DETERMINATIONS OF P, AND CP, FOR HEAVY MESONS AND TESTS FOR THEIR VIOLATIONS WITHOUT POLARIZATION EXPERIMENTS

HAL Id: jpa-00224540

https://hal.archives-ouvertes.fr/jpa-00224540

Submitted on 1 Jan 1985

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

DETERMINATIONS OF P, AND CP, FOR HEAVY MESONS AND TESTS FOR THEIR VIOLATIONS

WITHOUT POLARIZATION EXPERIMENTS

C. Nelson

To cite this version:

C. Nelson. DETERMINATIONS OF P, AND CP, FOR HEAVY MESONS AND TESTS FOR THEIR

VIOLATIONS WITHOUT POLARIZATION EXPERIMENTS. Journal de Physique Colloques, 1985,

46 (C2), pp.C2-261-C2-268. �10.1051/jphyscol:1985229�. �jpa-00224540�

JOURNAL DE PHYSIQUE

Colloque C2, supplément au n°2, Tome 46, février 1985

page C2-261

DETERMINATIONS OF P, AND CP, FOR HEAVY MESONS AND TESTS FOR THEIR VIOLATIONS WITHOUT POLARIZATION EXPERIMENTS

C.A. Nelson

Department of Physics, State University of New York at Binghamton, Binghamton, New York 13901, U.S.A.

Résumé - Les résultats présentés sont d'un grand intérêt car ils peuvent être utilisés sur les "collider" modernes pour effectuer des tests de symétrie fondamentale par analyse de la désintegration séquentielle de X •*- V1V2. Les résultats permettent la détermination empirique de P et de CP pour les misons lourds ainsi que la réalisation de tests pour leur violation sans expérience de polarisation.

Abstract - Powerful results are tabulated which can be used at modern colliders to make fundamental symmetry tests by analysis of sequential decays of X + V1V2. By generalization of the ty$ parity test which has recently been used to determine the parity of the r|c, the P (or CP) quantum number can always be determined for X of any spin J which decays P (or respectively CP) invariantly into VV or VV where each vector meson decays into two spin-0 bosons, or is (0. P can also always be determined from a mode like K + K °. A neutral spin-0 technipion and an elementary Higgs particle, for instance, can be distinguished by such CP invariant decay modes and by <j>p , <j)J, JT, or i£ sufficiently massive by <f>Z° or JZ° where J/\JJ and Z° go into a lepton-antilepton pair. Generalization to the gZ° and gg decay channels, g = gluon jet, which would be relevant to new resonance physics, for example, at the CERN collider is discussed.

There are also very simple tests for possible violations of P, of the com- bination of C plus isospin, of both P and CP, and of both C and CP.

The practicality and state-of-the-art property of the c)><|> parity test /1/ has been recently demonstrated by its use /2/ by the Mark III collaboration at SLAC-SPEAR to determine the parity of the t) . Less than twenty events were needed to measure the dependence of the decay correlation function

I((ji) = 1 + 6 cos2<f)

on the azimuthal angle <j> between the two <f> -* K+KT decay planes and to show agreement with B = -1 (pseudoscalar), instead of 0 <_ 6 <_ 1 (scalar). This (j)(j) parity test /1/

for a spin-zero particle was proposed by Ngee-Pong Chang and myself in 1978 as an analogue of Yang's parity test / 3 / for the ir°. By means of the h'elicity formalism / 4 / , it was soon elegantly generalized / 5 / by Trueman for a decaying X particle of any spin J.

In the last few months the test has been extended /6,7/ to other V1V2 decay modes, for X of any spin J, including those of neutral X particles with odd charge- conjugation and those of charged X states. It has also been found that a spin-0 technipion and an elementary Higgs particle can be distinguished by a decay mode like (jxj) or JJ (identical vector mesons), K*°K ° (particle-antiparticle pair), <j)p°,

<J)J, JT, or if sufficiently massive by cfiZ0 or JZO where j/t|i and Z° go into a lepton- antilepton pair. In this talk we will summarize these new results, explain what has to be measured, and tabulate what can be learned from analysis of specific V1V2 decay modes.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985229

c2-262

JOURNAL DE PHYSIQUE

The advantages of t h i s t y p e of t e s t a r e t h a t

it

i s r i g o r o u s , t h a t t h e s i g n a t u r e s a r e s t r i k i n g , t h a t t h e P/CP determination i s independent of t h e p o l a r i z a t i o n s t a t e of t h e decaying

X

system (and so t h e t e s t i s independent of t h e production mechan- ism), t h a t t h e P/CP determination never f a i l s f o r

J=0

o r when t h e r e i s a Vlt*.V2 exchange p r o p e r t y , and t h a t t h e t e s t i s normally a p p l i c a b l e i n semi-inclusive p r o d u c t i o n experiments s i n c e many X decay modes y i e l d observed s t a t e s with only charged p a r t i c l e s .

