C++ Interface to Tauola
funct_3pi.f
1 C **********************************************************
2 C library of functions used in calculation of currents
3 C references:
4 C [1] arXiv:0911.4436 (hep-ph) D. Gomez Dumm et al. (tau -> 3pi nu)
5 C [2] arXiv:0911.2640 (hep-ph) D. Gomezz Dumm et al. (tau -> KKpi nu)
6 C [3] arXiv:0807.4883 (hep-ph) D. R. Boito et al. (tau -> Kpi nu)
7 C [4] P. Roig, talk at (tau -> 2 pi nu)
8 C [5] arXiv:0803.2039 (hep-ph) E. Arganda et al., Appendix B (tau -> KK nu)
9 C **********************************************************
10 
11  FUNCTION alp1_rpt(Q,S,T,M1SQ,M2SQ,M3SQ,
12  $ MMM,MMM2,GGG)
13  IMPLICIT NONE
14  REAL Q,S,T
15  DOUBLE PRECISION M1SQ,M2SQ,M3SQ,
16  & mmm,mmm2,ggg
17 C **********************************************************
18 C COMPLEX FUNCTION ALP1_RPT;
19 C one-resonance contribution to
20 C F3pi_rcht(iform=1,2) at f3pi_rcht.f;
21 C corrected formula (8) of REF [1] including rho1,
22 C the factor sqrt(2)*FV_RPT*GV_RPT/(3.*FPI_RPT**3) is included in
23 C F3pi_rcht(iform1=1,2) at f3pi_rcht.f
24 C **********************************************************
25  REAL U
26  include '../parameter.inc'
27  include '../funct_declar.inc'
28 
29  u= q-s-t+m1sq+m2sq+m3sq
30  alp1_rpt = - 3.*s/(1.+beta_rho)*
31  $ (1./(s-mmm**2+i*mmm*grho_rcht(s,mmm))+
32  $ beta_rho/(s-mmm2**2+i*mmm2*grho1_rcht(s,mmm2,ggg)))
33  $ +(2.*gv_rpt/fv_rpt-1.)*
34  $ ((2.*q-2.*s-u)/(1.+beta_rho)*
35  $ (1./(s-mmm**2+i*mmm*grho_rcht(s,mmm))+
36  $ beta_rho/(s-mmm2**2+i*mmm2*grho1_rcht(s,mmm2,ggg)))+
37  $ (u-s)/(1.+beta_rho)*
38  $ (1./(t-mmm**2+i*mmm*grho_rcht(t,mmm))+
39  $ beta_rho/(t-mmm2**2+i*mmm2*grho1_rcht(t,mmm2,ggg))))
40 
41  RETURN
42 
43  END
44 
45 
46 
47  FUNCTION beta_rpt(Q,S,T,M1SQ,M2SQ,M3SQ,MMM,MMM2,GGG)
48  IMPLICIT NONE
49  REAL Q,S,T
50  DOUBLE PRECISION M1SQ,M2SQ,M3SQ,MMM,MMM2,GGG
51 C **********************************************************
52 C COMPLEX FUNCTION BETA_RPT ; two-resonance contribution to
53 C F3pi_rcht(iform=1,2) at f3pi_rcht.f;
54 C corrected formula (8) of REF [1] including rho1,
55 C the factor 4*FA_RPT*GV_RPT/(3.*FPI_RPT**3)*QQ/D_a1(QQ)
56 C is included in F3pi_rcht(iform1=1,2) at f3pi_rcht.f
57 C **********************************************************
58  include '../parameter.inc'
59  include '../funct_declar.inc'
60 
61  REAL U,LAM0_RPT,LAM1_RPT,LAM2_RPT,FF1_RPT,FF2_RPT,FF_REL
62 
63  ff_rel = fpi_rpt*fpi_rpt/(fv_rpt*fv_rpt)
64 
65  lam1_rpt = fpi_rpt*fpi_rpt/(2.d0*sqrt(2.d0)*fa_rpt*gv_rpt)
66  lam2_rpt = -(1.-2.*ff_rel)*lam1_rpt
67  lam0_rpt = (lam1_rpt + lam2_rpt)/4.
