New interactions: past and future experiments Michele Maltoni Departamento de F´ ısica Te´ orica & Instituto de F´ ısica Te´ orica Universidad Aut´ onoma de Madrid Neutrino 2008, Christchurch, New Zealand – May 27, 2008 I. Non-standard interactions with matter Violation of fundamental principles Neutrino magnetic moment II. Models with extra sterile neutrinos Long-range leptonic forces III. Neutrino decay and decoherence Mass-varying neutrinos . . . Summary
I. Non-standard interactions with matter 2 Lagrangian formalism • Effective low-energy Lagrangian for standard neutrino interactions with matter: √ √ 2 G F ∑ 2 G F ∑ g f ν β γ µ L ℓ β ][ ¯ f γ µ Lf ′ ]+ h.c. ν β γ µ L ν β ][ ¯ f γ µ P f ] L eff � � SM = − 2 [ ¯ − 2 P [ ¯ β P , β where P ∈ { L , R } , ( f , f ′ ) form an SU ( 2 ) doublet, and g f P is the Z coupling to fermion f : L = 1 L = sin 2 θ W − 1 L = − 2 3 sin 2 θ W + 1 L = 1 3 sin 2 θ W − 1 g ν g ℓ g u g d 2 , 2 , 2 , 2 , R = − 2 R = 1 g ν g ℓ R = sin 2 θ W , 3 sin 2 θ W , 3 sin 2 θ W ; g u g d R = 0 , • here we consider NC-like non-standard neutrino-matter described by: √ 2 G F ∑ ε fP ν α γ µ L ν β ][ ¯ f γ µ P f ] ; L eff αβ [ ¯ NSI = − 2 P , α , β note that ε fP αβ is Hermitian; • for convenience, we also define the vector component ε fV αβ = ε fL αβ + ε fR αβ . Michele Maltoni <michele.maltoni@uam.es> N EUTRINO 2008, C HRISTCHURCH , 27/05/2008
I. Non-standard interactions with matter 3 Bounds from non-oscillation experiments (Flavor Conserving) ν e e → ν e LSND − 0 . 03 < ε eL 0 . 004 < ε eR ee < 0 . 08 ee < 0 . 15 good [1, 2] ν e e → ¯ ν e ¯ Reactors − 1 < ε uL − 0 . 4 < ε uR ν e q → ν q ee < 0 . 3 ee < 0 . 7 CHARM mild [3] − 0 . 3 < ε dL − 0 . 6 < ε dR ν e q → ν q ee < 0 . 3 ee < 0 . 5 CHARM mild [3] | ε eL | ε eR ν µ e → ν e µµ | < 0 . 03 µµ | < 0 . 03 CHARM II good [1, 3] | ε uL − 0 . 008 < ε uR ν µ q → ν q µµ | < 0 . 003 µµ < 0 . 003 NuTeV strong [3] | ε dL − 0 . 008 < ε dR ν µ q → ν q µµ | < 0 . 003 µµ < 0 . 015 NuTeV strong [3] e + e − → ν ¯ − 0 . 5 < ε eL − 0 . 3 < ε eR νγ ττ < 0 . 2 ττ < 0 . 4 LEP mild [1, 4] | ε uL | ε uR τ decay ττ | < 1 . 4 ττ | < 3 rad. corrections poor [3] | ε dL | ε dR τ decay ττ | < 1 . 1 ττ | < 6 rad. corrections poor [3] (limits at 90% CL varying one parameter at a time ) [1] J. Barranco et al. , arXiv:0711.0698 . [2] J. Barranco et al. , Phys. Rev. D73 (2006) 113001 [ hep-ph/0512195 ]. [3] S. Davidson et al. , JHEP 03 (2003) 011 [ hep-ph/0302093 ]. [4] Z. Berezhiani and A. Rossi, Phys. Lett. B535 (2002) 207 [ hep-ph/0111137 ]. Michele Maltoni <michele.maltoni@uam.es> N EUTRINO 2008, C HRISTCHURCH , 27/05/2008
