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2
3*AJW 1 version of CURR from KORALB.
4 SUBROUTINE CURR_CLEO(MNUM,PIM1,PIM2,PIM3,PIM4,HADCUR)
5C ==================================================================
6C AJW, 11/97 - based on original CURR from TAUOLA:
7C hadronic current for 4 pi final state
8C R. Fisher, J. Wess and F. Wagner Z. Phys C3 (1980) 313
9C R. Decker Z. Phys C36 (1987) 487.
10C M. Gell-Mann, D. Sharp, W. Wagner Phys. Rev. Lett 8 (1962) 261.
11C BUT, rewritten to be more general and less "theoretical",
12C using parameters tuned by Vasia and DSC.
13C ==================================================================
14
15 COMMON / PARMAS / AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU
16 * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1
17 * ,AMK,AMKZ,AMKST,GAMKST
18C
19 REAL*4 AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU
20 * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1
21 * ,AMK,AMKZ,AMKST,GAMKST
22C
23 REAL PIM1(4),PIM2(4),PIM3(4),PIM4(4)
24 COMPLEX HADCUR(4)
25
26 INTEGER K,L,MNUM,K1,K2,IRO,I,J,KK
27 REAL PA(4),PB(4),PAA(4)
28 REAL AA(4,4),PP(4,4)
29 REAL A,XM,XG,G1,G2,G,AMRO2,GAMRO2,AMRO3,GAMRO3,AMOM,GAMOM
30 REAL FRO,COEF1,FPI,COEF2,QQ,SK,DENOM,SIG,QQA,SS23,SS24,SS34,QP1P2
31 REAL QP1P3,QP1P4,P1P2,P1P3,P1P4,SIGN
32 REAL PKORB,AMPA
33 COMPLEX ALF0,ALF1,ALF2,ALF3
34 COMPLEX LAM0,LAM1,LAM2,LAM3
35 COMPLEX BET1,BET2,BET3
36 COMPLEX FORM1,FORM2,FORM3,FORM4,FORM2PI
37 COMPLEX BWIGM,WIGFOR,FPIKM,FPIKMD
38 COMPLEX AMPL(7),AMPR
39 COMPLEX BWIGN
40C
41 BWIGN(A,XM,XG)=1.0/CMPLX(A-XM**2,XM*XG)
42C*******************************************************************************
43C
44C --- masses and constants
45 IF (G1.NE.12.924) THEN
46 G1=12.924
47 G2=1475.98
48 FPI=93.3E-3
49 G =G1*G2
50 FRO=0.266*AMRO**2
51 COEF1=2.0*SQRT(3.0)/FPI**2
52 COEF2=FRO*G ! overall constant for the omega current
53 COEF2= COEF2*0.56 ! factor 0.56 reduces contribution of omega from 68% to 40 %
54
55C masses and widths for for rho-prim and rho-bis:
56 AMRO2 = 1.465
57 GAMRO2= 0.310
58 AMRO3=1.700
59 GAMRO3=0.235
60C
61 AMOM = PKORB(1,14)
62 GAMOM = PKORB(2,14)
63 AMRO2 = PKORB(1,21)
64 GAMRO2= PKORB(2,21)
65 AMRO3 = PKORB(1,22)
66 GAMRO3= PKORB(2,22)
67C
68C Amplitudes for (pi-pi-pi0pi+) -> PS, rho0, rho-, rho+, omega.
69 AMPL(1) = CMPLX(PKORB(3,31)*COEF1,0.)
70 AMPL(2) = CMPLX(PKORB(3,32)*COEF1,0.)*CEXP(CMPLX(0.,PKORB(3,42)))
71 AMPL(3) = CMPLX(PKORB(3,33)*COEF1,0.)*CEXP(CMPLX(0.,PKORB(3,43)))
72 AMPL(4) = CMPLX(PKORB(3,34)*COEF1,0.)*CEXP(CMPLX(0.,PKORB(3,44)))
73 AMPL(5) = CMPLX(PKORB(3,35)*COEF2,0.)*CEXP(CMPLX(0.,PKORB(3,45)))
74C Amplitudes for (pi0pi0pi0pi-) -> PS, rho-.
