What If U e3 2 < 10 4? Neutrino Factories and Other Matters

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1 What If U e3 < 0 4? Neutrino Factories and Other Matters André de Gouvêa University DUSEL Theory Workshop Ohio State University, April 4 6, 008 April 5, 008 tiny U e3 : now what?

2 Outline. What are We Aiming At?. Reach of Next-Generation Experiments 3. New Neutrino Beams: Neutrino Factories & β-beams 4. Where Will We Be? 5. Really Tiny U e3 What Can We Still Measure? 6. Expectations? April 5, 008 tiny U e3 : now what?

3 The Goal of Neutrino Oscillation Experiments (m 3 ) (m ) (m ) ( m ) sol What is the ν e component of ν 3? (θ 3 0?) Is CP-invariance violated in neutrino oscillations? (δ 0, π?) ( m ) atm ν e ν µ ( m ) atm Is ν 3 mostly ν µ or ν τ? (θ 3 > π/4, θ 3 < π/4, or θ 3 = π/4?) ν τ What is the neutrino mass hierarchy? ( m 3 > 0?) ( m ) sol normal hierarchy (m ) (m ) (m 3 ) inverted hierarchy MORE IMPORTANT: test the three neutrino mixing hypothesis. Are we missing anything? (New Physics?) April 5, 008 tiny U e3 : now what?

4 Marching Orders Say we knew U e3 was very small, say U e3 < 0 4. Which long-baseline experiment should we pursue under these circumstances? April 5, 008 tiny U e3 : now what?

5 U e3 Reach of Next-Generation Experiments: Reactors: ultimate reach around U e3 > 0 3 : shape-dominated analysis in huge reactor experiments. Atmospheric Neutrinos: INO-like detector sensitive to oscillation questions if U e3 > 0. Conventional Neutrino Beams (π µν): sensitive to oscillation questions if U e3 > 0 (next) and, ultimately, U e3 > 0 4 (next-next). Potential improvements: bigger (Hyper-K), better (liquid argon) detectors. Project X-type proton beams... April 5, 008 tiny U e3 : now what?

6 #cp (") André de Gouvêa.5 LAR 00kt LE 80 km 4 mrad +LAR 00kt LE 700 km 57 mrad 0 0 ProjectX pots: 60x0 &+60x0 & LAR 00kt 60GeV WBB 300 km 0 mrad 0 0 ProjectX pots: 60x0 &+60x0 & 3 % Discovery Potential for #cp$0 and ($") REALLY OPTIMISTIC? #cp (") Normal Hierarchy Inverted Hierarchy -3 0 NOvA 5kt ME 80 km 4 mrad 0 0 ANU pots: 5x0 &+5x0 & NOvA 5kt ME 80 km 4 mrad 0 0 SNUMI pots: 30x0 &+30x0 & NOvA 5kt ME 80 km 4 mrad 0 0 ProjectX pots: 60x0 &+60x0 & LAR 00kt LE 80 km 4 mrad +LAR 00kt LE 700 km 57 mrad 0 0 ProjectX pots: 60x0 &+60x0 & LAR 00kt 60GeV WBB 300 km 0 mrad 0 0 ProjectX pots: 60x0 &+60x0 & Normal Hierarchy % Discovery Potential for sin (! 3 )$0 0 - #cp (") sin (! 3 ) NOvA 5kt ME 80 km 4 mrad 0 0 ANU pots: 5x0 %+5x0 % NOvA 5kt ME 80 km 4 mrad 0 0 SNUMI pots: 30x0 %+30x0 % NOvA 5kt ME 80 km 4 mrad 0 0 ProjectX pots: 60x0 %+60x0 % LAR 00kt LE 80 km 4 mrad +LAR 00kt LE 700 km 57 mrad 0 0 ProjectX pots: 60x0 %+60x0 % LAR 00kt 60GeV WBB 300 km 0 mrad 0 0 ProjectX pots: 60x0 %+60x0 % Normal Hierarchy Inverted Hierarchy 95%C.L for discovering sign$m sin (! 3 ) Inverted Hierarchy sin (! 3 ) [N. Saulidou, Project X at FNAL, Preliminary ] April 5, 008 tiny U e3 : now what?

7 How do we do better: Need Qualitatively Better Beam! Remember, the pion beam is messy and dirty. We don t know the neutrino energy spectrum or flux very well, plus we don t have a pure ν µ beam: there is always a ν e contamination from kaons and muons... Two ideas well-developed in the market: β-beams: pure ν e or ν e beam from β-decaying boosted nucleus in storage ring. Main search modes ν e ν e, ν e ν µ. low energy ( 400 MeV) versus high energy ( GeV.5 GeV) Neutrino Factories: ν e and ν µ beam (or vice-versa) from muon storage ring. First step towards a muon collider! April 5, 008 tiny U e3 : now what?

8 P eµ sin θ 3 sin θ 3 P eτ cos θ 3 sin θ 3 P µµ,µτ sin θ 3 April 5, 008 tiny U e3 : now what?

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12 What About the Other Parameters? If U e3 is tiny, we will still run the next-generation experiments and not measure it. In the mean time, we will measure all sorts of other things, mostly from ν µ disappearance. For example, we don t know this about θ 3 (atmospheric angle):. Is it maximal (sin θ 3 = /)?. Is sin θ 3 > / or sin θ 3 < /? Limited information regarding () from disappearance channel. ( ) m P µµ = sin θ 3 sin 3 L + subleading. 4E In order to resolve this issue, need more information from reactors, atmospheric neutrinos, P eτ cos θ 3 (which requires τ appearance and θ 3 0. Beyond the reach of next-generation LBL experiments. Requires Neutrino Factory). April 5, 008 tiny U e3 : now what?

