Tes tj ng minimal seesaw models at hadron co lm iders Arindam Das Korea Neutrino Research Center, Seoul National University, Korea Institute for Advanced Study 18th July, 2017 Neu ts inos at ti e High Energy Fron tj er
Wolfgang Pauli, Enrico Fermi energy momentum conservation ‘Little neutral one’ going to be the most attractive key now a days more care needed amongst many open questions of the SM
Quick Historical Raymond Davis Jr. (1914-2006) Homestake experiment site at Homestake gold mine in Lead, South Dakota Development of the neutrino oscillation experiments John Bahcall Kamiokande, Japan; SAGE, former Soviet Union; GALLEX, Italy; (1934-2005) Super Kamiokande, Japan; Sudbury Neutrino Observatory, Canada
Some Results More'Mysteries'' Super['Kamiokande,'Sudbury'Neutrino'Observatory''1999',' Neutrino'oscilla$on'between'mass'and'flavor'eigenstates' Neutrinos'are'very'special'' Neutrino'oscilla$on'data' ∆ m 2 7 . 6 × 10 − 5 eV 2 SNO 21 | ∆ m 31 | 2 2 . 4 × 10 − 3 eV 2 Super − K sin 2 2 θ 12 0 . 87 KamLAND , SNO sin 2 2 θ 23 0 . 999 T2K 0 . 90 MINOS sin 2 2 θ 13 0 . 084 DayaBay2015 0 . 1 RENO 0 . 09 DoubleChooz
Unresolved'Issues' All the MYSTERIES are not solved ⇥ � ⇥ � ⇥ ν 1 ν e U PMNS ν 2 ν µ ⌅ ⇤ ⌅ ⌅ = ⇤ ν 3 ν τ � ''''Bruno'' � 'Masami'''''' Ziro'Maki' Shoichi'Sakata' Pontecorvo' Nakagawa' ⇤ ⌅ s 13 e − i δ c 12 c 13 s 12 c 13 ⌥ � � 1 , e i ρ , e i φ ⇥ ⌥ � ⌥ � × diag , = ⌥ � − s 12 c 23 − c 12 s 23 s 13 e i δ c 12 c 23 − s 12 s 23 s 13 e i δ s 23 c 13 ⌥ � ⌥ � ⌥ � ⇧ ⌃ s 12 s 23 − c 12 c 23 s 13 e i δ − c 12 s 23 − s 12 c 23 s 13 e i δ c 23 c 13 , e i φ ⇥ ⇥ We'are'looking'for'' Is δ ⇤ = 0 ? Can'we'measure'' , e i ρ , e ?' and'' − π 2 Tes$ng'the'UNITARITY'of'''' U P MNS
Type of neutrino mass still unknown Neutrino'Mass':'What'Type' Paul'Dirac,'FRS'(1902[1984)' Eeore'Majorana','(1906['?')' = m ν ν R ν L +'H.'c.' = m ν ν c L ν L +'H.'c.' L → r ← L → r ← L → r ← L → r ← ← → ← ← R → ← R → R → µ ' Fermion'Number'Conserving' µ µ µ Fermion'Number'Viola$ng' Can'be'tested'in'neutrinoless'double'beta'decay'and' collider'experiments'
Lightest mass eigenstate: Not fixed yet m 1 < m 2 < m 3 : Normal Hierarchy m 3 < m 1 < m 2 : Inverted Hierarchy Normal Hierarchy Inverted Hierarchy
Birth'of'(a)'new'idea/'s':'genera$on'of'neutrino' mass' Weinberg'Operator''in'SM'(d=5),'PRL'43,'1566(1979)' ⇥ L H ⇥ c T H within'the'Standard' L 'Model' M The'dimension'5'operator'can'be'realized'in'the'following'ways' H' H' ⇧ L , ⇧ L , H' H' ⇧ L , ⇧ L , Majorana'mass'term'is'generated'by'the'breaking'of'the'lepton'numbers'by'2'units.'
Minkowski(1977),'Yanagida'(1979),'Gell[Mann,'Ramond,' Seesaw'Mechanism' Gell-Mann, Glashow, Minkowski, Mohapatra, Ramond, Slansky'(1979),''Glashow'(1980),'Mohapatra'and'Senjanovic' Senjanovic, Slansky, Yanagida (1980)' SU(3) SU(2) U(1) Y R − 1 � � ν L L ⊃ − Y αβ L HN β 2 m αβ R N β D � α N N α C R + H.c.. − 1 � L = 1 2 e L 2 − 1 e R 1 1 � � H 0 M D = Y D v − 1 √ 2 . H = 1 2 H − 2 0 N R 1 1 � � 0 M D M ν = . M T m N D Naturally'explains'the'small' neutrino'mass'' N M T m ν = − M D m − 1 D .
