P-Conserving, C- and T- violation in Effective Field Theory Chien - PowerPoint PPT Presentation

P-Conserving, C- and T- violation in Effective Field Theory Chien Yeah Seng Amherst Center for Fundamental Interactions (ACFI), Physics Department, University of Massachusetts Amherst In collaboration with Basem El-Menoufi and Michael J. Ramsey-Musolf Time-reversal Tests in Nuclear and Hadronic Processes workshop, ACFI, 7 November 2014

Outline Outline 1. Some Background 2. Effective PCTV Operators 3. Numerical estimations of the dim-5 contribution to T-violating experimental observables 4. Conclusion

1. Some Background

I need: • Baryon number violation • C and CP-violation • Interaction out of thermal equilibrium Assuming CPT: T-violation  CP-violation Andrei Sakharov CP-violation  C-conservation, P-violation OR C-violation, P-conservation

• Standard Model T-violation only comes from the complex phase in the CKM-matrix. • Characterized by Jarlskog invariant: J º 3E-5. \ SM background is small! • C-even P-odd: tightly constrained by EDM searches. • C-odd P-even: less constrained by experiments. One reason: particles/ particle systems with definite C-parity are few and difficult to prepare in large quantities.

Limits on C-even, P-odd observables: EDM Particle Current Upper Bound on EDM (e cm) Electron 8.7E-29 Mercury 3.1E-29 Proton 7.9E-25 Neutron 2.9E-26 And a lot more!

Limits on C-odd observables: neutral ϕ -decays C-Odd Decay Decay Width (eV) Channel π Ø 3 g < 2.4E-7 η Ø π 0 g < 1E-1 η Ø 2 π 0 g < 7E-1 η Ø 3 π 0 g < 8E-2 η Ø 3 g < 2.1E-2 η Ø π 0 e + e - < 5E-2 η Ø π 0 m + m - < 7E-3 (PDG 2014) (C=(-1) l+s for L + L - system)

• Another C-oven, P-even observable: the “D-coefficient” in the polarized neutron β -decay          2 ( )  d G V p p p p p p   2 2         ˆ ( 1 3 ) | | ( 1 ( )) F ud e e e g p E E a s A B D     5 ( 2 ) A e e n dE d d E E E E E E     e e e e e Ando, McGovern and Sato, Phys.Lett. B677 (2009) 109-115 • Current experimental limit:       4 ( 0 . 96 1 . 89 1 . 01 ) 10 D Mumm et al, Phys.Rev.Lett. 107 (2011) 102301 (strictly speaking the D-coefficient could be a function of the energies of the outgoing particles)

2. Effective PCTV operators

• EFT analysis: write down higher-order PCTV operators that consist of SM fields. • PCTV interaction cannot arise via tree-level boson exchange in a renormalizable gauge theory ( Herczeg, Hyperfine Interact, 75, 127 (1992) ) • Lowest-dimension flavor-conserving PCTV operators have dimension 7. ( Conti and Khriplovich, Phys.Rev.Lett. 68 (1992) 3262-3265 ) Ramsey-Musolf, Phys.Rev.Lett. 83 (1999) 3997-4000

Direct vs Indirect Probe • Direct probe: Look for PCTV-observables. E.g. a PCTV 4-quark operator:   ˆ        ( ) O q i q D D q q q    4 1 5 1 2 5 2 could directly generate a PCTV nucleon-nucleon interaction, or generate a long-range ρ NN-operator: ˆ               ( ) O NN i N N      which then generate a PCTV nucleon-nucleon interaction.        p n n p (Question: how about operators like: ?) 5 5

• Indirect probe: the PCTV operator can generate PVTV observables (such as EDMs) via electroweak loop- corrections. Ramsey-Musolf, Phys.Rev.Lett. 83 (1999) 3997-4000 Indirect probes usually set more stringent bounds because PVTV observables are more constrained experimentally.

• How about flavor non-diagonal operators? Consider a “pseudo-Chern-Simons” (pCS) type of interaction coming from gauging the axial anomaly of QCD under SU(2) L XU(1) Y : ~ ˆ     ~ O p n e F   L L (S. Gardner, Hadronic Probes of Fundamental Symmetries workshop, 2014); Harvey, Hill and Hill, hep-ph/0708.1281v2 Before integrating out the W-boson, it looks like: ~ ˆ   ~ O p nW F   (gauge invariance is ensured by some complicated anomaly analysis) • We think it is subject to EDM constraints as well via loop corrections like: g p n n W Unless there’s some peculiar cancelation between diagrams.

