T exture mo dels, neutrino observ ables and Leptogenesis - PDF document

T exture mo dels, neutrino observ ables and Leptogenesis Martin Hirsch Univ ersit y of Southampton 1. Neutrino oscillation data and neutrino masses 2. T exture mo dels, U (1) family symmetries and O (1) co e�cien ts 3. Neutrino observ ables and Leptogenesis 4. Summary � M. Hirsc h and S.F. King, in preparation

Neutrino masses: Exp erimen tal facts A) Limits (PDG2000): m � 3 eV � e m � 190 k eV � � m � 18 : 2 MeV � � h m i � (0 : 2 � 0 : 6) eV � B) \Hin ts" on non-zero neutrino masses: ) A tmospheric neutrinos: Ratio of � =� ev en ts disagrees with exp ectation, e � Sup erKamiok ande con�rms earlier exp erimen ts with high statistics ) Solar neutrinos 5 exp erimen ts (using 3 exp erimen tal tec hniques) observ e less neutrinos than exp ected ) neutrinos as hot dark matter (HDM) Small ( O [ eV ]) neutrino mass migh t help structure formation ) LSND exp erimen t

Neutrino masses and the seesa w mec hanism ) In the SM neutrinos are massless, b ecause N � � do es R not exist ) Supp ose N exists, add the follo wing mass terms: L = m � N + M N N D L M ) Giv es the follo wing mass matrix (one generation notation): 0 1 0 m D M = : B C � N @ m M A D M ) Assuming m � M , one arriv es at the famous seesa w D M form ula: 2 m D m ' � M M ) Smallness of observ ed neutrino masses explained b y large mass scale M M ) Ho w ev er, seesa w mec hanism alone do es not �x relativ e size of di�eren t en tries in the mass matrix

F rogatt-Nielson mec hanism Assume some hea vy singlet � exists. Additional exotic v ector matter with mass M allo ws an expansion parameter � to b e V generated b y a F roggatt-Nielsen mec hanism, � < � > < � > = = � � 0 : 22 M M V V Assign U (1) c harges to L , N , etc: i Ri H (0) (+ insertions) h � i (1) (M) H' ( l + n ) 3 3 L ( l ) N ( n ) 3 3 3 3 The ab o v e diagram generates mass term: j l j + n m � � h H i 3 3 L ;N 3 3 Ev en if coupling at v ertex is of O (1), strong suppression can b e generated!

U (1) F amily Symmetry and T extures Using basic idea of F rogatt-Nielsen mec hanism, assign �a v our c harges (F C) to all �elds, leading to mass matrices of the form: 0 1 j l + n j j l + n j j l + n j a � a � a � 1 1 1 2 1 3 11 12 13 B C j l + n j j l + n j j l + n j B C Y � a � a � a � 2 1 2 2 2 3 B C � 21 22 23 B C B C j l + n j j l + n j j l + n j a � a � a � @ A 3 1 3 2 3 3 31 32 33 0 1 j 2 n + � j j n + n + � j j n + n + � j A � A � A � 1 1 2 1 3 11 12 13 B C j n + n + � j j 2 n + � j j n + n + � j B C M � A � A � A � 1 2 2 2 3 B C RR 12 22 23 B C B C j n + n � j j n + n + � j j 2 n + � j A � A � A � @ A 1 3 2 3 3 13 23 33 ) Since � is � � 1, a high p o w er in the exp onen t leads to v ery small en tries in the mass matrices, so-called texture zeros Example (F C1): l = � 2, l = 0, l = 0, n = � 2, n = 1, 1 2 3 1 2 n = 0 and � = 0, leads to (after the seesa w): 3 0 1 0 1 4 2 2 4 2 2 � � � � � � B C B C F C 1 B 2 C B 2 2 2 C m � + O : � 1 1 � � � B C B C LL B C B C B C B C 2 2 2 2 � 1 1 � � � @ A @ A ) Adv an tage: Smallness of mass and relativ e size of en tries can b e easily �xed ) Disdv an tage: Co e�cien ts a and A (assumed to b e O (1) ij ij couplings) not predicted

O (1) co e�cien ts Basic idea: ) Since O (1) co e�cien ts not predicted, assume them to b e a random n um b ers ) Cho ose in terv al for co e�cien ts suc h that texture struc- ture of mass matrix is not destro y ed ) Run a h uge sample of mo dels in a computer program ) Plot the distributions with cor- lo garithmic al ly binne d rect relativ e normalisation for eac h mo del ) A mo del is then considered to b e a \go o d" mo del, if the p eaks of the distributions coincide with (or are close to) the preferred exp erimen tal v alue

The atmospheric angle Figure: The atmospheric angle for 5 di�eren t mo dels 8 (10 random sets p er mo del): a) red: F C1, b) F C2 (dot-dashes), c) F C3 (thic k dots), d) F C4 (thin dots), e) blue: neutrino mass anarc h y (No structure in neutrino mass matrix). units arbitrary 0.15 0.2 0.3 0.5 0.7 1 s atm It is easy to generate large atmospheric angle!

