8
IL NUOVO CIMENTO VOL. 42 A, N. 1 1 Novembre 1977 Simple Symmetry Breaking and Decays of Charmed Mesons (*) C). ~M-, SINGICB Physics Depa~'tmen~, U~d'~'e.rsity o/ Wiscoq~sin. - .Madison,, Wis. 53706 (ricevuto il 10 Giugno ]977) Summary. -- We calculate the effects of simple symmetry breaking on the decay rates of charmed mesons using a ehir~l U4 effective Lagrangian to describe the mesons. We find that the D +, unlike the F + and D e, has no relatively large two-body decay into pseudoscalar mesons. Neutrino- induced tz-e+ events contain hints of these radically different decays of the D o and D +. Recent experiments in search of new particles have produced evidence for charmed mesons in neutrino-induced dilepton events (~.4), and in the inwriant- (*) To speed up publication, the author of this paper has agreed to not receive the proofs for correction. {**) Work supported in part by funds granted by the Wisconsin Alumni Research Foundation and in part by the Energy Research and Development Administration under contract E(11-1)-881, C00-575. (1} A. BENVENUTI, D. CLINE, W. T. FORD, R. I~ILAY, T. Y. LING, A. K. MANN, :R. ORR, D. D. REEDER, C. I~UBBIA, R. STEFANSKI, L. SULAK and F. WA~TDEREZ: Phys. Rev. Lett., 31, 419 (1975); 35, 1199, 1203, 1249 (1975). (2) B. BARISH, J. Y. BARTLETT, A. BODEK, K. W. BRO~vVN,D. BUCHHOLZ, 17. JACQUET, J. LEE, 17. S. MERRITT, 17. J. SCIULLI, L. STUTTE, H. SUTER, H. E. PISK and G. KRAFCzYs: Cal. Tech. report 68-485; Phys. t~ev. Lett., 36, 939 (1976). (a) J. VON KROGH, W. FRY, U. CAMERINI, D. CLINE, I{. J. LOVELESS, J. MAPP, I{. H. MARCH and D. D. REEDER: Phys. Rev. Lett., 36, 710 (1976). (4) J. BLIETSCHAU, H. DEDEN, P. J. HASER% W. KRENZ, D. LANSKE, J. MORFIN, G. H. BERTRAND-COREMANS, H. MULKENS, J. SACTON, W. VAN DONINCK, D. C. CUNDY, I. DANILCHENKO, D. HAIDT, A. LLORET, C. MATTEUZZI, F. MUSSET, K. MYKLEBOST, J. B. M. FATTISON, D. H. PERKINS, D. I)ITTUCK, P. ROMANO, H. WACtISMUTH, A. BLON- D:EL, V. BRISSON, ]3. I):EGRANGR, T. FRANCOIS, M. HAGUENAUER, L. KLIJBERG, U. 1N~GUY:EN-KHAC, P. P:ETIAU, A. ROUSSET, P. VAN DAIvI,A. ALDROVANDI, E. BELLOTTI, S. BONETTI, D. CAVALLI, E. FIORINI, A. I°ULLIA, M. I~OLLI~R, B. AUBERT, D. ]SLU]~i, 25

Simple symmetry breaking and decays of charmed mesons

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IL NUOVO CIMENTO VOL. 42 A, N. 1 1 Novembre 1977

Simple Symmetry Breaking and Decays of Charmed Mesons (*) C).

~M-, SINGICB

Physics Depa~'tmen~, U~d'~'e.rsity o/ Wiscoq~sin. - .Madison,, Wis. 53706

(ricevuto il 10 Giugno ]977)

Summary. - - We calculate the effects of simple symmet ry breaking on the decay rates of charmed mesons using a ehir~l U 4 effective Lagrangian to describe the mesons. We find tha t the D +, unlike the F + and D e, has no re la t ively large two-body decay into pseudoscalar mesons. Neutrino- induced tz-e+ events contain hints of these radical ly different decays of the D o and D +.

