Update on the post-sphaleron baryogenesis model prediction for neutron-antineutron oscillation time
Bhupal Dev
Washington University in St. Louis
Theoretical Innovations for Future Experiments Regarding B Violation University of Massachusetts, Amherst August 4, 2020 Outline
Post-Sphaleron Baryogenesis [Babu, Mohapatra, Nasri (PRL ’06)]
A UV-complete model [Babu, BD, Mohapatra (PRD ’08)]
Low-energy constraints (Neutrino masses and mixing, FCNC, BAU)
Upper limit on n − n¯ oscillation time [Babu, BD, Fortes, Mohapatra (PRD ’13)]
2020 update (in light of recent lattice, neutrino and LHC results) [Babu, Chauhan, BD, Mohapatra, Thapa (work in progress)]
Conclusion
2 Post-sphaleron baryogenesis: Deep connection between BAU and n − n¯ oscillation. BAU is generated below 100 GeV, after the EW sphalerons go out-of-equilibrium. [Babu, Mohapatra, Nasri (PRL ’06)] Low reheating temperature consistent with wide range of inflation models.
More compelling than EW baryogenesis. [Ann Nelson (INT Workshop ’17)]
Why PSB is Compelling?
BAU requires B violation. [Sakharov (JETP Lett. ’67)] 16 ∆B = 1: Proton decay constraints require very high scale ∼ 10 GeV. [Nath, Fileviez Perez (Phys. Rept. ’07)] ∆B = 2: Induced by dimension-9 operator 1 L = qqqqqq eff Λ5 High-dimension implies scale can be as low as Λ ∼ 106 GeV.
Observable signature: n − n¯ oscillation. [Phillips, Snow, Babu et al. (Phys. Rept. ’16)]
3 Why PSB is Compelling?
BAU requires B violation. [Sakharov (JETP Lett. ’67)] 16 ∆B = 1: Proton decay constraints require very high scale ∼ 10 GeV. [Nath, Fileviez Perez (Phys. Rept. ’07)] ∆B = 2: Induced by dimension-9 operator 1 L = qqqqqq eff Λ5 High-dimension implies scale can be as low as Λ ∼ 106 GeV.
Observable signature: n − n¯ oscillation. [Phillips, Snow, Babu et al. (Phys. Rept. ’16)] Post-sphaleron baryogenesis: Deep connection between BAU and n − n¯ oscillation. BAU is generated below 100 GeV, after the EW sphalerons go out-of-equilibrium. [Babu, Mohapatra, Nasri (PRL ’06)] Low reheating temperature consistent with wide range of inflation models.
More compelling than EW baryogenesis. [Ann Nelson (INT Workshop ’17)]
3 Naturally realized in quark-lepton unified models, with S identified as the Higgs boson of B − L breaking. Yukawa couplings that affect PSB and n − n¯ are the same as the ones that generate neutrino masses via seesaw. Requiring successful BAU and observed neutrino oscillation parameters lead to a concrete, quantitative prediction for n − n¯ amplitude.
Basic Idea of PSB
A (pseudo)scalar S decays to baryons, violating B. ∆B = 1 is strongly constrained by proton decay and cannot lead to successful PSB. ∆B = 2 decay of S, if violates CP and occurs out-of-equilibrium, can generate BAU below T = 100 GeV. The same ∆B = 2 operator leads to n − n¯.
4 Basic Idea of PSB
A (pseudo)scalar S decays to baryons, violating B. ∆B = 1 is strongly constrained by proton decay and cannot lead to successful PSB. ∆B = 2 decay of S, if violates CP and occurs out-of-equilibrium, can generate BAU below T = 100 GeV. The same ∆B = 2 operator leads to n − n¯. Naturally realized in quark-lepton unified models, with S identified as the Higgs boson of B − L breaking. Yukawa couplings that affect PSB and n − n¯ are the same as the ones that generate neutrino masses via seesaw. Requiring successful BAU and observed neutrino oscillation parameters lead to a concrete, quantitative prediction for n − n¯ amplitude.
