Post-Sphaleron Baryogenesis and N −N Oscillations

Post-Sphaleron Baryogenesis and n n Oscillations −

K.S. Babu

Oklahoma State University INT Workshop on Neutron-Antineutron Oscillations University of Washington, Seattle October 23 – 27, 2017

Based on: K. S. Babu, R. N. Mohapatra (2017) (to appear); K. S. Babu, R. N. Mohapatra and S. Nasri, hep-ph/0606144; hep-ph/0612357; K. S. Babu, P. S. Bhupal Dev and R. N. Mohapatra, arXiv:0811.3411 [hep-ph]; K. S. Babu, P. S. Bhupal Dev, E. C. F. S. Fortes and R. N. Mohapatra, arXiv:1303.6918 [hep-ph]

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 1 / 26 Outline

Idea of post-sphaleron baryogeneis

Explicit models based on SU(2)L SU(2)R SU(4)C symmetry × ×

Relating baryogenesis with neutron-antineutron oscillation

Other experimental tests

Conclusions

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 2 / 26 Generating Baryon Asymmetry of the Universe

Observed baryon asymmetry: nB nB −11 Y∆B = − = (8.75 0.23) 10 s ± × Sakharov conditions must be met to dynamically generate Y∆B

I Baryon number (B) violation I C and CP violation I Departure from thermal equilibrium All ingredients are present in Grand Uniﬁed Theories. However, in simple GUTs such as SU(5), B L is unbroken − Electroweak sphalerons, which are in thermal equilibrium from T = (102 1012) GeV, wash out any B L preserving asymmetry− generated at any T > 100 GeV− Kuzmin, Rubakov, Shaposhnikov (1985) K.S. Babu (OSU) Post-Sphaleron Baryogenesis 3 / 26 Generating baryon asymmetry (cont.)

Sphaleron: Non-perturbative conﬁguration of the electroweak theory Leads to eﬀective interactions of left-handed fermions:

sL s Y L tL OB+L = (qi qi qi Li ) cL b i L

Obeys ∆B = ∆L = 3 Sphaleron dL bL

Sphaleron can convert lepton asymmetry to ν dL τ baryon asymmetry – Leptogenesis mechanism u νµ L ν (Fukugita, Yanagida (1986)) e Post-sphaleron baryogenesis: Baryon number is generated below 100 GeV, after sphalerons go out of equilibrium (Babu, Nasri, Mohapatra (2006))

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 4 / 26 Post-Sphaleron Baryogenesis

A scalar (S) or a pseudoscalar (η) decays to baryons, violating B ∆B = 1 is strongly constrained by proton decay and cannot lead to successful post-sphaleron baryogenesis ∆B = 2 decay of S/η can generate baryon asymmetry below T = 100 GeV: S/η 6 q; S/η 6 q → → Decay violates CP, and occurs out of equilibrium Naturally realized in quark-lepton unified models, with S/η identified as the Higgs boson of B L breaking − ∆B = 2 connection with n n oscillation ⇒ − Quantitative relationship exists in quark-lepton unified models based on SU(2)L SU(2)R SU(4)C × ×

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 5 / 26 Conditions for Post-Sphaleron Baryogenesis

At high temperature, T above the masses of S/η and the mediators, the B-violating interactions are in equilibrium: 2 ∗ 1/2 T Γ∆B6=0(T ) H(T ) = 1.66(g ) MPl As universe cools, S/η freezes out from the plasma while relativistic at T = T∗ with T∗ MS/η.(Number density of S/η ≥ is then comparable to nγ.)

