00001
00002 COMPLEX FUNCTION F3PI(IFORM,QQ,SA,SB)
00003
00004
00005
00006
00007
00008
00009
00010
00011
00012
00013
00014
00015
00016
00017
00018
00019
00020
00021
00022
00023
00024
00025
00026
00027
00028
00029
00030 INTEGER IFORM
00031 REAL QQ,SA,SB
00032
00033
00034 REAL PKORB
00035 COMPLEX BWIGML
00036
00037
00038
00039
00040 CHARACTER*(*) CRNAME
00041 PARAMETER( CRNAME = 'F3PI' )
00042
00043 INTEGER IFIRST,IDK
00044 REAL MRO,GRO,MRP,GRP,MF2,GF2,MF0,GF0,MSG,GSG
00045 REAL M1,M2,M3,M1SQ,M2SQ,M3SQ,MPIZ,MPIC
00046 REAL S1,S2,S3,R,PI
00047 REAL F134,F150,F15A,F15B,F167
00048 REAL F34A,F34B,F35,F35A,F35B,F36A,F36B
00049 COMPLEX BT1,BT2,BT3,BT4,BT5,BT6,BT7
00050 COMPLEX FRO1,FRO2,FRP1,FRP2
00051 COMPLEX FF21,FF22,FF23,FSG1,FSG2,FSG3,FF01,FF02,FF03
00052 COMPLEX FA1A1P,FORMA1
00053
00054
00055
00056
00057
00058 DATA IFIRST/0/
00059
00060
00061
00062 IF (IFIRST.EQ.0) THEN
00063 IFIRST = 1
00064
00065 MRO = 0.7743
00066 GRO = 0.1491
00067 MRP = 1.370
00068 GRP = 0.386
00069 MF2 = 1.275
00070 GF2 = 0.185
00071 MF0 = 1.186
00072 GF0 = 0.350
00073 MSG = 0.860
00074 GSG = 0.880
00075 MPIZ = PKORB(1,7)
00076 MPIC = PKORB(1,8)
00077
00078
00079 PI = 3.14159
00080 BT1 = CMPLX(1.,0.)
00081 BT2 = CMPLX(0.12,0.)*CEXP(CMPLX(0., 0.99*PI))
00082 BT3 = CMPLX(0.37,0.)*CEXP(CMPLX(0.,-0.15*PI))
00083 BT4 = CMPLX(0.87,0.)*CEXP(CMPLX(0., 0.53*PI))
00084 BT5 = CMPLX(0.71,0.)*CEXP(CMPLX(0., 0.56*PI))
00085 BT6 = CMPLX(2.10,0.)*CEXP(CMPLX(0., 0.23*PI))
00086 BT7 = CMPLX(0.77,0.)*CEXP(CMPLX(0.,-0.54*PI))
00087
00088 PRINT *,' In F3pi: add (rho-pi S-wave) + (rhop-pi S-wave) +'
00089 PRINT *,' (rho-pi D-wave) + (rhop-pi D-wave) +'
00090 PRINT *,' (f2 pi D-wave) + (sigmapi S-wave) + (f0pi S-wave)'
00091 END IF
00092
00093
00094 F3PI = CMPLX(0.,0.)
00095
00096
00097
00098
00099 R = PKORB(4,11)