We w i l l f i r s t c o n s i d e r t h e following s e q u e n t i a l decay of an

X system of any s p i n J X +

v1 v2

Spin

0

mesons A1, B1, ...

I n t h e X r e s t frame t h e nine h e l i c i t y amplitudes a r e s p e c i f i e d by

where X

=

XI-X2 and @ ,

^@

a r e t h e p o l a r and azimuthal a n g l e s of V l . By Lorentz- i n v a r i a n c e t h e g e n e r a l decay c o r r e l a t i o n f u n c t i o n is 161

+ Bd(01,02)

cos 2$

+ Bx(01,02) s i n 2+

where t h e p o l a r a n g l e s el and 82 f o r

A 1

and A2 momenta a r e defined

/5,6/ a s i n F i g .

1. I n p a r t i c u l a r , although t h e azimuthal a n g l e 4 i s i n v a r i a n t under Lorentz b o o s t s

V1

r e s t frame

v1 -z

V2

r e s t frame

Y

I

Fig. 1 - D e f i n i t i o n of a n g l e s

$,

el, 8 f o r s e q u e n t i a l decay of

2 X+V1V2.

along

z,

81 and 82 a r e defined r e s p e c t i v e l y i n t h e V1 and V2 r e s t frames. The

c o e f f i c i e n t s i n 1 ( 8 1 , 8 2 , ~ ) a r e very simple:

2 2 2

~ ( 0 ₁

,e

₂) =

i.8

^[-y(l) s i n 2 e s i n

₁

₂

+ y ( 2 )

cos

e ₁

^COS

e

₂

2 2 2

+

y(3) s i n 2 e 0 s 0

+ y 4

c o B s i n e 2 ]

1 1

(1)

1

( 2 ) +

+

^{4 3 ) +}

where t h e o v e r a l l normalization

i s

determined by 1 =

y + ^{1; y}

^{1 ( 4 )}

and$ =

E

laA

A 12.

1 2 The a ' s ,

8'

amplitudes i n t e g r a t e d i n s t a n c e , i

s , and y ' s a r e q u a d r a t i c f u n c t i o n s , s e e Appendix, of t h e n i n e h e l i c i t y and w i t h & can be simply determined by measurement of t h e a s s o c i a t e d d i s t r i b u t i o n s o r e q u i v a l e n t l y by measurement of I(B1,e2,(). For .f X -t V1V2

i s

P o r CP i n v a r i a n t , then

a,

= 6, = 0 and

=

t

⁽¹

+

aocos@

+

cos 2$),

c

⁼

Ig,

₉

and

i'lO. ^{. . . .}

0 -1 -1 0

=

S

( 1

- a

cos(

+

B ~ C O S 2 + ) , w i t h

Note t h a t t h e a ' s , B's, and y ' s appear v e r y simply

i n

t h e s e i n t e g r a t e d distribu:

t i o n s , w i t h a appearing i n t h e i r o v e r a l l n o r m a l i z a t i o n s . Therefore, we have chosen t o express I ( & ,e7,$) i n terms of t h e s e parameters. A

-

Note a l s o t h a t t h e f o u r auad- r a n t s i n

B1,e2

acceptance have been s e p a r a t e l y i n t e g r a t e d over t o i s o l a t e

a,

because t h e s i g n of t h e

a,

cos$ term

is

quadrant dependent 1 6 1 .

