Functions
double	mzdelta (int i, int k)

double	mzvscalar (int n, double p, double q)

double	mzvmod2 (int n, double *p)

void	mzboost (int flag, double p, double q, double *q_prime)

double	mzenergy (double m, double p_x, double p_y, double p_z)

double	mzpolar (double *p)

double	mzazimuthal (double *p)

double	mzcospolar (double *p)

double	mzangle (double p, double q)

double	mzrnd (double a, double b)

double	mzcomplexmod (double Re_z, double Im_z)

double	mz_E_to_s (double E)

double	mz_legendre_polynomial (int n, double x)

double	mz_linear_extrapolation (double x1, double y1, double x2, double y2, double x)

Function Documentation

double mz_E_to_s ( double E )

function mz_E_to_s

arguments:

E: pbar energy in lab (GeV)

returns:

cm-energy square s of pbar p system

Definition at line 410 of file mzfunctions.cxx.

References exit(), i, mp, mzvmod2(), P, printf(), and s.

                           {
   double s;
 
   double M=mp;
 
   double p_p[4];           //lab frame: 4-mom p    (proton target)
   double pbar_p[4];        //lab frame: 4-mom pbar (anti-proton beam)
   double pbarp_p[4];       //lab frame: 4-mom pbarpsystem
   double P;                //lab frame: pz pbar
 
 
   //check argument range
   if(E<M){
     printf("ERROR: function mz_E_to_s called with argument E out of range \n");
     printf("    => E should be larger than the proton mass M = %5.3f GeV\n",M);
     printf("\n\n");
     exit(1);
   }
 
 
   //4-mom of p (lab frame)
   p_p[0]=M;
   p_p[1]=0.;
   p_p[2]=0.;
   p_p[3]=0.;
 
 
   //4-mom of pbar (lab frame)
   P=pow((E*E-M*M),0.5);
 
   pbar_p[0]=E;
   pbar_p[1]=0.;
   pbar_p[2]=0.;
   pbar_p[3]=P;
 
 
   //4-mom pbarpsystem (lab frame)
   for(int i=0; i<4; i++){
     pbarp_p[i]=p_p[i]+pbar_p[i];
   }
 
   s=mzvmod2(4,pbarp_p);
 
   return s;
 }

double mz_legendre_polynomial	(	int	n,
		double	x
	)

function mz_legendre_polynomial

INPUT:

n -> polynomial degree, [0,10] x -> independent variable, [-1,1]

returns:

P_{n}(x)

Definition at line 470 of file mzfunctions.cxx.

References exit(), printf(), x, and y.

Referenced by mz_pp_to_pipi_vandewi_sigma_legendre().

                                               {
   double y;
 
   //checking parameter range...
   if( !( (n>=0)&&(n<=10) ) ){
     printf("ERROR: function  mz_legendre_polynomial called with n out of range \n");
     printf("    => n should be contained in the interval [0,10]\n");
     printf("\n\n");
     exit(1);
   }
 
   if( !( (x>=-1.0)&&(x<=1.0) ) ){
     printf("ERROR: function  mz_legendre_polynomial called with x out of range \n");
     printf("    => x should be contained in the interval [-1.0,1.0]\n");
     printf("\n\n");
     exit(1);
   }
 
 
   if(n==0){
     y=1.0;
   }
 
   if(n==1){
     y=x;
   }
 
   if(n==2){
     y=(1.0/2.0)*(3.0*pow(x,2.0) -1.0);
   }
 
   if(n==3){
     y=(1.0/2.0)*(5.0*pow(x,3.0) -3.0*x);
   }
 
   if(n==4){
     y=(1.0/8.0)*(35.0*pow(x,4.0) -30.0*pow(x,2.0) +3.0);
   }
 
   if(n==5){
     y=(1.0/8.0)*(63.0*pow(x,5.0) -70.0*pow(x,3.0) +15.0*x);
   }
 
   if(n==6){
     y=(1.0/16.0)*(231.0*pow(x,6.0) -315.0*pow(x,4.0) 
                  +105.0*pow(x,2.0) -5.0);
   }
 
