Bridges of Low-E observables with Leptogenesis in mu-tau Reflection Symmetry

Transcript

1 rdges of Low-E observables wth Leptogeness n mu-tau Reflecton Symmetry Y.H.Ahn (Academa Snca) Wth S.K.Kang, C.S.Km, T.P.Nguyen (hep-ph ) Consequences of mu-tau reflecton Symmetry Connecton CP-volaton n neutrno oscllaton to Leptogeness va RG runnng Numercal Results and Summary Sngapore/008 1

2 Present Knowledges Δ m = ev, sn θ = 0.3 ; θ = from Δ m =.4 10 ev, sn = 0.50 ; θ = 45.0 from Atm -Large Mxng Angle sn θ = σ (Malton et al : New J. Phys. 6, 1) θ Nothng s known about all 3 CPV phases, CP ϕ, 1 ϕ Cosmologcal lmt(ncludng the WMAP 3-years results) Upper bound on masses m < 0.14 ev (95% C.L) Starts to Dsfavor the degenerate spectrum of neutrnos (JCAP10,104, astro-ph/ ) η = Sngapore/008

3 Constructon mass matrx m In the flavor bass (,, ) e μ Data m = U Dag.( m, m, m ) U 1 3 T U U μ3 3 e3 U μ U 1 = U Orthorgonalty of wth and : U = U for all = 1,,3 μ 3 1 u1 u u3 U = υ1 υ υ3 wth u = real υ1 υ υ 3 If ths matrx s PMNS, Standard acton s nvarant under μ ξ ξ c c μ m = m m = m ( ξ : phase factors), e eμ μμ Sngapore/008 3

4 Constructon mass matrx m Sm S m wth μ - nterchange operator : S μ Reflecton Symmetry (Harrson-Scott, 00; Grmus-Lavoura, 003) eff = eff = Consder the Lagrangan of the lepton sector from whch the Seesaw-mech. works L m 1 c = LYN φ LYllRφ N M R N + hc.. Take a bass where charged lepton Yukawa couplng matrx s dagonal M : 3 3 symmetrc matrx n flavor space R Y = Dag.( f, f, f ) where n general f : complex e μ α Sngapore/008 4

5 y mposng the CP transpormaton & L μ- symmetry m μ = = S S * LM R SMRS f (real) & f f Y Y e CP-nvarance of M = m = Sm S eff eff Re-basng: R M a be be φ T T φ R M R R, R Y φ M 3 a3 be 3 b3 φ 1 1 M = V V = M Y = V = a be be φ e φ 3 3 m m m ee eμ e T 1 eff = υ R = 0 eμ μμ mμ me mμ m m Y M Y m m m Sngapore/008 5

6 Consequences of μ- reflecton symmetry snθ cos = 0 & CP-volaton s Maxmal θ 3 13 π = 4 CP Maxmal Atmospherc mxng CP π = ϕ 1, = 0 or π (Maj. CP-volatng phases) CP n Oscllaton : J CP = 1 sn θ1 sn θ3 sn θ13 cos θ13 sn C 8 1 θ 4 sn θ for θ P μ - reflecton symmetry ndcates that the CP-asymmetry P( ) P( ) s maxmal μ e 13 μ e As long as θ 0, Non-vanshng would be a sgnal of CP-volaton J CP Sngapore/008 6

7 CPV responsble for AU H All com λ ω λχ κωcos φ1 ωcos φ13 b3 λχ κω cos φ1 χ κ κ cos φ3 YY = + Δ + Δ ωcos Δφ13 κcos Δφ3 pts. of YY are real and + + Δ Δ μ - reflected Y Leptogeness s Not possble (v een n flavored-leptogeness at M 1 1<10 GeV) μ - Impose the μ- reflecton symmetry for the neutrno sectors at the GUT scale. Assumpton: Two heavy Mj. s are exact degenerate n mass and M1 = M M 3 Effects of the parameter a3 and φ3 on low energy neutrno phenomenology and leptogeness are neglgbly small take a = 0 and φ = 0 at the GUT scale 3 3 Sngapore/008 7

8 d T ln( Q/ Λ) RGE: MR = q (YY )MR M R(YY ), t, q 1() SM(SSM) dt + = = 16π Re-basng M = V M V = Dag.( M, M, M ) Y = V Y T T R R R R 1 3 R Snce M changes wth the evoluton of the scale, the untary matrx depends on the scale, too d V = V A wth A = A R R R VR dt d Dagonal Part: M = qm ( YY ), A = 0 dt Mk + M j M j Mk Off-dagonal Part: Ajk = q Re[( YY ) jk ] + q Im[( YY ) jk ], M M M + M wth j k k j j k RGE: d 3 9 3? Y (Y Y ) T = Y T g Y g Y Y A Y SM dt d 3 Y Y T? T = 3 g g 1 + (Y Y + 3 Y Y ) + A Y SSM dt 5 Sngapore/008 8