Inverse(Seesaw(Mechanism(:(Mohapatra(1986),(Mohapatra(&(Valle((1986)(((( SU(2) U(1) Y − 1 / 2 � L 2 − 1 / 2 H 2 N j 0 1 R N j 0 1 L Relevant(Part(of(the(Lagrangian( j j j L − m ij N i L − Y D ij � i L mass ⊃ − µ ij (( N L ) c ) i N R + H . c . R N L HN m D = Y D √ 2 v ν L → t N R → v N L → r ← N L ← N R ← ν L v t m D m D M M µ
0 0 m D − 1 ) µ ( m D M − 1 ) T m T m ν = ( m D M M ν = 0 M D M T 0 µ − 1 ∼ O (1) If µ ∼ g m D M ll, O ( m ν ), LightS(heavy(mixing(could(be(large(and(Heavy(neutrino(can(be( • It will be dis produced(at(LHC( − 1 � 1, b e phenomenological constraints , R =( m D M
Phenomenological Constraints on N and R s ⌫ ' N ⌫ m + R N m , m D m − 1 ⇣ ⌘ 1 � 1 = U MNS 2 ✏ N h ✏ = R ∗ R T Nonunitarity: JHEP 10 (2006) 084 U T MNS m ν U MNS = diag( m 1 , m 2 , m 3 ) JHEP 12(2007) 061 In the presence of ✏ , the mixing matrix N is not unitary, namely N † N 6 = 1. L CC = � g 2 W µ ` α � µ P L � � N α j ⌫ m j + R α j N m j p + H . c ., g h ⌫ m i � µ P L ( N † N ) ij ⌫ m j + N m i � µ P L ( R † R ) ij N m j L NC = � Z µ 2 cos ✓ W n oi ⌫ m i � µ P L ( N † R ) ij N m j + H . c . + ,
N R Fixing(the(Matrices((((((((and(( , N , R • We consider the two generations of heavy neutrinos s 13 e i δ c 12 c 13 s 12 c 13 − s 12 c 23 − c 12 s 23 s 13 e i δ c 12 c 23 − s 12 s 23 s 13 e i δ U MNS = s 23 c 13 s 12 s 23 − c 12 c 23 s 13 e i δ − c 12 s 23 − s 12 c 23 s 13 e i δ c 23 c 13 × diag (1 , e i ρ , 1) • We fix the parameters by the following neutrino oscillation data sin 2 θ 12 0.87 sin 2 θ 23 1.00 sin 2 θ 13 0.092 ∆ m 2 12 = m 2 2 − m 2 7 . 6 × 10 − 5 eV 2 1 ∆ m 2 23 = | m 2 3 − m 2 2 . 4 × 10 − 3 eV 2 2 |
For the minimal scenario we consider the Normal Hierarchy(NH) and Inverted Hierarchy(IH) cases as ✓q ◆ q ✓ ◆ q q ∆ m 2 23 � ∆ m 2 ∆ m 2 D IH = diag 23 , 0 12 , ∆ m 2 ∆ m 2 12 + ∆ m 2 D NH = diag 0 , 12 , 23 as M N = m 1 N = m 2 we assume degenerate case N , Light neutrino mass matrix for type-I seesaw can be simplified 1 p MNS D NH / IH U † p m D m T m D = m ν = D = U ∗ M N U ∗ D NH / IH O, MNS , MNS M N p 0 1 0 1 1 ( ∆ m 2 23 � ∆ m 2 0 0 12 ) 0 4 B C B C p p 1 1 D NH = ( ∆ m 2 D IH = ( ∆ m 2 A , 12 ) 0 0 23 ) B C B C 4 4 B C B C @ @ A 1 ( ∆ m 2 23 + ∆ m 2 0 12 ) 0 0 4
How can we write O Application Casas- Ibarra Conjecture ⇥ 0 1 0 1 0 1 @ cos( X + iY ) sin( X + iY ) @ cosh Y i sinh Y @ cos X sin X @ A = O = A A � sin( X + iY ) cos( X + iY ) � i sinh Y cosh Y � sin X cos X e X and Y are real parameters. Due to non unitarity, the elements of N are highly constrained by the precession experiments of the W, Z decays and the LFV processes γ Phenomenologies: JHEP Lee and Shrock: 09 (2010) 108 Phys. Rev. D16, 1444 PRD 84, 013005 (2011) (1977). JHEP 08 (2012) 125 W + W + JHEP 09 (2013) 023(E) µ − e − N B ( < 4 . 2 × 10 − 13 ) EPJ C 76, (2016) no.8, 434 µ → e � B ( < 4 . 5 × 10 8 ) PLB 666, (2008)16-22 ⌧ → e � B ( < 12 . 0 × 10 − 8 ) PLB 666, (2008)16-22 ⌧ → µ �
