| 1 | SUBROUTINE DECAY6(AM0,AM3,AM4,AM5,PARAMA,PARAMB,PARAMC,AMPMX,MODE)
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| 2 |
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| 3 | C-----------------------------------------------------------------------
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| 4 | C DECAY (INTO 3 PARTICLES)
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| 5 | C
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| 6 | C TREATES DECAY INTO 3 PARTICLES; FULLY CONSERVING ENERGY AND MOMENTA
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| 7 | C KINEMATIC RANGE PARAMETRISATION SEE PHYS. LETT. 204B (1988) 90-91
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| 8 | C FOR LEPTONIC KAON DACAY: THE POLARIZATION OF THE MUON AND
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| 9 | C THE NEUTRINO PRODUCTION IS INCLUDED.
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| 10 | C THIS SUBROUTINE IS CALLED FROM ETADEC, KDECAY, AND PI0DEC
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| 11 | C ARGUMENTS:
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| 12 | C AM0 = MASS OF DECAYING PARTICLE
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| 13 | C AM3, AM4, AM5 = MASSES OF RESULTING PARTICLES
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| 14 | C PARAMA = DALITZ AMPLITUDE PARAMETER (SEE BELOW)
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| 15 | C PARAMB = DALITZ AMPLITUDE PARAMETER (SEE BELOW)
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| 16 | C PARAMC = DALITZ AMPLITUDE PARAMETER (SEE BELOW)
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| 17 | C AMPMX = MAXIMUM AMPLITUDE OF DALITZ PLOT
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| 18 | C MODE = 1 FOR DECAY KAON ----> 3 PIONS
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| 19 | C = 2 FOR DECAY ETA ----> 3 PIONS OR 2 PIONS + GAMMA
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| 20 | C FOR DECAY PI(0) ----> ELECTRON + POSITRON + GAMMA
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| 21 | C = 3 FOR DECAY KAON ----> PION + MUON + NEUTRINO
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| 22 | C = 4 FOR DECAY KAON ----> PION + ELECTRON + NEUTRINO
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| 23 | C
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| 24 | C AMPLITUDE PARAMETERS PARAMA, PARAMB, PARAMC ARE DEPENDENT ON MODE:
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| 25 | C FOR MODE=1: PARAMA = G DALITZ AMPLITUDE PARAMETRISATION SEE
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| 26 | C PARAMB = H PHYS. LETT. 204B (1988) 181 - 193
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| 27 | C PARAMC = K
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| 28 | C
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| 29 | C FOR MODE=2: PARAMA = A DALITZ AMPLITUDE PARAMETRISATION SEE
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| 30 | C PARAMB = DUMMY PHYS. LETT. 204B (1988) 173 - 175;
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| 31 | C PARAMC = DUMMY J.G. LAYTER ET.AL. PHYS.REV.D7(1973)2565
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| 32 | C
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| 33 | C FOR MODE>2: PARAMA = LAMBDA-PLUS DALITZ AMPLITUDE PARAMETRISATION
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| 34 | C PARAMB = LAMBDA-ZERO SEE PHYS. LETT. 204B (1988)
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| 35 | C PARAMC = DUMMY 182 - 194
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| 36 | C
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| 37 | C DESIGN : D. HECK IK3 FZK KARLSRUHE
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| 38 | C-----------------------------------------------------------------------
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| 39 |
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| 40 | IMPLICIT NONE
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| 41 | *KEEP,CONST.
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| 42 | COMMON /CONST/ PI,PI2,OB3,TB3,ENEPER
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| 43 | DOUBLE PRECISION PI,PI2,OB3,TB3,ENEPER
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| 44 | *KEEP,DECAY.
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| 45 | COMMON /DECAY/ GAM345,COS345,PHI345
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| 46 | DOUBLE PRECISION GAM345(3),COS345(3),PHI345(3)
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| 47 | *KEEP,PAM.
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| 48 | COMMON /PAM/ PAMA,SIGNUM
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| 49 | DOUBLE PRECISION PAMA(6000),SIGNUM(6000)
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| 50 | *KEEP,PARPAR.
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| 51 | COMMON /PARPAR/ CURPAR,SECPAR,PRMPAR,OUTPAR,C,
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| 52 | * E00,E00PN,PTOT0,PTOT0N,THICKH,ITYPE,LEVL
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| 53 | DOUBLE PRECISION CURPAR(14),SECPAR(14),PRMPAR(14),OUTPAR(14),
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| 54 | * C(50),E00,E00PN,PTOT0,PTOT0N,THICKH
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| 55 | INTEGER ITYPE,LEVL
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| 56 | *KEEP,PARPAE.
