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EvtVubNLO.hh
1 //--------------------------------------------------------------------------
2 //
3 // Environment:
4 // This software is part of the EvtGen package developed jointly
5 // for the BaBar and CLEO collaborations. If you use all or part
6 // of it, please give an appropriate acknowledgement.
7 //
8 // Copyright Information: See EvtGen/COPYRIGHT
9 // Copyright (C) 1998 Caltech, UCSB
10 //
11 // Module: EvtGen/EvtVubNLO.hh
12 //
13 // Description:
14 // Class to generate inclusive B to X_u l nu decays according to various
15 // decay models. Implemtented are ACCM, parton-model and a QCD model.
16 //
17 // Modification history:
18 //
19 // Sven Menke January 17, 2001 Module created
20 //
21 //------------------------------------------------------------------------
22 
23 #ifndef EVTVUBNLO_HH
24 #define EVTVUBNLO_HH
25 
26 #include <vector>
27 #include "EvtGenBase/EvtDecayIncoherent.hh"
28 
29 class EvtParticle;
30 class RandGeneral;
31 
32 class EvtVubNLO:public EvtDecayIncoherent {
33 
34 public:
35 
36  EvtVubNLO() {}
37  virtual ~EvtVubNLO();
38 
39  std::string getName();
40 
41  EvtDecayBase* clone();
42 
43  void initProbMax();
44 
45  void init();
46 
47  void decay(EvtParticle *p);
48 
49 
50 private:
51 
52  // cache
53  double _lbar;
54  double _mupi2;
55 
56  double _mb; // the b-quark pole mass in GeV
57  double _mB;
58  double _lambdaSF;
59  double _b; // Parameter for the Fermi Motion
60  double _kpar;
61  double _mui; // renormalization scale (preferred value=1.5 GeV)
62  double _SFNorm; // SF normalization
63  double _dGMax; // max dGamma*p2 value;
64  int _nbins;
65  int _idSF;// which shape function?
66  double * _masses;
67  double * _weights;
68 
69  double _gmax;
70  int _ngood,_ntot;
71 
72 
73  double tripleDiff(double pp, double pl, double pm);
74  double SFNorm(const std::vector<double> &coeffs);
75  static double integrand(double omega, const std::vector<double> &coeffs);
76  double F10(const std::vector<double> &coeffs);
77  static double F1Int(double omega,const std::vector<double> &coeffs);
78  double F20(const std::vector<double> &coeffs);
79  static double F2Int(double omega,const std::vector<double> &coeffs);
80  double F30(const std::vector<double> &coeffs);
81  static double F3Int(double omega,const std::vector<double> &coeffs);
82  static double g1(double y, double z);
83  static double g2(double y, double z);
84  static double g3(double y, double z);
85 
86  static double Gamma(double z);// Euler Gamma Function
87  static double dgamma(double t, const std::vector<double> &c){ return pow(t,c[0]-1)*exp(-t);}
88  static double Gamma(double z, double tmax);
89 
90  // theory parameters
91  inline double mu_i(){return _mui;} // intermediate scale
92  inline double mu_bar(){return _mui;}
93  inline double mu_h(){return _mb/sqrt(2.0);} // high scale
94  inline double lambda1(){return -_mupi2;}
95 
96  // expansion coefficients for RGE
97  static double beta0(int nf=4){return 11.-2./3.*nf;}
98  static double beta1(int nf=4){return 34.*3.-38./3.*nf;}
99  static double beta2(int nf=4){return 1428.5-5033./18.*nf+325./54.*nf*nf;}
100  static double gamma0(){return 16./3.;}
101  static double gamma1(int nf=4){return 4./3.*(49.85498-40./9.*nf);}
102  static double gamma2(int nf=4){return 64./3.*(55.07242-8.58691*nf-nf*nf/27.);} /* zeta3=1.20206 */
103  static double gammap0(){return -20./3.;}