R e c e n t e x p e r i m e n t s in s ea r ch of n e w p a r t i c l e s h a v e p r o d u c e d ev idence for

c h a r m e d mesons in n e u t r i n o - i n d u c e d d i l e p t o n e v e n t s (~.4), a n d in t h e i n w r i a n t -

(*) To speed up publication, the author of this paper has agreed to not receive the proofs for correction. {**) Work supported in par t by funds granted by the Wisconsin Alumni Research Foundat ion and in par t by the Energy Research and Development Administrat ion under contract E(11-1)-881, C00-575. (1} A. BENVENUTI, D. CLINE, W. T. FORD, R. I~ILAY, T. Y. LING, A. K. MANN, :R. ORR, D. D. REEDER, C. I~UBBIA, R. STEFANSKI, L. SULAK and F. WA~TDEREZ: Phys. Rev. Lett., 31, 419 (1975); 35, 1199, 1203, 1249 (1975). (2) B. BARISH, J. Y. BARTLETT, A. BODEK, K. W. BRO~vVN, D. BUCHHOLZ, 17. JACQUET, J. LEE, 17. S. MERRITT, 17. J. SCIULLI, L. STUTTE, H. SUTER, H. E. PISK and G. KRAFCzYs: Cal. Tech. repor t 68-485; Phys. t~ev. Lett., 36, 939 (1976). (a) J. VON KROGH, W. FRY, U. CAMERINI, D. CLINE, I{. J. LOVELESS, J. MAPP, I{. H. MARCH and D. D. REEDER: Phys. Rev. Lett., 36, 710 (1976). (4) J. BLIETSCHAU, H. DEDEN, P. J. HASER% W. KRENZ, D. LANSKE, J. MORFIN, G. H. BERTRAND-COREMANS, H. MULKENS, J. SACTON, W. VAN DONINCK, D. C. CUNDY, I. DANILCHENKO, D. HAIDT, A. LLORET, C. MATTEUZZI, F. MUSSET, K. MYKLEBOST, J. B. M. FATTISON, D. H. PERKINS, D. I)ITTUCK, P. ROMANO, H. WACtISMUTH, A. BLON- D:EL, V. BRISSON, ]3. I):EGRANGR, T. FRANCOIS, M. HAGUENAUER, L. KLIJBERG, U. 1N~GUY:EN-KHAC, P. P:ETIAU, A. ROUSSET, P. VAN DAIvI, A. ALDROVANDI, E. BELLOTTI, S. BONETTI, D. CAVALLI, E. FIORINI, A. I°ULLIA, M. I~OLLI~R, B. AUBERT, D. ]SLU]~i,

25

26 M. SINGER

mass spectra of KT~ sys tems produced in e+e- unnihilations (5,6). I t is our purpose to examine the weak decays of the D +, D O and F + mesons (7-14) by means of a phenomenological chiral U4 Lagrangian to describe the pseudo- scalar mesons and their currents .

The phenomenological Lagrangian we use is a s t ra ight forward extension

to U4 of a successful U3 model proposed b y CRo~I~ (is). The s t rong LagTangian is (where repea ted indices denote summat ion)

~ 2 - - b + a b a 3qtl (1) ~¢s = ~ [~,M~ ~,Mo --A~(Mb -]- Mb+~)] -f- (~, ~',

wi th (1~)

a] M~ = exp

mass terms)

(a, b ---- 1, ..., 4)