For T < T∗, decay rate of S/η is a constant. S/η drifts and occasionally decays. As the universe cools, H(T ) slows; at some temperature Td , the constant decay rate of S/η becomes comparable to H(Td ). S/η decays at T Td generating B. ∼ −1 Post-sphaleron mechanism assumes Td = (10 100) GeV. −

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 6 / 26 Dilution of Baryon Asymmetry

S/η 6q decay occurs atTd MS/η. There is no wash out eﬀect→ from back reactions

However, S/η decay dumps entropy into the plasma. This results in a dilution: s g −1/40.6(Γ M )1/2 T d before ∗ η Pl d ≡ safter ' rMη ' Mη

Mη cannot be much higher than a few TeV, or else the dilution will be too strong

There is a further dilution of order 0.1, owing to the change of g∗ from 62.75 at 200 MeV to 5.5 after recombination

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 7 / 26 Summary of Constraints on PSB

Pseudoscalar η must have ∆B = 2 decays

Such decays should have CP violation to generate B asymmetry

η should freeze-out while relativistic: T∗ Mη. This requires η to be feebly interacting, and a singlet of≥ Standard Model

Td , the temperature when η decays, should lie in the range Td = (100 MeV 100 GeV) − η should have a mass of order TeV, or else baryon asymmetry will suﬀer a dilution of Td /Mη

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 8 / 26 Quark-Lepton Symmetric Models

Quark-lepton symmetric models based on the gauge group SU(2)L SU(2)R SU(4)C have the necessary ingredients for PSB × × There is no ∆B = 1 processes since B L is broken by 2 units. Thus there is no rapid proton decay. Symmetry− may be realized in the 100 TeV range There is baryon number violation mediated by scalars, which are the partners of Higgs that lead to seesaw mechanism Scalar ﬁelds S/η arise naturally as Higgs bosons of B L breaking − Yukawa coupling that aﬀect PSB and n n oscillations are the same as the ones that generate neutrino− masses

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 9 / 26 Quark-Lepton Symmetric Models

Models based on SU(2)L SU(2)R SU(4)C (Pati-Salam) × × Fermions, including νR , belong to (2, 1, 4) (1, 2, 4) ⊕ Symmetry breaking and neutrino mass generation needs Higgs ﬁeld ∆(1, 3, 10). Under SU(2)L U(1)Y SU(3)C : × × 8 ∗ 2 ∗ 4 ∗ 2 ∗ ∆(1, 3, 10) = ∆uu(1, − , 6 ) ⊕ ∆ (1, − , 6 ) ⊕ ∆ (1, + , 6 ) ⊕ ∆ue (1, , 3 ) 3 ud 3 dd 3 3 4 ∗ 8 ∗ 2 ∗ ⊕ ∆uν (1, − , 3 ) ⊕ ∆ (1, , 3 ) ⊕ ∆ (1, , 3 ) ⊕ ∆ee (1, 4, 1) 3 de 3 dν 3 ⊕ ∆νe (1, 2, 1) ⊕ ∆νν (1, 0, 1) .

∆uu, ∆ud , ∆dd are diquarks, ∆ue , ∆uν, ∆de , ∆dν are leptoquarks, and ∆νν is a singlet that breaks the symmetry Diquarks generate B violation, leptoquarks help with CP violation, and singlet ∆νν provides the ﬁeld S/η for PSB

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 10 / 26 Quark-Lepton Symmetric Models (cont.)

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 0 + ∆νν ∆ ∆ ∆ + λ ∆νν ∆uu∆ ∆ + h.c. 2 dd ud ud dd dd 0 fij = gij = hij and λ = λ from gauge symmetry. We also introduce a scalar χ(1, 2, 4) which couples to ∆(1, 3, 10) via( µχχ∆ χνχν∆νν + ...) ⊃ Among the phases of ∆νν and χν, one combination is eaten by B L gauge boson. The other, is a pseudoscalar η: − (ρ1 + vR ) (ρ2 + vB ) 2η2vR η1vB ∆ = eiη1/vR , χ = eiη2/vB , η = νν ν p 2− 2 √2 √2 4vR + vB Advantage of using η 6 q is that η has a ﬂat potential due to a shift symmetry →

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 11 / 26 Baryon violating decay of η

η 6q and η 6q decays violate B: → → u d

u d

∆uu d ∆dd u

∆dd ∆ud η η

∆dd d ∆ud d d u

d d

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 12 / 26 Baryon violating decay of η (cont.)

