Observation of the π0 → e+e− decay

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  • V01ume 738, num6er 3 PHY51C5 LE77ER5 27 Fe6ruary 1978

    085ERVA710N 0F 7HE n 0 --, e+e - DECAY

    J. F15CHER, P. EX7ERMANN, 0. 6U15AN, R. MERM0D, 8. M0REL, L. R055ELE7 1 and R. 5ACH07 2

    Un1ver51ty 0f 6eneva, 5w1t2er1and

    and

    P. 8L0CH, 6 .8UNCE a, 8. DEVAUX, A.M. D1AMAN7-8ER6ER 4, N. D0-DUC, 6. MAREL and R. 7URLAY Ddpartement de Phy514ue de5 Part1cu1e5 E1dmenta1re5, Centre dEtude5 Nuc1~a1re5, 5ac1ay, France

    Rece1ved 14 N0vem6er 1977 Rev15ed manu5cr1pt rece1ved 2 January 1978

    We have 065erved f0r the f1r5t t1me the very rare n ~ e+e - decay. 7he ta99ed n5 c0me fr0m K + ~ ~r+n decay51n +2.4 f119ht. We f1nd the 6ranch1n9 rat10 t0 6e (2.23 -1.1 ) 10-7 (90% C.L.). 7h15 va1ue 15 we11 a60ve the QED un1tary 11m1t and

    c0me51n r0u9h a9reement w1th a 5ec0nd-0rder e1ectr0ma9net1c pr0ce55 med1ated 6y vect0r me50n5.

    7he very rare decay m0de 0f the 7r 0 1nt0 an e1ec- tr0n-p051tr0n pa1r 15 0ne 0f the n0n-5tran9e c0unter- part5 0f the K 0 ~ #+/a- decay [1 ]. 1t 15 5upp05ed t0 pr0ceed ma1n1y thr0u9h e1ectr0ma9net1c 1nteract10n [2,3] and perhap5 thr0u9h neutra1 weak 1nteract10n [4]. 7here 15 a 10wer 60und t0 the n 0 ~ e+e - 6ranch- 1n9 rat10 pred1cted 6y 4uantum e1ectr0dynam1c5, the un1tar1ty 11m1t, wh1ch 91ve5 [3]

    1"(n 0 ~ e+e- ) /F (n 0 ~ a11) > 4.75 X 10 -8 .

    7h15 11m1t re11e5 0n1y 0n the a55umpt10n 0f a tw0- ph0t0n 1ntermed1ate 5tate and d0e5 n0t depend 0n the m0de1 u5ed t0 c0up1e the ph0t0n5 t0 the n 0. Var10u5 m0de15 [2,3,5] pred1ct a 6ranch1n9 rat10 6etween 1 and a60ut 3 t1me5 the un1tar1ty 11m1t.

    We have 065erved the n 0 ~ e+e - decay m0de 6y 5tudy1n9 a 1ar9e 5amp1e 0f n 0 Da11t2 decay5 0r 0 e+e-7) f0r wh1ch the 315 n0t detected. 7he ta99ed

    1 Pre5ent addre55: Ferm11a6, 8atav1a, 1L 60510, U5A. 2 Pre5ent addre55: CERN, 1211 6eneva 23, 5w1t2er1and. a Pre5ent addre55: Un1v. 0f W15c0n51n, Mad150n, W1 53706,

    U5A. 4 Pre5ent addre55: 5LAC, 5tanf0rd, CA 94305, U5A.

    n 05 are pr0duced 6y K ~ n+n 0 decay5 1n f119ht, a11 char9ed part1c1e5 are mea5ured 1n a ma9net1c 5pectr0m- eter and the e1ectr0n5 are 1dent1f1ed 6y Cerenk0v c0unter5. We refer the reader t0 the preced1n9 1etter [6] f0r the 5tudy 0f the Da11t2 decay m0de 1t5e1f, f0r the de5cr1pt10n 0f the apparatu5 and f0r the def1n1t10n 0f the exper1menta1 5amp1e5.

