#include <bubble.h>

Inheritance diagram for ql::Bubble< TOutput, TMass, TScale >:

Collaboration diagram for ql::Bubble< TOutput, TMass, TScale >:

Public Member Functions
	Bubble ()
	The Constructor.

	~Bubble ()
	The Destructor.

void	integral (vector< TOutput > &res, TScale const &mu2, vector< TMass > const &m, vector< TScale > const &p)
	Computes the Bubble integral automatically. More...

void	BB0 (vector< TOutput > &res, TScale const &mu2, TMass const &m0, TMass const &m1, TScale const &s) const
	General configuration I(s;m0,m1) More...

void	BB1 (vector< TOutput > &res, TScale const &mu2, TMass const &m) const
	Special configuration I(m2;0,m2) More...

void	BB2 (vector< TOutput > &res, TScale const &mu2, TMass const &m) const
	Special configuration I(0;0,m2) More...

void	BB3 (vector< TOutput > &res, TScale const &mu2, TMass const &s) const
	Special configuration I(s;0,0) More...

void	BB4 (vector< TOutput > &res, TScale const &mu2, TMass const &m, TScale const &s) const
	Special configuration I(s;0,m2) More...

void	BB5 (vector< TOutput > &res, TScale const &mu2, TMass const &m0, TMass const &m1) const
	Special configuration I(0;m0,m1) More...

Public Member Functions inherited from ql::Topology< TOutput, TMass, TScale >
	Topology (string name="None")
	Topology<TOutput, TMass>::Topology. More...

	Topology (const Topology &obj)
	Topology<TOutput, TMass>::Topology. More...

virtual	~Topology ()
	Topology<TOutput, TMass>::~Topology.

string const &	getName () const
	Get topology name.

Public Member Functions inherited from ql::Tools< TOutput, TMass, TScale >
	Tools ()
	The Constructor.

	~Tools ()
	The Destructor.

bool	iszero (TMass const &psq) const
	Check for zeros. More...

TOutput	cLn (TOutput const &z, TScale const &isig) const
	Log of complex argument with explicit sign for imag part. More...

TOutput	cLn (TScale const &x, TScale const &isig) const

TOutput	fndd (int const &n, TOutput const &x, TScale const &iep) const
	The fndd function. More...

TOutput	Lnrat (TOutput const &x, TOutput const &y) const
	Computes the ratio of logs. More...

TOutput	Lnrat (TScale const &x, TScale const &y) const

TMass	ddilog (TMass const &x) const
	Computes the dilog function for real argument. More...

TOutput	denspence (TOutput const &z, TScale const &isig) const
	Spence's function. More...

TOutput	spencer (TOutput const &zrat1, TOutput const &zrat2, TScale const &ieps1, TScale const &ieps2) const
	Spence's function for ratio arguments. More...

TOutput	xspence (TOutput const (&z1)[2], TScale const (&im1)[2], TOutput const &z2, TScale const &im2) const
	Difference of complex Spence's function. More...

TOutput	cspence (TOutput const &z1, TScale const &im1, TOutput const &z2, TScale const &im2) const
	Complex Spence's function. More...

TOutput	Li2omrat (TScale const &x, TScale const &y) const
	Expression for dilog(1-(x-iep)/(y-iep)). More...

TOutput	Li2omrat (TOutput const &x, TOutput const &y, TScale const &ieps1=-1, TScale const &ieps2=-1) const

TOutput	Li2omx2 (TScale const &v, TScale const &w, TScale const &x, TScale const &y) const
	Expression for dilog(1-(v-iep)(w-iep)/(x-iep)/(y-i*ep)). More...

TOutput	Li2omx2 (TOutput const &v, TOutput const &w, TOutput const &x, TOutput const &y, TScale const &ieps1=-1, TScale const &ieps2=-1) const

TOutput	cLi2omx2 (TOutput const &z1, TOutput const &z2, TScale const &ieps1=-1, TScale const &ieps2=-1) const

TOutput	Li2omx (TMass const &x1, TMass const &x2, TScale const &ieps1, TScale const &ieps2) const
	Calculate Li[2](1-(x1+ieps1)*(x2+ieps2)) More...