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| 57 | DOUBLE PRECISION GAMMA,COSTHE,PHI,H,T,X,Y,CHI,BETA,GCM,ECM
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| 58 | EQUIVALENCE (CURPAR(2),GAMMA), (CURPAR(3),COSTHE),
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| 59 | * (CURPAR(4), PHI ), (CURPAR(5), H ),
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| 60 | * (CURPAR(6), T ), (CURPAR(7), X ),
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| 61 | * (CURPAR(8), Y ), (CURPAR(9), CHI ),
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| 62 | * (CURPAR(10),BETA), (CURPAR(11),GCM ),
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| 63 | * (CURPAR(12),ECM )
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| 64 | *KEEP,POLAR.
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| 65 | COMMON /POLAR/ POLART,POLARF
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| 66 | DOUBLE PRECISION POLART,POLARF
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| 67 | *KEEP,RANDPA.
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| 68 | COMMON /RANDPA/ FAC,U1,U2,RD,NSEQ,ISEED,KNOR
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| 69 | DOUBLE PRECISION FAC,U1,U2
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| 70 | REAL RD(3000)
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| 71 | INTEGER ISEED(103,10),NSEQ
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| 72 | LOGICAL KNOR
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| 73 | *KEEP,RUNPAR.
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| 74 | COMMON /RUNPAR/ FIXHEI,THICK0,HILOECM,HILOELB,
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| 75 | * STEPFC,NRRUN,NSHOW,PATAPE,MONIIN,
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| 76 | * MONIOU,MDEBUG,NUCNUC,
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| 77 | * CETAPE,
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| 78 | * SHOWNO,ISHW,NOPART,NRECS,NBLKS,MAXPRT,NDEBDL,
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| 79 | * N1STTR,MDBASE,
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| 80 | * DEBDEL,DEBUG,FDECAY,FEGS,FIRSTI,FIXINC,FIXTAR,
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| 81 | * FIX1I,FMUADD,FNKG,FPRINT,FDBASE
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| 82 | * ,GHEISH,GHESIG
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| 83 | COMMON /RUNPAC/ DSN,HOST,USER
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| 84 | DOUBLE PRECISION FIXHEI,THICK0,HILOECM,HILOELB
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| 85 | REAL STEPFC
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| 86 | INTEGER NRRUN,NSHOW,PATAPE,MONIIN,MONIOU,MDEBUG,NUCNUC,
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| 87 | * SHOWNO,ISHW,NOPART,NRECS,NBLKS,MAXPRT,NDEBDL,
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| 88 | * N1STTR,MDBASE
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| 89 | INTEGER CETAPE
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| 90 | CHARACTER*79 DSN
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| 91 | CHARACTER*20 HOST,USER
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| 92 |
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| 93 | LOGICAL DEBDEL,DEBUG,FDECAY,FEGS,FIRSTI,FIXINC,FIXTAR,
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| 94 | * FIX1I,FMUADD,FNKG,FPRINT,FDBASE
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| 95 | * ,GHEISH,GHESIG
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| 96 | *KEND.