    We 5tart fr0m 5amp1e 1 wh1ch c0nta1n5 1.13 X 105 K decay5 w1th an e+e - pa1r, a n + (0r/a ) and p055161e neutra15 1n the f1na1 5tate. F1r5t we re5tr1ct 0ur5e1ve5 t0 we11-ta99ed n0~5 c0m1n9 fr0m K + ~ n+n 0 decay5 6y re4u1r1n9 the m1551n9 ma55 t0 the n + (M~+) t0 11e 6etween 110 and 160 MeV/c 2 (5ee f19. 1 0fref. [6]). 5ec0nd1y we c0ncentrate 0n event5 w1th an e+e - effec- t1ve ma55 (Mee) c105e t0 the n 0 ma55 (m7r) 6y app1y1n9 the f0110w1n9 cut: 121.5 ~

  • V01ume 738, num6er 3 PHY51C5 LE77ER5 27 Fe6ruary 1978

    the reC0n5trUCt10n perf0rmed 6y the pattern rec09n1- t10n pr09ram. 1n 1 0 ca5e5, the 5park cham6er5 6ef0re the ma9net have rec0rded m0re than 3 track5 wh1ch a11 p01nt t0 the vertex. We attr16ute th05e event5 t0 Da11t2 decay5 1n wh1ch the rea1 7 c0nvert5 1nt0 an e1ectr0n pa1r at the entrance 0f the 5pectr0meter. 7he5e 4-e1ectr0n event5 can fake h19h effect1ve ma55e5 Mee 1f 0n1y 0ne e1ectr0n 0f each pa1r (and 0f the r19ht 519n) pa55e5 the ma9net1c 6arr1er * 1.8ut 51nce they have a very c1ear 519nature 1n the 5park cham6er5, the5e react10n5 can 6e e11m1nated 1n a 5tra19htf0rward way. A M0nte Car10 51mu1at10n pred1ct5 an upper 11m1t 0f 1 5 5uch event5, 1n 900d a9reement w1th the 065erved num6er. We a150 e11m1nate 3 0ther event5 wh1ch have a h1t 1n the 3 c0unter5. After th15 5u6trac- t10n 0f c1ear1y m151dent1f1ed event5, we 06ta1n a 5amp1e 0f 24 event5.

    7he c0rre5p0nd1n9 x d15tr16ut10n 15 pre5ented 1n f19. 1. A5 an 1nd1cat10n, we 5h0w the exper1menta1 d15- tr16ut10n d0wn t0 x = 0.8.1n the ran9e 0.8 0.22.

    At th15 1eve1 a1ready, we 5ee that the num6er 0f event5 w1th x > 0.94 cann0t 6e acc0unted f0r 6y the ta11 0f the Da11t2 decay5. (A 1ar9er va1ue 0f the f0rm- fact0r 510pe d0e5 n0t he1p 519n1f1cant1y.) We 1nterpret the5e event5 a5 6e1n9 part1y due t0 d1rect n decay5 1nt0 tw0 e1ectr0n5, a5 5u99e5ted 6y the f0110w1n9 ar9u- ment5: (1) rec0n5truct10n err0r5, wh1ch w0u1d 1ncrea5e the ma55 0f n0rma1 Da11t2 pa1r5, are very un11ke1y 6ecau5e, f0r h19h x va1ue5, the e + and e - traject0r1e5 are we11 5eparated 1n the 5park cham6er5, (11) the ma55 5ca1e x 15 ca116rated c0rrect1y, a5 dem0n5trated 1n the preced1n9 1etter, and (111) the5e event5 11e 1n the ran9e expected f0r K + --> ~r+~r 0, 1r 0 ~ e+e - decay5 a5 5h0wn 6y the 51mu1at10n curve wh1ch 15 p10tted 1n f19. 1 (da5hed 11ne) w1th an ar61trary 5ca1e fact0r. N0t1ce

    ,1 D0u61e Da11t2 decay5 (~r --, e+e-e+e -) 6e10n9 t0 the 5ame cate90ry 6ut they are 5tr0n91y 5uppre55ed 6y the tr199er and d0 n0t c0ntr16ute 519n1f1cant1y.

