Post-Sphaleron Baryogenesis and n n Oscillations. K.S. Babu

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1 Post-Sphaleron Baryogenesis an n n Oscillations K.S. Bab Oklahoma State University INT Workshop on Netron-Antinetron Oscillations University of Washington, Seattle October 23 27, 2017 Base on: K. S. Bab, R. N. Mohapatra (2017) (to appear); K. S. Bab, R. N. Mohapatra an S. Nasri, hep-ph/ ; hep-ph/ ; K. S. Bab, P. S. Bhpal Dev an R. N. Mohapatra, arxiv: [hep-ph]; K. S. Bab, P. S. Bhpal Dev, E. C. F. S. Fortes an R. N. Mohapatra, arxiv: [hep-ph] K.S. Bab (OSU) Post-Sphaleron Baryogenesis 1 / 26

2 Otline Iea of post-sphaleron baryogeneis Explicit moels base on SU(2) L SU(2) R SU(4) C symmetry Relating baryogenesis with netron-antinetron oscillation Other experimental tests Conclsions K.S. Bab (OSU) Post-Sphaleron Baryogenesis 2 / 26

3 Generating Baryon Asymmetry of the Universe Observe baryon asymmetry: Y B = n B n B = (8.75 ± 0.23) s Sakharov conitions mst be met to ynamically generate Y B Baryon nmber (B) violation C an CP violation Departre from thermal eqilibrim All ingreients are present in Gran Unifie Theories. However, in simple GUTs sch as SU(5), B L is nbroken Electroweak sphalerons, which are in thermal eqilibrim from T = ( ) GeV, wash ot any B L preserving asymmetry generate at any T > 100 GeV Kzmin, Rbakov, Shaposhnikov (1985) K.S. Bab (OSU) Post-Sphaleron Baryogenesis 3 / 26

4 Generating baryon asymmetry (cont.) Sphaleron: Non-pertrbative configration of the electroweak theory Leas to effective interactions of left-hane fermions: O B+L = i (q i q i q i L i ) c L sl s L t L b L Obeys B = L = 3 L Sphaleron b L Sphaleron can convert lepton asymmetry to baryon asymmetry Leptogenesis mechanism (Fkgita, Yanagia (1986)) L L νe νµ ν τ Post-sphaleron baryogenesis: Baryon nmber is generate below 100 GeV, after sphalerons go ot of eqilibrim (Bab, Nasri, Mohapatra (2006)) K.S. Bab (OSU) Post-Sphaleron Baryogenesis 4 / 26

5 Post-Sphaleron Baryogenesis A scalar (S) or a pseoscalar (η) ecays to baryons, violating B B = 1 is strongly constraine by proton ecay an cannot lea to sccessfl post-sphaleron baryogenesis B = 2 ecay of S/η can generate baryon asymmetry below T = 100 GeV: S/η 6 q; S/η 6 q Decay violates CP, an occrs ot of eqilibrim Natrally realize in qark-lepton nifie moels, with S/η ientifie as the Higgs boson of B L breaking B = 2 connection with n n oscillation Qantitative relationship exists in qark-lepton nifie moels base on SU(2) L SU(2) R SU(4) C K.S. Bab (OSU) Post-Sphaleron Baryogenesis 5 / 26

6 Conitions for Post-Sphaleron Baryogenesis At high temperatre, T above the masses of S/η an the meiators, the B-violating interactions are in eqilibrim: Γ B 0 (T ) H(T ) = 1.66(g ) 1/2 T 2 M Pl As niverse cools, S/η freezes ot from the plasma while relativistic at T = T with T M S/η. (Nmber ensity of S/η is then comparable to n γ.) For T < T, ecay rate of S/η is a constant. S/η rifts an occasionally ecays. As the niverse cools, H(T ) slows; at some temperatre T, the constant ecay rate of S/η becomes comparable to H(T ). S/η ecays at T T generating B. Post-sphaleron mechanism assmes T = ( ) GeV. K.S. Bab (OSU) Post-Sphaleron Baryogenesis 6 / 26

7 Diltion of Baryon Asymmetry S/η 6q ecay occrs att M S/η. There is no wash ot effect from back reactions However, S/η ecay mps entropy into the plasma. This reslts in a iltion: s before g 1/4 0.6(Γ η M Pl ) 1/2 T s after rm η M η M η cannot be mch higher than a few TeV, or else the iltion will be too strong There is a frther iltion of orer 0.1, owing to the change of g from at 200 MeV to 5.5 after recombination K.S. Bab (OSU) Post-Sphaleron Baryogenesis 7 / 26

8 Smmary of Constraints on PSB Pseoscalar η mst have B = 2 ecays Sch ecays shol have CP violation to generate B asymmetry η shol freeze-ot while relativistic: T M η. This reqires η to be feebly interacting, an a singlet of Stanar Moel T, the temperatre when η ecays, shol lie in the range T = (100 MeV 100 GeV) η shol have a mass of orer TeV, or else baryon asymmetry will sffer a iltion of T /M η K.S. Bab (OSU) Post-Sphaleron Baryogenesis 8 / 26

