Baryon Oscillations and CP Violation. David McKeen University of Pittsburgh INT Workshop INT-17-69W, Oct. 26, 2017

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1 Baryon Oscillations and CP Violation David McKeen University of Pittsburgh INT Workshop INT-17-69W, Oct. 26, 2017

2 Outline CP & neutron oscillations How to engineer CPV in neutron oscillation Heavy flavor baryon oscillations and CPV Contribution to the baryon asymmetry of the Universe

3 See also talk by Vainshtein Vainshtein & Berezhiani, Gardner (& Jafari, & Yan) (DM & Ann Nelson ) Neutron Oscillation Lagrangian The general Lagrangian containing neutron bilinear with B-preserving and B-violating terms In terms of 2-comp., LH Weyl spinors (B = +1), (B = 1) n = = i 2 L = ni µ n + L B + L 6B L B = n (m n P L + m np R ) n L 6B = n c ( 1 P L + 2P R ) n + n ( 2 P L + 1P R ) n c L = i µ@ µ + i µ@ µ + L B + L 6B L B = m n +h.c. L 6B = h.c. How does this behave wrt CP?

4 See also talk by Vainshtein Vainshtein & Berezhiani, Gardner (& Jafari, & Yan) (DM & Ann Nelson ) Neutron Oscillation Lagrangian! C m n! m n, C 1! C 2! P m n! P m n, 1! P 2!,! CP CP m n! m CP n, 1,2! 1,2 CP L = i µ@ µ + i µ@ µ + L B + L 6B L B = m n +h.c. L 6B = h.c. 3 phases, 2 fields, naively can t remove all but can rotate to remove or 1 2! cos +sin,! sin + cos

5 (Ipek, DM, & Nelson) Neutron Oscillation Hamiltonian Express fields in terms of creation/ annihilation operators = X s = X s Z Z d 3 p 1 p hx s (2 ) 3/2 p 2Ep a s pe ip x + yp s b s p e ip xi d 3 p 1 p hx s (2 ) 3/2 p 2Ep b s pe ip x + yp s a s p e ip xi n; p, si = a s p 0i, n; p, si = b s p k0i Can then compute Hamiltonian hi; p, s Z d 3 x L j; p 0,s 0 i p!0 =(2 ) 3 (3) (p p 0 ) H ss0 ij H = 1 m + 2 n m n! ss 0 Remaining phase can be removed by rephasing states

6 Neutron Oscillation Hamiltonian Can easily incorporate B fields, decays in this H = mn ss 0 (µ n B d n E) M 12 ss 0 L (µ n id n ) F µ µ +h.c. M 12 ss0 m n ss 0 +(µ n B d n E) i 2 n n ss 0 M 12 = Gives transition probs. P ni! ni = 2 H cosh 2 t cos mt e nt 2 p µ 2 nb 2 + H 12 H 21 i H 12,21 = M 12, ,21 CPV is, e.g., P ni! ni P ni! ni 1= 2Im (M ) M /4 Im (M )

7 CPV in Neutron Oscillations Is measurable CPV possible? Need 12 n! pe + e, n! pe e dim-12, 3 body, so extremely suppressed Need to consider new state lighter than neutron u γ m p m e <m <m p + m e L g ū d + y d + m +h.c. n d guarantees stability of, p φ Z 2 subgroup of B d χ number preserved

8 CPV in Neutron Oscillations Is measurable CPV possible? Need 12 L g ū d + y d + m +h.c. 12 egy 3 QCD m 2 m 2 n So GeV! 2 m 2 n m GeV m / p gy n n n n χ χ M 12 3 QCD gy! 2 m m 2 m 2 n m P n! n P n!n 1 / 12 M 12 m 2 m 2 n! 3 M 1 MeV M 1 MeV GeV 10 8 GeV m / p gy 4 1 MeV M Oscillations also suppressed by M 12 n. 10 5

9 (Aitken, DM, Neder, & Nelson) Heavy Flavor Oscillations What if B =2operators had S =4? ū u K 0 s s 0 n K s s n K K is kinematically forbidden! 2m N < 4m K Dominant constraints could be from colliders 12, M 12 could be much larger Kuzmin ( 96)

10 (Aitken, DM, Neder, & Nelson) Heavy Flavor Oscillation Model L int g ud ū R d c R y id id c R +H.c. u R ū R d R φ m χ χ φ d R Same model as described by Nelson but different regime: m m d R 0 d R u B B B B n n n n χ χ 12 M 12 d d long-lived / m5 m 4 Need 2 i for phase diff.

11 Including weak interactions What if B =2operators had S =4? but Chirally suppressed. Matching: u/d K + /K 0 C BB (q R q R q R ) 2! 4 f 3 2 trb CBB B +..., p/n p/n u W ± d L L u u s d R R u/d s s s K 0 K + /K 0 ( Combine with strangeness changing operators G F p 2 V us V udf f 3 2 trb CBB h B +... Can estimate constraints on heavy flavor transition amplitudes from n osc./dnd

12 Heavy Flavor Oscillations What if B =2operators had S =4? 2m N < 4m K but u/d K + /K 0 p/n u W ± L u s d R R s s K 0 p/n d L u u/d s K + /K 0

13 Collider constraints Produce color triplet scalars easily d i d i ū j ū j j

14 Collider constraints Also produced through RPV coupling u di Monteux d ūjj Resonant production is important!

15 Collider constraints Scan over scalar masses m = 200 MeV ( ) ( ) ϕ ( )

16 Production in the early Universe Need a way to produce the baryons out of equilibrium Simplest possibility is long-lived 3 Same as in model described by Nelson, similar to postsphaleron scenario of Babu, Dev, Mohapatra In this case, decoherence is important

17 Boltzmann equations for radiation, long-lived fermion, heavy B Need density matrix Tulin, Yu, Zurek Change of variables to symmetric/asymmetric components Decoherence due to

18 Baryon asymmetry calculation: ( ) cb M 12 B = 10 2, ( ) 12 M 12 = Γ - - χ σ ( B + B_ ) ( ) Γ B Γ B + B _ η ( ) η Sudden decay approx: Can get observed asymmetry!

19 Probing this scenario q b q 0 branchings can be O(10 3 ) [ ] P B! B M B 10 5 Further work in progress

20 Conclusions Having measurable CPV in baryon oscillations requires common final states for baryon & antibaryon In the neutron system, this is very constrained Heavy baryons are less constrained and could exhibit a large degree of CPV This could be relevant to baryon asymmetry of the Universe

CP Violation, Baryon violation, RPV in SUSY, Mesino Oscillations, and Baryogenesis

CP Violation, Baryon violation, RPV in SUSY, Mesino Oscillations, and Baryogenesis David McKeen and AEN, arxiv:1512.05359 Akshay Ghalsasi, David McKeen, AEN., arxiv:1508.05392 (Thursday: Kyle Aitken, David