Is there any interesting operator in lower dimension? • We can write down a dim-5, flavor non- conserving PCTV operator:   c       ( ) L iv u dW d uW   PCTV  2 TV which could arise from dim-6 T-violating operators before EWSB: ˆ         ( ) i d H Q Q H d B  1 R L L R   i i ˆ         ( ) i i d H Q Q H d W  2 R L L R 2 2 ~ ~ ˆ         ( ) i u H Q Q H u B  3 R L L R   ~ i i ~ ˆ         ( ) i i u H Q Q H u W  4 R L L R 2 2

Perform a set of linear combinatio ns : 2 ˆ ˆ     ' 1 1 c w 2 ˆ ˆ    ' 2 3 c w ˆ ˆ ˆ ˆ ˆ          ' ( ) 2 ( ) t 3 1 3 2 4 w ˆ ˆ ˆ ˆ ˆ            ' ( ) 2 ( ) t 4 1 3 2 4 w   After EWSB and neglecting and terms : Z W W ˆ      ' (tree - level d - EDM) vi d dF  1 5 ˆ      ' (tree - level u - EDM) vi u uF  2 5 ˆ         ' ( - ) (PCTV operator) vi d uW u dW   3 ˆ            ' ( ) (" weak trans ition EDM" ) vi d uW u dW   4 5 5

3. Numerical estimations of the dim-5 contribution to T-violating experimental observables

(a). D-coefficient induced by the dim-5 operator      n p p u d n g u u T p n q Nucleon tensor charge W μ ig             ( ...) iM V u g g iF q u  5 ud p V A n 2 2 The imaginary part of F induces a D-coefficient º 1): With our dim-5 operator we obtain (set g V 4 2 g v       ( ) { 2 ( 1 )( ) 4 } T D E c g m m E   2 2 e A n p e ( 1 3 ) g V g ud A TV

using:  1 . 038 g (lattice calculation, hep-ph1303.6953) T with a typical energy of the outgoing electron:  ( . ) 0 . 25 MeV K E e   0 . 76 MeV E e and the current bound on the D-coefficient:    4 | | 4 10 D we obtain: J. Martin, JLab Hall C Summer Meeting, 2007 c    4 - 2 4 10 GeV  TV 2

(b). Nucleon EDM induced by the dim-5 operator W Quark EDMs could be generated via diagrams like: d d u u Since the PCTV operator already breaks chiral symmetry so there’s no quark-mass g suppression to the EDM. Naïve dimensional analysis (NDA) estimation: eV g v m ~ ln ud W d c    2 2 q 16 TV

For order of magnitude estimation, assume: d ~ d n q Current neutron EDM bound:      26 -12 2 . 9 10 cm 1.5 10 GeV d n e e m By naively ta king ln ~ 1 we get : W  c  10  12 - 2 GeV  TV 2 •This is a much more stringent bound than that set by direct PCTV observables! •Question: how do we distinguish effects between tree- level PVTV operators and loop-level PCTV operators?

• More rigorous analysis: compute the mixing of various dim-6 T-violating operators, and run it down from Λ TV to EW scale. W ˆ         ( ) i d H Q Q H d B  1 R L L R   Q d i i ˆ L R         ( ) i i d H Q Q H d W  2 R L L R 2 2 B ~ ~ H ˆ         ( ) i u H Q Q H u B  3 R L L R B   ~ ~ i i ˆ         ( ) i i u H Q Q H u W  4 R L L R 2 2 Q d ˆ      L R . i d H Q H H h c 5 R L ~ ~ ~ ˆ      . W H i u H Q H H h c 6 R L CALCULATION IN PROGRESS!

Ø 3 g (c). P-even ϕ induced by the dim-5 operator Ø 3 g • The dim-5 PCTV operator could induce a ϕ decay which is C-odd and P-even via diagrams like:   q q   W W  q q 

• Effective Operator Analysis: write down lowest order ϕ Ø 3 g operators in terms of ϕ , F μν (and its dual) and derivatives. • Useful rules:    0 F F F   ~    0 F F F   ~    0 F              0 F F F    0 (EOM) F  • The effective C-violating, P-conserving ϕ Ø 3 g operator begins at dim-9! Only ONE independent operator: ~ ˆ        ( )( ) O CVPC F F F      3