C++ Interface to Tauola
f3pi_rcht.f
1 C JAK = 5
2 C
3  COMPLEX FUNCTION f3pi_rcht(IFORM,QQ,SA,SB)
4  IMPLICIT NONE
5  INTEGER IFORM
6  REAL QQ,SA,SB
7 C.......................................................................
8 C.
9 C. F3PI - RchT version of the hadronic curent used in TAUOLA
10 C. References: [1] arXiv:0911.4436 (hep-ph) P. Roig et al.
11 C. eqs (5)-(9), (32) gives the main part of the current
12 C (the part without the sigma contribution)
13 C. [2] arXiv:1203.3955,
14 C. the manual for the 3pi current without the sigma contribution
15 C. [3] http://annapurna.ifj.edu.pl/~wasm/RChL/RChLa1.pdf
16 C eq (3) the sigma meson contribution to the 3 pi current
17 C. Inputs : QQ,SA,SB - invariant masses**2 [GeV**2]
18 C. : IFORM formfactor no.
19 C. Outputs : F3PI_RCHT formfactor value
20 C.
21 C. COMMON : RCHT_3PI content is defined in this routine
22 C.
23 C. Calls : functions from file ./funct_rpt.f, ./fa1rchl.f
24 C. Called : from file ../formf.f
25 C. Author : O.S
26 C. Created :
27 C. Modified : 1. Feb 2011
28 C a part with scalars added on the 1st May 2012
29 C.......................................................................
30  include '../parameter.inc'
31  include '../funct_declar.inc'
32 
33  COMMON / decpar / gfermi,gv,ga,ccabib,scabib,gamel
34  real*4 gfermi,gv,ga,ccabib,scabib,gamel
35  COMMON / taukle / bra1,brk0,brk0b,brks
36  real*4 bra1,brk0,brk0b,brks
37  INTEGER J3PI
38  REAL wid_a1_fit
39 *
40  CHARACTER*(*) CRNAME
41  parameter( crname = 'F3PI' )
42 *
43  INTEGER IDK
44  DOUBLE PRECISION M1,M2,M3,M1SQ,M2SQ,M3SQ
45  REAL GGMA1
46  REAL S1,S2,S3,FACT_RPT
47 *
48  REAL R_RPT,KAP_RPT,FACT_ADD_RPT
49  COMPLEX ALP21_RPT,ALP22_RPT,ALP11_RPT,ALP12_RPT
50  $ ,BETA1_RPT,BETA2_RPT,BETA1_RPT_RHO1,ALP11_RPT_RHO1
51  $ ,ALP21_RPT_RHO1,ALP22_RPT_RHO1
52  COMPLEX FA1RCHL
53  INTEGER IFIRST
54  DATA ifirst/0/
55 
56 C. GENERAL INITIALIZATION
57 C. ======================
58 
59  IF (ifirst.EQ.0) THEN
60  ifirst = 1
61  print *,' In F3pi: chpt + 1 resonance + 2 resonance (RchT)'
62  END IF
63 
64 C******************************************
65 C Initilisation of the mass of the particles
66 C*****************************************
67  call rchl_parameters(5)
68 
69 C. We impose isospin symmetry requesting that charged and neutral pion mass
70 C. are equal. This may need to be changed MMPI_AV = (2.*MPIC+MPIZ)/3.
71 
72  m1 = mmpi_av
73  m2 = mmpi_av
74  m3 = mmpi_av
75 
76 
77 C. normalization factor to compensate on different
78 C. convention for normalization constant used in TAUOLA and
79 C. TAUOLA documentation on one side and paper [1] on other.
80  fact_add_rpt = 1./fpi_rpt
81 
82 
83 
84 C. FUNCTION VALUE, GENERAL CASE
85 C. ============================
86 
87 C Function value set to 0
88  f3pi_rcht = cmplx(0.,0.)
89 
90 C. First determine whether we are doing pi-2pi0 or 3pi.
91 C. we CH3PI GET information (eg from phase space geneator of tauola.f)
92 C. whether it is 3 prong J3pi=1 or 1 prong J3pi=2 final state of 3 pion.
93  CALL ch3piget(j3pi)
94 
95  IF (j3pi.EQ.2) THEN ! it is pi 2pi0
96  idk = 1
97  r_rpt = -1.
98  kap_rpt = 0.5
99  ELSE IF(j3pi.EQ.1) THEN ! it is 3pi
100  idk = 2
101  r_rpt = 1.
102  kap_rpt = 1.
103  END IF
104 
105  m1sq = m1*m1
106  m2sq = m2*m2
107  m3sq = m3*m3
108 
109 
110 C. Calculation, IFORM = 1 or 2.
111 C. VECTOR 3 PION FORM FACTORS
112 C. ============================
113  IF (iform.EQ.1.OR.iform.EQ.2) THEN
114  s1 = sa ! t variable in [2] (!!! vec1 = v2 !!!)
115  s2 = sb ! s variable in [2]
116  s3 = qq-sa-sb+m1sq+m2sq+m3sq
117 
118  IF (s3.LE.0..OR.s2.LE.0.) RETURN
119 
120 C. FUNCTIONS BETA_RPT, ALP1_RPT are coded in ./funct_rpt.f
121 C. they are defined in Eq (6) of [2]
122  beta1_rpt = beta_rpt(qq,s1,s2,m1sq,m2sq,m3sq,mro,mrho1,grho1)
123  alp11_rpt = alp1_rpt(qq,s1,s2,m1sq,m2sq,m3sq,mro,mrho1,grho1)
124 
125  f3pi_rcht = - 2.*sqrt(2.)/(3.*fpi_rpt) -
126  $ sqrt(2.)*fv_rpt*gv_rpt/(3.*fpi_rpt**3)*alp11_rpt +
127  $ 4.*fa_rpt*gv_rpt/(3.*fpi_rpt**3)*beta1_rpt*qq
128  $ *fa1rchl(qq)
129 
130 C. FA1RCHL(QQ) is the a1 propagator, is it coded in ./fa1rchl.f
131 
132 
133  f3pi_rcht = f3pi_rcht * r_rpt
134 
135 C.
136 C. The contribution from the scalar (sigma) resonance
137 C.
138  IF(ff3piscal.EQ.1) THEN
139 C. This parametrization does not fit
140  IF(j3pi.EQ.1) THEN
141  f3pi_rcht = f3pi_rcht + (
142  & sqrt(2.)*(r0scal_3pi(qq,s1)+r0scal_3pi(qq,s2)) +
143  & (r2scal_3pi(qq,s1)+r2scal_3pi(qq,s2))
144  & )
145  ELSE IF(j3pi.EQ.2) THEN
146  f3pi_rcht = f3pi_rcht - (
147  & (r0scal_3pi(qq,s1)+r0scal_3pi(qq,s2)) -
148  & sqrt(2.)*(r2scal_3pi(qq,s1)+r2scal_3pi(qq,s2))
149  & )
150  ENDIF
151  ELSE IF(ff3piscal.EQ.2) THEN
152 C. A new parametrization 10.02.2013 for the scalar contribution
153 C. analytical formulae in [3], eqs (3)-(6),
154 C. functions BWsig(Mm,Gg,Qx), FFsig(QQ,Qx) coded in ./funct_rpt.f
155 C.
156  IF(j3pi.EQ.1) THEN
157  f3pi_rcht = f3pi_rcht +
158  & sqrt(2.)*fv_rpt*gv_rpt/(3.*fpi_rpt**3)*
159  & (alpsig*bwsig(msig,gsig,s1)*ffsig(qq,s1) +
160  & betasig*bwsig(msig,gsig,s2)*ffsig(qq,s2))
161  & +4.*fa_rpt*gv_rpt/(3.*fpi_rpt**3)*
162  & (gamsig*bwsig(msig,gsig,s1)*ffsig(qq,s1) +
163  & delsig*bwsig(msig,gsig,s2)*ffsig(qq,s2))
164  $ *fa1rchl(qq)
165  ELSE IF(j3pi.EQ.2) THEN
166  f3pi_rcht = f3pi_rcht - (
167  & sqrt(2.)*fv_rpt*gv_rpt/(3.*fpi_rpt**3)*
168  & alpsig*bwsig(msig,gsig,s3)*ffsig(qq,s3)
169  & +4.*fa_rpt*gv_rpt/(3.*fpi_rpt**3)*
170  & gamsig*bwsig(msig,gsig,s3)*ffsig(qq,s3)
171  $ *fa1rchl(qq) )
