TAUP 2009 July 2 nd Probing θ 13 with global neutrino data analysis Antonio Palazzo CSIC/IFIC, AHEP group, Valencia Based on work done in collaboration with: G.L. Fogli. E. Lisi, A. Marrone, A.M. Rotunno
Ou Outl tlin ine � In Intr troduc ductio ion � The s he stan anda dard 3 d 3 ν fr fram amew ework; � On the tr On the track of k of θ 13 13 � Hin Hints fr ts from: m: � 1) 1) Atmo mosphe spheric da c data; � 2) 2) Sol Solar & KamLAND r & KamLAND; � 3) 3) MINOS ( MINOS ( ν e a app ppea earanc ance da e data); a); � ns � Fu Futu ture p e persp spective an e and c d conc nclusio sions 2
The s he stan anda dard 3 d 3 ν fr fram amew ework k � 3
The l he leptonic m c mix ixin ing � Dirac CP-violating phase unknown Explicit form: 4
The n he neu eutr trin ino ma o mass sp ss spectr trum � ? NH � NH IH � IH ν 3 + Δ m 2 ν 2 ν 2 δ m 2 ν 1 ν 1 - Δ m 2 ν 3 5
Experim Ex imen ental Sensi l Sensitivi vitie ies � lea eadin ding � Atmospheric, LBL (disapp.) sub-lea sub-l eadin ding � Solar, KamLAND CHOOZ, MINOS (app.) 6
Cons Co nstr train aints fr ts from gl m glob obal 3 l 3 ν ana analysis a ysis as of 20 s of 2008 08 � Fogli et. al. [PRD 78, 033010 (2008)] High precision on both mass splittings, now determined by “artificial” neutrino sources experiments (KamLAND for δ m 2 , MINOS for Δ m 2 ). Estimates of the two leading mixing angles is less accurate (especially θ 23 ), and experiments using “natural” ν ’s play a crucial role in their determination. A preference for θ 13 > 0 at a non-negligible C.L (90%) emerged in 2008 [Fogli, Lisi, Marrone, A.P, Rotunnno, PRL 101, 141801 (2008), arXiv:0806.2649,hep-ph]. This brings us to focus on … 7
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The CHOOZ experiment � eactor ν e ● Sea Searche hed f d for r disa disapp ppea earanc ance of r e of rea E ~ few MeV L = 1 km ● L/E range comparable to atmospheric ν → probes the same Δ m 2 ● No disappearance signal was found (1998) 9
“His Historical” u upp pper bo r bound o d on n θ 13 13 e establ blishe ished in 1998 d in 1998 � CHOOZ exclusion plot Exclusion plot in the ( Δ m 2 , θ 13 13 ) plane Atm Δ m 2 scale (now) +LBL set with precision by 10
The role of global analyses in pinning down θ 13 Since then the 3 Sinc e then the 3 ν gl glob obal ana l analyse yses ha s have sho e shown a sl n a slow b w but p t progressi ssive � enhanc enhancem emen ent in the sensi t in the sensitivi vity t ty to o θ 13 13 . � In the pa In the past the t they ha y have fir e first c t corrobo oborated ( d (atmo mosphe spheric ana c analyse yses), an ), and � then s then str tren engthen gthened ( d (sol solar+KamLAND ana r+KamLAND analyse yses) the CHOO ) the CHOOZ u Z upp pper l r lim imit. � It is then not a c It is then n t a compl mplete su e surprise tha ise that the t they n y now s w start t t to be sensi o be sensitive � to v o value ues of s of θ 13 13 bel below the CHOO w the CHOOZ l Z lim imit. � Wha hat ins t instea ead (pl d (plea easan santl tly) su y) surprise ises u s us is tha s is that, f , for the fir r the first t t tim ime, the , the � neu eutr trin ino da o data p a poin int t t towa wards a n ds a non-z n-zero v o value of ue of θ 13 13 – p – provi vidin ding thr g three ee in inde depen enden dent an t and c d convergin ing h g hin ints in th ts in this dir is directio ion. n. � 11
Hin Hint n. t n. I � Da Date: e: � 20 2006 06 � Da Data: a: � Atm. + LBL( + LBL(disa disapp pp.) + CHOO .) + CHOOZ � 12
Numerical results of 3 ν global analysis (2006) G.L. Fogli, E. Lisi, A. Marrone, A.P., Prog. Part. Nucl. Phys. 57, 742 (2006) � We f e found a h d a hin int f t for � θ 13 13 > 0 > 0 � in the 3 in the 3 ν ana analysis of ysis of � Atm. + LBL + CHOO + LBL + CHOOZ Z � t fit ~ 0.015 Best fit Be is ~ 1 sigma 1 sigma � a awa way fr y from z m zero � The hint persists after inclusion of the latest disappearance LBL results (MINOS) 13
Tracing the origin of the “atmospheric hint” Atmospheric data present a small excess of sub-GeV electron-like events . � This can be partially explained by 3 ν subleading effects driven by the “ solar ” splitting δ m 2. � Indeed, from an estimate of the order of magnitude of the MSW potential : � - Δ m 2 -driven for multi-GeV we see tha we see that in SK da t in SK data ea a earth ma th matter e r effects a ts are: e: � - δ m 2 -driven for sub-GeV 14 14