00100 IF (R.EQ.0.) THEN
00101
00102 IDK = 1
00103 M1 = MPIZ
00104 M2 = MPIZ
00105 M3 = MPIC
00106 ELSE
00107
00108 IDK = 2
00109 M1 = MPIC
00110 M2 = MPIC
00111 M3 = MPIC
00112 END IF
00113 M1SQ = M1*M1
00114 M2SQ = M2*M2
00115 M3SQ = M3*M3
00116
00117
00118
00119
00120
00121
00122
00123
00124
00125
00126
00127
00128
00129 IF (IFORM.EQ.1.OR.IFORM.EQ.2) THEN
00130 S1 = SA
00131 S2 = SB
00132 S3 = QQ-SA-SB+M1SQ+M2SQ+M3SQ
00133 IF (S3.LE.0..OR.S2.LE.0.) RETURN
00134
00135 IF (IDK.EQ.1) THEN
00136
00137
00138 F134 = -(1./3.)*((S3-M3SQ)-(S1-M1SQ))
00139 F150 = (1./18.)*(QQ-M3SQ+S3)*(2.*M1SQ+2.*M2SQ-S3)/S3
00140 F167 = (2./3.)
00141
00142
00143 FRO1 = BWIGML(S1,MRO,GRO,M2,M3,1)
00144 FRP1 = BWIGML(S1,MRP,GRP,M2,M3,1)
00145 FRO2 = BWIGML(S2,MRO,GRO,M3,M1,1)
00146 FRP2 = BWIGML(S2,MRP,GRP,M3,M1,1)
00147 FF23 = BWIGML(S3,MF2,GF2,M1,M2,2)
00148 FSG3 = BWIGML(S3,MSG,GSG,M1,M2,0)
00149 FF03 = BWIGML(S3,MF0,GF0,M1,M2,0)
00150
00151 F3PI = BT1*FRO1+BT2*FRP1+
00152 1 BT3*CMPLX(F134,0.)*FRO2+BT4*CMPLX(F134,0.)*FRP2+
00153 1 BT5*CMPLX(F150,0.)*FF23+
00154 1 BT6*CMPLX(F167,0.)*FSG3+BT7*CMPLX(F167,0.)*FF03
00155
00156
00157 ELSEIF (IDK.EQ.2) THEN
00158
00159
00160 F134 = -(1./3.)*((S3-M3SQ)-(S1-M1SQ))
00161 F15A = -(1./2.)*((S2-M2SQ)-(S3-M3SQ))
00162 F15B = -(1./18.)*(QQ-M2SQ+S2)*(2.*M1SQ+2.*M3SQ-S2)/S2
00163 F167 = -(2./3.)
00164
00165
00166 FRO1 = BWIGML(S1,MRO,GRO,M2,M3,1)
00167 FRP1 = BWIGML(S1,MRP,GRP,M2,M3,1)
00168 FRO2 = BWIGML(S2,MRO,GRO,M3,M1,1)
00169 FRP2 = BWIGML(S2,MRP,GRP,M3,M1,1)
00170 FF21 = BWIGML(S1,MF2,GF2,M2,M3,2)
00171 FF22 = BWIGML(S2,MF2,GF2,M3,M1,2)
00172 FSG2 = BWIGML(S2,MSG,GSG,M3,M1,0)
00173 FF02 = BWIGML(S2,MF0,GF0,M3,M1,0)
00174
00175 F3PI = BT1*FRO1+BT2*FRP1+
00176 1 BT3*CMPLX(F134,0.)*FRO2+BT4*CMPLX(F134,0.)*FRP2
00177 1 -BT5*CMPLX(F15A,0.)*FF21-BT5*CMPLX(F15B,0.)*FF22