   if(n==7){
     y=(1.0/16.0)*(429.0*pow(x,7.0) -693.0*pow(x,5.0) 
                   +315.0*pow(x,3.0) -35.0*x);
   }
 
   if(n==8){
     y=(1.0/128.0)*(6435.0*pow(x,8.0) -12012.0*pow(x,6.0)
                    +6930.0*pow(x,4.0) -1260.0*pow(x,2.0) 
                    +35.0);
   }
 
   if(n==9){
     y=(1.0/128.0)*(12155.0*pow(x,9.0) -25740.0*pow(x,7.0) 
                    +18018.0*pow(x,5.0) -4620.0*pow(x,3.0) 
                    +315.0*x);
   }
 
   if(n==10){
     y=(1.0/256.0)*(46189.0*pow(x,10.0) -109395.0*pow(x,8.0)
                    +90090.0*pow(x,6.0) -30030*pow(x,4.0)
                    +3465.0*pow(x,2.0) -63.0);
   }
 
   return y;
 }

double mz_linear_extrapolation	(	double	x1,
		double	y1,
		double	x2,
		double	y2,
		double	x
	)

funtion mz_linear_extrapolation

INPUT:

(x1,y1) first point in (x,y)-plane (x2,y2) second point in (x,y)-plane

x independent variable

RETURNS:

y=f(x), with f the linear function atisfying y1=f(x1) and y2=f(x2)

Definition at line 558 of file mzfunctions.cxx.

References a, b, exit(), printf(), and y.

Referenced by mz_pp_to_pipi_sigma().

 {
   double y;
   double a,b;
 
   //checking parameter range...
   if(x2==x1){
     printf("ERROR: function  mz_linear_extrapolation called with x_2=x_1 \n");
     printf("    => argument x_2 should be different from argument x_1 \n");
     printf("\n\n");
     exit(1);
   }
 
   a = (y1-y2)/(x1-x2);
   b = y1-a*x1;
 
   y = a*x+b;
 
   return y;
 }

double mzangle	(	double *	p,
		double *	q
	)

function mzangle

input: 4-mom p, 4-mom q output: angle between 3-dim components of p, q in range [0,180]

Definition at line 310 of file mzfunctions.cxx.

References acos(), alpha, mzvmod2(), mzvscalar(), and PI.

 {
  double PI=acos(-1.0);
 
  double alpha;
 
  double scalar, pmod, qmod, cosalpha;
 
  pmod=pow(mzvmod2(3,p),0.5);
  qmod=pow(mzvmod2(3,q),0.5);
 
  scalar=mzvscalar(3,p,q);
 
  if(pmod==0.0){
     cerr << "WARNING: mzangle called with p[1]=p[2]=p[3]=0.0 " << endl;
     return 9999.;
  }
 
  if(qmod==0.0){
     cerr << "WARNING: mzangle called with q[1]=q[2]=q[3]=0.0 " << endl;
     return 9999.;
  }
 
 
  cosalpha=scalar/(pmod*qmod);
 
  if(cosalpha > 1.0) cosalpha=1.0;
  if(cosalpha < -1.0) cosalpha=-1.0;
 
  alpha=acos(cosalpha) * 180.0 / PI;
 
 
  return alpha;
 }

double mzazimuthal ( double * p )

function mzazimuthal

input: 4-mom p output: azimuthal angle phi in range [0,180]

Definition at line 258 of file mzfunctions.cxx.

References acos(), atan2(), phi, and PI.

 {
  double PI=acos(-1.0);
 
  double phi;
 
  if ( (p[1]==0.) && (p[2]==0.0) ) {
    cerr << "WARNING: mzazimuthal called with p[1]=p[2]=0.0 " << endl;
    return 9999.;
  }
 
 
  phi=atan2(p[2],p[1])*180.0/PI;
 
 
  if (phi<0.0) phi = phi + 360.0;
 
  return phi;
 }

void mzboost	(	int	flag,
		double *	p,
		double *	q,
		double *	q_prime
	)

function mzboost

input: flag=0 lab->CM, flag=1 CM->lab p 4-mom of CM particle (M!=0) in lab frame q 4-mom of test particle in lab frame (flag=0) / CM frame (flag=1)

output: q_prime 4-mom of test particle in the CM frame (flag=0) / lab frame (flag=1)

Definition at line 123 of file mzfunctions.cxx.