TOutput	cLi2omx3 (TOutput const &z1, TOutput const &z2, TOutput const &z3, TScale const &ieps1, TScale const &ieps2, TScale const &ieps3) const
	Calculate Li[2](1-(z1+ieps1)(z2+ieps2)(z3+ieps3)) More...

TOutput	L0 (TMass const &x, TMass const &y) const

TOutput	L1 (TMass const &x, TMass const &y) const

TOutput	R3int (TOutput const &p, TOutput const &s1, TOutput const &s2, TOutput const &t1) const

TOutput	R3int (TOutput const &p, TOutput const &s1, TOutput const &s2, TOutput const &t1, TOutput const &t2, TOutput const &t3, TOutput const &t4) const

TOutput	R2int (TOutput const &a, TOutput const &b, TOutput const &y0) const

TOutput	Rint (TOutput const &y, TOutput const &z, TScale const &ieps) const

void	R (TOutput &r, TOutput &d, TOutput const &q) const
	Tools<TOutput, TMass, TScale>::R. More...

TOutput	Zlogint (TOutput const &z, TScale const &ieps) const
	Tools<TOutput, TMass, TScale>::qlZlogint. More...

TOutput	ltspence (int const &i_in, TOutput const &z_in, TScale const &s) const

TOutput	li2series (TOutput const &z, TScale const &isig) const

TOutput	ltli2series (TOutput const &z1, TScale const &s) const

TOutput	eta2 (TOutput const &a, TOutput const &b) const

TOutput	eta3 (TOutput const &a, TOutput const &b, TOutput const &c) const

TOutput	eta5 (TOutput const &a, TOutput const &b, TOutput const &c, TOutput const &d, TOutput const &e) const

TOutput	xetatilde (TOutput const (&z1)[2], TScale const (&im1)[2], TOutput const &z2, TScale const &im2, TOutput const (&l1)[2]) const

TOutput	xeta (TOutput const (&z1)[2], TScale const (&im1)[2], TOutput const &z2, TScale const &im2, TScale const &im12, TOutput const (&l1)[2]) const

int	eta (TOutput const &z1, TScale const &s1, TOutput const &z2, TScale const &s2, TScale const &s12) const

int	etatilde (TOutput const &c1, TScale const &im1x, TOutput const &c2, TScale const &im2x) const

void	kfn (TOutput(&res)[3], TScale &ieps, TMass const &xpi, TMass const &xm, TMass const &xmp) const
	The K-function. More...

void	solveabc (TMass const &a, TMass const &b, TMass const &c, TOutput(&z)[2]) const
	Solution of the quadratic equation. More...

void	solveabcd (TOutput const &a, TOutput const &b, TOutput const &c, TOutput const &d, TOutput(&z)[2]) const
	Solution of the quadratic equation passing the discriminant. More...

void	solveabcd (TOutput const &a, TOutput const &b, TOutput const &c, TOutput(&z)[2]) const

void	ratgam (TOutput &ratp, TOutput &ratm, TScale &ieps, TMass const &p3sq, TMass const &m3sq, TMass const &m4sq) const
	Ratio function. More...

void	ratreal (TMass const &si, TMass const &ta, TMass &rat, TScale &ieps) const
	Ratio function. More...

Public Member Functions inherited from ql::LRUCache< size_t, vector< TOutput > >
	LRUCache (int const &size=1)
	LRUCache constructor. More...

	LRUCache (const LRUCache &obj)

void	setCacheSize (int const &size)
	Set the Cache size.

int const &	getCacheSize () const
	Get the Cache size.

void	store (size_tconst &key, vector< TOutput >const &value)
	Store the cached data.

bool	get (size_tconst &key, vector< TOutput > &out)
	Get the cached data.

Additional Inherited Members
Public Types inherited from ql::LRUCache< size_t, vector< TOutput > >
typedef std::pair< size_t, vector< TOutput > >	key_value_pair_t

typedef std::list< key_value_pair_t >::iterator	list_iterator_t

Protected Member Functions inherited from ql::Topology< TOutput, TMass, TScale >
bool	checkCache (TScale const &, vector< TMass > const &, vector< TScale > const &)
	< Check stored cached results More...

void	storeCache (TScale const &, vector< TMass > const &, vector< TScale > const &)
	Topology<TOutput, TMass>::storeCache.