To i l l u s t r a t e t h e c o n c l u s i v e n a t u r e of t h e P/CP d e t e r m i n a t i o n , we c o n s i d e r t h e c a s e of a P i n v a r i a n t X + V1V2 decay mode w i t h a V1"V2 exchange p r o p e r t y so

where t h e

5

f a c t o r f o r each of t h e following decay modes i s :

@+

i d e n t i c a l v e c t o r mesons =

+1

(Bose S t a t i s t i c s r e q u i r e d ) K*~c*o

_, *+ *-

K K p a r t i c l e - a n t i p a r t i c l e C = Cn of

X

(C i n v a r i a n c e r e q u i r e d )

*+-*0 *+-*0 I+21V

K K , D D (C p l u s i s o s p i n i n v a r i a n c e r e q u i r e d ) 5 = Cn(-) Then /5,6/

(B

6,. a

=

a o )

JOURNAL DE PHYSIQUE

2 Re(a++aoo*) 2 rip

1

^{a h}

1

²

a =

& ,

^{f o r}

5

=

*l

s o f o r 5 = +1, t h e p a r i t y

np

^{of X i s given by}

'.

⁼

t ^*

k l i f B = a = O . ^{sgn sgn a i f}

^{B, B}

^{= 0}

Our r e s u l t s 161 f o r a

X

-t

VIVZ

which

i s

P o r CP i n v a r i a n t a r e given i n Table

1:

The n o t a t i o n V1 =

v1

^{means V1} i s i t s own a n t i p a r t i c l e . Note from Table I t h a t many decay modes y i e l d observed s t a t e s w i t h only charged p a r t i c l e s , e.g. K*' + +

7 1 f ( l ~ + ~ - ) ; t h a t modes without a Vl*V2 property determine qp o r y ~ p times t h e s i g n a t u r e

(-lJ;

and t h a t by

B

and C, t h e i n c o n c l u s i v e s i t u a t i o n can be i s o l a t e d e m p i r i c a l l y i f i t should occur. Omitted from t h e t a b l e i s t h e f a c t t h a t from a mode w i t h a V l + + V 2 p r o p e r t y , t h e s i g n a t u r e

(-)J

of X can be determined except i n c e r t a i n circumstances / 5 , 6 / .

TABLE I Measure

X

n e u t r a l

a,$ =>

X

charged a , ~ =>

Examples

This same c l a s s of s e q u e n t i a l decay modes provides simple e m p i r i c a l t e s t s f o r p o s s i - b l e symmetry v i o l a t i o n s f o r X of any s p i n J. Associated w i t h t h e g e n e r a l decay c o r r e l a t i o n f u n c t i o n I(Bl,82,$) given a t t h e beginning of t h i s t a l k , we have

161

Table

I1

and Table 111. I n c o n s i d e r i n g Table

I T ,

n o t e t h a t i t i s s u f f i c i e n t t o e m p i r i c a l l y demonstrate t h e presence o f s i n @ and/or s i n 24 terms e i t h e r i n I(B1,82,$) o r i n t h e i n t e g r a t e d d i s t r i b u t i o n s . I n considering Table 111, r e c a l l t h a t C0(B1,02)

i s

t h e d i s t r i b u t i o n t h a t appears when I(01,B2,$) i s i n t e g r a t e d over t h e e n t i r e range o f t h e azimuthal a n g l e $. I n r a t h e r s p e c i a l circumstances, i . e . , f o r s p e c i a l values o f a A , A q , from 1(01,82,$)

i t

can be e m p i r i c a l l y shown 161 t h a t

Case have Case

NO Vl-V2

Case No V1'+

V2

V1++V2 exchange b u t V1

=-TI

^{and with}

p r o p e r t y . V2 = V2. V1

# q1

and/or V2

# V2.

qp(-) J i f P good J

' I ~

i f P

good qp(-) i f

P good

yCP i f CP good

Y (-lJ

i f CP good

CP

np

i f P good Q ~ ( - ) ~ i f

P good

*

^{k f}

$0,

pop0 $PO, up0, u$ K , P K , w K ,

*o-*o

*+ *-

^{k o}

^a

⁺

K

K

, K K

P P I P , ~ P -

*+-k0

* *

K

K , D D _C, and o t h e r s K

+DI

v v

Never F a i l s J=0 Never F a i l s ; J>1 i n c o n c l u s i v e i f both la,+[ = 0 ( a c c i d e n t a l ) and l a

001

^{= O .}

t h e r e a r e symmetry v i o l a t i o n s even i f both of t h e above t e s t s d o n ' t show any evi- I L

dence f o r such a v i o l a t i o n .

P

bad.

TABLE I1 I f Measure f o r

any J:

X n e u t r a l s i n $ and/or s i n 2$

( i . e .

ax#

0 and/or

Bx#

0.)

X

charged

Same a s above.