4 w w w w 0 ± ∓ (1,1,15)wMc & 1400 TeV (from KL → µ e ) w w [Valencia, Willenbrock (PRD ’94)]
SU(2)L × SU(2)R × U(1)B−L × SU(3)c [Mohapatra, Pati (PRD ’75)] w [Senjanović, Mohapatra (PRD ’75)] w w w (1, 3, 10)wvBL (& 200 TeV) [Mohapatra, Marshak (PRL ’80)] w w
SU(2)L × U(1)Y × SU(3)c
No ∆B = 1 processes since B − L is broken by two units.
Quark-Lepton Symmetric Model
SU(2)L × SU(2)R × SU(4)c [Pati, Salam (PRD ’74)]
5 w w w w (1, 3, 10)wvBL (& 200 TeV) [Mohapatra, Marshak (PRL ’80)] w w
SU(2)L × U(1)Y × SU(3)c
No ∆B = 1 processes since B − L is broken by two units.
Quark-Lepton Symmetric Model
SU(2)L × SU(2)R × SU(4)c [Pati, Salam (PRD ’74)] w w w w 0 ± ∓ (1,1,15)wMc & 1400 TeV (from KL → µ e ) w w [Valencia, Willenbrock (PRD ’94)]
SU(2)L × SU(2)R × U(1)B−L × SU(3)c [Mohapatra, Pati (PRD ’75)] [Senjanović, Mohapatra (PRD ’75)]
5 Quark-Lepton Symmetric Model
SU(2)L × SU(2)R × SU(4)c [Pati, Salam (PRD ’74)] w w w w 0 ± ∓ (1,1,15)wMc & 1400 TeV (from KL → µ e ) w w [Valencia, Willenbrock (PRD ’94)]
SU(2)L × SU(2)R × U(1)B−L × SU(3)c [Mohapatra, Pati (PRD ’75)] w [Senjanović, Mohapatra (PRD ’75)] w w w (1, 3, 10)wvBL (& 200 TeV) [Mohapatra, Marshak (PRL ’80)] w w
SU(2)L × U(1)Y × SU(3)c
No ∆B = 1 processes since B − L is broken by two units.
5 (B − L)-breaking Scalars
Under SU(2)L × U(1)Y × SU(3)c , 8 2 4 ∆(1, 3, 10) = ∆ (1, − , 6∗) ⊕ ∆ (1, − , 6∗) ⊕ ∆ (1, + , 6∗) uu 3 ud 3 dd 3 2 4 ⊕ ∆ (1, , 3∗) ⊕ ∆ (1, − , 3∗) ue 3 uν 3 8 2 ⊕ ∆ (1, , 3∗) ⊕ ∆ (1, , 3∗) de 3 dν 3 ⊕ ∆ee (1, 4, 1) ⊕ ∆νe (1, 2, 1) ⊕ ∆νν (1, 0, 1) .
∆uu, ∆ud , ∆dd (diquarks) generate B violation.
∆νν (singlet) breaks the B − L symmetry and provides a real scalar field S for PSB:
1 0 ∆νν = vBL + √ (S + iG ) 2
6 The real scalar field S can decay into 6q and 6q¯, thus violating B by two units. S must be the lightest of the (1, 3, 10) multiplet to forbid its B-conserving
decays involving on-shell ∆qq.
Diquark Interactions and B-violating Decay of S
Interactions of color-sextet diquarks and B-violating couplings:
fij hij gij LI = ∆dd di dj + ∆uuui uj + √ ∆ud (ui dj + uj di ) 2 2 2 2 λ + ∆ ∆ ∆ ∆ + λ0∆ ∆ ∆ ∆ + H.c. 2 νν dd ud ud νν uu dd dd 0 Boundary conditions: fij = gij = hij and λ = λ in the PS symmetry limit. Couplings only to RH quarks due to L-R embedding.