Protected Attributes inherited from ql::Topology< TOutput, TMass, TScale >
string	_name

size_t	_key

TScale	_mu2

vector< TMass >	_m

vector< TScale >	_p

vector< TOutput >	_val

ContainerHasher< TMass, TScale > *	_ch

Protected Attributes inherited from ql::Tools< TOutput, TMass, TScale >
TScale	_pi

TScale	_pi2

TScale	_pio3

TScale	_pio6

TScale	_pi2o3

TScale	_pi2o6

TScale	_pi2o12

TScale	_zero

TScale	_half

TScale	_one

TScale	_two

TScale	_three

TScale	_four

TScale	_five

TScale	_six

TScale	_ten

TScale	_eps

TScale	_eps4

TScale	_eps7

TScale	_eps10

TScale	_eps14

TScale	_eps15

TScale	_xloss

TScale	_neglig

TScale	_reps

TOutput	_2ipi

TOutput	_ipio2

TOutput	_ipi

TOutput	_czero

TOutput	_chalf

TOutput	_cone

TOutput	_ctwo

TOutput	_cthree

TOutput	_cfour

TOutput	_ieps

TOutput	_ieps2

TOutput	_ieps50

Detailed Description

template<typename TOutput = complex, typename TMass = double, typename TScale = double>
class ql::Bubble< TOutput, TMass, TScale >

The Bubble integral.

Parses automatically the topology and computes the integral

Member Function Documentation

template<typename TOutput , typename TMass , typename TScale >

void ql::Bubble< TOutput, TMass, TScale >::BB0	(	vector< TOutput > &	res,
		TScale const &	mu2,
		TMass const &	m0,
		TMass const &	m1,
		TScale const &	s
	)		const

General configuration I(s;m0,m1)

The integral is defined as in the general case but with the first term:

\[ I_{2}(s; m_0^2, m_1^2) = \Delta + 2 - \ln \left( \frac{m_0 m_1}{m_0^2} \right) + \frac{m_0^2-m_1^2}{s} \ln \left(\frac{m_1}{m_0} \right) - \frac{m_0 m_1}{s} \left(\frac{1}{r}-r \right) \ln r \]

with

\[ x^2 + \frac{m_0^2 + m_1^2 - s - i \epsilon}{m_0 m_1} +1 = (x+r)\left(x+\frac{1}{r} \right) \]

Implementation of the formulae of Denner and Dittmaier [7].

Returns: the output object res[0,1,2] the coefficients in the Laurent series

Parameters

mu2	is the squre of the scale mu
m0	is the square of the first mass of the internal line
m1	is the square of the second mass of the internal line
s	is the square of the four-momentum external line

template<typename TOutput , typename TMass , typename TScale >

void ql::Bubble< TOutput, TMass, TScale >::BB1	(	vector< TOutput > &	res,
		TScale const &	mu2,
		TMass const &	m
	)		const

Special configuration I(m2;0,m2)

The integral is defined as:

\[ I_{2}^{D=4-2 \epsilon}(m^2; 0, m^2)=\left( \frac{\mu^{2}}{m^{2}} \right)^{\epsilon} \left[ \frac{1}{\epsilon} + 2 \right] + O(\epsilon) \]

Implementation of the formulae of Denner and Dittmaier [5].

Returns: the output object res[0,1,2] the coefficients in the Laurent series

Parameters

mu2	is the squre of the scale mu
m	is the squares of the mass of the internal line

template<typename TOutput , typename TMass , typename TScale >

void ql::Bubble< TOutput, TMass, TScale >::BB2	(	vector< TOutput > &	res,
		TScale const &	mu2,
		TMass const &	m
	)		const

Special configuration I(0;0,m2)

The integral is defined as:

\[ I_{2}^{D=4-2 \epsilon}(0; 0, m^2)= \left( \frac{\mu^{2}}{m^{2}} \right)^{\epsilon} \left[ \frac{1}{\epsilon} + 1 \right] + O(\epsilon) \]

Implementation of the formulae of Denner and Dittmaier [5].