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| 97 |
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| 98 | DOUBLE PRECISION ABYM,AMPLI,AMPMX,AM0,AM3,AM34I,AM34SQ,AM35SQ,
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| 99 | * AM4,AM5,APARAL,APERPN,AUXA,AUXB,AUX1,AUX2,AUX2A,
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| 100 | * AUX3,AUX4,AUX4A,AUX5,AUX6,
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| 101 | * AUX7,AUX8,AUX10,AUX12,AUX14,BBYM,BOFQ,
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| 102 | * CM0SQ,CM3SQ,CM3SQI,CM4SQ,CM5SQ,COSALF,COSBET,
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| 103 | * COSFI4,COSOME,COSPHI,COSPSI,COS3CM,COS4CM,COS5CM,
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| 104 | * DISCR,EPIPRM,E3CM,E3STAR,E4CM,E5CM,E5STAR,FACT,
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| 105 | * GRLAMD,OMEGA,PA,PARAMA,PARAMB,PARAMC,PB,PC,PSI,
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| 106 | * P3CM,P3SQ,P4CM,P4SQ,P5CM,P5SQ,ROOT1,ROOT2,
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| 107 | * SINALF,SINBET,SINFI4,SINFI5,SINOMG,SINPHI,SINPSI,
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| 108 | * SINT4,SINT4I,SINT5I,SIN3CM,S0,TBYMSS,XIT,XI0
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| 109 | INTEGER MODE
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| 110 | C-----------------------------------------------------------------------
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| 111 |
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| 112 | IF ( DEBUG ) WRITE(MDEBUG,444) AM0,AM3,AM4,AM5
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| 113 | 444 FORMAT(' DECAY6: AM0',1P,E10.3,' AM3',E10.3,' AM4',E10.3,
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| 114 | * ' AM5',E10.3)
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| 115 |
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| 116 | C CALCULATE AUXILIARY QUANTITIES
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| 117 | CM0SQ = AM0**2
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| 118 | CM3SQ = AM3**2
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| 119 | CM4SQ = AM4**2
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| 120 | CM5SQ = AM5**2
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| 121 | AUX1 = (AM3 + AM4)**2
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| 122 | AUX2A = (AM0 - AM5)**2
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| 123 | AUX2 = AUX2A - AUX1
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| 124 | AUX3 = (AM3 + AM5)**2
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| 125 | AUX4A = (AM0 - AM4)**2
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| 126 | AUX4 = AUX4A - AUX3
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| 127 | AUX5 = CM3SQ - CM4SQ
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| 128 | AUX6 = CM0SQ - CM5SQ
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| 129 | AUX7 = 0.5D0 / AM0
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| 130 | IF ( MODE .EQ. 1 ) THEN
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| 131 | AUX8 = (AM0 - AM3)**2
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| 132 | S0 = OB3 * ( CM0SQ + CM3SQ + CM4SQ + CM5SQ )
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| 133 | AUX10 = 1.D0 / PAMA(8)**2
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| 134 | ELSEIF ( MODE .EQ. 2 ) THEN
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| 135 | AUX14 = 1.D0 / (AM0 - AM3 - AM4 - AM5)
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| 136 | ELSEIF ( MODE .EQ. 3 .OR. MODE .EQ. 4 ) THEN
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| 137 | CM3SQI = 1.D0 / CM3SQ
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| 138 | AUX12 = (CM0SQ + CM3SQ - CM4SQ) * AUX7
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| 139 | C XI0 IS XI(0); GRLAMD IS GREAT LAMBDA
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| 140 | XI0 = ( CM0SQ - CM3SQ) * CM3SQI * (PARAMB - PARAMA)
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| 141 | GRLAMD = -XI0 * PARAMA
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| 142 | ELSE
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| 143 | WRITE(MONIOU,*) 'DECAY6: UNEXPECTED MODE =',MODE
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| 144 | RETURN
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| 145 | ENDIF
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| 146 |
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| 147 | 100 CALL RMMAR( RD,3,1 )
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| 148 | C ARE INVARIANT MASS SQUARES INSIDE BOUNDARY OF DALITZ PLOT?
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| 149 | AM34SQ = AUX2 * RD(1) + AUX1
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| 150 | AM35SQ = AUX4 * RD(2) + AUX3
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| 151 | AM34I = 0.5D0 / SQRT(AM34SQ)
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| 152 | E3STAR = (AUX5 + AM34SQ) * AM34I
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| 153 | E5STAR = (AUX6 - AM34SQ) * AM34I
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| 154 | ROOT1 = SQRT(E3STAR**2 - CM3SQ )
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| 155 | ROOT2 = SQRT(E5STAR**2 - CM5SQ )
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| 156 | DISCR = AM35SQ - (E3STAR + E5STAR)**2