References i, L, m, mzdelta(), and mzvmod2().

Referenced by mz_pp_to_leplep_vandewi_event(), and mz_pp_to_pipi_vandewi_event().

 {
   int i,k;
 
   double m;
   double gamma;
   double p_uni[4];
 
   double L[4][4];
   double LI[4][4];
 
   double mztemp;
 
 
 
   //computing matrix L(p)
 
   m=pow(mzvmod2(4,p),0.5);
   gamma=p[0]/m;
 
 
   for (i=1; i<=3; i++) {
     p_uni[i]=p[i]/pow(mzvmod2(3,p),0.5);
   }
 
 
   L[0][0]=gamma;
 
 
   for (i=1; i<=3; i++) {
     L[0][i] = p_uni[i] * pow((gamma*gamma - 1.0),0.5);
     L[i][0] = L[0][i];
   }
 
 
   for (i=1; i<=3; i++) {
     for (k=1; k<=3; k++) {
       L[i][k] = mzdelta(i,k) + (gamma -1.0)*p_uni[i]*p_uni[k];
     }
   }
 
 
 
 
   //inverting matrix L(p)
 
   LI[0][0]=L[0][0];
 
   for (i=1; i<=3; i++) {
     LI[0][i] = -1.0*L[i][0];
     LI[i][0] = -1.0*L[0][i];
   }
 
   for (i=1; i<=3; i++) {
     for (k=1; k<=3; k++) {
       LI[i][k] = L[k][i];
     }
   }
 
 
 
   //boosting 4-mom q
 
   for (i=0; i<=3; i++) {
     mztemp = 0.0;
     for (k=0; k<=3; k++) {
       if (flag==0) mztemp = mztemp + LI[i][k]*q[k];
       if (flag==1) mztemp = mztemp + L[i][k]*q[k];
     }
     q_prime[i] =mztemp;
   }
 
 }

double mzcomplexmod	(	double	Re_z,
		double	Im_z
	)

function mzcomplexmod

arguments:

Re_z = real part of complex number z Im_z = imaginary part of complex number z

returns:

modulus of complex number z

Definition at line 389 of file mzfunctions.cxx.

References y.

                                              {
   double y;
 
   y=pow(Re_z*Re_z + Im_z*Im_z,0.5);
 
   return y;
 }

double mzcospolar ( double * p )

function mzcospolar

input: 4-mom p output: cos of polar angle theta

Definition at line 285 of file mzfunctions.cxx.

References mzvmod2().

 {
   double costheta;
   
   double pmod;
 
   pmod=pow(mzvmod2(3,p),0.5);
   
   if(pmod==0.0){
     cerr << "WARNING: mzcospolar called with p[1]=p[2]=p[3]=0.0 " << endl;
     return 9999.;
   }
 
   costheta  = p[3]/pmod;
 
   return costheta;
 }

double mzdelta	(	int	i,
		int	k
	)

Author: Manuel Zambrana zambr.nosp@m.ana@.nosp@m.kph.u.nosp@m.ni-m.nosp@m.ainz..nosp@m.de and Dmitry Khaneftd khane.nosp@m.ftd@.nosp@m.kph.u.nosp@m.ni-m.nosp@m.ainz..nosp@m.de

Mainz, May 2011

function mzdelta

input: i,k integers output: kroneker delta(i,k)

Definition at line 30 of file mzfunctions.cxx.

References d.

Referenced by mzboost().

 {
   double d;
 
   if( k==i )
   {
     d=1.0;
   }
   else{
     d=0.0;
   }
 
   return d;
 }

double mzenergy	(	double	m,
		double	p_x,
		double	p_y,
		double	p_z
	)

input: mass m, 3-mom components px, py, pz of a particle

output: energy of the particle

Definition at line 207 of file mzfunctions.cxx.