9 For an exact degeneracy n mass M = M Sngularty! To remove ths sngularty at the degeneracy scale Λ Impose = 0 Re[( YY ) 1( 1) ( 0)] Can always be satsfed by performng c s 0 α α H1 wth R( α) = s c 0 tan α = α α H11 H H 11 0 H 13 T At the GUT scale: H ( 0) YY ( 0) = RYY R = 0 H H 3 H 13 H 3 H 33 Re[ H 1( 1) ( 0)] = 0 No sngularty Im[ H 1(1) ( 0)] = 0 μ - symmetry 1 Y = RY where H H α H α H α H H α H α = cos + sn + sn, = cos + sn H H α H α H α H H α H α = cos sn + sn, = cos sn Sngapore/008 Real! 9

10 YY, Y and N b a a b b M For convenence, m0 υ, λ, χ, ω, κ, η M b b b b M M Degree of degeneracy : N 1 M d 4H1 N = q(1 N)[ H 11 H ] = q dt sn α 1 N qb t wth = 3 3 R Re[ H 1( M)] = Re[ H 1( M)] pb3 y μ t Im[ H ( )] = Im[ H ( )] 3 y t I 1 M 1 M pb3 μ 4( λχ + κω cos Δφ1) sn α p = 1 for SM (SSM) 3 R κ ω where μ = sn α + κω cos α cos Δ φ and = κωsn Δφ I 1 μ 1 Sngapore/008 10

11 RG mproved Drac neutrno Yukawa matrx for SM 3 y y11 εy1 y1 εy t y1 ( εy + y1) t 3 y Y ( M) y1 + εy11 y + εy1 t y + ( εy1 y) t 0 y3 y3 for SSM ε 3 ε and y y 3 y = b λc + χs y = b κs e + ωc e y = b φ φ1 where ( ), ( ), 11 3 α α 1 3 α α 3 3 φ φ1 ( ), ( ), y = b χc λs y = b κc e ωs e 1 3 α α 3 α α 3y R ε : corrected by Degeneracy ε μ y : corrected by Y tself μ - reflected Y s broken by y Such small RG effects can trgger leptogeness. Sngapore/008 11

12 RG mproved the effectve neutrno mass matrx Herarchcal lght neutrno spectrum RG effects from Seesaw to EW scale on m eff as well as U PMNS are expected to be very small even n SSM case As a results of the RG effects, m m m (1 + a ) meff m0 m m m O y m m m ee eμ eμ 4 eμ μμ μ (1 + a ) + ( ) eμ(1 + a ) μ(1 + a ) μμ(1+ a ) a = y 3 y t SM t SSM Ψ Ψ e e y Re-phasng as and μ μ m e e (1 + a ) meff m0 e m a O y Φ Φ ee eμ eμ Φ 4 eμ μμ μ (1 + ) + ( ) Φ eμe (1 + a ) mμ(1 + a ) μμ(1+ a ) R G correcton term a 0 recovers μ- symmetry Sngapore/008 1

13 Ψ where Φ=Ω, λω cosφ + κλ cosφ ω cos φ + κ cos φ Ω= Ψ cos cos + ( ) eμ μμ O η = λω + κ χ + λχκω cos Δ φ, κ + ω ++ κω cos Δφ + O( η ) eμ μμ 1 CP θ3 CP π cos a κ + ω Φ Δ = + Φ λ χ sn π κ + ω θ3 a Δ tan Φ 4 λ + χ tanθ ( κχ + ωλ) cos Φ ( κ + ω ) 1 Sngapore/008 13

14 θ 13 θ 13 ( κχ + λω) ( λ + χ ) sn Φ 4 ( κ + ω ) where sn Φ ( ) λ + χ κ + ω I μ Exstence of θ 0 s very Important 13 because t may be related wth Lepton ccp (measurable va Osc.) JCP θ 13 sn λ I + θ1 χ μ { λχ( κ ω ) + κω( λ χ )cos Δφ 4 1} 4 16( κ + ω ) θ can teach us about How 13 roken μ- symmetry s responsble for the orgn of AU n our scenaro. Sngapore/008 14

15 Radatvely generated leptonc CP-Asymmetry ε ε ε I e μ ee ee 1() ε R R 16πh1() μ μ μ 1() 1() ε ± t + O t I με ± ε + 3πh1() ( ) μ 1 t O( t ) R μ I 3 με ε ± + + 3πh1() 3 μ 1 3 y t O( t ) R μ ε 1() I 3 με y 16π h 1() t + Ot ( ) ε ε ε I e μ ee ε ee 1() R R 48πh1() μ 3 μ μ 1() 1() ε I με 4ε 96πh1() 3 + t + O t μ 1 + t O( t ) R + μ ( ) I με ε πh1() 9 μ 1 y t O( t ) R μ ε 1() I μ ε y 4π h 1() t + Ot ( ) Sngapore/008 15