9 Qark-Lepton Symmetric Moels Qark-lepton symmetric moels base on the gage grop SU(2) L SU(2) R SU(4) C have the necessary ingreients for PSB There is no B = 1 processes since B L is broken by 2 nits. Ths there is no rapi proton ecay. Symmetry may be realize in the 100 TeV range There is baryon nmber violation meiate by scalars, which are the partners of Higgs that lea to seesaw mechanism Scalar fiels S/η arise natrally as Higgs bosons of B L breaking Ykawa copling that affect PSB an n n oscillations are the same as the ones that generate netrino masses K.S. Bab (OSU) Post-Sphaleron Baryogenesis 9 / 26

10 Qark-Lepton Symmetric Moels Moels base on SU(2) L SU(2) R SU(4) C (Pati-Salam) Fermions, incling ν R, belong to (2, 1, 4) (1, 2, 4) Symmetry breaking an netrino mass generation nees Higgs fiel (1, 3, 10). Uner SU(2) L U(1) Y SU(3) C : (1, 3, 10) = (1, 8 3, 6 ) (1, 2 3, 6 ) (1, + 4 3, 6 ) e(1, 2 3, 3 ) ν(1, 4 3, 3 ) e (1, 8 3, 3 ) ν (1, 2 3, 3 ) ee(1, 4, 1) νe(1, 2, 1) νν(1, 0, 1).,, are iqarks, e, ν, e, ν are leptoqarks, an νν is a singlet that breaks the symmetry Diqarks generate B violation, leptoqarks help with CP violation, an singlet νν provies the fiel S/η for PSB K.S. Bab (OSU) Post-Sphaleron Baryogenesis 10 / 26

11 Qark-Lepton Symmetric Moels (cont.) Interactions of color sextet iqarks an B violating coplings: L I = f ij 2 i j + h ij 2 i j + g ij 2 2 ( i j + j i ) + λ 2 νν + λ νν + h.c. f ij = g ij = h ij an λ = λ from gage symmetry. We also introce a scalar χ(1, 2, 4) which coples to (1, 3, 10) via (µχχ χ ν χ ν νν +...) Among the phases of νν an χ ν, one combination is eaten by B L gage boson. The other, is a pseoscalar η: νν = (ρ 1 + v R ) e iη 1/v R, χ ν = (ρ 2 + v B ) e iη 2/v B, η = 2η 2v R η 1 v B 2 2 4v 2 R + vb 2 Avantage of sing η 6 q is that η has a flat potential e to a shift symmetry K.S. Bab (OSU) Post-Sphaleron Baryogenesis 11 / 26

12 Baryon violating ecay of η η 6q an η 6q ecays violate B: η η K.S. Bab (OSU) Post-Sphaleron Baryogenesis 12 / 26

13 Baryon violating ecay of η (cont.) B-violating ecay rate of η: Γ η Γ(η 6q) + Γ(η 6 q) = Here P is a phase space factor: ( ) P 12 M π λ 2 Tr(f f )[Tr(ĝ ĝ)] 2 13 η M 8 M 4 { (M P = /M S, M /M S 1) (M /M S = M /M S = 2). T is obtaine by setting this rate to Hbble rate. For T = (100 MeV 100 GeV), f g h 1, M M η neee η has a competing B = 0 for-boy ecay moe, which is necessary to generate CP asymmetry: η () ν ν The six-boy an for-boy ecays shol have comparable withs, or else B asymmetry will be too small K.S. Bab (OSU) Post-Sphaleron Baryogenesis 13 / 26

14 η () ν ν Baryon conserving ecay of η R R ν R ν ν R ν η ν R ν η ν R ν R R This generates absorptive part an CP violation in η 6q: η ν R ν R ν ν K.S. Bab (OSU) Post-Sphaleron Baryogenesis 14 / 26

15 η ν ν has a with: Baryon Asymmetry Γ η Γ(η ν ν) + Γ(η ν ν) = Here P is a phase space factor, P For λ = 1, Γ 6 ( ) Γ 4 M4 ν R M 4 Baryon asymmetry: ( f 2 Im(λ λ) M 2 ) ɛ B 8π( λ 2 + Γ 4 /Γ 6 ) Mν 2 R ( ) P 1024π 5 [Tr(ˆf ˆf )] 3 M 5 η Mν 4 R With M νr 100 M, Γ 4 Γ 6. This choice maximizes ɛ B : ɛ B ( f 2 λ ) Im( 8π λ ) For f λ 1, reasonable baryon asymmetry is generate with a iltion 10 3 K.S. Bab (OSU) Post-Sphaleron Baryogenesis 15 / 26

16 Other constraints for sccessfl baryogenesis η mst freeze ot at T M η. Interactions of η with lighter particles mst be weak. The scattering processes freeze ot as esire, owing to the shift symmetry in η. η ν η ν R ν η ν ν R R η ν R ν η η K.S. Bab (OSU) Post-Sphaleron Baryogenesis 16 / 26

