#include "HADRONS++/Current_Library/VA_B_DPi.H" using namespace HADRONS; using namespace ATOOLS; void VA_B_DPi::SetModelParameters( struct GeneralModel _md ) { m_Vxx = _md("Vxx",Tools::Vcb); } void VA_B_DPi::Calc(const ATOOLS::Vec4D_Vector& moms, bool m_anti) { Vec4D pB = moms[p_i[0]]; Vec4D pD = moms[p_i[1]]; Vec4D pPi= moms[p_i[2]]; double mB = p_masses[0]; double mD = p_masses[1]; Vec4D vB = pB/mB; //4-velocity of B meson Vec4D vD = pD/mD; //4-velocity of D double w = vB*vD; //four velocity transfer Complex dmb = Complex(0.0460,-0.5*0.00001); double g = 0.5; double alpha3 = 0.690; // See table I in G&R's paper double alpha1 = -1.430; double alpha2 = -0.140; double f0=0.093; // The pion decay constant set to 93 MeV Complex dmt3 = Complex (0.563,-0.5*0.191); Complex dmt1 = Complex(0.392,-0.5*1.040); Complex dmt2 = Complex(0.709,-0.5*0.405); double betas=0.285; double betap=0.280; double betad=0.260; double betasp=betas*betas+betap*betap; double betasd=betas*betas+betad*betad; double lambdabar=0.750; double xi = exp(lambdabar*lambdabar*(1.0-w*w)/(4*betas*betas)); double xi1= -1.0*sqrt(2.0/3.0)*(lambdabar*lambdabar*(w*w-1.0)/(4*betas*betas))* exp(lambdabar*lambdabar*(1.0-w*w)/(4*betas*betas)); double rho1= sqrt(1.0/2.0)*(lambdabar/betas)* pow((2*betas*betap/(betasp)),2.5)* exp(lambdabar*lambdabar*(1.0-w*w)/(2*betasp)); double rho2= sqrt(1.0/8.0)*(lambdabar*lambdabar/(betas*betas))* pow((2*betas*betad/(betasd)),3.5)* exp(lambdabar*lambdabar*(1.0-w*w)/(2*betasd)); Complex h,a1,a2,a3; Complex hnr,a1nr,a2nr,a3nr; Complex hr,a1r,a2r,a3r; // Non-resonance part hnr = g*xi*(1.0/(pPi*vB+dmb))/(2*f0*mB*mD); // in the original paper: hnr = g*xi*(1.0/(pPi*vB+dmb-i*eps)-1.0/(pPi*vD-dmd+i*eps))/(2*f0*mB*mD) a1nr= -1.0*g*xi*(1+w)*(1.0/(pPi*vB+dmb))/(2*f0); // a1nr= -1.0*g*xi*(1+w)*(1.0/(pPi*vB+dmb-i*eps)-1.0/(pPi*vD-dmd+i*eps))/(2*f0) a2nr= g*xi*((pPi*(vB+vD))/(pPi*vB+dmb))/(2*f0*mB); // a2nr= g*xi*((pPi*(vB+vD))/(pPi*vB+dmb-i*eps))/(2*f0*mB) a3nr= Complex(0.0,0.0); // a3nr= -1.0*g*xi*((pPi*(vB+vD))/(pPi*vD-dmd+i*eps))/(2*f0*mD) // Resonance part hr = alpha2*rho2*(w-1)*(1.0/(pPi*vB+dmt2))/(6*f0*mB*mD) + alpha3*xi1*(1.0/(pPi*vB+dmt3))/(2*f0*mB*mD); // hr = alpha2*rho2*(w-1)*(1.0/(pPi*vB+dmt2)-1.0/(pPi*vD-dmt2))/(6*f0*mB*mD) + // alpha3*xi1*(1.0/(pPi*vB+dmt3)-1.0/(pPi*vD-dmt3))/(2*f0*mB*mD) a1r= -1.0*alpha2*rho2*(w*w-1)*(1.0/(pPi*vB+dmt2))/(6*f0) - alpha3*xi1*(1+w)*(1.0/(pPi*vB+dmt3))/(2*f0); // a1r= -1.0*alpha2*rho2*(w*w-1)*(1.0/(pPi*vB+dmt2)-1.0/(pPi*vD+dmt2))/(6*f0) - // alpha3*xi1*(1+w)*(1.0/(pPi*vB+dmt3)-1.0/(pPi*vD-dmt3))/(2*f0) a2r= alpha1*rho1*((pPi*vB)/(pPi*vB+dmt1))/(2*f0*mB) + alpha2*rho2*(0.5*pPi*(w*vD-vB)+pPi*(vD-w*vB))/ (3*f0*mB*(pPi*vB+dmt2)) + alpha3*xi1*((pPi*(vB+vD))/(pPi*vB+dmt3))/(2*f0*mB); // a2r= alpha1*rho1*((pPi*vB)/(pPi*vD-dmt1)+(pPi*vB)/(pPi*vB+dmt1))/(2*f0*mB) + // alpha2*rho2*(1/(pPi*vB+dmt2)*(1/6*(w*pPi*vD-pPi*vB)+1/3*(pPi*vD-*w*pPi*vB)) + // 0.5*1/(pPi*vD-dmt2)*(pPi*vB-w*pPi*vD))/(f0*mB) + // alpha3*xi1*((pPi*(vB+vD))/(pPi*vB+dmt3))/(2*f0*mB) a3r= -1.0*alpha1*rho1*((pPi*vB)/(pPi*vB+dmt1))/(2*f0*mD) - alpha2*rho2*((pPi*(vD-w*vB))/(pPi*vB+dmt2))/(2*f0*mD); // a3r= -1.0*alpha1*rho1*((pPi*vB)/(pPi*vD-dmt1)+(pPi*vB)/(pPi*vB+dmt1))/(2*f0*mD) - // alpha2*rho2*(1/(pPi*vD-dmt2)*(1/6*(w*pPi*vB-pPi*vD)+1/3*(pPi*vB-*w*pPi*vD)) + // 0.5*1/(pPi*vB+dmt2)*(pPi*vD-w*pPi*vB))/(2*f0*mD) - // alpha3*xi1*((pPi*(vB+vD))/(pPi*vD-dmt3))/(2*f0*mB) // Sum h=hnr+hr; a1=a1nr+a1r; a2=a2nr+a2r; a3=a3nr+a3r; Insert( m_Vxx * sqrt(mB*mD) * (Complex(0.0,1.0)*h*mB*mD*cross(vB,vD,pPi)+ a1*pPi+a2*mB*vB+a3*mD*vD) , 0); } DEFINE_CURRENT_GETTER(VA_B_DPi,"VA_B_DPi") void ATOOLS::Getter<Current_Base,ME_Parameters,VA_B_DPi>:: PrintInfo(std::ostream &st,const size_t width) const { st<<"\\paragraph{Parametrization} \n" <<" \\[ \\mathcal{J^{B\\to D \\pi}_\\mu} = V_{cb} \\sqrt{M_B M_D} \\left( \n" <<" -i h M_B M_D \\epsilon_{\\mu\\nu\\rho\\sigma}v_B^\\nu v_D^\\rho p_\\pi^\\sigma \n" <<" + A_1 p_{\\pi\\mu} + A_2 M_B v_{B\\mu} + A_3 M_D v_{D\\mu} \\right) \\]\n" <<" \\begin{itemize} \n" <<" \\item Particle order: 0 = $B$, 1 = $D$, 2 = $\\pi$ \n" <<" \\item Example: $ B \\to D \\; \\pi \\; l \\; \\nu_l $ \n" <<" \\item Reference: Goity, Roberts \\cite{Goity:1994xn}; EvtGen\\cite{Lange:2001uf} \n" <<" \\end{itemize} \n\n" <<"\\paragraph{Available parameters} \n" <<" No parameters. \n"<<std::endl; }