 2006) (dashed: 2%, solid: 5% matter density uncertainty)

21. March 30, 2007IDS CERN - Walter Winter21  13 precision measurement Bands: dependence on  (worst case, median, best case) Bands: dependence on  (worst case, median, best case) (Gandhi, Winter, 2006) Example: sin 2 2  13 = 0.001: Example: sin 2 2  13 = 0.001:

22. March 30, 2007IDS CERN - Walter Winter22 Resolving the  23 degeneracy 4000 km alone: Problems with degs for intermediate  13 4000 km alone: Problems with degs for intermediate  13 7200 km alone: No sensitivity for small  13 7200 km alone: No sensitivity for small  13 4000 km + 7200 km: Good for all  13 4000 km + 7200 km: Good for all  13 (Gandhi, Winter, 2006)

23. March 30, 2007IDS CERN - Walter Winter23 Null result if solar effects neglected: Null result if solar effects neglected: But solar term: Note that i.e., effect increases with baseline! But solar term: Note that i.e., effect increases with baseline! MSW effect sensitivity for  13 =0 (Winter, 2004) (Freund et al, 1999) 55

24. March 30, 2007IDS CERN - Walter Winter24 Physics case for a very long NF baseline sin 2 2  13 10 -1 10 -3 „Large“ Reduced impact of matter density uncertainty Better CP violation performance Precise matter density measurement Guaranteed mass hierarchy sensitivity Correlation and degeneracy resolution Improved precision measurement of  CP Information on the matter density Maximized  13 and mass hier. sens. reach Correlation and degeneracy resolution Improved precision measurement of  CP MSW effect sensitivity Potentially future mass hier. sensitivity 10 -2 10 -4 „Medium“ „Small“ „Zero“ Helps for the  23 measurement Helps for octant degeneracy resolution Improves  13 precision measurement (see: Gandhi, Winter, 2006)

25. March 30, 2007IDS CERN - Walter Winter25 Summary Magic baseline description holds for all practical applications, but use  Ref instead of mean density Magic baseline description holds for all practical applications, but use  Ref instead of mean density Two baseline setup rather insensitive to very long baseline length (but: VL baseline clearly helps) Two baseline setup rather insensitive to very long baseline length (but: VL baseline clearly helps) Geophysics spin-off may prefer specific detector locations; needs more investigation Geophysics spin-off may prefer specific detector locations; needs more investigation Physics case for very long baseline no matter how big  13 is (if neutrino factory is built) Physics case for very long baseline no matter how big  13 is (if neutrino factory is built)