L. M. CI{OUNET, P. HEUSSE, M. JAFFRE, L. JAIYNEAU, C. LONGUEMARE, A. M. LUTZ, C. PASCAl:D, J. P. VIALLE, F. W. BITLLOCK, T. W. JONES, A. G. ~ICHETTE and G. WYATT : Phys. Lett., 60 B, 207 (1976). (5) G. GOLDHABER, F. ~VJ[. PIERRE, G. S. ABRAMS, M. S. ALAI~I, A. M. BOYARSKI, M. BREIDENBACH, W. C. CARITIt'ERS, W. CHINOWSKY, S. C. COOPER, R. G. DEVoE, J. M. DORFAN, G. J. I~ELDMAN, C. ]~. ~RIEDBERG, D. ]~-~RYBERGER, G. HANSON, Z. JAROS, A. D. JOHNSON, J. A. KADYK, R. R. LARSEN, D. LLIKE, V. Li)TH, H. L. LYNCH, R. J. MADARAS', C. C. MOREItOUSE, H. K. NGUYEN, J. M. PATERSON, M. L. PERL, I. PERUZZI, M. PICCOLO, T. P. PUN, P. RAPIDIS, B. RICHTER, B. SADOULET, R. H. SCHINDLER, R. F. SCHWITTERS, J. SIEGRIST, W. TANENBAUM, Cx. H. TRILLING, 1 ~. ~V~ANNUCCI, J. S. WH1TA~ZER and J. E. WISS: Phys. Rev. Lett., 37, 255 (1976). (6) I. PERUZZI, M. PICCOLO, G. J. IFELDMAN, H. K. NGIYYEN, J. E. WISs, G. S. ABRAMS, M. S. ALAM, A. M. BOYARSKI, M. BREIDENBACH, W. C. CARITHERS, W. CHtlNOWSKY, R. G. DEVoE, J. M. DORFAN, G. E. :FISCHER, C. E. FRIEDBERG, D. ~RYBERGEI~, G. GOLD- HABER, G. HANSON, J. A. JAROS, A. D. JOHNSON, J. A. KADYK, R. n . LARSEN, D. Li3KE, V. Li)TI-I, H. L. LYNCH, R. J. ~ADARAS, C. C. MOREHOUSE, J. M. PATERSON, M. L. PERL, F. M. PIERRE, W. P. PUN, P. •APIDIS, B. RICHTER, R. H. SCHINDLER, R. F. SCHWITTERS, J. SIEGRIST, W. TANENBAUM, G. H. TRILLING, F. VANNUCCI and J. S. WHITAKER: Phys. t~ev. I~ett., 37, 569 (1976). (v) M. GAILLARD, B. LEE and J. R0SNER: Rev. Mod. Phys., 47, 277 (1975). (s) G. ALTAI~ELLI, N. CABIBBO and L. MAIANI: Phys. Rev. Left., 35, 635 (1975); Nucl. Phys., 88 B, 285 (1975). (9) R. KINGSLEY, S. TREI~AN, F. WILCZEK and A. ZEE: Phys. l~ev. D, 11, 1919 (1975); 12, 106 (1975). (lo) S. 0KUBO: Phys. Rev. D, 11, 3261 (1975). (11) M. KHANNA: Phys. Rev. D, 13, 1266 (1976). (12) M. EINI~ORN and C. QUIGG: Phys. l~ev. Left., 35, 1114 (1975); Phys. l~ev. D, 12, 2015 (1975). (13) Z. I4~ANDASWAMy, J. SCHECHTER and M. SINGER: Phys. t~ev. D, 13, 3151 (1976). (14) S. B. BORCHAI~DT and V. S. MATHUR: Phys. Bey. IJett., 36, 1287 (1976). (15) j . A. CRONIN: Phys. Rev., 161, 1483 (1967). (16) In fact M1 nonlinear Lagrangians are equivalent to order 4. For a proof for the SU s nlodel, see appendix A of J. SCHECtlTER and Y. UEDA: Phys. Rev., 188, 2184 (1968). The extension to S U s is straightforward.

S I M P L E SYM1E[I~TRY B R : E A K I N G AzND D E C A Y S O F C ~ I A R M E D M E S O N S 27

and

(2) A~ : A~6~ (no sum).

The ~ ' s are then the :t6-plet of pseudoscalar mesons (17), while ] is a constant parameter of dimension (mass). The symmetry-breaking parameters Aa generate most meson masses. In fact, assuming isotopic-spin invariance, we have

2 A I = A o = m,:,

(3) J~ = 2m~-- m~ ,

Equat ion (1) also gives the mass-squ~red sum rule

(~) ~ = ~ , + ~ - ~ .

From eq. (1) now we calculate the hudronic vector and axial vector currents W b b . ( a)~ and (A~)~.

(5.~) ~ i ~ M ]~ " ~ ~ ... (Vo)~,: ~]~[M, + ~ : ~ 9 ~ o + ,

i (5.2) (A~)z= ~ p{M, ~M+}~ :

O re) c '~ d b c d a

= 1 ~ + 5 ~ [ ~ o ~ o , ~ - ~ ~ ~ . . . .

Using the Glashow-Iliopoutos-Maiani (GIM) model (is) for weak interactions, and the hadronic currents in eq. (5), we obtain the following effective La- grangian densities for leptonie pseudoscalar decay:

G (6.1) ~¢.(~) = i~-~eos 0 o t ~ - t ~ ( 1 + 7~)~,

G (6.2) ~ , ( K ) ---- i ~ s i n O c ] ~ K - f i V ~ ( 1 + y~)v~ ,

G (6.3) ~q~,(D) ---- - - i ~/-~sinOc]~,D-fi y~(1 + y~)v~,

G (6.~) ~e~(F) = i ~ . cos Ool~-fty~(~ + y~)~.

