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Physics Letters B 788 (2019) 535–541

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Constraining P and CP violation in the main decay of the neutral

Sigma hyperon

Shankar Sunil Nair, Elisabetta Perotti, Stefan Leupold

∗

Institutionen för fysik och astronomi, Uppsala Universitet, Box 516, S-75120 Uppsala, Sweden

a r t i c l e i n f o a b s t r a c t

Article history:

Received

13 February 2018

Received

in revised form 30 August 2018

Accepted

9 September 2018

Available

online 28 November 2018

Editor:

V. Metag

Keywords:

Radiative

decays of hyperons

Electric

dipole moment

violation

On general grounds based on quantum ﬁeld theory the decay amplitude for 

→γ consists of a parity

conserving magnetic and a parity violating electric dipole transition moment. Because of the subsequent

self-analyzing weak decay of the  hyperon the interference between magnetic and electric dipole tran-

sition

moment leads to an asymmetry in the angular distribution. Comparing the decay distributions for

the 

hyperon and its antiparticle gives access to possible C and CP violation. Based on ﬂavor SU(3)

symmetry the present upper limit on the neutron electric dipole moment can be translated to an upper

limit for the angular asymmetry. It turns out to be far below any experimental resolution that one can

expect in the foreseeable future. Thus any true observation of a CP violating angular asymmetry would

constitute physics beyond the standard model, even if extended by a CP violating QCD theta-vacuum-

angle

term.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

There is much more matter than antimatter in the universe. If

this is not just by chance but has a dynamical origin, then an ex-

planation

of this baryon asymmetry should come from the realm

of particle physics. Based on Sakharov’s conditions [1]this has

spurred the search for baryon decays and reactions that show CP

violation [2]. (Here C denotes charge conjugation symmetry and

Pparity symmetry.) Two directions of such searches are weak de-

cays

of baryons [3–5] and electric dipole moments (EDMs) [6,7].

the present work we propose to study a reaction that is in

between these two types of reactions, the decay of the neutral

ground-state Sigma hyperon to a photon and a Lambda hyperon,



→ γ . This electromagnetic baryon decay could in principle

show an interference between a parity conserving and a parity vi-

olating

amplitude. The latter would come from an electric dipole

transition moment (the former from a magnetic transition mo-

ment).

Note that the  hyperon decays further into pion and

proton on account of the weak interaction [8]. The possible in-

terference

in the ﬁrst decay can then be observed as an angular

asymmetry in the decay products of the, in total, three-body decay



→γπ

−

p. Comparing the asymmetry parameters for the parti-

Corresponding author.

E-mail

address: stefan.leupold@physics.uu.se (S. Leupold).

cle decay, 

→γ , and for the corresponding antiparticle decay,



→γ

, one can search for C and CP violation.

Let

us add right away that the conservative expectation is that

one would not ﬁnd an effect of P, C or CP violation in this decay.

This will be substantiated by our explicit estimates given below.

Yet, if theory predicts that something is very small, then it might

be worth checking this experimentally. Even if one “only” estab-

lishes

an upper limit, this can help to constrain beyond-standard-

model

developments. Needless to add that if one found an effect

not predicted by established theory, then this would be sensa-

tional.

Actually

already in 1962 the interplay of magnetic and electric

dipole transition moment for the 

decay has been addressed in

[9], though under the implicit assumption of CP conservation. In

the present work we will be more general. In addition, to the best

of our knowledge, the search for such interference effects, albeit

suggested so early, has never been conducted. With recent and on-

going

experiments on hyperon production (e.g. at ELSA [10], J-LAB

[11,12], GSI [13,14], BEPC II [15,16], KEKB [17], CESR [18]) and

in particular with the upcoming PANDA experiment [19,20]as a

hyperon–antihyperon factory, it is absolutely timely to establish at

least upper limits for the angular asymmetry of the 

decay.

The

process 

→ γ  constitutes the main decay of the

ground state 

. Its lifetime is governed by this decay [8]. There-

fore

the 

lives much longer than hadronic resonances that decay

https://doi.org/10.1016/j.physletb.2018.09.065

0370-2693/

SCOAP

536 S.S. Nair et al. / Physics Letters B 788 (2019) 535–541

on account of the strong interaction, but much shorter than weakly

decaying particles. This makes the analysis of 

decays challeng-

ing,

as already pointed out in [9]. Hopefully these problems can be

diminished by the increasing production rate of 

particles and

detector quality.

