1. Atmospheric n’s in a large LAr Detector
G.Battistoni, A.Ferrari, C.Rubbia, P.R.Sala & F.Vissani

2. Motivations to continue the study of atmospheric neutrinos
There is still interest in continuing the study of atmospheric neutrinos:
the confirmation of SK results with a technology having a large reduction of experimental systematics with respect to water Čerenkov
the search for subleading contributions in the mixing matrix;
a possible (in principle) precision measurement of q23
a possible discrimination of Normal vs Inverted Hierarchy of masses
Tiny effects!!
Can a very large LAr detector be the tool to perform these new investigations (“Precision Physics”)? How does it compare to SK?
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

3. This work: FLUKA + NUX with 3-f oscillations with matter effects
(A.Rubbia)
FLUKA + NUX with 3-f oscillations with matter effects
Earth density profile:
PREM model
Atmospheric neutrino Fluxes
Dm223 = 2.5 x 10-3eV2 (positive)
Dm212 = 8.x10-5eV2
q12 = 34o
q23 = 40o, 45o , 50o
q13 = 0o, 3o , 5o , 10o
dCP = 0o
A.Strumia & F.V.
hep-ph/
1000 Kton year exposure
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

4. Event selection and definition
LAr
Super-Kamiokande
Thresh. for e event
10 MeV
100 MeV
(single prong)
Thresh. for muon
event
50 MeV
200 MeV
600 MeV
(Multi-prong)
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

5. ne CC Simulated Event Gallery
How SubGeV ne events will appear in ICARUS in one of its projective views (full detector desponse simulation using FLUKA)
Pp = 401 MeV/c
En = 340 MeV
Pe = 241 MeV/c
Pp = 336 MeV/c
En = 961 MeV
Pe = 493 MeV/c
Pp = 416 MeV/c
Pp = 399 MeV/c
Pp = 424 MeV/c
En = 534 MeV
Pe = 416 MeV/c
Pp = 303 MeV/c
En = 840 MeV
Pe = 509 MeV/c
Pp = 504 MeV/c
En = 585 MeV
Pe = 433 MeV/c
Pp = 398 MeV/c
En = 949 MeV
Pe = 479 MeV/c
En = 653 MeV
Pe = 500 MeV/c
Pp = 525 MeV/c
Pp = 278 MeV/c
En = 568 MeV
Pe = 493 MeV/c
En = 323 MeV
Pe = 294 MeV/c
En = 806 MeV
Pe = 789 MeV/c
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

6. ne CC Simulated Event Gallery
En = 549 MeV
Pe = 609 MeV/c
Pp = 198 MeV/c
En = 978 MeV
Pe = 528 MeV/c
Pp = 543 MeV/c
En = 510 MeV
Pe = 471 MeV/c
En = 220 MeV
Pe = 195 MeV/c
Pp = 136 MeV/c
En = 849 MeV
Pe = 595 MeV/c
En = 743 MeV
Pe = 727 MeV/c
En = 799 MeV
Pe = 745 MeV/c
En = 422 MeV
Pe = 378 MeV/c
Pp = 116 MeV/c
En = 770 MeV
Pe = 409 MeV/c
En = 954 MeV
Pe = 637 MeV/c
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

7. The “standard” nm analysis:
Beware of containment:
but we have good news about the possibility of using MS to measure muon energy
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

8. A slightly less standard opportunity
Direction reconstruction
using lepton+recoiling proton
In general:
a superior capability
in pointing
a better resolution
in L/E
Minimum Goal: ~ kton yr
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

9. The Precision Physics case
Solar n and KamLAND experiments contributed to determine with relatively high precision Dm212 and q12
At present the only determination of q23 come from atmospheric neutrinos and has a large uncertainty. How close is q23 to /4? Is it larger or lower than /4? (“octant ambiguity”)
q23 < /4  |<nm|n3>| > |<nt|n3>|
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

10. The determination of q23 in atm. neutrino exp.
DIscussion previously proposed by P.Lipari
Essentially the best determination of 2 q23 comes from the analysis of Multi-GeV muon-like events
(in SK ~ 6 ev/Kton yr)
At present: 36° < q23 < 54°
The “solar” (12) sector generates significant effects on Sub-GeV neutrinos which might help resolve the octant ambiguity. This is true even in case q13 = 0
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

11. Oscillation effects in e-like events in the q13 = 0 approximation
Fosce = F0e P(ne  ne) F0m P(nm  ne) F0e ,F0m : n flux w/o osc.
= F0e [ P(ne  ne) + r P(nm  ne) ] r = F0m / F0e : m/e flux ratio
= F0e [ 1 – P r cos2 q23 P12 ] P12 = |Aem|2 : 2n transition probability ne  nmt in matter
driven by Dm212
(Fosce / F0e) – 1 = P12 (r cos2 q23 – 1)
screening factor for low energy n (r ~ 2)
~ 0 if cos2 q23 = (sin2 q23 = 0.5)
< 0 if cos2 q23 < (sin2 q23 > 0.5)
> 0 if cos2 q23 > (sin2 q23 < 0.5)
Important only in SubGeV region where
Dm212L/E is sufficiently large
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