00178 1 -BT6*CMPLX(F167,0.)*FSG2-BT7*CMPLX(F167,0.)*FF02
00179
00180
00181 END IF
00182
00183 ELSE IF (IFORM.EQ.3) THEN
00184 S3 = SA
00185 S1 = SB
00186 S2 = QQ-SA-SB+M1SQ+M2SQ+M3SQ
00187 IF (S1.LE.0..OR.S2.LE.0.) RETURN
00188
00189 IF (IDK.EQ.1) THEN
00190
00191
00192 F34A = (1./3.)*((S2-M2SQ)-(S3-M3SQ))
00193 F34B = (1./3.)*((S3-M3SQ)-(S1-M1SQ))
00194 F35 =-(1./2.)*((S1-M1SQ)-(S2-M2SQ))
00195
00196
00197 FRO1 = BWIGML(S1,MRO,GRO,M2,M3,1)
00198 FRP1 = BWIGML(S1,MRP,GRP,M2,M3,1)
00199 FRO2 = BWIGML(S2,MRO,GRO,M3,M1,1)
00200 FRP2 = BWIGML(S2,MRP,GRP,M3,M1,1)
00201 FF23 = BWIGML(S3,MF2,GF2,M1,M2,2)
00202
00203 F3PI =
00204 1 BT3*(CMPLX(F34A,0.)*FRO1+CMPLX(F34B,0.)*FRO2)+
00205 1 BT4*(CMPLX(F34A,0.)*FRP1+CMPLX(F34B,0.)*FRP2)+
00206 1 BT5*CMPLX(F35,0.)*FF23
00207
00208
00209 ELSEIF (IDK.EQ.2) THEN
00210
00211
00212 F34A = (1./3.)*((S2-M2SQ)-(S3-M3SQ))
00213 F34B = (1./3.)*((S3-M3SQ)-(S1-M1SQ))
00214 F35A = -(1./18.)*(QQ-M1SQ+S1)*(2.*M2SQ+2.*M3SQ-S1)/S1
00215 F35B = (1./18.)*(QQ-M2SQ+S2)*(2.*M3SQ+2.*M1SQ-S2)/S2
00216 F36A = -(2./3.)
00217 F36B = (2./3.)
00218
00219
00220 FRO1 = BWIGML(S1,MRO,GRO,M2,M3,1)
00221 FRP1 = BWIGML(S1,MRP,GRP,M2,M3,1)
00222 FRO2 = BWIGML(S2,MRO,GRO,M3,M1,1)
00223 FRP2 = BWIGML(S2,MRP,GRP,M3,M1,1)
00224 FF21 = BWIGML(S1,MF2,GF2,M2,M3,2)
00225 FF22 = BWIGML(S2,MF2,GF2,M3,M1,2)
00226 FSG1 = BWIGML(S1,MSG,GSG,M2,M3,0)
00227 FSG2 = BWIGML(S2,MSG,GSG,M3,M1,0)
00228 FF01 = BWIGML(S1,MF0,GF0,M2,M3,0)
00229 FF02 = BWIGML(S2,MF0,GF0,M3,M1,0)
00230
00231 F3PI =
00232 1 BT3*(CMPLX(F34A,0.)*FRO1+CMPLX(F34B,0.)*FRO2)+
00233 1 BT4*(CMPLX(F34A,0.)*FRP1+CMPLX(F34B,0.)*FRP2)
00234 1 -BT5*(CMPLX(F35A,0.)*FF21+CMPLX(F35B,0.)*FF22)
00235 1 -BT6*(CMPLX(F36A,0.)*FSG1+CMPLX(F36B,0.)*FSG2)
00236 1 -BT7*(CMPLX(F36A,0.)*FF01+CMPLX(F36B,0.)*FF02)