In general, ∆ud could couple to both LH and RH quark bilinears, leading to EDM. [Bell, Corbett, Nee, Ramsey-Musolf (PRD ’19)]
7 Diquark Interactions and B-violating Decay of S
Interactions of color-sextet diquarks and B-violating couplings:
fij hij gij LI = ∆dd di dj + ∆uuui uj + √ ∆ud (ui dj + uj di ) 2 2 2 2 λ + ∆ ∆ ∆ ∆ + λ0∆ ∆ ∆ ∆ + H.c. 2 νν dd ud ud νν uu dd dd 0 Boundary conditions: fij = gij = hij and λ = λ in the PS symmetry limit. Couplings only to RH quarks due to L-R embedding.
In general, ∆ud could couple to both LH and RH quark bilinears, leading to EDM. [Bell, Corbett, Nee, Ramsey-Musolf (PRD ’19)]
The real scalar field S can decay into 6q and 6q¯, thus violating B by two units. S must be the lightest of the (1, 3, 10) multiplet to forbid its B-conserving
decays involving on-shell ∆qq.
7 Conditions for PSB:
ΓS→6q ≤ H(TEW), and ΛQCD ≤ Td ≤ TEW. S → 6q must be the dominant decay mode (over S → Zf f¯, ZZ) =⇒ v 100 TeV. √ BL & Vacuum stability restricts vBL from being arbitrarily large: λvBL . 2 πM∆. −1/4 √ sbefore g∗ 0.6 ΓS MPl Td Not too much dilution: d ≡ ' ∼ =⇒ MS 17 TeV. safter nS MS /s(Td ) MS .
Thermal History of S Decay
P 12 M13 Γ ≡ Γ(S → 6q) + Γ(S → 6q¯) = |λ|2Tr(f †f )[Tr(ˆg †gˆ)]2 S S π9 · 225 · 45 4 M8 M4 ∆ud ∆dd
−4 where P = 1.13 × 10 is a phase space factor (for M∆ud /MS , M∆dd /MS 1).
8 Thermal History of S Decay
P 12 M13 Γ ≡ Γ(S → 6q) + Γ(S → 6q¯) = |λ|2Tr(f †f )[Tr(ˆg †gˆ)]2 S S π9 · 225 · 45 4 M8 M4 ∆ud ∆dd
−4 where P = 1.13 × 10 is a phase space factor (for M∆ud /MS , M∆dd /MS 1).
Conditions for PSB:
ΓS→6q ≤ H(TEW), and ΛQCD ≤ Td ≤ TEW. S → 6q must be the dominant decay mode (over S → Zf f¯, ZZ) =⇒ v 100 TeV. √ BL & Vacuum stability restricts vBL from being arbitrarily large: λvBL . 2 πM∆. −1/4 √ sbefore g∗ 0.6 ΓS MPl Td Not too much dilution: d ≡ ' ∼ =⇒ MS 17 TeV. safter nS MS /s(Td ) MS . 8 CP Asymmetry
W ui ui
dβ dβ ∆ud ∆ud uj W
uj dα dα s 2 2 m2 2 m2 8g ∗ ∗ mt mj mW β β wave ' − † δi3=(ˆgiαgˆjαVjβ Viβ ) 2 2 1 − 2 + 2 − 4 2 64π Tr(f f ) mt − mj mt mt mt 2 2 2 2 2 2 mW mβ mβ mβ mt mβ × 2 1 − 2 + 2 − 4 2 + 1 + 2 2 + 2 − 1 mt mt mW mt mW mW
2 2 (i,j6=3) 8g ∗ ∗ mβ mj 3mW 2hp1 · p2i vertex ' − † =(ˆgiαgˆjβ Viβ Vjα) 2 1 + ln 1 + 2 32π Tr(f f ) mW 2hp1 · p2i mW
2 2 (i=3,j6=3) 8g δi3 ∗ ∗ mβ mj 3mW 2hp1 · p2i vertex ' − † =(ˆgiαgˆjβ Viβ Vjα) 2 1 + ln 1 + 2 32π Tr(f f ) mW 2hp1 · p2i mt (Updated calculation) 9 Flavor Violation
Diquark fields lead to flavor violation, both at tree and loop levels.