68 
69  u= q-s-t+m1sq+m2sq+m3sq
70 
71  ff1_rpt = -lam0_rpt*m1sq/q +lam1_rpt*s/q+lam2_rpt
72  ff2_rpt = -lam0_rpt*m1sq/q +lam1_rpt*t/q+lam2_rpt
73 
74  beta_rpt = -3.*(lam1_rpt+lam2_rpt)*s/(1.+beta_rho)*
75  $ (1./(s-mmm**2+i*mmm*grho_rcht(s,mmm))+
76  $ beta_rho/(s-mmm2**2+i*mmm2*grho1_rcht(s,mmm2,ggg)))+
77  $ ff1_rpt*(2.*q+s-u)/(1.+beta_rho)*
78  $ (1./(s-mmm**2+i*mmm*grho_rcht(s,mmm))+
79  $ beta_rho/(s-mmm2**2+i*mmm2*grho1_rcht(s,mmm2,ggg)))+
80  $ ff2_rpt*(u-s)/(1.+beta_rho)*
81  $ (1./(t-mmm**2+i*mmm*grho_rcht(t,mmm))+
82  $ beta_rho/(t-mmm2**2+i*mmm2*grho1_rcht(t,mmm2,ggg)))
83 
84  RETURN
85 
86  END
87 
88  FUNCTION alp1_rpt_rho1(Q,S,T,M1SQ,M2SQ,M3SQ,
89  $ MMM,MMM2,GGG)
90  IMPLICIT NONE
91  REAL Q,S,T
92  DOUBLE PRECISION M1SQ,M2SQ,M3SQ,
93  & mmm,mmm2,ggg
94 C **********************************************************
95 C COMPLEX FUNCTION ALP1_RPT_RHO1;
96 C one-resonance contribution to
97 C F3pi_rcht(iform=1,2) at f3pi_rcht.f;
98 C corrected formula (8) of REF [1] including rho1,
99 C the factor sqrt(2)*FV_RPT*GV_RPT/(3.*FPI_RPT**3) is included in
100 C F3pi_rcht(iform1=1,2) at f3pi_rcht.f
101 C **********************************************************
102  REAL U
103  include '../parameter.inc'
104  include '../funct_declar.inc'
105 
106  u= q-s-t+m1sq+m2sq+m3sq
107  alp1_rpt_rho1 = - 3.*s
108  $ /(s-mmm2**2+i*mmm2*grho1_rcht(s,mmm2,ggg))
109  $ +(2.*gv1_rpt/fv1_rpt-1.)*
110  $ ( (2.*q-2.*s-u)
111  $ /(s-mmm2**2+i*mmm2*grho1_rcht(s,mmm2,ggg))+
112  $ (u-s)/(t-mmm2**2+i*mmm2*grho1_rcht(t,mmm2,ggg)) )
113 
114  RETURN
115 
116  END
117 
118 
119 
120  FUNCTION beta_rpt_rho1(Q,S,T,M1SQ,M2SQ,M3SQ,MMM,MMM2,GGG)
121  IMPLICIT NONE
122  REAL Q,S,T
123  DOUBLE PRECISION M1SQ,M2SQ,M3SQ,MMM,MMM2,GGG
124 C **********************************************************
125 C COMPLEX FUNCTION BETA_RPT_RHO1 ; two-resonance contribution to
126 C F3pi_rcht(iform=1,2) at f3pi_rcht.f;
127 C corrected formula (8) of REF [1] including rho1,
128 C the factor 4*FA_RPT*GV_RPT/(3.*FPI_RPT**3)*QQ/D_a1(QQ)
129 C is included in F3pi_rcht(iform1=1,2) at f3pi_rcht.f
130 C **********************************************************
131  include '../parameter.inc'
132  include '../funct_declar.inc'
133 
134  REAL U,LAM0_RPT,LAM1_RPT,LAM2_RPT,FF1_RPT,FF2_RPT,FF_REL
135 
136  ff_rel = fpi_rpt*fpi_rpt/(fv1_rpt*fv1_rpt)
137 
138  lam1_rpt = fpi_rpt*fpi_rpt/(2.d0*sqrt(2.d0)*fa_rpt*gv1_rpt)
139  lam2_rpt = -(1.-2.*ff_rel)*lam1_rpt
140  lam0_rpt = (lam1_rpt + lam2_rpt)/4.
141 
142  u= q-s-t+m1sq+m2sq+m3sq
143 
144  ff1_rpt = -lam0_rpt*m1sq/q +lam1_rpt*s/q+lam2_rpt
145  ff2_rpt = -lam0_rpt*m1sq/q +lam1_rpt*t/q+lam2_rpt
146 
147  beta_rpt_rho1 = -3.*(lam1_rpt+lam2_rpt)*s
148  $ /(s-mmm2**2+i*mmm2*grho1_rcht(s,mmm2,ggg)) +
149  $ ff1_rpt*(2.*q+s-u)
150  $ /(s-mmm2**2+i*mmm2*grho1_rcht(s,mmm2,ggg))+
151  $ ff2_rpt*(u-s)
152  $ /(t-mmm2**2+i*mmm2*grho1_rcht(t,mmm2,ggg))
153 
154  RETURN
155 
156  END
157 
158 
159 
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