00237
00238
00239 END IF
00240 END IF
00241
00242
00243 FORMA1 = FA1A1P(QQ)
00244 F3PI = F3PI*FORMA1
00245
00246 RETURN
00247 END
00248
00249 COMPLEX FUNCTION BWIGML(S,M,G,M1,M2,L)
00250
00251
00252
00253 REAL S,M,G,M1,M2
00254 INTEGER L,IPOW
00255 REAL MSQ,W,WGS,MP,MM,QS,QM
00256
00257 MP = (M1+M2)**2
00258 MM = (M1-M2)**2
00259 MSQ = M*M
00260 W = SQRT(S)
00261 WGS = 0.0
00262 IF (W.GT.(M1+M2)) THEN
00263 QS=SQRT(ABS((S -MP)*(S -MM)))/W
00264 QM=SQRT(ABS((MSQ -MP)*(MSQ -MM)))/M
00265 IPOW = 2*L+1
00266 WGS=G*(MSQ/W)*(QS/QM)**IPOW
00267 ENDIF
00268
00269 BWIGML=CMPLX(MSQ,0.)/CMPLX(MSQ-S,-WGS)
00270
00271 RETURN
00272 END
00273
00274 COMPLEX FUNCTION FA1A1P(XMSQ)
00275
00276
00277
00278
00279 REAL XMSQ
00280 REAL PKORB,WGA1
00281 REAL XM1,XG1,XM2,XG2,XM1SQ,XM2SQ,GG1,GG2,GF,FG1,FG2
00282 COMPLEX BET,F1,F2
00283 INTEGER IFIRST/0/
00284
00285 IF (IFIRST.EQ.0) THEN
00286 IFIRST = 1
00287
00288
00289 XM1 = PKORB(1,10)
00290 XG1 = PKORB(2,10)
00291 XM2 = PKORB(1,17)
00292 XG2 = PKORB(2,17)
00293 BET = CMPLX(PKORB(3,17),0.)
00294
00295 GG1 = XM1*XG1/(1.3281*0.806)
00296 GG2 = XM2*XG2/(1.3281*0.806)
00297
00298 XM1SQ = XM1*XM1
00299 XM2SQ = XM2*XM2
00300 END IF
00301
00302 GF = WGA1(XMSQ)
00303 FG1 = GG1*GF
00304 FG2 = GG2*GF
00305 F1 = CMPLX(-XM1SQ,0.0)/CMPLX(XMSQ-XM1SQ,FG1)
00306 F2 = CMPLX(-XM2SQ,0.0)/CMPLX(XMSQ-XM2SQ,FG2)
00307 FA1A1P = F1+BET*F2
00308
00309 RETURN
00310 END
00311
00312 FUNCTION WGA1(QQ)
00313
00314
00315
00316
00317
00318
00319 REAL QQ,WGA1
00320 DOUBLE PRECISION MKST,MK,MK1SQ,MK2SQ,C3PI,CKST
00321 DOUBLE PRECISION S,WGA1C,WGA1N,WG3PIC,WG3PIN,GKST
00322 INTEGER IFIRST
00323
00324
00325 IF (IFIRST.NE.987) THEN
00326 IFIRST = 987
00327
00328
00329 MKST = 0.894D0
00330 MK = 0.496D0
00331 MK1SQ = (MKST+MK)**2
00332 MK2SQ = (MKST-MK)**2
00333
00334 C3PI = 0.2384D0**2
00335 CKST = 4.7621D0**2*C3PI
00336 END IF
00337
00338
00339
00340
00341 S = DBLE(QQ)
00342 WG3PIC = WGA1C(S)
00343 WG3PIN = WGA1N(S)
00344
00345
00346 GKST = 0.D0
00347 IF (S.GT.MK1SQ) GKST = SQRT((S-MK1SQ)*(S-MK2SQ))/(2.*S)
00348
00349 WGA1 = SNGL(C3PI*(WG3PIC+WG3PIN)+CKST*GKST)
00350
00351 RETURN
00352 END
00353
00354 DOUBLE PRECISION FUNCTION WGA1C(S)
00355
00356
00357
00358 DOUBLE PRECISION S,STH,Q0,Q1,Q2,P0,P1,P2,P3,P4,G1_IM
00359
00360 PARAMETER(Q0 = 5.80900D0,Q1 = -3.00980D0,Q2 = 4.57920D0,
00361 1 P0 = -13.91400D0,P1 = 27.67900D0,P2 = -13.39300D0,
00362 2 P3 = 3.19240D0,P4 = -0.10487D0)
00363
00364 PARAMETER (STH = 0.1753D0)
00365
00366
00367 IF(S.LT.STH) THEN
00368 G1_IM = 0.D0
00369 ELSEIF((S.GT.STH).AND.(S.LT.0.823D0)) THEN
00370 G1_IM = Q0*(S-STH)**3*(1. + Q1*(S-STH) + Q2*(S-STH)**2)
00371 ELSE
00372 G1_IM = P0 + P1*S + P2*S**2+ P3*S**3 + P4*S**4
00373 ENDIF
00374
00375 WGA1C = G1_IM
00376 RETURN
00377 END
00378
00379 DOUBLE PRECISION FUNCTION WGA1N(S)
00380
00381
00382
00383 DOUBLE PRECISION S,STH,Q0,Q1,Q2,P0,P1,P2,P3,P4,G1_IM
00384
00385 PARAMETER(Q0 = 6.28450D0,Q1 = -2.95950D0,Q2 = 4.33550D0,
00386 1 P0 = -15.41100D0,P1 = 32.08800D0,P2 = -17.66600D0,
00387 2 P3 = 4.93550D0,P4 = -0.37498D0)
00388
00389 PARAMETER (STH = 0.1676D0)
00390
00391
00392 IF(S.LT.STH) THEN
00393 G1_IM = 0.D0
00394 ELSEIF((S.GT.STH).AND.(S.LT.0.823D0)) THEN
00395 G1_IM = Q0*(S-STH)**3*(1. + Q1*(S-STH) + Q2*(S-STH)**2)
00396 ELSE
00397 G1_IM = P0 + P1*S + P2*S**2+ P3*S**3 + P4*S**4
00398 ENDIF
00399
00400 WGA1N = G1_IM
00401 RETURN
00402 END