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14 Deciding that θ 3 is not maximal with LBL experiments 5 Conventional Beams 5 JPARC SK 5 NuMI off axis 0 3 ev True value of m ev True value of m ev True value of m True value of sin Θ True value of sin Θ True value of sin Θ 3 5 After ten years 5 JPARC HK 5 NuFact II 0 3 ev True value of m ev True value of m ev True value of m April 5, True value of sin Θ True value of sin Θ True value of sin Θ 3 Antusch et al., PRD70, (004). tiny U e3 : now what?

15 What if U e3 is vanishingly small? (m 3 ) (m ) (m ) ( m ) sol ( m ) atm ν e ν µ ( m ) atm Is ν 3 mostly ν µ or ν τ? (θ 3 > π/4, θ 3 < π/4, or θ 3 = π/4?) ν τ What is the neutrino mass hierarchy? ( m 3 > 0?) ( m ) sol normal hierarchy (m ) (m ) (m 3 ) inverted hierarchy Still Work To Do: these won t be resolved if U e3 0 April 5, 008 tiny U e3 : now what?

16 Example: Determining the Mass Hierarchy via Oscillations vanishing U e3 route hep-ph/ , hep-ph/05070, hep-ph/ In the case of two-flavors, the mass-hierarchy can only be determined in the presence of matter effects: vacuum neutrino oscillations are not sensitive to the mass hierarchy. In the case of three-flavors, this is not the case: vacuum neutrino oscillation probabilities are sensitive to the neutrino mass hierarchy. This does not depend on whether U e3 vanishes or not. April 5, 008 tiny U e3 : now what?

17 Survival probabilities ( only relevant ones in the U e3 0 limit): ( P αα = 4 U α U α sin L ( 4 U α U α3 sin 3 L ( 4 U α U α3 sin 3 L ij m ij/e. Note that 3 = 3. It is easy to see how the different hierarchies lead to different results. In the normal case, 3 > 3, while in the inverted case 3 < 3. Hence, all one needs to do is establish which frequency is associated to which amplitude (governed by the U αi s). ) ) ), April 5, 008 tiny U e3 : now what?

18 P µµ L=95 km m 3 = ev m 3 = ev (s) m 3 = ev (d) m = ev, sin θ = 0.83, sin θ 3 = E (GeV) The small L problem: in this case x = m cos θ (= ev ). This would be the situation at a short baseline experiment: even with quasi-infinite statistics one would still end up with two different values of m 3, one for each hierarchy hypothesis. April 5, 008 tiny U e3 : now what?

19 P µµ P µµ E (GeV) L=6000 km E (GeV) m 3 = ev m 3 = ev (d) m = ev, sin θ = 0.83, sin θ 3 = There is hope! But can we see the fast oscillations at low energies? April 5, 008 tiny U e3 : now what?

20 Theoretical Expectations? [Albright and Chen, hep-ph/060837] April 5, 008 tiny U e3 : now what?

21 generic predictions for subleading parameters. Note correlations between U e3 and cos θ 3, plus dependency on mass-hierarchy. Case Texture Hierarchy U e3 cos θ 3 (n.s.) cos θ 3 Solar Angle m A 3 m 0 Normal m O() m O() 3 m B m 3 0 Inverted m m m 3 m 3 O() 0 0 m C 3 m 0 0 Inverted m m 3 O() m 3 cos θ m m Anarchy m 3 Normala > 0. O() O() a One may argue that the anarchical texture prefers but does not require a normal mass hierarchy. [enlarged from AdG, PRD69, (004)] Textures are another way to parametrize neutrino mixing and to try and understand salient features: U e3, cos θ 3, m m 3, etc. Usually quark independent. April 5, 008 tiny U e3 : now what?

22 Concluding Thoughts: If U e3 < 0 4, we will probably need qualitatively different neutrino beams. Ultimate machine: neutrino factory. Of course, we won t know that U e3 < 0 4 until we get there. Along the way, we will measure other parameters more precisely, and may meet some surprises along the way. If U e3 0 4, there is still work to do: atmospheric parameters, mass hierarchy (really challenging). On the flip side, we need a neutrino factory or other new neutrino beam if we want to do precision neutrino oscillation measurements. Is this something the community is interested in? Typical neutrino factories are high energy (E µ > 0 GeV) and long baseline (L > 3000 km). Where does DUSEL fit into this? Work needed! April 5, 008 tiny U e3 : now what?

23 Back-ups April 5, 008 tiny U e3 : now what?

24 How does one compare the two mass hierarchies and determines which one is correct? The question I address is the following: For a positive choice of m 3 = m + 3, is there a negative choice for m 3 = m 3 that yields identical oscillation probabilities? If the answer is yes, then one cannot tell one mass hierarchy from the other. If the answer is no, then one can, in principle, distinguish the two possibilities. More concretely: fix m + 3 (which I ll often refer to as m 3) and define x so that m 3 = m+ 3 + x. Question: Is there a value of x that renders P ( m + 3 ) = P ( m 3 )? Note: x is such that m 3 is negative. It turns out that x s that almost do the job are of order m. April 5, 008 tiny U e3 : now what?