Stronger r e s u l t s a r e obtained f o r J = 0 ,

1

because f o r J = 0 , ah = 0 only i f hl=hp, a n d f o r J = l , a f o o n l y i f

I x I = I x - X I ( ~ .

^{1 2}

All2

1 2

Case have Case No V l + + V Case No Vl++ V2 V l t f y 2 exchange b u t Vl

=-PI

an$ w i t h

p r o p e r t y . V2 = Vg. V1

# V1

and/or V2 #

V2.

Both Both

P

bad

P

bad

and and

CP bad.

CP

bad.

P

bad.

P

bad.

TABLE 111

I f

Measure f o r

any J : X n e u t r a l Asymmetric

co(e13e2) o r

1(81,82>44 under

e

^{- 8}

1 2

( i . e . y

PO) X- +

charged

Same a s above.

I n Table I V we l i s t s e v e r a l t e s t s which could be used, f o r i n s t a n c e

/7/,

t o d i s t i n - g u i s h between a J = 0 Higgs (YCp = +1) and a technipion (YCp = -1). [Ref. 6 and J . D e l l f A q u i l l a and C . A. Nelson, SUNY-BING Report i n p r e p a r a t i o n . ]

Case V1V2 Case V1V2

i d e n t i c a l p a r t i c l e s . a p a r t i c l e - a n t i p a r t i c l e p a i r .

Bose s t a t i s t i c s bad, Both C bad, and

C

bad, and a l s o a l s o CP bad.

CP bad.

Case

*+-*o *+-*o

K K , ^{D D} ,...

Combination of

C and i s o s p i n i n v a r i a n c e i s bad.

C2-266

JOURNAL DE PHYSIQUE

Technipion TABLE I V

VlV2 decay mode:

9$, -..

i d e n t i c a l v e c t o r mesons

Higgs

* * ^*+ *-

K ° K O , K K

, ...

p a r t i c l e - a n t i p a r t i c l e p a i r

Same a s above.

Same a s above.

Same a s above.

Same a s above.

Same a s above.

Same a s above.

Same a s above.

Dependence of t h e

8

values on f i n i t e l e p t o n masses i s normally n o t an important c o r r e c t i o n , s i n c e i f t h e l e p t o n mass dependence i s included, t h e e f f e c t i s only t o r e p l a c e

The $ v e c t o r meson r e s u l t s a l s o hold i f )I i s replaced by pO, w,

and s i m i l a r l y J/J, can be replaced by $(3685),

T,

T(10,350) a l l of which have l a r g e l e p t o n i c branching r a t i o s . Note t h a t t h e s i g n a t u r e s a r e n o t a s maximal

/1/

f o r a decay

mode

y i e l d i n g any l e p t o n - a n t i l e p t o n p a i r s s i n c e , u n l i k e f o r a boson c u r r e n t , t h e muon c u r r e n t i n t h e associate! v e c t o r meson r e s t frame can couple t o v e c t o r meson p o l a r i z a t i o n s o u t s i d e t h e pp decay plane.

Note a l s o t h a t t h e r e s u l t s a r e t h e same f o r each o f t h e ZO modes a s f o r t h e i r pre- ceding e n t r y i n Table I V because t h e presence of both a parity-conserving and a p a r i t y - v i o l a t i n g n e u t r a l c u r r e n t coupling only a f f e c t s t h e o v e r a l l normalization,

.

A c o r r o l l a r y i s t h a t a l l of Table I V i s simultaneously r e l e v a n t f o r d i s t i n - guishing / 7 / between a J=O system of even p a r i t y and one of odd p a r i t y .

This same type of P/CP t e s t g e n e r a l i z e s t o g ~ O and gg decay channels, g = gluon j e t , which would be r e l e v a n t t o new resonance p h y s i c s , f o r example / 8 , 9 / , a t t h e CERN

c o l l i d e r . The e x c l u s i v e $Zo and JZO channels may be hard t o observe due t o small branching r a t i o s . Although i t seems q u i t e d i f f i c u l t to experimentally i s o l a t e gluon j e t s , i t should be p o s s i b l e t o choose an enriched j e t sample with a leading v e c t o r meson decaying i n t o a LL p a i r which has been most l i k e l y produced from t h e high z fragmentation of a gluon. Assuming t h a t t h i s v e c t o r meson a r i s e s from t h e gluon, and t h a t

i t s

p o l a r i z a t i o n on t h e average follows t h a t

o f

t h e gluon j e t , t h e p o l a r i z a t i o n s o f t h e l e a d i n g v e c t o r meson and Z0 would be t h e same a s those of t h e primary gluon p l u s ZO. From t h e above r e s u l t s f o r JZ', t h i s reasoning then i n d i - c a t e s t h a t

B

w i l l be n e g a t i v e ( p o s i t i v e ) f o r a gluon-jet pl_us ZO mode t h a t a r i s e s r e s p e c t i v e l y from

a

y ~ p =

-1 (yep

= f l ) s o u r c e

x

^where

x

=

X.