16 χ λ ee = sn α + λχcos α ee = ( χ λ )cos α λχsn α = Δ μ ( κ ω )cos α κωsn αcos φ1 h1 = H 11 b3 ( κ + χ )sn α + ( ω + λ )cos α + { λχ + κωcosδφ1 sn α} h = H b ( κ + χ ) cos α + ( ω + λ ) sn α { λχ + κωcosδφ sn α} 3 1 ee R μ H ( λχ + κω cos Δφ ) = = s justfed from tan α =... H11 H λ + ω χ κ From the Yukawa-Drac neutrno overall scale, b m M (174GeV) = ye 0.05eV 10 GeV υ TeV Leptogeness!! ε α I and ε A lnk between θ and Leptogeness μ 13 ε ε and ε ε due to 1 and ( e μ h h O ε ) O( ε ) O( ε ) α 1 α 1 Sngapore/008 16

17 Wash-out Parameters m K s c e 0 1 ( χ α + λ α) m m K c c e 0 ( χ α λ α) m m K ( κ s + ω c + κωs c cos Δφ ) μ, 0 1 α α α α 1 m m K ( κ c + ω s κωs c cos Δφ ) μ, 0 α α α α 1 m Snce K can be much less than one and O( ε ) O( ε ) O( ε ) e e μ the lepton asym. for electron flavor n the WK washout regme leads to the d omnant contrbuton to the lepton asym., whch can be enough to gve rse to successful baryogeness. Sngapore/008 17

18 Case-I: Weak Wash-out K > 1, K > 1, K < 1 e, μ, μ, e 1 Numercally SM K 10 1, K e 5 SSM K 10 1, K 80 (tan β = 1), 40 (tan β = 10 60) e 5 The resultng baryon-to-photon rato η can be smply approxmated as f η f 3 e 10 ε e KK Chooz angle θ 13 Sngapore/008 18

19 How tan β s correlated wth the mxng angle θ 13 β 0.1 h tan 1 e R I K K μ μ 1 How the baryon asymmetry η s senstve to the CP-volatng observable measurable J CP through Oscllaton f Sngapore/008 19

20 η ε 3y η ε π 1 M 1 ln f e e e K( K) 4 Λ K( K) SM The predcton of η s suppressed by 10 K, 8 e e.., 4 8 order of magntude compared wth η η s too small to gve successful leptogeness. f SSM The predcton of η s suppressed by 8 10 (1 tan ) + β K e Radatvely nduced ε y = y (1 + tan β) 4 4 1( ) SM for large tan β t can be hghly enhanced. Lower lmt of tan β from the CM observaton h tan β tan β 60 R I t μ μ Sngapore/008 0

21 Case-II: Strong Wash-out K μ > e,, 1, 1 The resultng baryon-to-photon rato η can be approxmately gven by η α ε κ wth κ = f α α 10 α f K K K α α In the ST wash-out case, the resultng baryon asym. s too small to gve a successful leptogeness n the SM. SSM Numercally, κ 10 > κ 10 κ > κ 10, for tan β 3 e κ e 1 μ, μ, e > κ 10 κ > κ 4 10, for tan β < 3 1 μ, μ, e Flavor dependent washout factors almost equally contrbute to leptogeness. η f can be smply approxmated as an order of magntude f 11 η 10 (1 + tan β ) At least tan β 7 s needed for flavored leptogeness to successfully work. Sngapore/008 1

22 η s not senstve to θ any more, nstead of that, senstve to θ f 13 1 Sngapore/008

23 A correlaton between tan β and θ : 1 best-ft η tan β 1 xy SM 1 wth x η = f y f In order for the predcton of η to be consstent wth the rght amount of baryon asymmetry, tanβ 7 The best-ft value of η and the current measurements of θ favors whch can be measurable n the upcomng LL neutrno oscllaton experments. J CP Sngapore/008 3

24 Concluson We showed that CP volaton responsble for the generaton of baryon asymmetry of our unverse can be drectly lnked wth CP volaton measurable through neutrno oscllaton as well as neutrno mxng angles θ and θ We expect that n addton to the reactor and long baselne neutrno experments for precse measurng neutrno mxng angles and CP volaton, the measurements for the supersymmetrc parameter tanβ at future collder experments would serve as an ndrect test of our scenaro of baryogeness based on the μ - reflecton symmetry. Sngapore/008 4