∗ † † † † 1 fi`f α β 1 [(ff ) (ff ) + (ff ) (ff ) ] H = − kj (d γ d α )(d γµd β ) + ij `k ik `j ∆dd 8 M2 kR µ iR jR `R 256π2 M2 ∆dd ∆dd h α α β µ β α β β µ α i × (d jR γµdiR )(d kR γ d`R ) + 5(d jR γµdiR )(d kR γ d`R ) . ∗ 1 g g h β β i H = − bij bkl (uα γ uα )(d γµd β ) + (uα γ d α )(d γµuβ ) ∆ud 32 M2 kR µ iR `R jR kR µ iR `R jR ∆ud 1 1 1 + (gg †) (gg †) + (gg †) (gg †) 256π2 64 M2 bb ij bb `k bb ik bb `j ∆ud h α α β µ β α β β µ α i × (d jR γµdiR )(d kR γ d`R ) + 5(d jR γµdiR )(d kR γ d`R )
∆dd di d s d s d s ∆dd di dj ∆dd ∆dd s d s d d s ∆dd dj
10 Take M M M , with M 3 TeV, M 5 TeV, M 200 TeV. ∆ud . ∆dd ∆uu ∆ud & ∆dd & ∆uu & Update: M∆qq & 7.5 TeV from LHC dijet constraint. [CMS Collaboration (1911.03947)] Could be relaxed to some extent for specific flavor structures.
FCNC Constraints
Process Diagram Constraint on Couplings 2 M∆ Tree |f f ∗ | ≤ 7.04 × 10−4 dd 22 33 1 TeV M P3 ∗ ∆dd ∆mB Box |fi3f | ≤ 0.14 s i=1 i2 1 TeV M P3 ∗ ∆ud Box |gˆi3gˆ | ≤ 1.09 i=1 i2 1 TeV 2 M∆ Tree |f f ∗ | ≤ 2.75 × 10−5 dd 11 33 1 TeV M P3 ∗ ∆dd ∆mB Box |fi3f | ≤ 0.03 d i=1 i1 1 TeV M P3 ∗ ∆ud Box |gˆi3gˆ | ≤ 0.21 i=1 i1 1 TeV 2 M∆ Tree |f f ∗ | ≤ 6.56 × 10−6 dd 11 22 1 TeV M P3 ∗ ∆dd ∆m Box |fi2f | ≤ 0.01 K i=1 i1 1 TeV M P3 ∗ ∆ud Box |gˆi1gˆ | ≤ 0.10 i=1 i2 1 TeV 2 M∆ ∆m Tree |h h∗ | ≤ 3.72 × 10−6 uu D 11 22 1 TeV
M P3 ∗ ∆uu Box |hi2h | ≤ 0.01 i=1 i1 1 TeV
11 FCNC Constraints
Process Diagram Constraint on Couplings 2 M∆ Tree |f f ∗ | ≤ 7.04 × 10−4 dd 22 33 1 TeV M P3 ∗ ∆dd ∆mB Box |fi3f | ≤ 0.14 s i=1 i2 1 TeV M P3 ∗ ∆ud Box |gˆi3gˆ | ≤ 1.09 i=1 i2 1 TeV 2 M∆ Tree |f f ∗ | ≤ 2.75 × 10−5 dd 11 33 1 TeV M P3 ∗ ∆dd ∆mB Box |fi3f | ≤ 0.03 d i=1 i1 1 TeV M P3 ∗ ∆ud Box |gˆi3gˆ | ≤ 0.21 i=1 i1 1 TeV 2 M∆ Tree |f f ∗ | ≤ 6.56 × 10−6 dd 11 22 1 TeV M P3 ∗ ∆dd ∆m Box |fi2f | ≤ 0.01 K i=1 i1 1 TeV M P3 ∗ ∆ud Box |gˆi1gˆ | ≤ 0.10 i=1 i2 1 TeV 2 M∆ ∆m Tree |h h∗ | ≤ 3.72 × 10−6 uu D 11 22 1 TeV
M P3 ∗ ∆uu Box |hi2h | ≤ 0.01 i=1 i1 1 TeV
Take M M M , with M 3 TeV, M 5 TeV, M 200 TeV. ∆ud . ∆dd ∆uu ∆ud & ∆dd & ∆uu & Update: M∆qq & 7.5 TeV from LHC dijet constraint. [CMS Collaboration (1911.03947)] Could be relaxed to some extent for specific flavor structures. 11 Neutrino Masses and Mixing
The FCNC constraints enforce the Yukawa texture: [Babu, BD, Mohapatra (PRD ’08)] 0 0.95 1 ! f = 0.95 0 0.01 . 1 0.01 −0.06
In the type-II seesaw dominance, Mν ∝ f =⇒ inverted mass hierarchy.
Our 2008 fit yielded a “large" θ13, (serendipitously) close to the 2012 Daya Bay measurement. NEUTRINO MASS HIERARCHY, NEUTRON-ANTINEUTRON ... PHYSICAL REVIEW D 79, 015017 (2009) 34 0.35 0.52
33 0.34 0.51 0.5 32 0.33 solar 2
12 23 0.49 m θ θ ∆ 2 2 / 31 0.32 sin sin