 {
   double E;
 
   E=pow(m*m +p_x*p_x +p_y*p_y +p_z*p_z,0.5);
 
   return E;
 }

double mzpolar ( double * p )

function mzpolar

input: 4-mom p output: polar angle theta in range [0,180]

Definition at line 223 of file mzfunctions.cxx.

References acos(), mzvmod2(), PI, and theta.

 {
   double PI=acos(-1.0);
 
   double theta;
 
   double pmod;
   double costheta;
 
   pmod=pow(mzvmod2(3,p),0.5);
   
   if(pmod==0.0){
     cerr << "WARNING: mzpolar called with p[1]=p[2]=p[3]=0.0 " << endl;
     return 9999.;
   }
 
   costheta  = p[3]/pmod;
 
   if(costheta > 1.0) costheta=1.0;
   if(costheta < -1.0) costheta=-1.0;
 
   theta = acos(costheta) * 180.0 / PI ;
 
 
   return theta;
 }

double mzrnd	(	double	a,
		double	b
	)

function mzrnd

arguments:

a = inf[a,b] b = sup[a,b]

returns:

random number in interval [a,b]

Definition at line 353 of file mzfunctions.cxx.

References a, exit(), printf(), ranlxd(), x, and y.

Referenced by mz_pp_to_leplep_vandewi_event(), and mz_pp_to_pipi_vandewi_event().

                                 {
   double y;
 
   int dim=1;
   double rvec[dim];
   double x;
 
   //check arguments
   if(b<=a){
     printf("ERROR: function mzrnd called with arguments b<=a \n");
     printf("    => argument b should be larger than argument a \n");
     printf("\n\n");
     exit(1);
   }
 
   ranlxd(rvec,dim);  //generate random number in interval [0,1]
   x=rvec[0];
   y=(b-a)*x + a; 
 
   return y;
 }

double mzvmod2	(	int	n,
		double *	p
	)

function mzvmod2

input: int n, 4-vector p

output:

n=2 -> returns p[1]*p[1] + p[2]*p[2] n=3 -> returns p[1]*p[1] + p[2]*p[2] + p[3]*p[3] n=4 -> returns p[0]*p[0] -p[1]*p[1] -p[2]*p[2] -p[3]*p[3]

Definition at line 93 of file mzfunctions.cxx.

References exit(), m2(), mzvscalar(), and printf().

Referenced by mz_E_to_s(), mz_pp_to_leplep_vandewi_event(), mz_pp_to_pipi_vandewi_event(), mz_pp_to_pipi_vandewi_init(), mzangle(), mzboost(), mzcospolar(), and mzpolar().

 {
   double m2;
 
 
   if( !(n==2||n==3||n==4) ){
     printf("ERROR: function mzvmod2 called with flag n out of range \n");
     printf("    => n should take the value 2,3 or 4 \n");
     printf("\n\n");
     exit(1);
   }
 
 
   m2 = mzvscalar(n,p,p);
 
   return m2;
 }

double mzvscalar	(	int	n,
		double *	p,
		double *	q
	)

function mzvscalar

input: int n, 4-vector p, 4-vector q

output:

n=2 -> returns p[1]*q[1] + p[2]*q[2] n=3 -> returns p[1]*q[1] + p[2]*q[2] + p[3]*q[3] n=4 -> returns p[0]*q[0] -p[1]*q[1] -p[2]*q[2] -p[3]*q[3]

Definition at line 53 of file mzfunctions.cxx.

References exit(), printf(), and s.

Referenced by mzangle(), and mzvmod2().

 {
   double s;
 
 
   if( !(n==2||n==3||n==4) ){
     printf("ERROR: function mzvscalar called with flag n out of range \n");
     printf("    => n should take the value 2,3 or 4 \n");
     printf("\n\n");
     exit(1);
   }
 
 
   if (n==2) {
     s = p[1]*q[1] + p[2]*q[2];
   }
 
   if (n==3) {
     s = p[1]*q[1] + p[2]*q[2] + p[3]*q[3];
   }
 
   if (n==4) {
     s = p[0]*q[0] -1.0*p[1]*q[1] -1.0*p[2]*q[2] -1.0*p[3]*q[3];
   }
 
   return s;
 }

Functions

Function Documentation