A gg mode can a r i s e from an

X

where X

_= 5.

Our r e s u l t s f o r any s p i n J f o r t h e VV,

W,

and V1V2 decay channel where V1 = V 1 and V2 = V2 apply and so a s p i n 0 system, f o r example, would have 11p = +sgn

B

f o r

5

=

+1.

I n summary, we p o i n t a g a i n t o t h e four accompanying t a b l e s and t o t h e advantages o f t h i s type of t e s t f o r P/CP determination which we l i s t e d a t t h e beginning.

These r e s u l t s demonstrate t h a t c o l l i d e r s should be a b l e t o make fundamental sym- metry t e s t s a t very high e n e r g i e s by a n a l y s i s of s e q u e n t i a l decays.

We thank E. Berger and W . K . Tung f o r s e p a r a t e remarks.

[This work was p a r t i a l l y supported by t h e U. S. Department of Energy under Contract NO. DE-AC02-83ER4018. ]

Appendix: The

a's,

B's, and y h

I n t h e general decay c o r r e l a t i o n f u n c t i o n I(B1, $) t h e parameters c h a r a c t e r i z i n g t h e i n t e g r a t e d d i s t r i b u t i o n s a r e

(a: ¹

^{l a}

73;

XlX2 A112 a = R e ( a a* + a a* - a

*

^{00 00}

^--

^+oao-

*

- a a * ) / a ^{o+ -0}

ax

= -1m (same)

/&

J

-

By P i n v a r i a n c e , a-X = np(-) a X

,

o r by CP i n v a r i a n c e f o r V1 =

yl,

V2 = V

1 2 1 2 2

a-\1,-\2

= yep(-) J

ahli2,

s o

ax

=

BX

= 0 .

C2-268 JOURNAL

DE PHYSIQUE

By

CP

i n v a r i a n c e f o r a

W,

o r ~i mode, a-X

SO

ax

=

6

=

y

=

0.

1 2

^{X X}

By t h e p r e s e n c e o f a

Vl++V2

exchange p r o p e r t y a

aA2hl . ^yX

⁼

References

1. MANG, N. P. and NELSON,

C. A . ,

Phys. Rev. L e t t . 60 (1978) 1617; Phys. Rev. J @ (1979) 2923.

2.

BALTRUSAITIS,

R. M . ,

e t . a l . , Phys. Rev. L e t t . 52 (1984) 2126.

3. YANG,

C . N.,

Phys. Rev. 11 (1950) 242; 11 (1950) 722.

4. JACOB, M. and

WICK, G.

C., Ann. Phys. (N.Y.) 1, (1959) 404.

5 . TRUEMAN, T. L., Phys. Rev. D18 (1978) 3423.

6 . NELSON, C .

A., Phys.

Rev.

030 (1984) 107; (Oct.

1,

1984).

7. E x o t i c

J"

quantum numbers f o r b i d d e n t o t h e n o n r e l a t i v i s t i c

qq

system p r o v i d e a u s e f u l s i g n a t u r e f o r m u l t i q u a r k and g l u o n bound s t a t e s , and f o r r e l a t i v i s t i c dynamics a s was emphasized i n Ref. 1. Of c o u r s e , J ~ C quantum numbers ( i n par- t i c u l a r t h e p a r i t y quantum number) a l s o p r o v i d e a n i m p o r t a n t s i g n a t u r e f o r s q u a r k v e r s u s q u a r k c o n s t i t u e n t s i n

t h e

c a s e of supersymmetric dynamics.

8. ARNISON,

G.,

e t . a l . , Phys. L e t t . (1984) 115. BAGNAIA, P., e t . a l . , Phys.

L e t t . a (1984) 105.

9. BERGER,

E .

L. and JACOB,

M . ,

r e p o r t ANLHEP-PR-84-25, Ref.TH.3919-CERN.