atm 0.48 2
m 30 0.31 ∆ 0.47
29 0.3 0.46
28 0.29 0.45 0.015 0.02 0.025 0.03 0.015 0.02 0.025 0.03 0.015 0.02 0.025 0.03 2 2 2 sin θ13 sin θ13 sin θ13
FIG. 1. We give the predictions for neutrino oscillation parameters for the allowed ranges of the diquark scalar couplings in our Update:model. Normal Note the lowerhierarchy limit on the possible13 of about by 0.1. making f22 6= 0, but at the expense of f13 (and n − n¯). A more exhaustiveSecond, we predict parameter that the neutrinoless scan double for neutrino -decay massBetween fits1 (includingT 100 TeV, nonzero the ÁB 2δ interaction) currently experiments should observe a Majorana neutrino mass at rates go like ¼ CP underway.the 10–20 meV level which is perhaps within reach of the f6 next round of neutrinoless double -decay experiments. À ÁB 2 11 T (16) In Fig. 1, we present two scatter plots that display the ð ¼ Þ 2 9 ð Þ preference of oscillation parameters in our model. To and are therefore in equilibrium if some of the f ’s are obtain this plot, we have allowed the neutrino oscillation ij above 0.3 as in our case. parameters to vary within the current experimental limits Below T 1 TeV, the ÁB 2 processes such as the 12 and we also allow a more general CKM-like form for the decay S 6qc 6qc, qc;qc ¼ S 5 qc; qc occur at U . We clearly see the lower bound on the from them. r r l 13 a rate given! by þ ð Þþ ! ð Þ We will see below that this form of the f matrix satisfies the baryon asymmetry constraints as well as the n n 6 13 100fud;12 T constraints. À À ÁB 2 ; (17) ð ¼ Þ 2 9 6M 12 ð Þ ð Þ where M TeV, the average mass of the Á c c , Á c c V. ORIGIN OF MATTER d d u d particles which are still in equilibrium. The Áucuc is about Before proceeding to the discussion of how baryon 100 TeV and hence its contribution to these processes is asymmetry arises in this model, let us first sketch the more suppressed compared to that of Ádcdc , Áucdc . This cosmological sequence of events starting at the SU 4 c decay then goes out of equilibrium somewhat below the ð Þ scale that leads up to this. For temperatures above the TeV temperature range. One impact of this is that these SU 4 c scale of about 100 TeV, there is no B L violation. interactions being in equilibrium above T TeV erase any ð Þ À The sphalerons are active and therefore erase any preexist- preexisting baryon asymmetry as discussed above. ing B L asymmetry in the Universe. So if there was a By the time the Universe cools to a temperature near or þ primordial GUT scale generated baryon asymmetry that slightly below MS, its decay channels can start if the rates conserved B L [like