    50.

    40.

    t~ 30 .

    a: 20 . uJ =.

    10.

    0 .

    5 2

    /

    .80 .84 .88 .92 .96 1.00 1.0*1. 1.08 x

    F19.1. e+e - effect1ve-ma55 d15tr16ut10n 6ef0re k1nemat1c f1t. H15t09ram: exper1menta1 5amp1e, d0t5: M0nte Car10 51mu1a- t10n. 7he expected d15tr16ut10n 0f ~r --, e+e - decay5 (da5hed 11ne) 15 p10tted w1th an ar61trary 5ca1e fact0r. 7he d0u61e arr0w5 repre5ent the 3 61n5 0f ta61e 1.

    that the centre 0f 9rav1ty 0f th15 curve 15 5h1fted fr0m x = 1 t0 x = 0.99 6y the 6rem55trah1un9 1n the appa- ratu5 * 2.7h15 curve ref1ect5 a150 0ur x re501ut10n. Let u5 a150 remark that n0 k1nemat1ca1 f1t 15 perf0rmed 50 far.

    We n0w 1nve5t19ate p055161e 50urce5 0f c0ntam1na- t10n. A11 the K + decay m0de5 wh1ch c0u1d c0ntam1nate are 51mu1ated 6y M0nte Car10 techn14ue5 6ut the 0n1y 0ne5 c0ntr16ut1n9 m0re than 0.1% are the f0110w1n9: the K~r2-Da11t2 decay, the d1rect K + ~ rr+e+e - decay and the 4-e1ectr0n react10n5 ment10ned a60ve. 7he re5u1t5 are pre5ented 1n ta61e 1.1n 0rder t0 dem0n- 5trate the 1nterna1 c0n515tency 0f 0ur c0mputat10n, we def1ne 1ncrea51n9 1nterva15 1n x (61n5 1, 2 and 3, centered at x = 0.99), 1n each 0ne we ca1cu1ate the num6er 0f 7r 0 ~ e+e- cand1date5 d1v1ded 6y the re1a- t1ve acceptance 0f the 61n and we 5h0w th15 num6er t0 6e 1ndependent 0f the 61n w1dth. 7he5e 61n5 are a150 1nd1cated 0n f19. 1.

    1n the 6ack9r0und e5t1mate5 we make the f0110w1n9 a55umpt10n5. F0r the K~r2-Da11t2 decay5, we u5e the f0rm-fact0r 510pe a = 0.1 1 [6]. F0r the K + ~ 1r+e+e - decay5, we take the 6ranch1n9 rat10 0f ref. [7] and a un1f0rm pha5e-5pace d15tr16ut10n. And f0r the 4-e1ec-

    :~2 7he effect 0f 1nterna1 6rem55trah1un9 1n the ~r --* e+e - decay 15 n0t 1nc1uded. R0u9h e5t1mate5 5h0w that 1t d0e5 n0t chan9e the w1dth 0f the curve and ha5 0n1y 11tt1e effect 0n the 065erved rate.

    365

  • v01ume 738, num6er 3

    7a61e 1 8ack9r0und 5u6tract10n (n0 k1nemat1ca1 f1t).

    PHY51C5 LE77ER5 27 Fe6ruary 1978

    81n 1 81n 2 81n 3 0.97~

  • V01ume 738, num6er 3 PHY51C5 LE77ER5 27 Fe6ruary 1978

    1.06

    1004 - -

    1 .02 - - m

    1.00 - -

    m ,96 - -

    .92 - -

    .90

    0 .

    1 1

    0 ) EX P

    1

    111 1 1 1

    m 11

    = 1 1 1 1 100. 200 . 300 . 400- 500,

    1.06

    1 .04

    1 .02

    1 .00

    .98

    .96

    .94

    .92

    .90

    1 1

    6) 1" - e + e-

    MC (x50) ~,~"

    fV =

    ~k~1,"

    [17 ~,~;)-..~... ~-~..~.~. -.

    == .