(17) Our notation for the charmed pseudoscal~rs is that of ref. (~). (iS) S. GLASHOW, J. ILIOPOULOS ,~nd L. MAIA•I: Phys Rev D, 2, 1285 (1970).

28

TABLE I. -- Widths/or some 2- and 3-body decays o] charmed mesons. of mass ~ 1.8 Geg.

M. S I N G E R

Here L is a heavy lepton

D + widths in S -1 D o widths in S -1 F + widths in S -1

/"(D+-~ ~+u) = 1.57- l0 s /"(F+-+ ~+u) == 3.08.10 *

/"(D+-~ L+v) = 4.72.108 F(F+-~ L%) = 3.35.101°

/"(D+-~ ]~°~t+v) = 1.06.1011 /"(DO--> K-~+v) = 5.28- 101° /"(1 ~+-+'r,e+u) -- 7.95" 101°

F(D +-+ K°e+~) = 1.09-1011 /"(D~-+ K-e+v) = 5.45-1019 /"(F +-~ ~[x+v) = 7.91-101°

F(D+-> K°n+) = 2.25.10 ~° /"(D °-+ K-~ +) = 2.56.10 ~2 /"(p +_> ~+~o) = 0

/"(F+-+ ~+'q) = 3.32" 101~

/"(F +-> K+K 9) -- 4.83" 10 lz

/"(D+-~ K-=+~ +) - 6.16" 1011 /"(D o -> r:-K°rc +) = 1.03" 1011 /"(F+-+ r~+~+r:-) : 7.84"10 ~

/" (F+~ r~+K+K-) = 2.66" 1011

I n t h e above , G is t h e F e r m i c o n s t a n t , 0 c is t h e C a b i b b o angle , a n d J, t h e

p i o n d e c a y c o n s t a n t , is also equa l to t h e K , D a n d F d e c a y c o n s t a n t s (19). F r o m

p i o n decay , we t h e n see t h a t /_~ 1 . 0 1 m : . I f a h e a v y c h a r g e d l e p t o n (L) of

mass ~ 1.8 G e V ex i s t s (20), t h e n eqs. (6.3) a n d (6.4) w i t h fiy~(1 + y~)v~ re-

p l a c e d b y /dJ~(14-75)v~ w o u l d desc r ibe t h e F , D - + L - t - v d e c a y s (~). T h e

l e p t o n i c - d e c a y w i d t h s of t h e F a n d D a re l i s t e d in t a b l e I .

F o r t h e d o m i n a n t s emi - l ep ton i c d e c a y s Kt3, Dta a n d Fta ~ we f ind t h e h a d r o n i c

p a r t of t h e m a t r i x e l e m e n t s (22) to b e

i (7.1) %/dPo~(~-(q) l (V~)~]K,(p)> -= ~-~ (p + q)~,

(7.2) V/dpoqo<Ko(q)l(V~)~lD+(p)} -= (p + q)~,

i (7.3) V/dpoqo<K-(q)l(V~),lD°(p)> -= ~ (p + q), ,

(7.4) ~dpoqo<~(q)J(V~)~,jF+(p)> = V ~ ( p + q) , .

W e f ind t h a t u s i n g th i s m o d e l g ives a c a l c u l a t e d / ' ( K . -+ ~:+e-v) = 7.34.106 S -1

as c o m p a r e d w i t h t h e e x p e r i m e n t a l v a l u e of 7 .52 .10~S -1. The o t h e r semi-

l e p t o n i c w i d t h s a r e l i s t e d in t a b l e I .

(19) j . KANDASWAMY, J. SCItECtITER and M. SINGER: Phys. Rev. ~Lett., 38, 933 (1977). (20) M. L. PERL: Proceedings o] the International ConJerence on the l~roduction o] Par- ticles with New Quantum Numbers, Universi ty of Wisconsin-Madison (April 22-24, 1976). (21) I. KARLINER: Phys. t~ev. Left., 36, 759 (1976). (22) The semi-leptonie 3-body decays occur via the vector current. This s ta tement is expected to hold on general grounds from a generalization of the conserved-vector- current hypothesis and the Ademollo-Gatto theorem.