that in most SU 5 and some are faster compared to the Hubble expansion rate. Let us À ð Þ SO 10 models], it will be erased by sphalerons. Any therefore estimate the various decay rates: ð Þ baryon asymmetry residing in B L violating interactions There are four decay modes which are competitive with À c c c will however survive. each other: (i) Sr 6q ; (ii) Sr Zf f ; (iii) Sr ZZ; 1! ! ! Below the SU 4 c scale, B L violating interactions and (iv) Sr e. We discuss them below. ð Þ À ! c arise e.g. SS eþeÀ, and will be in equilibrium together (i) S 6q : The diagram for this is given in Fig. 2. ! r with the ÁB 2 interactions. So together they will erase Since! M m , in its decay all modes will partici- ¼ S t any preexisting baryon or lepton asymmetry. Thus in mod- pate. Including all the modes, we find the decay rate els of this kind, baryon asymmetry of the Universe must be to be generated fresh below the sphaleron decoupling 3 2 13 temperature. c 36 Tr fyf MS À Sr 6q 9 ð ½ Þ 12 ; (18) In order to sketch how fresh baryon asymmetry arises in ð ! Þ ’ 2 6MÁ our model, we assume the following mass hierarchy be- ð Þ ð Þ where we have chosen 1 2 0:1. Taking tween the Sr field and the Ádcdc , Áucuc , Áucdc fields: ¼ as an example a typical set of parameters MÁ m MÁucuc 100 TeV ; ð Þ 1The S W W is suppressed by W W mixing pa- r ! þ À L À R where mt is the top quark mass. rameter which can be adjusted to be small. 015017-5 Connection with n − n¯ Oscillation [Mohapatra, Marshak (PRL ’80)] Tree-level amplitude: f g 2 λv f 2 h λ0v Atree ' 11 11 BL + 11 11 BL . n−n¯ M2 M4 M4 M2 ∆dd ∆ud ∆dd ∆uu But f11 has to be vanishingly small to satisfy FCNC constraints. Go to one-loop level to set a lower bound on the ‘effective’ f11. 13 Loop-level n − n¯ d d t W − u ∆ud ∆ S dd b h i ∆ ud d d u g 2g g f V ∗ V λv m m A1−loop ' 11 13 13 ub td BL t b F hn¯|O2 |ni n−n¯ 128π2M2 m2 RLR ∆ud W where the loop factor is M2 M2 ∆ ∆ F = 1 1 ln ud − 1 ln dd M2 −M2 M2 m2 M2 m2 ∆ud ∆dd ∆ud W ∆dd W 2 2 1−(m /4m ) m2 + 1 t W ln t . M2 M2 1−(m2/m2 ) m2 ∆ud ∆dd t W W 14 Effective Operator Relevant effective operator: 2 T T T s ORLR = (uiR CdjR )(ukLCdlL)(dmR CdnR )Γijklmn, s with the color tensor Γijklmn = mik njl + nik mjl + mjk nil + njk mil . Matrix element in the MIT bag model: [Rao, Shrock (PLB ’82)] 2 −5 6 hn¯|ORLR |ni = −0.314 × 10 GeV Update: New lattice QCD result– Mike Wagman’s talk [Rinaldi, Syritsyn, Wagman, Buchoff, Schroeder, Wasem (PRL ’19; PRD ’19)] 2 with hn¯|Q5|ni = hn¯|Q6|ni and Q6 = −4ORLL. New matrix element is 16% smaller. 