Let

us relate and compare the process 

→γ  in more detail

to the mentioned searches for CP violation in weak baryon de-

cays

and for EDMs. In our case there is an interference between

two amplitudes, a large and a small one. The ﬁrst one is related

to the magnetic transition moment. This amplitude is parity con-

serving

and compatible with Quantum Electrodynamics (QED) and

Quantum Chromodynamics (QCD). The second one is related to

the electric dipole transition moment and is parity violating. Thus

one expects small effects right away. This is in contrast to similar

radiative decays where both amplitudes are caused by the weak

interaction, for instance 

→ γ [21]; see also the note on “Ra-

diative

Hyperon Decays” from the Particle Data Group [8]. For the

weak radiative decays the angular asymmetry is appreciably large,

but the difference between particle and antiparticle decay is in

most cases so far unmeasurably small. Only recently ﬁrst evidence

for a CP violating decay of the 

baryon has been reported [5].

For our case we expect very small effects for the angular asymme-

try

and for the particle–antiparticle differences.

Though

nature violates all discrete symmetries P, C and CP,

this

happens to different degrees and different interactions behave dif-

ferently.

Therefore in an analysis of the decay 

→γ  it is useful

to distinguish conceptually between a scenario of C violation but

CP conservation and a scenario of C conservation but CP violation.

We will present observables to test both scenarios for the process

of interest. Yet for our concrete estimates we will focus on strong

CP violation.

From

an experimental point of view, the strong interaction con-

serves

P, C and CP separately. Yet from the theory side it would

be natural to expect CP violation in QCD based on the non-trivial

topological structure of the non-abelian gauge theory [23]. Such a

“theta-vacuum-angle term” is C conserving but P and CP violat-

ing.

In particular, it gives rise to an EDM of the neutron. So far, no

EDM of the neutron has been experimentally established [24], but

the very small upper limit raises the question of why CP violation

in the strong sector is so unnaturally small (the “strong-CP prob-

lem”)

[25]. Note that the weak CP violation leads to an EDM of the

neutron that is many orders of magnitude below the experimental

upper limit [6]. Therefore we focus on possible strong CP violation

in the following. As we will show below, our decay 

→ γ  is

related to the neutron EDM via the approximate SU(3) ﬂavor sym-

metry

[26]. In the framework of chiral perturbation theory, one

can take care of the explicit symmetry breaking in a systematic

way [27–29]. Based on the experimental upper limit of the neu-

tron

EDM we will provide an upper limit for the CP violating effect

on the Sigma decay chain.

The

rest of the paper is structured in the following way: In

the next section we will present a general parametrization of the

transition moments for radiative decay amplitudes of baryons, dis-

cuss

the impact of C and CP symmetry/violation and relate all this

to the angular asymmetries of baryon and antibaryon decays. In

section 3 we will calculate all relevant decay widths and angu-

lar

distributions. In section 4 we will determine an upper limit for

those effects caused by strong CP violation, which is in turn related

to the QCD theta-vacuum-angle term. Here baryon chiral perturba-

tion

theory [27–29]can be used to relate the neutron EDM to the

In quantum ﬁeld theory the third discrete symmetry, time reversal symmetry T,

is intimately tied to CP via the CPT theorem [22]. In our decay, time reversal ar-

guments

are not directly applicable because we do not study the inverse formation

process γ →

. Therefore we focus on CP instead of T.



decay. Finally a summary and an outlook will be provided in

section 5.

2. Transition moments and angular decay asymmetries

For the coupling of baryons to the electromagnetic current J

we follow in principle [28]but adopt the deﬁnition of the photon

momentum to our decay process:

B



)|J

|B(p)=e



) 

(q) u

(p) (1)

with q := p − p



and



(q) =





−m



)



+(m



) q



)

−



μν

)

−



μν

). (2)

If B and B



have the same intrinsic parity then the functions

) and F

) are the P conserving Dirac and Pauli transition

form factors. F

) and F

) are the P violating Lorentz invari-

ant

transition form factors and are termed the anapole form factor

and the electric dipole form factor, respectively. We note in pass-

ing

that ideas how to access the q

dependence of F

and F

for

the transition of 

to  have been presented in [30].

For

the neutron, the Pauli form factor at the photon point is

related to the anomalous magnetic moment by [8]

2,n

(0) =κ

≈−1.91 (3)

while the EDM of the neutron is given by

3,n

(0). (4)

The decay 

→ γ  is only sensitive to the magnetic (dipole)

transition moment [8,30]

:= F

2,

(0) ≈1.98 (5)

and the electric dipole transition moment (EDTM)







3,

(0). (6)

The (transition) charge must vanish, F

1,

(0) = 0, and the anapole

moment F

A,

does not contribute for real photons, technically

based on q

= 0 and q



= 0 where 

denotes the polarization

vector of the photon. In section 4 we will relate the electromag-

netic

properties of the neutron and of the 

– transition.

Following

[8]the successive decay  → π

−

p is parametrized

by the matrix element

(A −Bγ

) u



(7)

where A and B are complex numbers. To stay in close analogy

to this parametrization we write the decay matrix element for the

ﬁrst decay 

→γ  as



(a σ

μν

−b σ

μν

) u



(−i)q



μ∗

. (8)

The two decay parameters a and b are related to the transition

moments via

a =





, b = id



. (9)

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