0 1 1 . 288 ⇥ 10 − 5 8 . 76356 ⇥ 10 − 3 0 . 994 ± 0 . 00625 B C |NN † | = 1 . 288 ⇥ 10 − 5 1 . 046 ⇥ 10 − 2 A . 0 . 995 ± 0 . 00625 B C B C @ 8 . 76356 ⇥ 10 − 3 1 . 046 ⇥ 10 − 2 0 . 995 ± 0 . 00625 ce NN † ' 1 � ✏ , ⌧ → e � ' � 0 0 1 < 1 . 288 ⇥ 10 − 5 < 8 . 76356 ⇥ 10 − 3 0 . 006 ± 0 . 00625 B C | ✏ | = < 1 . 288 ⇥ 10 − 5 < 1 . 046 ⇥ 10 − 2 0 . 005 ± 0 . 00625 B C B C @ A < 8 . 76356 ⇥ 10 − 3 < 1 . 046 ⇥ 10 − 2 0 . 005 ± 0 . 00625 ⌧ → µ � µ → e � 1 1 D NH / IH U † p D NH / IH O ∗ O T p ✏ ( � , ⇢ , Y ) = ( R ∗ R T ) NH / IH = m D m T = U MNS MNS . D m N M 2 N
p t ✏ ( � , ⇢ , Y ) is independent of X since 0 0 1 @ cosh 2 Y + sinh 2 Y − 2 i cosh Y sinh Y O ∗ O T = A cosh 2 Y + sinh 2 Y 2 i cosh Y sinh Y @ A Now we perform a scan for the parameter set { � , ⇢ , Y } and identify an allowed region for which ✏ ( � , ⇢ , Y ) satisfies the experimental constraints in Eq. (17). set M N = 100 GeV a − ⇡ ≤ � , ⇢ ≤ ⇡ with the interval of 20 and 0 ≤ y ≤ 14 with the interval of 0 . 01875. π
NH Case Das, Okada: arXiv:1702.04688 0.001 10 - 6 10 - 6 10 - 10 10 - 9 » V 11 2 » V 12 2 10 - 14 10 - 12 10 - 18 10 - 15 10 - 18 10 - 22 - 3 - 2 - 1 0 1 2 3 - 3 - 2 - 1 0 1 2 3 d d 0.001 10 - 5 10 - 6 10 - 9 10 - 9 » V 11 2 » V 12 2 10 - 13 10 - 12 10 - 17 10 - 15 10 - 18 10 - 21 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 Y Y Mixing parameters vary between 10 -5 -10 -20 , similar behavior is obtained for the other elements
IH Case 0.001 10 - 6 10 - 6 10 - 10 » V 11 2 » V 12 2 10 - 9 10 - 14 10 - 12 10 - 18 10 - 15 10 - 18 10 - 22 - 3 - 2 - 1 0 1 2 3 - 3 - 2 - 1 0 1 2 3 d d 0.001 10 - 5 10 - 6 10 - 9 10 - 9 » V 11 2 » V 12 2 10 - 13 10 - 12 10 - 17 10 - 15 10 - 18 10 - 21 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 Y Y Mixing parameters vary between 10 -5 -10 -19 , similar behavior is obtained for the other elements
NH Case 10 - 5 10 - 6 V eN 2 + V m N 2 V eN 2 + V m N 2 10 - 10 V eN V m N * 2 V eN V m N * 2 10 - 10 10 - 15 10 - 14 10 - 20 10 - 18 10 - 25 10 - 30 10 - 22 - 3 - 2 - 1 0 1 2 3 0 2 4 6 8 10 12 14 Y d IH Case 0.001 10 - 5 10 - 6 V eN 2 + V m N 2 V eN 2 + V m N 2 10 - 10 V eN V m N * 2 V eN V m N * 2 10 - 9 10 - 15 10 - 12 10 - 20 10 - 15 10 - 25 10 - 30 10 - 18 - 3 - 2 - 1 0 1 2 3 0 2 4 6 8 10 12 Y d
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