Baryon Oscillations and CP Violation David McKeen University of Pittsburgh INT Workshop INT-17-69W, Oct. 26, 2017
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
See also talk by Vainshtein Vainshtein & Berezhiani, Gardner (& Jafari, & Yan) (DM & Ann Nelson 1512.05359) 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 @ 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 = 1 + 2 +h.c. How does this behave wrt CP?
See also talk by Vainshtein Vainshtein & Berezhiani, Gardner (& Jafari, & Yan) (DM & Ann Nelson 1512.05359) 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 = 1 + 2 +h.c. 3 phases, 2 fields, naively can t remove all but can rotate to remove or 1 2! cos +sin,! sin + cos
(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 2 1+ 2 2 m n! ss 0 Remaining phase can be removed by rephasing states
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 12 12 n ss 0 M 12 = 1 + 2 Gives transition probs. P ni! ni = 2 H 21 2 2 cosh 2 t cos mt e nt 2 p µ 2 nb 2 + H 12 H 21 i H 12,21 = M 12,21 2 12,21 CPV is, e.g., P ni! ni P ni! ni 1= 2Im (M 12 12 ) M 12 2 12 2 /4 Im (M 12 12 )
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
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 10 47 GeV! 2 m 2 n m 16 10 8 GeV m / p gy n n n n χ χ M 12 3 QCD gy! 2 m m 2 m 2 n m 2 1 4 P n! n P n!n 1 / 12 M 12 m 2 m 2 n! 3 M 1 MeV 3. 10 14 4 M 1 MeV 10 33 GeV 10 8 GeV m / p gy 4 1 MeV M Oscillations also suppressed by M 12 n. 10 5
(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)
(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.
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 2 10 8 4 f 3 2 trb CBB h B +... Can estimate constraints on heavy flavor transition amplitudes from n osc./dnd
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
Collider constraints Produce color triplet scalars easily d i d i ū j ū j j 1601.07453 1308.2631
Collider constraints Also produced through RPV coupling u di Monteux d ūjj 1601.03737 Resonant production is important!
Collider constraints Scan over scalar masses m = 200 MeV ( ) ( ) ϕ ( )
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
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
Baryon asymmetry calculation: ( ) - - - cb M 12 B = 10 2, ( ) 12 M 12 =0.3 - - - - Γ - - χ σ ( B + B_ ) ( ) Γ B Γ B + B _ η ( ) η Sudden decay approx: Can get observed asymmetry!
Probing this scenario q b q 0 branchings can be O(10 3 ) [1708.05808] P B! B M 12 2 2 B 10 5 Further work in progress
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