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

• bservables
• 4. Conclusion

• 1. Some Background

I need:

• Baryon number violation
• C and CP-violation
• Interaction out of thermal

equilibrium

Andrei Sakharov

Assuming CPT: T-violation CP-violation

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:

Jº3E-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.

Particle Current Upper Bound on EDM (e cm) Electron 8.7E-29 Mercury 3.1E-29 Proton 7.9E-25 Neutron 2.9E-26

Limits on C-even, P-odd observables: EDM And a lot more!

Limits on C-odd observables: neutral ϕ

• decays

C-Odd Decay Channel Decay Width (eV) πØ3g < 2.4E-7 ηØπ0 g < 1E-1 ηØ2π0 g < 7E-1 ηØ3π0 g < 8E-2 ηØ3 g < 2.1E-2 ηØπ0 e+e- < 5E-2 ηØπ0 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

)) ( ˆ 1 ( | | ) 3 1 ( ) 2 ( ) (

2 2 5 2        

 E E p p D E p B E p A s E E p p a E E p g V G d d dE d

e e e e n e e e e A ud F e e

                  

Ando, McGovern and Sato, Phys.Lett. B677 (2009) 109-115

• Current experimental limit:

4

10 ) 01 . 1 89 . 1 96 . (



     D

Mumm et al, Phys.Rev.Lett. 107 (2011) 102301 (strictly speaking the D-coefficient could be a function of the energies of the

• utgoing 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

which then generate a PCTV nucleon-nucleon interaction.

• Direct probe: Look for PCTV-observables. E.g. a PCTV

4-quark operator:

Direct vs Indirect Probe

N N i O NN ) ( ˆ

   

   

     

    

2 5 2 1 5 1 4

) ( ˆ q q q D D q i O q    

   

   

could directly generate a PCTV nucleon-nucleon interaction, or generate a long-range ρNN-operator:

  

    p n n p

5 5

(Question: how about operators like: ?)

• Indirect probe: the PCTV operator can generate PVTV
• bservables (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 :

  

   F e n p O

L L

~ ~ ˆ

(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:

  

 F nW p O ~ ~ ˆ

(gauge invariance is ensured by some complicated anomaly analysis)

• We think it is subject to EDM constraints as well via loop corrections

like:

n p g 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:

) (

2 PCTV   

 

   

  uW d dW u c iv

TV

L

which could arise from dim-6 T-violating operators before EWSB:

i R i L L i R R L L R i R i L L i R R L L R

W u H Q Q H u i B u H Q Q H u i W d H Q Q H d i B d H Q Q H d i

           

                ) ~ 2 2 ~ ( ˆ ) ~ ~ ( ˆ ) 2 2 ( ˆ ) ( ˆ

4 3 2 1

       

   

) EDM" ition weak trans (" ) ( ' ˆ

• perator)

(PCTV )

• (

' ˆ EDM)

• u

level

• (tree

' ˆ EDM)

• d

level

• (tree

' ˆ : terms and neglecting and EWSB After ) ˆ ˆ ( 2 ) ˆ ˆ ( ' ˆ ) ˆ ˆ ( 2 ) ˆ ˆ ( ' ˆ ˆ 2 ' ˆ ˆ 2 ' ˆ : ns combinatio linear

• f

set a Perform

5 5 4 3 5 2 5 1 4 2 3 1 4 4 2 3 1 3 3 2 1 1      

                 

           

                            dW u uW d vi dW u uW d vi uF u vi dF d vi W W Z t t c c

w w w w

• 3. Numerical estimations of the

dim-5 contribution to T-violating experimental observables

(a). D-coefficient induced by the dim-5 operator

n p T

u u g n d u p

 

  

Nucleon tensor charge n p q

n A V p ud

u q iF g g u V ig iM ...) ( 2 2

5

   

    

   

The imaginary part of F induces a D-coefficient

} 4 ) )( 1 ( 2 { ) 3 1 ( 2 4 ) (

2 2 e p n A TV A ud T e

E m m g v c g V g g E D        

With our dim-5 operator we obtain (set gV º1): Wμ

038 . 1 

T

g

MeV 76 . MeV 25 . ) . (   

e e

E E K

using: (lattice calculation, hep-ph1303.6953) with a typical energy of the outgoing electron: and the current bound on the D-coefficient:

4

10 4 | |



  D

we obtain:

2

• 4

2

GeV 10 4



  TV c

• J. Martin, JLab Hall C

Summer Meeting, 2007

(b). Nucleon EDM induced by the dim-5 operator

d u u d g W Quark EDMs could be generated via diagrams like: Since the PCTV operator already breaks chiral symmetry so there’s no quark-mass suppression to the EDM. Naïve dimensional analysis (NDA) estimation:

 

W TV ud q

m v c g eV d ln 16 ~

2 2



q n

d d ~

• 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?

2

• 12

2

GeV 10  TV c GeV 10 1.5 cm 10 9 . 2

• 12

26

e e dn    



: get we 1 ~ ln king naively ta By 

W

m

For order of magnitude estimation, assume: Current neutron EDM bound:

• More rigorous analysis: compute the mixing of various

dim-6 T-violating operators, and run it down from ΛTV to EW scale.

c h H H Q H u i c h H H Q H d i W u H Q Q H u i B u H Q Q H u i W d H Q Q H d i B d H Q Q H d i

L R L R i R i L L i R R L L R i R i L L i R R L L R

. ~ ~ ~ ˆ . ˆ ) ~ 2 2 ~ ( ˆ ) ~ ~ ( ˆ ) 2 2 ( ˆ ) ( ˆ

6 5 4 3 2 1

           

       

                 

           

L

Q

L

Q

R

d

R

d W B H H B W

CALCULATION IN PROGRESS!

(c). P-even ϕ Ø3g induced by the dim-5 operator

• The dim-5 PCTV operator could induce a ϕ

Ø3g decay which is C-odd and P-even via diagrams like:

q q q q W W      

• Effective Operator Analysis: write down lowest
• rder ϕØ3g
• perators in terms of ϕ, Fμν

(and its dual) and derivatives.

• Useful rules:

(EOM) ~ ~            

                 

F F F F F F F F F F F

• The effective C-violating, P-conserving ϕØ3g
• perator

begins at dim-9! Only ONE independent operator:

      

 F F F OCVPC ) ~ )( ( ˆ

3

  



• An “overestimated” NDA analysis: P-even ηØ3g

LEC:

CVPC

O g

   3

ˆ



 L

q q W   

2 2 3 2 2

1 16 1 ~

 

 F m v ge c g

W TV



That gives:

5 19 4 2 10 2 3 2

GeV 10 ~ ) 2 ( 32 2 1 ~ ) 3 (



   

TV

c k g m m



  

 

k (assuming k~mη /3) With current data:

• 5

6 tot ,

10 1.6 ) 3 BR( GeV, 10 30 . 1      



 



This leads to:

2

• 4

2

GeV 10  TV c

Not very useful!

3-particle phase space (SM flavor-diagonal T-violations are many-loop suppressed) Replacing η by π does not help because mπ <mη causes a large suppression.

Summary Summary

• Current direct bounds on PCTV observables are

far less stringent than their PVTV counterparts.

• Lowest-order PCTV operators with SM fields

have dimension 5, and could arise from dim-6 T- violating operators before EWSB

• Induced PVTV observables such as EDMs place

the most stringent bound on PCTV interactions.

• Current ηØ3g

data does not seem to set any significant constraint on the dim-5 PCTV interactions.