Returns: the output object res[0,1,2] the coefficients in the Laurent series

Parameters

mu2	is the squre of the scale mu
m	is the squares of the mass of the internal line

template<typename TOutput , typename TMass , typename TScale >

void ql::Bubble< TOutput, TMass, TScale >::BB3	(	vector< TOutput > &	res,
		TScale const &	mu2,
		TMass const &	s
	)		const

Special configuration I(s;0,0)

The integral is defined as:

\[ I_{2}^{D=4-2 \epsilon}(s; 0, 0)= \left( \frac{\mu^{2}}{-s-i \epsilon} \right)^{\epsilon} \left[ \frac{1}{\epsilon} + 2 \right] + O(\epsilon) \]

Implementation of the formulae of Denner and Dittmaier [5].

Returns: the output object res[0,1,2] the coefficients in the Laurent series

Parameters

mu2	is the squre of the scale mu
s	is the four-momentum squared of the external line

template<typename TOutput , typename TMass , typename TScale >

void ql::Bubble< TOutput, TMass, TScale >::BB4	(	vector< TOutput > &	res,
		TScale const &	mu2,
		TMass const &	m,
		TScale const &	s
	)		const

Special configuration I(s;0,m2)

The integral is defined as:

\[ I_{2}^{D=4-2 \epsilon}(s; 0, m^2)= \left( \frac{\mu^{2}}{m^2} \right)^{\epsilon} \left[ \frac{1}{\epsilon} + 2 + \frac{m^2-s}{s} \ln \left( \frac{m^2-s-i \epsilon}{m^2} \right) \right] + O(\epsilon) \]

Implementation of the formulae of Denner and Dittmaier [5].

Returns: the output object res[0,1,2] the coefficients in the Laurent series

Parameters

mu2	is the squre of the scale mu
m	is the squares of the mass of the internal line
s	is the four-momentum squared of the external line

template<typename TOutput , typename TMass , typename TScale >

void ql::Bubble< TOutput, TMass, TScale >::BB5	(	vector< TOutput > &	res,
		TScale const &	mu2,
		TMass const &	m0,
		TMass const &	m1
	)		const

Special configuration I(0;m0,m1)

The integral is defined as in the general case but with the first term:

\[ I_{2}^{\epsilon=0}(0; m_0^2, m_1^2) = \ln \left( \frac{\mu}{m_0^2} \right) - f_0 \left( \frac{m0}{m0-m1} \right) \]

Implementation of the formulae of Denner and Dittmaier [5].

Returns: the output object res[0,1,2] the coefficients in the Laurent series

Parameters

mu2	is the squre of the scale mu
m0	is the square of the first mass of the internal line
m1	is the square of the second mass of the internal line

template<typename TOutput , typename TMass , typename TScale >

void ql::Bubble< TOutput, TMass, TScale >::integral	(	vector< TOutput > &	res,
		TScale const &	mu2,
		vector< TMass > const &	m,
		vector< TScale > const &	p
	)

virtual

Computes the Bubble integral automatically.

The integral is defined as:

\[ I_{2}^{D=4-2 \epsilon}(p^2; m_1^2, m_2^2)= \mu^{2 \epsilon} \left[ \frac{1}{\epsilon} - \int_{0}^{1} da \ln (-a (1-a) p^2 + am_{2}^2 + (1-a) m_{1}^{2} - i \epsilon ) \right] + O(\epsilon) \]

Implementation of the formulae of Denner and Dittmaier [5].

Parameters

res	output object res[0,1,2] the coefficients in the Laurent series
mu2	is the squre of the scale mu
m	are the squares of the masses of the internal lines
p	are the four-momentum squared of the external lines

Implements ql::Topology< TOutput, TMass, TScale >.

The documentation for this class was generated from the following files:

/home/carrazza/repo/github/qcdloop/src/qcdloop/bubble.h
/home/carrazza/repo/github/qcdloop/src/bubble.cc

Public Member Functions

Additional Inherited Members

Detailed Description

template<typename TOutput = complex, typename TMass = double, typename TScale = double> class ql::Bubble< TOutput, TMass, TScale >

Member Function Documentation

template<typename TOutput = complex, typename TMass = double, typename TScale = double>
class ql::Bubble< TOutput, TMass, TScale >