B-violating decay rate of η: 13 ! P 12 2 † † 2 Mη Γη ≡ Γ(η → 6q) + Γ(η → 6¯q) = |λ| Tr(f f )[Tr(ˆg gˆ)] π9 · 225 · 45 4 M8 M4 ∆ud ∆dd Here P is a phase space factor:

−4 1.13 × 10 (M∆ud /MS , M∆dd /MS 1) P = −4 1.29 × 10 (M∆ud /MS = M∆dd /MS = 2) .

Td is obtained by setting this rate to Hubble rate. For Td = (100 MeV 100 GeV), f g h 1, M∆ Mη needed − ∼ ∼ ∼ ud ∼ η has a competing B = 0 four-body decay mode, which is necessary to generate CP asymmetry: η (uu)∆uν∆uν → The six-body and four-body decays should have comparable widths, or else B asymmetry will be too small

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 13 / 26 Baryon conserving decay of η

η (uu)∆uν∆uν → uR uR

ν ν R ∆uν R ∆uν

η ∆uν η ∆uν νR νR uR uR

This generates absorptive part and CP violation in η 6q: → u d

νR ∆uν d ∆dd η ∆uν d νR ∆dd u d

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 14 / 26 Baryon Asymmetry

η uu∆uν∆uν has a width: → 5 ! ∗ ∗ P † 3 Mη Γη ≡ Γ(η → uu∆uν ∆uν ) + Γ(η → uu∆ − uν ∆ ) = [Tr(fˆ fˆ)] uν 1024π5 M4 νR Here P is a phase space factor, P 2 10−3 'M4× −9 νR For λ = 1, Γ6 (7 10 ) Γ4 M4 ' × × × ∆dd Baryon asymmetry: 2 ˜ M2 f Im(λλ) ∆dd B | | 2 2 ' 8π( λ + Γ4/Γ6) M | | νR

With MνR 100 M∆dd ,Γ4 Γ6. This choice maximizes B : ∼ × ∼ 2 ˜ −5 f λ B (8 10 ) | | Im( ) ∼ × × 8π λ For f λ 1, reasonable baryon asymmetry is generated with a dilution∼ d ∼ 10−3 ∼ K.S. Babu (OSU) Post-Sphaleron Baryogenesis 15 / 26 Other constraints for successful baryogenesis

η must freeze out at T Mη. Interactions of η with lighter particles must be weak. The scattering≥ processes freeze out as desired, owing to the shift symmetry in η.

η ∆uν η νR ∆uν

ν u η R R ν ∆uν η R ∆uν

u d

η ∆uu η ∆dd

∆dd ∆ud ∆dd ∆ud

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 16 / 26 Connection with n n oscillation − As η is associated with B L symmetry breaking, replacing η by the vacuum expectation value,−n n oscillation results: −

vB L vB L − − d d ∆dd ∆dd d ∆dd ∆ud u n ∆ n n ∆ n d uu d d ud d u d u u

Mη 3TeV , M∆ud 4TeV , M∆dd 50TeV , M∆uν 1TeV , vB−L 300TeV∼ is a consistent∼ choice ∼ ∼ ∼ Flavor dependence of baryon asymmetry can be ﬁxed via neutrino mass generation

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 17 / 26 Connection with neutrino oscillations

Quark-Lepton symmetry implies that the Yukawa couplings entering η decay and n n oscillation is the same as in neutrino mass generation −

In type-II seesaw mechanism for neutrino masses, Mν f .A consistent choice of f that yields inverted neutrino spectrum:∝  0 0.95 1  f =  0.95 0 0.01  1 0.01 0.06 This choice satisﬁes all ﬂavor changing constraints mediated by color sextet scalars The (1,1) entry will be relevant for n n oscillation. It is induced via a W boson loop −

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 18 / 26 Flavor changing constraints