I. Non-standard interactions with matter 4 Bounds from non-oscillation experiments (Flavor Changing) | ε eL | ε eR eµ | < 0 . 0005 eµ | < 0 . 0005 µ → 3 e rad. corrections strong [3] | ε uL | ε uR eµ | < 0 . 0008 eµ | < 0 . 0008 Ti µ → Ti e rad. corrections strong [3] | ε dL | ε dR eµ | < 0 . 0008 eµ | < 0 . 0008 Ti µ → Ti e rad. corrections strong [3] | ε eL | ε eR ν e e → ν e e τ | < 0 . 33 e τ | < 0 . 28 LEP+LSND+Rea mild [1, 4] | ε uL | ε uR ν e q → ν q e τ | < 0 . 5 e τ | < 0 . 5 CHARM mild [3] | ε dL | ε dR ν e q → ν q e τ | < 0 . 5 e τ | < 0 . 5 CHARM mild [3] | ε eL | ε eR ν µ e → ν e µ τ | < 0 . 1 µ τ | < 0 . 1 CHARM II good [1, 3] | ε uL | ε uR ν µ q → ν q µ τ | < 0 . 05 µ τ | < 0 . 05 NuTeV good [3] | ε dL | ε dR ν µ q → ν q µ τ | < 0 . 05 µ τ | < 0 . 05 NuTeV good [3] (limits at 90% CL varying one parameter at a time ) WARNING: bounds become weaker when correlations among parameters are included! [1] J. Barranco et al. , arXiv:0711.0698 . [3] S. Davidson et al. , JHEP 03 (2003) 011 [ hep-ph/0302093 ]. [4] Z. Berezhiani and A. Rossi, Phys. Lett. B535 (2002) 207 [ hep-ph/0111137 ]. Michele Maltoni <michele.maltoni@uam.es> N EUTRINO 2008, C HRISTCHURCH , 27/05/2008
I. Non-standard interactions with matter 5 NSI and neutrino oscillations • Equation of motion: lots of parameters: ν id � 1 0 · U † + V SM + V NSI ; � � ν ; 0 , ∆ m 2 21 , ∆ m 2 H = U · H d H d dt = H � 0 = diag ; 31 2 E ν s 13 e − i δ CP ν e c 12 c 13 s 12 c 13 − s 12 c 23 − c 12 s 13 s 23 e i δ CP c 12 c 23 − s 12 s 13 s 23 e i δ CP ν = ν µ � U = , ; c 13 s 23 s 12 s 23 − c 12 s 13 c 23 e i δ CP − c 12 s 23 − s 12 s 13 c 23 e i δ CP c 13 c 23 ν τ ε fV ε fV ε fV e τ ee eµ √ √ N f 2 G F N e ∑ ∗ ε fV ε fV ε fV V SM = ± 2 G F N e diag ( 1 , 0 , 0 ) ; V NSI = ± ; µ τ eµ µµ ∗ ε fV ∗ ε fV N e f ε fV e τ µ τ ττ • note that only the vector couplings ε fV αβ = ε fL αβ + ε fR αβ appear in propagation; • however, NC-like NSI can affect detection ( e.g. , ν e → ν e elastic scattering); ⋆ too much parameters ⇒ only partial analyses so far. . . Michele Maltoni <michele.maltoni@uam.es> N EUTRINO 2008, C HRISTCHURCH , 27/05/2008
I. Non-standard interactions with matter 6 Solar neutrinos • As in the SM case, solar neutrinos can be reduced to an effective 2 ν problem [5]: � � � � � � �� ν ∆ m 2 − cos2 θ 12 sin2 θ 12 ε f √ c 2 √ id � 13 0 0 ν , 21 � dt = ± 2 G F N e ( r ) ± 2 G F N f ( r ) sin2 θ 12 cos2 θ 12 ε f ε ′ 4 E ν 0 0 f eµ c 23 − ε fV e τ s 23 ) − s 13 [ ε fV µµ − ε fV ε f = c 13 ( ε fV µ τ ( c 2 23 − s 2 23 )+( ε fV ττ ) c 23 s 23 ] , � � ν e ν = ε ′ f = ε fV 23 + ε fV 23 − ε fV ee − 2 ε fV µ τ c 23 s 23 + 2 s 13 c 13 ( ε fV e τ c 23 + ε fV µµ c 2 ττ s 2 � , eµ s 23 ) ν a 13 ( ε fV 23 + ε fV 23 − ε fV ee + 2 ε fV − s 2 ττ c 2 µµ s 2 µ τ s 23 c 23 ) (neglecting for simplicity δ CP and the complex phases in ε fV αβ ); • Analyses in the literature [5, 6] focus on f = { u , d } , because (1) bounds on ε qV αβ are weaker, and (2) for f = e SK detection is also affected by NSI. • pre-Borexino solar data can be perfectly fitted by NSI only ( i.e. , ∆ m 2 21 = 0 ); • however, KamLAND requires ∆ m 2 21 ⇒ pure NSI solution no longer interesting. [5] M. Guzzo et al. , Nucl. Phys. B629 (2002) 479 [ hep-ph/0112310 ]. [6] A. M. Gago et al. , Phys. Rev. D65 (2002) 073012 [ hep-ph/0112060 ]. Michele Maltoni <michele.maltoni@uam.es> N EUTRINO 2008, C HRISTCHURCH , 27/05/2008
I. Non-standard interactions with matter 7 Solar neutrinos with both oscillations and NSI • Solar LMA solution is unstable with respect to the introduction of NSI [7, 8, 9]; • KamLAND is insensitive to NSI ⇒ it determines ∆ m 2 21 ; • bounds on ε q and ε ′ q from combined Solar+KamLAND analysis are very weak. 20 [9] Present [7] Future 15 LMA-II LMA-II ∆ m 2 (eV 2 ) LMA-I LMA-I 2 ∆χ 10 LMA-0 5 90% C.L. 90% C.L. 0 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 1 ε ε ’ tan 2 θ tan 2 θ [7] O. G. Miranda, M. A. Tortola, and J. W. F. Valle, JHEP 10 (2006) 008 [ hep-ph/0406280 ]. . C. de Holanda, and O. L. G. Peres, Phys. Lett. B591 (2004) 1 [ hep-ph/0403134 ]. [8] M. M. Guzzo, P [9] A. Friedland, C. Lunardini, and C. Pena-Garay, Phys. Lett. B594 (2004) 347 [ hep-ph/0402266 ]. Michele Maltoni <michele.maltoni@uam.es> N EUTRINO 2008, C HRISTCHURCH , 27/05/2008
I. Non-standard interactions with matter 8 Atmospheric neutrinos: the ν µ − ν τ channel • We consider NSI in the µ − τ sector [10] (note that ε fV µµ ≈ 0 from LAB data): � ∆ m 2 � � � ε fV �� � � ν − cos2 θ 23 sin2 θ 23 √ ν µ id � 0 µ τ ν , ν = 31 ∗ ε fV � � dt = ± 2 G F N f ( r ) ; sin2 θ 23 cos2 θ 23 ν τ ε fV 4 E ν µ τ ττ • determination of oscillation parameters is very stable ; 0 4 • 90% ( 3 σ ) bounds on NSI [11]: 10 F = √ [11] 2 /4 f = e f = e µµ | � | ε eV µ τ | ≤ 0 . 038 ( 0 . 058 ), ττ − ε e 2 ] -3 eV -1 3 ( e ) 10 | ε eV 2 + | ε e ττ | ≤ 0 . 12 ( 0 . 19 ); 31 [10 ★ � µτ | | ε uV µ τ | ≤ 0 . 012 ( 0 . 019 ), 2 | ε e -2 2 ∆ m 10 ( u ) | ε uV ττ | ≤ 0 . 039 ( 0 . 061 ); -3 1 � | ε dV 10 µ τ | ≤ 0 . 012 ( 0 . 019 ), 0 0.25 0.5 0.75 1 -1 -0.5 0 0.5 1 2 θ 23 ( d ) | ε e µτ | / F sin | ε dV ττ | ≤ 0 . 038 ( 0 . 060 ); • Bounds on ε fV ττ are much stronger than LAB ones. [10] N. Fornengo et al. , Phys. Rev. D65 (2002) 013010 [ hep-ph/0108043 ]. [11] M. C. Gonzalez-Garcia and M. Maltoni, Phys. Rept. 460 (2008) 1 [ arXiv:0704.1800 ]. Michele Maltoni <michele.maltoni@uam.es> N EUTRINO 2008, C HRISTCHURCH , 27/05/2008
Recommend
More recommend