15 Prediction for n − n¯ Oscillation Time −1 1−loop τn−n¯ ≡ δm = cQCD(µ∆, 1 GeV) An−n¯ . where cQCD is the RG running factor: [Winslow, Ng (PRD ’10)] 2 8/7 2 24/23 2 24/25 2 8/9 αs (µ∆) αs (mt ) αs (mb) αs (mc ) cQCD(µ∆, 1GeV) = 2 2 2 2 αs (mt ) αs (mb) αs (mc ) αs (1 GeV ) ' 0.18. 0.07 0.06 0.05 0.04 0.03 Probability 0.02 0.01 0.00 10. 100 8 Τ - n-n 10 sec H L [Babu, BD, Fortes, Mohapatra (PRD ’13)] 16 Updated Prediction for n − n¯ Oscillation Time 0.030 0.025 0.020 0.015 Probability 0.010 0.005 0.000 1 10 100 1000 τ - 8 n-n/(10 sec) [Babu, Chauhan, BD, Mohapatra, Thapa (preliminary result)] 17 Updated Prediction for n − n¯ Oscillation Time 0.030 0.025 0.020 ILL Super - K 0.015 Probability 0.010 0.005 0.000 1 10 100 1000 τ - 8 n-n/(10 sec) [Babu, Chauhan, BD, Mohapatra, Thapa (preliminary result)] 18 Updated Prediction for n − n¯ Oscillation Time 0.030 0.025 0.020 ILL Super - K 0.015 uuelimit ) ( future ESS ) limit ( future DUNE Probability 0.010 0.005 0.000 1 10 100 1000 τ - 8 n-n/(10 sec) [Babu, Chauhan, BD, Mohapatra, Thapa (preliminary result)] 19 Stay tuned. Conclusion Post-sphaleron baryogenesis is a compelling low-scale alternative to popular high-scale baryogenesis/leptogenesis. Directly links BAU with n − n¯ oscillation. In quark-lepton symmetric models, leads to a quantitative prediction for n − n¯ oscillation time. Deep connection between BAU, n − n¯ and Majorana neutrino mass. 9 11 τn−n¯ ≈ (10 − 10 ) sec is the preferred range from PSB. (Partly) within reach of future experiments. 20 Conclusion Post-sphaleron baryogenesis is a compelling low-scale alternative to popular high-scale baryogenesis/leptogenesis. Directly links BAU with n − n¯ oscillation. In quark-lepton symmetric models, leads to a quantitative prediction for n − n¯ oscillation time. Deep connection between BAU, n − n¯ and Majorana neutrino mass. 9 11 τn−n¯ ≈ (10 − 10 ) sec is the preferred range from PSB. (Partly) within reach of future experiments. Stay tuned. 20 Understanding the Upper Limit on n − n¯ Oscillation Time 1000 1000 500 500 sec ) sec ) 8 8 /( 10 /( 10 - 100 - 100 n - n - τ τ 50 50 10 10 5 10 15 20 25 30 35 40 5 10 15 20 MΔdd(TeV) MΔud(TeV) 1000 1000 500 500 sec ) sec ) 8 8 /( 10 /( 10 - 100 - 100 n - n - τ τ 50 50 10 10 6 8 10 12 14 16 18 500 1000 1500 2000 2500 3000 MS(TeV) vBL(TeV) 21 Baryon conserving decay of ⌘ ⌘ (uu) ! u⌫ u⌫ uR uR ⌫ ⌫ R u⌫ R u⌫ ⌘ u⌫ ⌘ u⌫ ⌫R ⌫R uR uR This generates absorptive part and CP violation in ⌘ 6q: ! u d ⌫R u⌫ d dd ⌘ u⌫ d ⌫R dd u d 2 0∗ 2 K.S. Babu (OSU) Post-Sphaleron Baryogenesis M 14 / 26 |f | =(λλ ) ∆dd ' 2 2 8π(|λ| + Γ4/Γ6) MνR Other diagrams for CP Violation 2 2 8 ∗ ∗ MZ mj mβ mj diamond ' =(ˆg fjmgˆ hnβ ) 1 − Figure† 2: Diamondnm β loopj diagram2 in2 the (X, Y, Z)2 