75 AMPL(6) = CMPLX(PKORB(3,36)*COEF1)
76 AMPL(7) = CMPLX(PKORB(3,37)*COEF1)
77C
78C rho' contributions to rho' -> pi-omega:
79 ALF0 = CMPLX(PKORB(3,51),0.0)
80 ALF1 = CMPLX(PKORB(3,52)*AMRO**2,0.0)
81 ALF2 = CMPLX(PKORB(3,53)*AMRO2**2,0.0)
82 ALF3 = CMPLX(PKORB(3,54)*AMRO3**2,0.0)
83C rho' contribtions to rho' -> rhopipi:
84 LAM0 = CMPLX(PKORB(3,55),0.0)
85 LAM1 = CMPLX(PKORB(3,56)*AMRO**2,0.0)
86 LAM2 = CMPLX(PKORB(3,57)*AMRO2**2,0.0)
87 LAM3 = CMPLX(PKORB(3,58)*AMRO3**2,0.0)
88C rho contributions to rhopipi, rho -> 2pi:
89 BET1 = CMPLX(PKORB(3,59)*AMRO**2,0.0)
90 BET2 = CMPLX(PKORB(3,60)*AMRO2**2,0.0)
91 BET3 = CMPLX(PKORB(3,61)*AMRO3**2,0.0)
92C
93 END IF
94C**************************************************
95C
96C --- initialization of four vectors
97 DO 7 K=1,4
98 DO 8 L=1,4
99 8 AA(K,L)=0.0
100 HADCUR(K)=CMPLX(0.0)
101 PAA(K)=PIM1(K)+PIM2(K)+PIM3(K)+PIM4(K)
102 PP(1,K)=PIM1(K)
103 PP(2,K)=PIM2(K)
104 PP(3,K)=PIM3(K)
105 7 PP(4,K)=PIM4(K)
106C
107 IF (MNUM.EQ.1) THEN
108C ===================================================================
109C pi- pi- p0 pi+ case ====
110C ===================================================================
111 QQ=PAA(4)**2-PAA(3)**2-PAA(2)**2-PAA(1)**2
112
113C Add M(4pi)-dependence to rhopipi channels:
114 FORM4= LAM0+LAM1*BWIGN(QQ,AMRO,GAMRO)
115 * +LAM2*BWIGN(QQ,AMRO2,GAMRO2)
116 * +LAM3*BWIGN(QQ,AMRO3,GAMRO3)
117
118C --- loop over five contributions of the rho-pi-pi
119 DO 201 K1=1,3
120 DO 201 K2=3,4
121C
122 IF (K2.EQ.K1) THEN
123 GOTO 201
124 ELSEIF (K2.EQ.3) THEN
125C rho-
126 AMPR = AMPL(3)
127 AMPA = AMPIZ
128 ELSEIF (K1.EQ.3) THEN
129C rho+
130 AMPR = AMPL(4)
131 AMPA = AMPIZ
132 ELSE
133C rho0
134 AMPR = AMPL(2)
135 AMPA = AMPI
136 END IF
137C
138 SK=(PP(K1,4)+PP(K2,4))**2-(PP(K1,3)+PP(K2,3))**2
139 $ -(PP(K1,2)+PP(K2,2))**2-(PP(K1,1)+PP(K2,1))**2
140
141C -- definition of AA matrix
142C -- cronecker delta
143 DO 202 I=1,4
144 DO 203 J=1,4
145 203 AA(I,J)=0.0
146 202 AA(I,I)=1.0
147C ... and the rest ...
148 DO 204 L=1,4
149 IF (L.NE.K1.AND.L.NE.K2) THEN
150 DENOM=(PAA(4)-PP(L,4))**2-(PAA(3)-PP(L,3))**2
151 $ -(PAA(2)-PP(L,2))**2-(PAA(1)-PP(L,1))**2
152 DO 205 I=1,4
153 DO 205 J=1,4
154 SIG= 1.0
155 IF(J.NE.4) SIG=-SIG
156 AA(I,J)=AA(I,J)
157 $ -SIG*(PAA(I)-2.0*PP(L,I))*(PAA(J)-PP(L,J))/DENOM
158 205 CONTINUE
159 ENDIF
160 204 CONTINUE
161C
162C --- lets add something to HADCURR
163C FORM1= FPIKM(SQRT(SK),AMPI,AMPI) *FPIKM(SQRT(QQ),AMPI,AMPI)
164C FORM1= AMPL(1)+AMPR*FPIKM(SQRT(SK),AMPI,AMPI)
165
166 FORM2PI= BET1*BWIGM(SK,AMRO,GAMRO,AMPA,AMPI)
167 1 +BET2*BWIGM(SK,AMRO2,GAMRO2,AMPA,AMPI)
168 2 +BET3*BWIGM(SK,AMRO3,GAMRO3,AMPA,AMPI)
169 FORM1= AMPL(1)+AMPR*FORM2PI
170C
171 DO 206 I=1,4
172 DO 206 J=1,4
173 HADCUR(I)=HADCUR(I)+FORM1*FORM4*AA(I,J)*(PP(K1,J)-PP(K2,J))
174 206 CONTINUE
175C --- end of the rho-pi-pi current (5 possibilities)
176 201 CONTINUE
177C
178C ===================================================================
179C Now modify the coefficient for the omega-pi current: =
180C ===================================================================