104  static double gammap1(int nf=4){return -32./3.*(6.92653-0.9899*nf);} /* ?? zeta3=1.202 */
105 
106 
107  // running constants
108 
109  static double alphas(double mu) ;
110  static double C_F(double mu){return (4.0/3.0)*alphas(mu)/4./EvtConst::pi;}
111 
112  // Shape Functions
113 
114  inline double lambda_SF(){ return _lambdaSF;}
115  double lambda_bar(double omega0);
116  inline double lambda2(){return 0.12;}
117  double mu_pi2(double omega0);
118  inline double lambda(double){ return _mB-_mb;}
119 
120  // specail for gaussian SF
121  static double cGaus(double b){return pow(Gamma(1+b/2.)/Gamma((1+b)/2.),2);}
122 
123  double M0(double mui,double omega0);
124  static double shapeFunction(double omega, const std::vector<double> &coeffs);
125  static double expShapeFunction(double omega, const std::vector<double> &coeffs);
126  static double gausShapeFunction(double omega, const std::vector<double> &coeffs);
127  // SSF (not yet implemented)
128  double subS(const std::vector<double> &coeffs );
129  double subT(const std::vector<double> &coeffs);
130  double subU(const std::vector<double> &coeffs);
131  double subV(const std::vector<double> &coeffs);
132 
133 
134  // Sudakov
135 
136  inline double S0(double a, double r){return -gamma0()/4/a/pow(beta0(),2)*(1/r-1+log(r));}
137  inline double S1(double /*a*/, double r){return gamma0()/4./pow(beta0(),2)*(
138  pow(log(r),2)*beta1()/2./beta0()+(gamma1()/gamma0()-beta1()/beta0())*(1.-r+log(r))
139  );}
140  inline double S2(double a, double r){return gamma0()*a/4./pow(beta0(),2)*(
141  -0.5*pow((1-r),2)*(
142  pow(beta1()/beta0(),2)-beta2()/beta0()-beta1()/beta0()*gamma1()/gamma0()+gamma2()/gamma0()
143  )
144  +(pow(beta1()/beta0(),2)-beta2()/beta0())*(1-r)*log(r)
145  +(beta1()/beta0()*gamma1()/gamma0()-beta2()/beta0())*(1-r+r*log(r))
146  );}
147  inline double dSudakovdepsi(double mu1, double mu2){return S2(alphas(mu1)/(4*EvtConst::pi),alphas(mu2)/alphas(mu1));}
148  inline double Sudakov(double mu1, double mu2, double epsi=0){double fp(4*EvtConst::pi);return S0(alphas(mu1)/fp,alphas(mu2)/alphas(mu1))+S1(alphas(mu1)/fp,alphas(mu2)/alphas(mu1))+epsi*dSudakovdepsi(mu1,mu2);}
149 
150  // RG
151  inline double dGdepsi(double mu1, double mu2){return 1./8./EvtConst::pi*(alphas(mu2)-alphas(mu1))*(gamma1()/beta0()-beta1()*gamma0()/pow(beta0(),2));}
152  inline double aGamma(double mu1, double mu2, double epsi=0){return gamma0()/2/beta0()*log(alphas(mu2)/alphas(mu1))+epsi*dGdepsi( mu1, mu2);}
153  inline double dgpdepsi(double mu1, double mu2){return 1./8./EvtConst::pi*(alphas(mu2)-alphas(mu1))*(gammap1()/beta0()-beta1()*gammap0()/pow(beta0(),2));}
154  inline double agammap(double mu1, double mu2, double epsi=0){return gammap0()/2/beta0()*log(alphas(mu2)/alphas(mu1))+epsi*dgpdepsi( mu1, mu2);}
155  inline double U1(double mu1, double mu2, double epsi=0){return exp(2*(Sudakov(mu1,mu2,epsi)-agammap(mu1,mu2,epsi)-aGamma(mu1,mu2,epsi)*log(_mb/mu1)));}
156  inline double U1lo(double mu1, double mu2){return U1(mu1,mu2);}
157  inline double U1nlo(double mu1, double mu2){return U1(mu1,mu2)*(1+2*(dSudakovdepsi(mu1,mu2)-dgpdepsi( mu1, mu2)-log(_mb/mu1)*dGdepsi( mu1, mu2)));}
158  inline double alo(double mu1, double mu2){return -2*aGamma(mu1,mu2);}
159  inline double anlo(double mu1, double mu2){return -2*dGdepsi(mu1,mu2);}
160 
161 };
162 
163 #endif
164 
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