model.2 16π Tr(f f ) MX MY mi + mα + 2hp1 · p2i We summarize the results of our calculations for the W ± exchange diagrams. If one of the external up–type quarks is the top quark, the corresponding quark line receives a wave function correction via W ± gauge boson exchange. The baryon asymmetry from this diagram is found to be 2 T wave 4 Im V ∗Mˆ V Mˆugg† ϵB 3α2 mW d 33 1+ 4 # 2 $ (5) Br ≃− 8 ! mt " mtmW (gg†)33 22 where Mˆ u = diag(mu,mc,mt), Mˆ d = diag(md,ms,mb)andV is the CKM matrix. Br stands for the branching ratio of Sr into 6q +6q. The vertex correction via the W boson exchange gives an asymmetry given by ϵvertex α ImTr[gT Mˆ Vg V Mˆ ] B 2 u † ∗ d . (6) Br ≃−4 Tr(g†g) Here we have assumed that M m . In the limit where m m ,wehavethesame Sr ≫ t Sr ≪ W asymmetry as in Eq. (6), but with a factor of (-1/4) multiplying it. Of course in this case, decays involving final state top quark are disallowed, which is to be implemented by removing the top quark contribution in the trace of Eq. (6).3 3 These W ± loops do not conflict with the theorem of Ref. [14] which states thatnobaryonasymmetry 9 Other diagrams for CP Violation Baryon conserving decay of ⌘ ⌘ (uu) ! u⌫ u⌫ uR uR ⌫ ⌫ R u⌫ R u⌫ ⌘ u⌫ ⌘ u⌫ ⌫R ⌫R u 2 u 2 8 ∗ ∗ R MZ mj mβ R mj diamond ' † =(ˆgnmfjmgˆβj hnβ ) 2 2 1 − 2 2 16π Tr(Figuref f ) 2: Diamond loop diagramM M in the (X, Y, Zm) model.+ mα + 2hp1 · p2i This generates absorptive part and CPX Y violation ini ⌘ 6q: ! We summarize the results of our calculations for the W exchange diagrams. If one u ±d of the external up–type quarks is the top quark, the corresponding quark line receives a ⌫R u⌫ wave function correction via W gauge boson exchange. The baryond asymmetry from this ± dd diagram is found to be ⌘ u⌫ d ⌫R dd u d wave 4 ˆ 2 T ˆ ϵ 3α2 m Im V ∗Md V Mugg† B 1+2 W 0∗ 2 33 (5) K.S. Babu (OSU) |f |Post-Sphaleron=(λλ4 ) Baryogenesis# M2 $ 14 / 26 Br ≃− 8 ! mt " mtmW∆(ggdd †)33 ' 2 2 8π(|λ| + Γ4/Γ6) Mν 22 where Mˆ u = diag(mu,mc,mt), Mˆ d = diag(md,ms,mb)andR V is the CKM matrix. Br stands for the branching ratio of Sr into 6q +6q. The vertex correction via the W boson exchange gives an asymmetry given by ϵvertex α ImTr[gT Mˆ Vg V Mˆ ] B 2 u † ∗ d . (6) Br ≃−4 Tr(g†g) Here we have assumed that M m . In the limit where m m ,wehavethesame Sr ≫ t Sr ≪ W asymmetry as in Eq. (6), but with a factor of (-1/4) multiplying it. Of course in this case, decays involving final state top quark are disallowed, which is to be implemented by removing the top quark contribution in the trace of Eq. (6).3 3 These W ± loops do not conflict with the theorem of Ref. [14] which states thatnobaryonasymmetry 9