∆dd , ∆uu, ∆ud ﬁelds lead to ﬂavor violation, at tree level as well as at loop:

f f ∗ † † † † 1 i` kj α α β µ β 1 [(ff )ij (ff )`k + (ff )ik (ff )`j ] H = − (d γµd )(d γ d ) + ∆F =2 8 M2 kR iR jR `R 256π2 M2 ∆dd ∆dd h α α β µ β α β β µ α i × (djR γµdiR )(dkR γ d`R ) + 5(djR γµdiR )(dkR γ d`R )

∆dd di d s d s d s d dj ∆dd ∆dd ∆dd i s d s d ∆dd dj d s

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 19 / 26 Flavor changing constraints

Table : Constraints on the product of Yukawa couplings in the PSB model 0 0 0 0 from K 0 K , D0 D , B0 B and B0 B mixing. − − s − s d − d K.S. Babu (OSU) Post-Sphaleron Baryogenesis 20 / 26 Prediction for n n oscillation − We take all PSB constraints, neutrino mass and mixing constraints, and FCNC constraints to estimate n n oscillation time − The ﬂavor structure of f has a zero in the (1,1) element. This entry is generated by a W boson loop.

d d t W − u ∆ud

vB L − ∆dd b

∆ ud d

d u

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 21 / 26 Prediction for n n oscillation (cont.) − Amplitude for n n oscillation: − 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 Loop induced amplitude: g 2g g f V ∗ V λv m m A1−loop 11 13 13 ub td BL t b F n¯ 2 n n−n¯ 128 2M2 m2 RLR ' π ∆ud W h |O | i Loop function: " # 1 1 M2 1 M2 F = ln ∆ud ln ∆dd M2 M2 M2 m2 − M2 m2 ∆ud − ∆dd ∆ud W ∆dd W 2 2 2 1 1 (mt /4mW ) mt + 2 2 − 2 2 ln 2 M M 1 (mt /m ) m ∆ud ∆dd − W W K.S. Babu (OSU) Post-Sphaleron Baryogenesis 22 / 26 Prediction for n n oscillation (cont.) − Eﬀective operator:

2 T T T s = (u CdjR )(u CdlL)(d CdnR )Γ ORLR iR kL mR ijklmn Matrix element in MIT bag model (Rao and Shrock):

n¯ 2 n = 0.314 10−5 GeV6 h |ORLR | i − × QCD correction: 8/7 24/23 24/25 " 2 # " 2 # " 2 # 2 8/9 αs (µ ) α (m ) αs (m ) α (m ) c (µ , 1GeV) = ∆ s t b s c QCD ∆ 2 2 2 2 αs (mt ) αs (mb) αs (mc ) αs (1 GeV )

−1 1−loop τ δm = cQCD(µ∆, 1 GeV) A n−n¯ ≡ n−n¯

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 23 / 26 Prediction for n n oscillation (cont.) −

1000 1000 500 500 L L 100 100 sec sec

8 50 8 50 10 10 H H - - n n - -

n 10 n 10 Τ 5 Τ 5

1 1 5 10 15 20 4 6 8 10 12

MDdd TeV MDud TeV

H L H L Figure : Scatter plots for τn−n¯ as a function of the ∆ masses M∆ud , M∆dd .

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 24 / 26 Prediction for n n oscillation (cont.) −

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 Figure : The likelihood probability for a particular value of τn−n¯ as given by the model parameters.

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 25 / 26 Conclusions

Post-sphaleron baryogenesis is an alternative to high scale leptogenesis

Directly linked with n n oscillation − In quark-lepton symmetric models, post-sphaleron baryogenesis can lead to quantitative prediction for n n oscillation time −

9 11 τn−n (10 10 ) sec. is the preferred range from PSB ≈ −

10 Within a concrete model, an upper limit of τn−n < 4 10 sec. is derived, which may be accessible to experiments ×

K.S. Babu (OSU) Post-Sphaleron Baryogenesis 26 / 26