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| 157 | C REJECT RANDOM NUMBERS, IF OUTSIDE KINEMATIC BOUNDARY OF DALITZ PLOT
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| 158 | IF ( DISCR .GT. -(ROOT1 - ROOT2)**2 ) GOTO 100
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| 159 | IF ( DISCR .LT. -(ROOT1 + ROOT2)**2 ) GOTO 100
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| 160 | C E3CM, E4CM, E5CM ARE ENERGIES IN THE C. M. SYSTEM
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| 161 | E4CM = (CM0SQ + CM4SQ - AM35SQ) * AUX7
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| 162 | E5CM = (CM0SQ + CM5SQ - AM34SQ) * AUX7
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| 163 | E3CM = AM0 - E4CM - E5CM
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| 164 |
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| 165 | IF ( MODE .EQ. 1 ) THEN
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| 166 | FACT = AUX10 * (AUX2A - 2.D0*AM0*(E5CM-AM5) - S0)
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| 167 | C AMPLITUDE OF SQUARED MATRIX ELEMENT (SEE PHYS. LETT. B204 (1988) 181)
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| 168 | AMPLI = 1.D0 + PARAMA*FACT + PARAMB*FACT**2 + PARAMC*( AUX10
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| 169 | * * ( AUX4A -AUX8 -2.D0*(E4CM-AM4-E3CM+AM3)*AM0 ) )**2
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| 170 |
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| 171 | ELSEIF ( MODE .EQ. 2 ) THEN
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| 172 | C AMPLITUDE OF SQUARED MATRIX ELEMENT (SEE PHYS. LETT. B204 (1988) 173)
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| 173 | C REF: J. G. LAYTER ET AL., PHYS. REV. D7 (1973) 2565
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| 174 | AMPLI = 1.D0 + PARAMA * ( 3.D0 * (E5CM - AM5) * AUX14 - 1.D0 )
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| 175 |
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| 176 | ELSE
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| 177 | C EPIPRM IS (ENERGY OF PION)PRIMED
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| 178 | EPIPRM = AUX12 - E3CM
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| 179 | C PA, PB, AND PC ARE THE A, B, AND C PARAMETERS
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| 180 | PA = AM0 * ( 2.D0 * E4CM * E5CM - AM0 * EPIPRM )
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| 181 | * + CM4SQ * ( 0.25D0 * EPIPRM - E5CM )
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| 182 | PB = CM4SQ * ( E5CM - 0.5D0 * EPIPRM )
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| 183 | PC = CM4SQ * EPIPRM * 0.25D0
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| 184 | C TBYMSS IS T DIVIDED BY MASS SQUARE OF PION
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| 185 | TBYMSS = (CM0SQ + CM3SQ - 2.D0 * AM0 * E3CM) * CM3SQI
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| 186 | C XIT IS XI(T)
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| 187 | XIT = XI0 + GRLAMD*TBYMSS
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| 188 | C AMPLITUDE OF SQUARED MATRIX ELEMENT (PHYS. LETT. B204 (1988) 183)
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| 189 | AMPLI = (1.D0 + PARAMA*TBYMSS)**2 * ( PA + XIT*PB + XIT**2 *PC )
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| 190 | ENDIF
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| 191 |
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| 192 | C REJECT RANDOM NUMBERS, IF RD(3) IS LARGER THAN DALITZ PLOT AMPLITUDE
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| 193 | IF ( RD(3)*AMPMX .GT. AMPLI ) GOTO 100
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| 194 |
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| 195 | IF (DEBUG) WRITE(MDEBUG,*)'DECAY6: E3CM,E4CM,E5CM=',
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| 196 | * SNGL(E3CM),SNGL(E4CM),SNGL(E5CM)
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| 197 | C P3CM, P4CM, P5CM ARE MOMENTA IN THE C.M. SYSTEM
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| 198 | C P3SQ, P4SQ, P5SQ ARE SQUARED MOMENTA IN C.M. SYSTEM
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| 199 | P5SQ = E5CM**2 - CM5SQ
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| 200 | P5CM = SQRT(P5SQ)
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| 201 | P4SQ = E4CM**2 - CM4SQ
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| 202 | P4CM = SQRT(P4SQ)
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| 203 | P3SQ = E3CM**2 - CM3SQ
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| 204 | P3CM = SQRT(P3SQ)
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| 205 | C ANGLE ALFA AND BETA ARE BETWEEN PARTICLE 3 AND 4 RSP. 3 AND 5
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| 206 | COSALF = (P5SQ - P3SQ - P4SQ) / (2.D0 * P3CM * P4CM)
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| 207 | SINALF = -SQRT(1.D0 - COSALF**2)
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| 208 | COSBET = (P4SQ - P3SQ - P5SQ) / (2.D0 * P3CM * P5CM)
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| 209 | SINBET = SQRT(1.D0 - COSBET**2)
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| 210 | C NOW SELECT RANDOM NUMBERS FOR THREE INDEPENDENT ANGLES IN CM-SYSTEM
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| 211 | C COS3CM AND PHI ARE ANGLES OF PARTICLE 3 RELATIVE TO DECAYING PARTICLE
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| 212 | CALL RMMAR( RD,3,1 )