181 IF (AMPL(5).EQ.CMPLX(0.,0.)) GOTO 311
182
183C Overall rho+rhoprime for the 4pi system:
184C FORM2=AMPL(5)*(BWIGN(QQ,AMRO,GAMRO)+ELPHA*BWIGN(QQ,AMROP,GAMROP))
185C Modified M(4pi)-dependence:
186 FORM2=AMPL(5)*(ALF0+ALF1*BWIGN(QQ,AMRO,GAMRO)
187 * +ALF2*BWIGN(QQ,AMRO2,GAMRO2)
188 * +ALF3*BWIGN(QQ,AMRO3,GAMRO3))
189C
190C --- there are two possibilities for omega current
191C --- PA PB are corresponding first and second pi-s
192 DO 301 KK=1,2
193 DO 302 I=1,4
194 PA(I)=PP(KK,I)
195 PB(I)=PP(3-KK,I)
196 302 CONTINUE
197C --- lorentz invariants
198 QQA=0.0
199 SS23=0.0
200 SS24=0.0
201 SS34=0.0
202 QP1P2=0.0
203 QP1P3=0.0
204 QP1P4=0.0
205 P1P2 =0.0
206 P1P3 =0.0
207 P1P4 =0.0
208 DO 303 K=1,4
209 SIGN=-1.0
210 IF (K.EQ.4) SIGN= 1.0
211 QQA=QQA+SIGN*(PAA(K)-PA(K))**2
212 SS23=SS23+SIGN*(PB(K) +PIM3(K))**2
213 SS24=SS24+SIGN*(PB(K) +PIM4(K))**2
214 SS34=SS34+SIGN*(PIM3(K)+PIM4(K))**2
215 QP1P2=QP1P2+SIGN*(PAA(K)-PA(K))*PB(K)
216 QP1P3=QP1P3+SIGN*(PAA(K)-PA(K))*PIM3(K)
217 QP1P4=QP1P4+SIGN*(PAA(K)-PA(K))*PIM4(K)
218 P1P2=P1P2+SIGN*PA(K)*PB(K)
219 P1P3=P1P3+SIGN*PA(K)*PIM3(K)
220 P1P4=P1P4+SIGN*PA(K)*PIM4(K)
221 303 CONTINUE
222C
223C omega -> rho pi for the 3pi system:
224C FORM3=BWIGN(QQA,AMOM,GAMOM)*(BWIGN(SS23,AMRO,GAMRO)+
225C $ BWIGN(SS24,AMRO,GAMRO)+BWIGN(SS34,AMRO,GAMRO))
226C No omega -> rho pi; just straight omega:
227 FORM3=BWIGN(QQA,AMOM,GAMOM)
228C
229 DO 304 K=1,4
230 HADCUR(K)=HADCUR(K)+FORM2*FORM3*(
231 $ PB (K)*(QP1P3*P1P4-QP1P4*P1P3)
232 $ +PIM3(K)*(QP1P4*P1P2-QP1P2*P1P4)
233 $ +PIM4(K)*(QP1P2*P1P3-QP1P3*P1P2) )
234 304 CONTINUE
235 301 CONTINUE
236 311 CONTINUE
237C
238 ELSE
239C ===================================================================
240C pi0 pi0 p0 pi- case ====
241C ===================================================================
242 QQ=PAA(4)**2-PAA(3)**2-PAA(2)**2-PAA(1)**2
243
244C --- loop over three contribution of the non-omega current
245 DO 101 K=1,3
246 SK=(PP(K,4)+PIM4(4))**2-(PP(K,3)+PIM4(3))**2
247 $ -(PP(K,2)+PIM4(2))**2-(PP(K,1)+PIM4(1))**2
248
249C -- definition of AA matrix
250C -- cronecker delta
251 DO 102 I=1,4
252 DO 103 J=1,4
253 103 AA(I,J)=0.0
254 102 AA(I,I)=1.0
255C
256C ... and the rest ...
257 DO 104 L=1,3
258 IF (L.NE.K) THEN
259 DENOM=(PAA(4)-PP(L,4))**2-(PAA(3)-PP(L,3))**2
260 $ -(PAA(2)-PP(L,2))**2-(PAA(1)-PP(L,1))**2
261 DO 105 I=1,4
262 DO 105 J=1,4
263 SIG=1.0
264 IF(J.NE.4) SIG=-SIG
265 AA(I,J)=AA(I,J)
266 $ -SIG*(PAA(I)-2.0*PP(L,I))*(PAA(J)-PP(L,J))/DENOM
267 105 CONTINUE
268 ENDIF
269 104 CONTINUE
270
271C --- lets add something to HADCURR
272C FORM1= FPIKM(SQRT(SK),AMPI,AMPI) *FPIKMD(SQRT(QQ),AMPI,AMPI)
273CCCCCCCCCCCCC FORM1=WIGFOR(SK,AMRO,GAMRO) (tests)
274C FORM1= FPIKM(SQRT(SK),AMPI,AMPI) *FPIKM(SQRT(QQ),AMPI,AMPI)
275 FORM1 = AMPL(6)+AMPL(7)*FPIKM(SQRT(SK),AMPI,AMPI)
276
277 DO 106 I=1,4
278 DO 106 J=1,4
279 HADCUR(I)=HADCUR(I)+FORM1*AA(I,J)*(PP(K,J)-PP(4,J))
280 106 CONTINUE
281C --- end of the non omega current (3 possibilities)
282 101 CONTINUE
283
284 ENDIF
285 END
286
287
288