17 Connection with n n oscillation As η is associate with B L symmetry breaking, replacing η by the vacm expectation vale, n n oscillation reslts: v B L v B L n n n n M η 3TeV, M 4TeV, M 50TeV, M ν 1TeV, v B L 300TeV is a consistent choice Flavor epenence of baryon asymmetry can be fixe via netrino mass generation K.S. Bab (OSU) Post-Sphaleron Baryogenesis 17 / 26

18 Connection with netrino oscillations Qark-Lepton symmetry implies that the Ykawa coplings entering η ecay an n n oscillation is the same as in netrino mass generation In type-ii seesaw mechanism for netrino masses, M ν f. A consistent choice of f that yiels inverte netrino spectrm: f = This choice satisfies all flavor changing constraints meiate by color sextet scalars The (1,1) entry will be relevant for n n oscillation. It is ince via a W boson loop K.S. Bab (OSU) Post-Sphaleron Baryogenesis 18 / 26

19 Flavor changing constraints,, fiels lea to flavor violation, at tree level as well as at loop: H F =2 = 1 f il fkj 8 M 2 ( α krγ µir α )(β jrγ µ β lr ) + 1 [(ff ) ij (ff ) lk + (ff ) ik (ff ) lj ] 256π 2 M 2 [( α ] jrγ µir α )(β krγ µ β lr ) + 5(α jrγ µ β ir )(β krγ µ lr α ) s s i s s s i j s j K.S. Bab (OSU) Post-Sphaleron Baryogenesis 19 / 26

20 Flavor changing constraints Process Diagram Constraint on Coplings ( M ) 2 Tree f 22 f TeV ( M ) m Bs Box 3i=1 f i3 fi TeV ( M ) Box 3i=1 ĝ i3 ĝi TeV ( M ) 2 Tree f 11 f TeV ( M ) m B Box 3i=1 f i3 fi TeV ( M ) Box 3i=1 ĝ i3 ĝi TeV ( M ) 2 Tree f 11 f TeV ( M ) m K Box 3i=1 f i2 fi TeV ( M ) Box 3i=1 ĝ i1 ĝi TeV ( ) m D Tree h 11 h22 M TeV ( ) Box 3i=1 h i2 hi1 M TeV Table : Constraints on the proct of Ykawa coplings in the PSB moel from K 0 K 0, D 0 D 0, B 0 s B 0 s an B 0 B0 mixing. K.S. Bab (OSU) Post-Sphaleron Baryogenesis 20 / 26

21 Preiction for n n oscillation We take all PSB constraints, netrino mass an mixing constraints, an FCNC constraints to estimate n n oscillation time The flavor strctre of f has a zero in the (1,1) element. This entry is generate by a W boson loop. t W vb L b K.S. Bab (OSU) Post-Sphaleron Baryogenesis 21 / 26

22 Preiction for n n oscillation (cont.) Amplite for n n oscillation: Loop ince amplite: A tree n n f 11g11λv 2 BL + f 11h 2 11 λ v BL M 2 M 4 M 4 M 2 A 1 loop n n g 2 g 11 g 13 f 13 V b V tλv BL 128π 2 M 2 ( mt m b m 2 W Loop fnction: [ ( 1 1 M 2 ) F = ln 1 M 2 M 2 M 2 mw (mt 2 /4mW 2 + ) ( ) m 2 M 2 M 2 1 (mt 2 /mw 2 ) ln t m 2 W ) F n O 2 RLR n M 2 ( M 2 ) ] ln mw 2 K.S. Bab (OSU) Post-Sphaleron Baryogenesis 22 / 26

23 Preiction for n n oscillation (cont.) Effective operator: ORLR 2 = (irc T jr )(klc T ll )(mrc T nr )Γ s ijklmn Matrix element in MIT bag moel (Rao an Shrock): n ORLR n 2 = GeV 6 QCD correction: c QCD (µ, 1GeV) = [ αs(µ 2 ) ] 8/7 [ ] α s(mt 2) 24/23 [ αs(m b 2) ] 24/25 [ α s(m 2 ] 8/9 c) α s(mt 2) α s(mb 2) α s(mc) 2 α s(1 GeV 2 ) n n δm = c QCD (µ, 1 GeV) τ 1 A 1 loop n n K.S. Bab (OSU) Post-Sphaleron Baryogenesis 23 / 26

24 Preiction for n n oscillation (cont.) Τ n n 10 8 sec Τ n n 10 8 sec M TeV M TeV Figre : Scatter plots for τ n n as a fnction of the masses M, M. K.S. Bab (OSU) Post-Sphaleron Baryogenesis 24 / 26

25 Preiction for n n oscillation (cont.) Probability n n Figre : The likelihoo probability for a particlar vale of τ n n as given by the moel parameters. K.S. Bab (OSU) Post-Sphaleron Baryogenesis 25 / 26

26 Conclsions Post-sphaleron baryogenesis is an alternative to high scale leptogenesis Directly linke with n n oscillation In qark-lepton symmetric moels, post-sphaleron baryogenesis can lea to qantitative preiction for n n oscillation time τ n n ( ) sec. is the preferre range from PSB Within a concrete moel, an pper limit of τ n n < sec. is erive, which may be accessible to experiments K.S. Bab (OSU) Post-Sphaleron Baryogenesis 26 / 26