172  ENDIF
173 
174 C.
175 C. The Coulomb interaction effects for the final pions
176 C. only for pi-pi+pi- should be included
177 C. Functions fattcoul(m1,m2,s),frepcoul(m1,m2,s) are coded in ./funct_rpt.f
178 C.
179  IF (fcoul.EQ.1.AND.(j3pi.EQ.1)) THEN ! it is 3pi
180  f3pi_rcht = f3pi_rcht*sqrt(fattcoul(m2,m3,s1)
181  & *fattcoul(m1,m3,s2)*frepcoul(m1,m2,s3))
182  END IF
183  ENDIF
184 
185 
186 C.
187 C. The factor 1/FACT_ADD_RPT = FPI_RPT comes to compensate an additional factor
188 C. in the hadronic current F3pi_rcht above compare with eq (6) in [2]
189 
190 
191  f3pi_rcht = f3pi_rcht/fact_add_rpt
192 
193 C. Calculation, for IFORM = 3 is not needed
194 C. =======================
195 C. F3PI_RCHT is set to zero in ../formf.f.
196 
197 C. Calculation, IFORM = 4.
198 C. PSEUDOSCALAR 3 PION FORM FACTOR
199 C. =======================
200  ELSEIF (iform.EQ.4) THEN
201  s1 = sa
202  s2 = sb
203  s3 = qq-sa-sb+m1sq+m2sq+m3sq
204 
205  IF (s3.LE.0..OR.s2.LE.0.) RETURN
206 
207 C. Functions ALP21_RPT, ALP22_RPT are Eq(10) in [2]
208 C. GRHO_RCHT, GRHO1_RCHT s1 or s2 dependent widths of rho or rho1
209 C. coded in ./funct_rpt.f
210  alp21_rpt = 3.*gv_rpt*s1*m1sq*(s3-s2)/
211  & (fv_rpt*qq*(qq-m1sq)*(1.+beta_rho))*
212  & (1./(s1-mro**2+i*mro*grho_rcht(s1,mro))+
213  & beta_rho/(s1-mrho1**2+i*mrho1*grho1_rcht(s1,mrho1,grho1)))
214  alp22_rpt = 3.*gv_rpt*s2*m1sq*(s3-s1)/
215  & (fv_rpt*qq*(qq-m1sq)*(1.+beta_rho))*
216  & (1./(s2-mro**2+i*mro*grho_rcht(s2,mro))+
217  & beta_rho/(s2-mrho1**2+i*mrho1*grho1_rcht(s2,mrho1,grho1)))
218 
219 C. PSEUDOSCALAR 3 PION FORM FACTOR. Eqs (9) in [2]
220  f3pi_rcht = sqrt(2.)/(3.*fpi_rpt*qq*(qq-m1sq))*
221  & m1sq*(3.*(s3-m3sq)-qq*(1.+2.*kap_rpt*r_rpt))
222 
223  f3pi_rcht = f3pi_rcht - sqrt(2.)*fv_rpt*gv_rpt/(3.*fpi_rpt**3)*
224  & ( alp21_rpt + alp22_rpt)
225 
226 C.
227 C. The factor 1/FACT_ADD_RPT = FPI_RPT comes to compensate an additional factor
228 C. in the hadronic current F3pi_rcht above compare with eq (9) in [2]
229  f3pi_rcht = r_rpt * f3pi_rcht/fact_add_rpt
230 
231 C.
232 C. The Coulomb interaction effects for the final pions
233 C. only for pi-pi+pi- should be included
234 C. Functions fattcoul(m1,m2,s),frepcoul(m1,m2,s) are coded in ./funct_rpt.f
235 C.
236  IF (fcoul.EQ.1.AND.(j3pi.EQ.1)) THEN ! it is 3pi
237  f3pi_rcht = f3pi_rcht*sqrt(fattcoul(m2,m3,s1)
238  & *fattcoul(m1,m3,s2)*frepcoul(m1,m2,s3))
239  END IF
240 
241  END IF
242 
243  RETURN
244  END
245 
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