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| 213 | COS3CM = 2.D0*RD(1) - 1.D0
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| 214 | SIN3CM = SQRT(1.D0 - COS3CM**2)
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| 215 | PHI345(1) = PI2 * RD(2)
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| 216 | COSPHI = COS( PHI345(1) )
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| 217 | SINPHI = SIN( PHI345(1) )
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| 218 | C ANGLE PSI GIVES ROTATION OF PLANE (3,4,5) RELATIVE TO PLANE (1,3)
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| 219 | PSI = PI2 * RD(3)
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| 220 | COSPSI = COS(PSI)
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| 221 | SINPSI = SIN(PSI)
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| 222 | C CALCULATE ALL NEEDED POLAR AND AZIMUTHAL ANGLES IN THE CM-SYSTEM
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| 223 | COS4CM = COS3CM * COSALF - SIN3CM * COSPSI * SINALF
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| 224 | IF ( ABS(COS4CM) .LT. 1.D0 ) THEN
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| 225 | SINT4 = SQRT(1.D0 - COS4CM**2)
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| 226 | SINT4I = 1.D0 / SINT4
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| 227 | AUXA = COS3CM * COSPSI * SINALF + SIN3CM * COSALF
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| 228 | COSFI4 = (COSPHI*AUXA-SINPHI*SINPSI*SINALF) * SINT4I
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| 229 | PHI345(2) = ACOS( MAX( -1.D0, MIN( 1.D0, COSFI4 ) ) )
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| 230 | SINFI4 = (SINPHI*AUXA+COSPHI*SINPSI*SINALF) * SINT4I
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| 231 | IF ( SINFI4 .LE. 0.D0 ) PHI345(2) = PI2 - PHI345(2)
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| 232 | ELSE
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| 233 | PHI345(2) = 0.D0
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| 234 | ENDIF
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| 235 | C CALCULATE GAMMA FACTORS AND POLAR ANGLES IN LABORATORY SYSTEM
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| 236 | GAM345(1) = GAMMA * (E3CM + BETA * P3CM * COS3CM) / AM3
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| 237 | COS345(1) = MIN( 1.D0, (BETA * E3CM + P3CM * COS3CM) * GAMMA
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| 238 | * / ( AM3 * SQRT(GAM345(1)**2 - 1.D0) ) )
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| 239 | GAM345(2) = GAMMA * (E4CM + BETA * P4CM * COS4CM) / AM4
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| 240 | COS345(2) = MIN( 1.D0, (BETA * E4CM + P4CM * COS4CM) * GAMMA
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| 241 | * / ( AM4 * SQRT(GAM345(2)**2 - 1.D0) ) )
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| 242 | C CALCULATE PARAMETERS OF PARTICLE 5, IF NEEDED
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| 243 | IF ( MODE .LE. 2 ) THEN
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| 244 | COS5CM = COS3CM * COSBET - SIN3CM * COSPSI * SINBET
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| 245 | IF ( ABS(COS5CM) .LT. 1.D0 ) THEN
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| 246 | SINT5I = 1.D0 / SQRT(1.D0 - COS5CM**2)
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| 247 | AUXB = COS3CM * COSPSI * SINBET + SIN3CM * COSBET
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| 248 | PHI345(3) = ACOS((COSPHI*AUXB-SINPHI*SINPSI*SINBET) * SINT5I)
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| 249 | SINFI5 = (SINPHI*AUXB+COSPHI*SINPSI*SINBET) * SINT5I
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| 250 | IF ( SINFI5 .LE. 0.D0 ) PHI345(3) = PI2 - PHI345(3)
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| 251 | ELSE
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| 252 | PHI345(3) = 0.D0
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| 253 | ENDIF
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| 254 | IF ( AM5 .NE. 0.D0 ) THEN
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| 255 | GAM345(3) = GAMMA * (E5CM + BETA * P5CM * COS5CM) / AM5
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| 256 | COS345(3) = MIN( 1.D0, (BETA * E5CM + P5CM * COS5CM) * GAMMA
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| 257 | * / ( AM5 * SQRT(GAM345(3)**2 - 1.D0) ) )
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| 258 | ELSE
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| 259 | C IF PARTICLE 5 IS GAMMA RAY OR NEUTRINO, THEN GAM345(3) IS THE ENERGY
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| 260 | GAM345(3) = GAMMA * (E5CM + BETA * P5CM * COS5CM)
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| 261 | COS345(3) = MIN( 1.D0, (BETA * E5CM + P5CM * COS5CM) * GAMMA
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| 262 | * / GAM345(3) )
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| 263 | ENDIF
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| 264 | ENDIF
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| 265 |
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| 266 | IF ( MODE .EQ. 3 ) THEN
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| 267 | C CALCULATION OF MUON POLARIZATION. WE FOLLOW THE DESCRIPTION OF
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| 268 | C L. JAUNEAU, IN: METHODS IN SUBNUCLEAR PHYSICS, VOL. 3, M. NIKOLIC ED.