12. A new measurement of q23 SubGeV: r~2
Also the nm rate is affected but this would be an extra term which adds to the “standard” 2-flavor oscillations
However, the general case of non vanishing q13
(and possibly dCP) plus matter effects is more complex
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

13. Cryodet Workshop, G.Battistoni
To give an idea:
osc. web calculator based on the code of F.V. (thanks to V.Vlachoudis CERN)
q12 = 34°
q13 = 3°
q23 = 50°
ne  ne
ne  nm
ne  nt
q12 = 34°
q13 = 0°
q23 = 50°
ne  ne
ne  nm
ne  nt
q12 = 34°
q13 = 0°
q23 = 40°
ne  ne
ne  nm
ne  nt
n’s from
nadir
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

14. Cryodet Workshop, G.Battistoni
Implications:
The knowledge of the absolute level of SubGeV ne can provide the best possible measurement of q23 and of its octant.
The unique features of a large LAr detector (>50 kton?) can provide an important measurement of of SubGeV ne with null or largely reduced experimental systematics. The ICARUS tecnology can explore for the first time the region with Pe<100 MeV/c (to be demonstrated by T600)
Of course, from the point of view of statistical significance, this requires a very high exposure.
How large?
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

15. Cryodet Workshop, G.Battistoni
Other possibilities
There are q13 induced oscillations which instead affect the MultiGeV region: these could be used to discriminate the hierarchy of masses (sign of Dm223) if n and anti-n could be distinguished (MSW resonance is present for n when Dm223>0 or for anti-n (when Dm223<0)
This measurement, which requires n/anti-n separation, might be more problematic for a LAr detector (magnet…)
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

16. ne + ne SubGeV CC interaction rates (kton yr)-1
No Osc.: 51.3 (62.8)
40o
45o
50o 0o
52.2
(63.9)
51.3
(62.8)
50.2
(61.7) 3o
51.7
(63.3)
50.9
(62.5)
49.7
(61.2) 5o
51.4
(63.0)
50.6
(62.2)
49.6
(61.1)
10o
50.8
(62.00)
50.4
(61.9)
49.3
(60.8)
q23
q13
En<1 GeV
Plepton<1 GeV/c
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

17. Cryodet Workshop, G.Battistoni
In graphic form...
q13 = 0o
q13 = 3o
q13 = 5o
q13 = 10o
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

18. Cryodet Workshop, G.Battistoni
Results for q13 = 0
q23 = 40o
q23 = 50o
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

19. Cryodet Workshop, G.Battistoni
Results for q13 = 0
Ratio
Ne/Ne0
q23 = 40o
q23 = 50o /
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

20. Cryodet Workshop, G.Battistoni
Results for q13 > 0
q13 = 5o
q13 = 10o
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

21. The problem of systematics
Leaving aside for a moment the question if such an extremely large exposure can be achieved:
The proposed measurement requires an absolute no-oscillation prediction affected by a systematic uncertainty not exceeding 1%. Is this achievable? (absolute level, ne/nm ratio)
Primary c.r. fluxes (maybe we can take this ~under control)
Neutrino-nucleus cross sections
Hadronic interactions and atm. shower development
is exactly 2 at low energy only if just p are there!
K/p?
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

22. Cryodet Workshop, G.Battistoni
A less naive method...
Of course it is hard to believe that one could rely on the absolute level of Ne prediction... (the c.r. flux normalization remains one of the most important uncertainties)
A better analysis is the ratio:
so that many common
systematics cancel out
The important topic remains the uncertainty as a function of energy
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

23. For example (q13 = 0) : it could be possible to achieve
a 3 s separation
even for ~500 kton yr
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

24. Considerations from SK
This topic has been debated at the end of 2004 in the context of a dedicated workshop
Requirements for SK: the measurement of q23 octant can be done with an exposure of at least 20 years of SK (depending on q13) to distinguish (Dc2~2) between the 2 mirror values of corresponding to sin2q23 = 0.96 with the present level of systematics
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni

25. Cryodet Workshop, G.Battistoni
Conclusions
A very large LAr TPC, in principle, can give new important contributions to neutrino physics, also with atmospheric neutrinos
It allows to detect low energy neutrinos with null or negligible experimental systematic error. An exposure of kton yr would allow be the minimum goal for this topic.
the sector of SubGeV ne, in particular, offers the possibility of performing new interesting measurements.
To perform new precision measurements a very large exposure (>500 kton yr) is anyway needed
Such a large exposure might be in part useless without an effort to reduce the existing systematic uncertainties (n fluxes, cross sections,...).
LNGS 13 Mar 2006
Cryodet Workshop, G.Battistoni