The solar angle Figure: The solar angle for 5 di�eren t mo dels: a) red: F C1, b) F C2 (dot-dashes), c) F C3 (thic k dots), d) F C4 (thin dots), e) blue: neutrino mass anarc h y. units arbitrary 0.001 0.01 0.1 1 s � Anarc h y prefers large solar angle Fla v our mo dels can b e constructed for either, large (F C1, F C3 and F C4) or small (F C2) solar angle

The \Cho oz angle" 2 2 Figure: s = 4 j U j (1 � j U j ) for 5 di�eren t mo dels: C e 3 e 3 a) red: F C1, b) F C2 (dot-dashes), c) F C3 (thic k dots), d) F C4 (thin dots), e) blue: neutrino mass anarc h y. units arbitrary 0.001 0.01 0.1 1 s C s � (0 : 1 � 0 : 3) Exp erimen tally: in SK region C Anarc h y prefers large s , p eaks at s = 1! C C Cho oz angle imp ortan t discriminator!

2 Ratio of � m 's 2 2 Figure: R � j � m j = j � m j for 5 di�eren t mo dels: 12 23 a) red: F C1, b) F C2 (dot-dashes), c) F C3 (thic k dots), d) F C4 (thin dots), e) blue: neutrino mass anarc h y. units arbitrary 10 - 5 10 - 4 10 - 3 10 - 2 10 - 1 10 0 R Spread in R h uge! Co e�cien ts a and A can not b e neglected! ij ij Small v alues of R disfa v our neutrino mass anarc h y

V ariation in range of co e�cien ts Figure: Solar angle for 3 di�eren t ranges of co e�cien ts for the mo del F C2: p p a) red: � [ 2 �; 1 = 2 � ], b) magen ta: � [0 : 82 ; 1 : 18], c) blue � [0 : 95 ; 1 : 05]. units arbitrary 0.001 0.01 0.1 1 s � Choice of co e�cien ts v ery imp ortan t! ) Theoretical w ork in texture mo dels should concen trate on calculation of co e�cien ts!

Leptogenesis ) CP violation in deca y of ligh test N comes from in terference R b et w een tree-lev el and one-lo op amplitude: y y y �( N ! L + H ) � �( N ! L + H ) R 1 j 2 j R 1 2 � = y y y �( N ! L + H ) + �( N ! L + H ) R 1 j 2 j R 1 2 0 2 2 1 1 M M 2 ! � � y 1 1 = I m ( Y Y ) f ( ) + g ( ) X B C � 1 i � y @ 2 2 A 8 � ( Y Y ) M M i 6 =1 � 11 i i � where p p 1 + x x 2 0 1 3 f ( x ) = x 1 � (1 + x ) ln ; g ( x ) = : 4 @ A 5 x 1 � x ) T exture mo dels �x order of magnitude of Y � ) T aking in to accoun t O (1) co e�cien ts � can b e calculated lik e an y lo w-energy observ able ) Con v ersion � $ Y dep ends on assumed thermal history B of the univ erse

� Y and for F C1-F C4 B 10 - 6 10 - 5 10 - 4 10 - 3 10 - 2 10 - 1 10 0 � 10 - 9 10 - 8 10 - 7 10 - 6 10 - 5 10 - 4 Y B

Neutrino observ ables for v arian ts of F C3 0.02 0.05 0.1 0.2 0.5 1 0.15 0.2 0.3 0.5 0.7 1 s s atm � 10 - 5 10 - 4 10 - 3 10 - 2 10 - 1 0.001 0.01 0.1 1 s R C ) V arian ts di�er only in l , while k eeping n and � constan t i i ) Keeps lo w-energy observ ables unc hanged, re-scales Y uk a w a matrix Mo dels l l l n n n � Colour: F actor: 1 2 3 1 2 3 F C3 -1 1 1 1 = 2 0 -1 = 2 -1 red 1 F C3a -2 2 2 1 = 2 0 -1 = 2 -1 blue 1 : 05 F C3b -3 3 3 1 = 2 0 -1 = 2 -1 magen ta 1 : 1 F C3c -4 4 4 1 = 2 0 -1 = 2 -1 green 1 : 15

Leptogenesis and LA-MSW solution: V arian ts of F C3 10 - 7 10 - 5 10 - 6 10 - 4 10 - 3 10 - 2 � 10 - 12 10 - 10 10 - 8 10 - 6 Y B ) without sp eci�c assumptions ab out Y uk a w a matrix, Leptogenesis indep enden t from lo w energy observ ables!

Leptogenesis and SA-MSW solution: V arian ts of F C2 10 - 4 10 - 3 10 - 2 10 - 1 10 0 10 - 5 10 - 4 10 - 3 10 - 2 10 - 1 10 0 s � s C 10 - 7 10 - 6 10 - 5 10 - 4 10 - 3 10 - 13 10 - 11 10 - 9 10 - 7 � Y B Mo dels l l l n n n � Colour: F actor: 1 2 3 1 2 3 F C2 -3 -1 -1 -3 0 -1 3 red 1 F C2a -4 -2 -2 -3 0 -1 3 blue 1 : 1 F C2b -4 -1 -1 -3 0 -1 3 magen ta 1 F C2c -5 -2 -2 -3 0 -1 3 green 1 : 1