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| 269 | C (GORDON + BREACH, NEW YORK, 1969), P. 123
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| 270 | C SEE ALSO: L.M. CHOUNET ET AL., PHYS. REP. 4 (1972) 199, APPENDIX 1.
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| 271 | C SEE ALSO: N. CABBIBO, A. MAKSYMOWICZ, PHYS. LETT. 9 (1964) 352
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| 272 | C (CORRECTIONS IN: PHYS. LETT. 11 (1964) 360; 14 (1965) 72)
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| 273 | C WE DEFINE BOFQ (READ: B OF Q), WHICH IS -B(Q**2)*4
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| 274 | BOFQ = 1.D0 - XIT
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| 275 | C ABYM AND BBYM (READ A BY M; B BY M) ARE THE QUANTITIES A/M AND B/M
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| 276 | ABYM = AM0 * ( BOFQ * EPIPRM - 2.D0 * E5CM )
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| 277 | BBYM = CM0SQ + 0.25D0 * CM4SQ * BOFQ**2 - BOFQ * AM0 * E4CM
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| 278 | C NOW CALCULATE THE COMPONENTS APARAL (PARALLEL TO MU DIRECTION) AND
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| 279 | C APERPN (PERPENDICULAR TO MU DIRECTION) USING QUANTITIES DEFINED IN
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| 280 | C KAON REST SYSTEM. NOTE OUR DEFINITION OF SINALF (ALWAYS WITH NEGATIVE
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| 281 | C SIGN) OPPOSITE TO CABBIBO'S SIN(PSI) AND JAUNEAU'S SIN(THETA)
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| 282 | APARAL = -P3CM*AM4*BBYM*COSALF - P4CM * ( AM0*ABYM - BBYM *
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| 283 | * ( P3CM*SINALF*(E4CM-AM4)/P4CM + AM0 - E3CM ) )
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| 284 | APERPN = P3CM*AM4*BBYM*SINALF
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| 285 | C NOW NORMALIZE THE PARALLEL COMPONENT OF POLARIZATION; POLART IS
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| 286 | C COSINE OF THE ANGLE BETWEEN MUON MOMENTUM AND POLARISATION
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| 287 | POLART = APARAL / SQRT(APARAL**2 + APERPN**2)
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| 288 | C THE POLARIZATION VECTOR LIES IN THE PLANE OF MOMENTA (PION,MUON).
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| 289 | C OMEGA IS THE ANGLE BY WHICH THE DECAY PLANE (PION,MUON) IS ROTATET
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| 290 | C AROUND THE DIRECTION OF MUON RELATIVE TO THE PLANE (KAON,MUON)
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| 291 | IF ( ABS(COS4CM) .LT. 1.D0 .AND. SINALF .NE. 0.D0 ) THEN
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| 292 | COSOME = (COS4CM*COSALF - COS3CM)*SINT4I/SINALF
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| 293 | OMEGA = ACOS( MAX( -1.D0, MIN( 1.D0, COSOME ) ) )
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| 294 | IF ( SINFI4 .NE. 0.D0 ) THEN
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| 295 | SINOMG = ( COSFI4 * ( COSALF - COS3CM*COS4CM ) * SINT4I
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| 296 | * - SIN3CM * COSPHI ) / (SINALF*SINFI4)
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| 297 | IF ( SINOMG .LT. 0.D0 ) OMEGA = PI2 - OMEGA
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| 298 | ENDIF
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| 299 | ELSE
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| 300 | OMEGA = 0.D0
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| 301 | ENDIF
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| 302 | POLARF = OMEGA
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| 303 | ENDIF
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| 304 |
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| 305 | RETURN
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| 306 | END
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