S I M P L E SYSIMETt~Y B R E A K I N G A N D D E C A Y S OF CI[AR.~IED M E S O N S 2 9

F o r n o n l e p t o n i c d e c a y s we a s s u m e t h a t t h e e f fec t ive w e a k L a g r a n g i a n is

p r o p o r t i o n a l to t h e 20 -d imens ionM p a r t ffa) of t h e GII~I i n t e r a c t i o n as fo l lows:

(8) ~ - G

2 ~ x [ s m 0o cos Oc(Ta, 7~, - - 274~ 7~,, + ' .4 .~

~ _ 2 "3 "1 "3 '1 ," 2 "2 "] "1 "2 - - s m 0 o ( h ~ 7 ~ , - - 74~7~) + cos 0o(Y4i,~2~ - - L v , 24,~) s in 0° cos 0°(j~, j ~ , - - "~ .a -2 .~ .~ -.,

H e r e x is a d imens ion l e s s p a r a m e t e r to be d e t e r m i n e d f r o m t h e K . -+ 2= r a t e .

The c u r r e n t s jo, z a r e t a k e n to be

(9) "~ ( V q @ b 5~((V~i A ¢ = (A°)#--~ + (o) , , ) ,

where (Vba), a n d A ~ ( a)i, a re g iven in eqs. (5.1) a n d (5.2). T h e r e s u l t s for some t y p i c a l

2 - b o d y d e c a y s a r e g iven b e l o w :

G (10.1) T(K~ --~ =+=-) ---- 7) x sin 9o cos 0c ](m~: - - m ~ ) ,

00.2)

(lO.3)

0o.~)

00.5)

I~(F + ~ = + = o ) = 0 ,

G I ' ( F + - + K+Ro ~ i ~ "~ ~ V~ x cos ~ Oc,

G = - - ~ x c o s ~ ~ ( m r - - .m=., ) T ( F +-> =+'q) i ~ 0° -~ 2

G T(D~ -+ K - n + ) = ~ x cos ~ 0o/(m~, - - , ~ ) ,

0o.6) G

T(D+-+ K°=+) = i - ;~x cos~-0o ](m~-- "4) 2 V z

F o r s i m p l i c i t y we h a v e se t T(D ° -~ K - = +) = ( i / v / ' 2 ) T ( D ° -> 1,2-=-I) Th is cor-

r e s p o n d s to negleetino" T(D o --> K-=+) wh ich sat isf ies AC = - - AS a n d is e x p e c t e d

to be s u p p r e s s e d b y sin 2 0 e. F r o m t h e e x p e r i n m n t M r a t e for (10.1) we f ind t h a t

2.14 (11) x ~ s i n0 c cos0° "

This d e t e r m i n e s t h e w i d t h s in t h i s m o d e l a n d t h e y a re l i s t e d in t a b l e I .

I t is i n t e r e s t i n g to n o t e t h e s u p p r e s s i o n of t h e F + - > =!,=o an , t D + - ~ Ko=+

decays . B o t h of t h e s e supp re s s ions can be u n d e r s t o o d in t e r m s of Bose sym-

(23) As noted in ref. (12), this contains the octet A I = ~- par t of the ]AS = 1 decays.

3{) M. SLNGER

merry for the final states. ]?or the F + _+~+~o mode, Bose symmet ry requires the 27: s tate to be an I ~ 2 state, while the F + is a singlet and the effective Lagrangian for a AS = AC decay has only a AI = 1 part . Since we are as- suming isotopic-spin invariance, T(F + _+ ~+~o) _-- 0. We have a similar sit- nat ion for the D + -+ ~o~+ mode, bu t in this c~se we are dealing ~vith V-spin. The D o has V-spin ---- 0, while the K ° and ~+ both have V-spin ~ ½. Bose sym- m e t ry requires the ~o~+ to be in a V-spin = 1 state, while the LagTangJan has only a AV = 0 par t (~). Since the SUa symmet ry is broken in the mass spectrum, the ra te for D + - + KO~ + is proport ional to the S Ua mass breaking.