Theoretical expectation for the excess The excess of expected electron events compared to the no-oscillation � case can be expressed as [Peres and Smirnov , Nucl. Phys. B 456, 204 (1999); 680, 479 (2004)] : � sub-GeV r = multi-GeV Notice that this observable is particularly useful to describe 3 ν sub-leading � effects since it exactly equals zero when: bo both th θ 13 13 = 0 & = 0 & δ m 2 = 0 = 0 � In the spirit of this qualitative discussion, it is helpful to assume that � the density of the earth is constant. Indeed, in this case we have that � this observable can be written as the sum of three different terms: 15
For the case of: we have: “ θ 13 term ” “ δ m 2 term ” “ Interference term ” mixing angles in matter “ swapping” relations two (non-equivalent) CP conserving cases 16
“Exact” numerical examples “ θ 13 term ” dominant “ δ m 2 term ” dominant “ Interference term ” dominant (only in sub-GeV) These terms help to fit the small electron excess in Sub-GeV and Multi-GeV � 17
Two non-equivalent CP-conserving cases 18 G.L. Fogli, E. Lisi, A. Marrone, A.P., Prog. Part. Nucl. Phys. 57, 742 (2006) �
Comparison with other existing analyses Escamilla , Latimer and Ernst (arXiv:0805.2924 [nucl-th]) Roa, Latimer, Ernst (arXiv:0904.3930 [nucl-th]) Atm. h hin int su t supp pported. d. Sim Simil ilar p r preferenc ence f e for c r cos δ sin sin θ 13 13 < 0 < 0 � Schwetz, Tortola, Valle (arXiv:0808.2016[hep-ph]) Atm. h hin int n t not su t supp pported. d. � Maltoni & Schwetz (arXiv:0812.3161[hep-ph]) Atm. h hin int n t not o t or pa r partially su y supp pported. d. � 19
Concluding remarks on the “atmospheric hint” There exist ongoing 3 ν analyses in SK after phase I, presented in recent PhD theses using SK-I+II data. � Unfortunately, none of the these analyses allows both θ 13 > 0 & dm 2 > 0, and thus they do not include the interference term. � It is also worth noticing that, at the current level of refinement, it is difficult to reproduce in detail the atmospheric analysis outside the SK collaboration, especially if one is looking for effects at the level of ~ 1 σ . � Therefore, it will be very important to see the next official SK oscillation analysis, which should hopefully include a complete treatment of three- flavor oscillations with both δ m 2 > 0 and θ 13 > 0. � Meanwhile, also in consideration of the partial agreement among different � independent analyses, it seems wise to consider the atmospheric hint having � a fragile status. � 20
Hin Hint n. t n. II II � Da Date: e: � June 20 e 2008 08 � Da Data: a: � Sol Solar & KamLAND r & KamLAND � 21
3 ν ana analysis of sol ysis of solar an r and KamLAND da d KamLAND data (20 a (2008) 08) � Notice that marginalization � over δ m 2 is practically � equivalent to fix this � parameter at its best fit � (determined KamLAND) Best fit ~ 0.021 is 1.2 sigma away from zero θ 13 Then we have a second, independent hint of θ 13 > 0 G.L Fogli, E. Lisi, A. Marrone, A.P., A.M. Rotunno � PRL 101, 141801 (2008) �
Origin: Tension between solar and KamLAND = 0 > 0 θ 13 13 = θ 13 13 > For θ 13 = 0 For θ 13 13 > 0 13 = Solar and KamLAND Solar data prefer higher θ 12 12 prefer different values of θ 12 KamLAND prefers lower θ 12 12 12 No overlap at 1 σ level Disagreement reduced* 23 *See also Balantekin and Yilmaz, J. Phys. G. 35, 075007 (2008)
Interplay is more evident in the plane spanned by the two mixing angles Sol Solar ( r (S) an ) and KamLAND (K d KamLAND (K) displ ) display di y differen ent c t correl elatio ions ns. � This r is ren ende ders their c s their combina mbinatio ion pa n particu cularly sensi y sensitive t e to o θ 13 13 � 24
Origin of the different correlations Di Differen ent r t rel elative sig e sign f n for ( r ( θ 12 12 , , θ 13 13 ) in P ) in P ee ee � of Solar (h of Sol r (hig igh-E do h-E domina inated) vs KamLAND d) vs KamLAND � High-E sol Hig h-E solar r � - + (adi diabatic MSW) c MSW) � - - KamLAND � KamLAND (vacuu cuum) � oscil cillatio ion pha n phase se � 25
How the tension increased in the past year 2005 2008 SNO-II SNO-III - Central value lower than before best fit of be t fit of θ 12 12 a at a t a � y lower v sl slig ightl tly value ue � - Error reduced when combined ran ange a e allowe wed f d for r θ 12 � y narrowed app ppreci ciabl bly - Apparently a small change but big en t big enoug ugh t h to g o give � rise t r ise to a sig o a signific ifican ant � tension w with KamLAND th KamLAND � 26
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