    1 "r 1 0. 100 . 200 . 300 .

    1 400.

    1 1

    500.

    K

    1 .06

    1 .04

    1 .02

    1 .00

    .98

    1 1 1 1 C) w~0~e + e),"

    MC (x50)

    ] 96 - - ~.

    . ; . - . . : ~ . . .94 ~.......'~, ~., ",,1.,., . . . .

    1~.~==:~ ~.~.:..:~..~.~,,- .92L~,k f ;~ ,~9,1 . ,m,,,.m, ~. . . ;

    .~01~ ~-~/~*-e~-~1~,-~--~. ," r 0. 100 . ;:00. 300 . 400 .

    1 1 1 d ) K+~1r * e+e -

    MC(x50)

    1.06

    ., 1-04 - -

    %=, 1

    1 .02 7= ~

    98 ~4~

    .96 L ~P 1

    ,50 1 0- 100-

    12 3 t

    1 " 1 1 ~00 300 400 . 500 . 500 .

    E) , (MeV) E 7 (MeV)

    F19. 2. (x, E,~) 5catter p10t5 after k1nemat1c f1t. (a) exper1menta15amp1e, (6) K + ~ 7r%r 0, ~r -- ee -, (c) K+~ ~r+rr 0, ~r ~ ee-r, (d) K ~ ~r+e~e -. 7he M0nte Car10 d15tr16ut10n51n (6), (c) and (d) are enhanced 50 t1me5 w11h re5pect t0 the actua1 rate5. Rad1at1ve c0rrect10n5 are 1nc1uded 1n (c) 0n1y. 7he vert1ca1 6ar5 repre5ent the 3 61n5 0f ta61e 2.

    7a61e 2 8ack9r0und 5u6tract10n (after 2C f1t).

    81n 1 81n 2 81n 3 0.96 < x < 1.00 0.94 < x < 1.02 0.91 < x < 1.05

    5 7 13 Exper1menta1 5amp1e

    K + ~ n+rr , 7r ~ e+e- 0.3

    K + ~ u+e+e - 0.6

    K + --, 4e react10n5 0.1

    C0rrected ~r 0 ~ e+e - 5amp1e 6.2

    1.2 6.5

    0.9 1.5

    0.3 0.5

    5.6 5.1

    367

  • V01ume 738, num6er 3 PHY51C5 LE77ER5 27 Fe6ruary 1978

    7a61e 3 ~r --* e+e - 6rancf11n9 rat105. F0r the def1n1t10n 0f the parame- ter5 h, A and mv, 5ee text.

    Exper1menta1 va1ue (2.23~+~: 4) X 10 -7

    Un1tar1ty 11m1t 0.47 X 10 -7

    Dre11 [5] h 2 = m7r2 0.48 X 10 -7

    = m~ 1.47 X 10 -7

    = 4m~ 2.50 X 10 -7

    8erman and A 2 = 10m~ 0.68 X 10 -7

    6effen [2] = 2rn~ 0.58 10 -7

    = 3 X 104m~ 0.48 X 10 -7

    2 Qu199 and rn v = m~ 0.61 X 10 -7

    Jack50n [3] = m~ 1.00 X 10 -7

    = 100m~ 1.50 X 10 -7

    t1ve part 0f the matr1x e1ement, 0ne 06ta1n5 the un1- tar1ty 11m1t 50 that:

    p(7r 0 ~ e+e-)/P(~r 0 --> ~p/) 1> 4.7 X 10 -8 .

    1n 0rder t0 take 1nt0 acc0unt the d15per51ve part 0f the matr1x e1ement 0ne ha5 t0 make 50me a55umpt10n 0n the f0rm fact0r t0 en5ure the c0nver9ence 0f the 1nte9ra1. Var10u5 m0de15 ex15t and f0r 50me 0f them we have rec0mputed the va1ue5 5ummar12ed 1n ta61e 3.