Final ly contr ibutions to the 3-body nonleptonic-deeay amplitudes in the t ree approximat ion arise f rom both 4-point weak vertices and from 2-point weak vertices and 4-point strong vertices. The re levant 4-point strong La- grangian is contained in eq. (1) and is seen to be

---- ~#00a00b ~ o ~ q-- :~ Aa%~c~°~%] •

Wi th the nota t ion tha t S~ ~ - ( p - q,)2, the results for some typical decays are given below:

(12.1)

G - - 2--2xsin0cv cos 0(~[-- S~ q- m~ q- m~],

(12.2) T(D+(p)--~ K-(q~) q- r:+(q2) q- ,~+(q3)) :

G -- 2 ,v~XC°S ~0o - - ' D ~ v ¢

2 "> [--6'1 q- m. ÷ m;~],

(12.3) T(F+(p) -->~-(q~) q- r:+(q~) + ~+(q3)) :

G 2m~: -- 2 V ~ xc°s~0°-m&-m~ [ - & + ,m~ + m~],

(12.4) G

T(F+(p) --> r~+(q~) q- K+(q~) q- K-(q3)) -- 2 VX x cos: Oc(-- S~ + m~(),

02.,5) T(D~(p)-->rc-(q~) q- r:+(q2) q- ~O(qa)) :

iG [$1 m~ m~ X, COS 2 0 c - ~ - - .)

--S,, ~ ,:, + + m . + m ~ ÷ ~ . . ~ . . .

S I M P L E S Y M M E T R Y B R E A K I N G AND DECAYS OF CHARMED MESONS 31

Calculations for the K - ~ 3~: mode give the s tandard current-a lgebraic result

t ha t F (K+-+~: -~+~ +) ----3.82.10~S -~ which is about 15~/o below the expcri-

mentu l value of 4.52.10~S -~. The res t of the 3-body widths for the charmed- par t ic le decays ~re l isted in t~ble I .

Discussion.

One of the methods used to look for charmed part icles is a search for peaks

in invar ian t -mass spectr~. I n the ca.se of the D O nnd D + mesons such peaks

are theoret ical ly expec ted in the K - ~ + and K-~+u + systems. These peaks

have been found (5,6). Reference to table I shows thut the D O und D + have

appreciable widths into these modes. A search for pe~ks in the ~-~ou+ or the

K°~: + should be difficult, since the widths for these decnys are about an order

of magni tude below the K - ~ + und K-~+~: + modes. A search for the F+-meson should then be eusiest in the K+K °, z+~, or in the smaller, bu t more easily

exper imenta l ly detectable mode ~+K+K -. The width for F + -+ ~+~+~- is grea t ly suppressed and it is expected to be well below the z+K+K - width.

Other possible tes ts for chnrmed mesons arc %-induced ~-c + events. Aguin

such events have been seen (3,4). I n this model the e+'s ~re ~ssumcd to h~ve

come f rom the semi-leptonic deeuys of ei ther F+'s, D+'s or D°'s. l~cference to ruble I shows t h a t only the D + hus an nppreciable branching r~tio in the

semi-leptonic mode. Also b y the Cabibbo-enhanced p~rt of the GIM mech-

unism, the D + should be produced in associution with a str,~nge purticle, 50 ~o of the t ime K ~. Therefore, each t ime a ~-e + final s tute is observed, i t hus most p robubly come f rom the re,~ction

v~ + ~N' -~- ~ . - + D + + (K~)°-I-...

I_~ e++~o+~o.

Thus each ~-e + event should be associated with 1.5 neutr~d kaons. Experi- men ta l ly there are now 1.8 ± 0.7 neut ra l K ' s per e,~ch ~z-e + event (.04).

I wish to t h a n k V. BA]~G]~]~, M. OLSSO~ T, C. GOE]~EL and J . SCHECItTE]¢

for m a n y helpful discussions. I also wish to t h a n k F. H.~J,z~,:N for this sug- gestions und for reading this manuscr ip t .

(24) j . yon KROGII: Proceedings ]rom the 1976 Inter~ational Neutrino Co~]e.re,~we, A achen, Germany, June 8-12, 1976.

32 M. s ING~'R

Q RIASSUNTO (*)

Si calcolano gli effet t i di n n a sempl ice r o t t u r a di s i m m e t r i a sui va lo r i di d e c a d i m e n t o di mesoni i n c a n t a t i , pe r mezzo di u n a l a g r a n g i a n a e f fe t t iva del ia s i m m e t r i a ch i ra le U 4 pe r descr ivere i mesoni . Si t r o v a che D + d i v e r s a m e n t e da F + e D o n o n subisce decadi - m e n t i a due eorpi r e l a t i v a m e n t e g r a n d i in meson i pseudosca la r i . Gli e v e n t i ~-e+ i n d o t t i dal n e u t r i n o con tengono p rove di ques t i d e c a d i m e n t i r a d i c a l m e n t e d i f ferent i di D o e D +.

(*) Traduz ione a eura della t~edazione.

PeBtoMe He ~o~yqezao.