    1n an ear1y attempt, Dre11 [5] u5e5 a d15per510n re1at10n and ch005e5 42 a5 the var1a61e. He a55ume5 the f0rm fact0r t0 6e c0n5tant up t0 42 = k2 and t0 van15h a60ve. He 15 adv0cat1n9 a va1ue 0f ~, 0f the 0rder 0f the nuc1e0n ma55.

    8erman and 6effen [2] 1ntr0duce a f0rm fact0r 51m11ar t0 a part1c1e pr0pa9at0r (f0r A 2 >> m2):

    r(K12, (4 - K1) 2, m 2) = A2/ (A 2 - K12 - (4 - K1)2-1e),

    where the parameter A c0rre5p0nd5 t0 the ma55 0f the pr0pa9ated part1c1e. 7h15 ]~arameter 15 re1ated t0 the n0-f0rm-fact0r 510pe a: A 2 = m2[a. W1th 0ur re5u1t a = 0.11 + 0.03 [6], we f1nd A 2 ~ 9rn 2 wh1ch 1ead5

    t0 a 6ranch1n9 rat10 R a60ut 3 t1me5 6e10w the exper1- menta1 va1ue. H19her va1ue5 0f A 2 1ncrea5e the d15cre- pancy.

    Qu199 and Jack50n [3] u5e a vect0r d0m1nance m0de1 and 06ta1n:

    r(K 2, (4 - K1 )2 , rn2) , = (f/rnv)62/(K21 + mv2) {(4 - K1) 2 + mv2),

    where m v 15 the ma55 0f the vect0r me50n. A9a1n the f0rm-fact0r 510pe 15 c0n5tra1n1n9 m v (m 2 = m2 /a) t0 ~0.5m0.8ut 0n1y a va1ue m v ~ 2rn0 c0u1d acc0unt f0r 0ur 6ranch1n9 rat10.

    1n c0nc1u510n the 065erved 2r 0 ~ e+e - 6ranch1n9 rat10 can 6e under5t00d w1th1n the framew0rk 0f e1ectr0ma9net1c 1nteract10n5 c0m61ned w1th the hyp0- the515 0f a vect0r d0m1nance 6ut n0 prec15e 4uant1ta- t1ve c0nc1u510n5 can 6e drawn 0n the ma55 0f the vec- t0r me50n 0r the type 0f m0de1 t0 6e u5ed. 0n the 0ther hand recent paper5 [9] are u51n9 the 7r 0 --> e+e - 6ranch1n9 rat10 a5 an 1nput t0 c0n5tra1n m0re 9enera1 5cheme5 0f 4uark-1ept0n c0up11n9.

    1t 15 a p1ea5ure t0 thank Pr0fe550r J.D. Jack50n f0r many he1pfu1 d15cu5510n5 1n updat1n9 the eva1uat10n 0f the m0de15. We w15h a150 t0 ackn0w1ed9e the eff1- c1ent 5upp0rt 0f the CERN c0mputer 5taff.

    Reference5

    [1] W.C. Caf1ther5 et a1., Phy5. Rev. Lett. 31 (1973) 1025; Y. Fuku5h1ma et a1., Phy5. Rev. Lett. 36 (1976) 348; M.J. 5h0chet et a1., Phy5. Rev. Lett. 39 (1977) 59.

    [2] 5.M. 8erman and D.A. 6effen, Nu0v0 C1ment0 18 (1960) 1193.

    [3] C. Qu199 and J.D. Jack50n, UCRL-18487 (1968) unpu6- f15hed.

    [4] 5. W01fram, RL-76-082 (1976) unpu6115hed. [5] 5.D. Dre11, Nu0v0 C1ment0 11 (1959) 693. [6] J. F15cher et a1., 5ee preced1n9 1etter. [7] P. 810ch et a1., Phy5. Lett. 568 (1975) 201. [8] Part1c1e Data 6r0up, Rev. M0d. Phy5.48 (1976) 51. [9] A. 50n1, Phy5. Lett. 528 (1974) 332;538 (1974) 280;

    J.C. Pat1 and A. 5a1am, Phy5. Rev. D11 (1975) 1137; P. Her2e9, Phy5. Rev. D16 (1977) 712.

    368