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Herwig  7.1.4

The a1ThreePionCLEODecayer class is designed to implement the decay of the $a_1$ to three pions using the model of Phys.Rev.D61:012002,2000, (hep-ex/9902022) (CLEO) which was fitted to the one charged and two neutral pion channel for the charged $a_1$ decay in $\tau \to a_1 -> \pi\pi\pi$. More...

#include <a1ThreePionCLEODecayer.h>

Inheritance diagram for Herwig::a1ThreePionCLEODecayer:

Public Member Functions

 a1ThreePionCLEODecayer ()
 Default constructor.
 
virtual int modeNumber (bool &cc, tcPDPtr parent, const tPDVector &children) const
 Which of the possible decays is required. More...
 
double me2 (const int ichan, const Particle &part, const ParticleVector &decay, MEOption meopt) const
 Return the matrix element squared for a given mode and phase-space channel. More...
 
virtual WidthCalculatorBasePtr threeBodyMEIntegrator (const DecayMode &dm) const
 Method to return an object to calculate the 3 body partial width. More...
 
virtual double threeBodyMatrixElement (const int imode, const Energy2 q2, const Energy2 s3, const Energy2 s2, const Energy2 s1, const Energy m1, const Energy m2, const Energy m3) const
 The matrix element to be integrated for the three-body decays as a function of the invariant masses of pairs of the outgoing particles. More...
 
virtual void dataBaseOutput (ofstream &os, bool header) const
 Output the setup information for the particle database. More...
 
Functions used by the persistent I/O system.
void persistentOutput (PersistentOStream &os) const
 Function used to write out object persistently. More...
 
void persistentInput (PersistentIStream &is, int version)
 Function used to read in object persistently. More...
 
- Public Member Functions inherited from Herwig::DecayIntegrator
 DecayIntegrator ()
 Default constructor.
 
virtual bool accept (tcPDPtr parent, const tPDVector &children) const
 Check if this decayer can perfom the decay for a particular mode. More...
 
virtual ParticleVector decay (const Particle &parent, const tPDVector &children) const
 For a given decay mode and a given particle instance, perform the decay and return the decay products. More...
 
int imode () const
 The mode being used for this decay.
 
void addMode (DecayPhaseSpaceModePtr mode, double maxwgt, const vector< double > wgts) const
 Add a phase-space mode to the list. More...
 
DecayMEPtr ME () const
 The helicity amplitude matrix element for spin correlations.
 
virtual bool twoBodyMEcode (const DecayMode &, int &mecode, double &coupling) const
 Specify the $1\to2$ matrix element to be used in the running width calculation. More...
 
virtual InvEnergy threeBodydGammads (const int imode, const Energy2 q2, const Energy2 s, const Energy m1, const Energy m2, const Energy m3) const
 The differential three body decay rate with one integral performed. More...
 
void setPartialWidth (const DecayMode &dm, int imode)
 Set the code for the partial width. More...
 
int findMode (const DecayMode &dm)
 Finds the phase-space mode corresponding to a given decay mode. More...
 
ParticleVector generatePhotons (const Particle &p, ParticleVector children)
 Members for the generation of QED radiation in the decays. More...
 
bool canGeneratePhotons ()
 check if photons can be generated in the decay
 
virtual double oneLoopVirtualME (unsigned int imode, const Particle &part, const ParticleVector &products)
 The one-loop virtual correction. More...
 
bool hasOneLoopME ()
 Whether or not the one loop matrix element is implemented.
 
virtual InvEnergy2 realEmissionME (unsigned int imode, const Particle &part, ParticleVector &products, unsigned int iemitter, double ctheta, double stheta, const LorentzRotation &rot1, const LorentzRotation &rot2)
 The real emission matrix element. More...
 
bool hasRealEmissionME ()
 Whether or not the real emission matrix element is implemented.
 
void persistentOutput (PersistentOStream &os) const
 Function used to write out object persistently. More...
 
void persistentInput (PersistentIStream &is, int version)
 Function used to read in object persistently. More...
 
- Public Member Functions inherited from Herwig::HwDecayerBase
 HwDecayerBase ()
 The default constructor.
 
virtual bool accept (const DecayMode &dm) const
 Check if this decayer can perfom the decay specified by the given decay mode. More...
 
virtual ParticleVector decay (const DecayMode &dm, const Particle &p) const
 Perform a decay for a given DecayMode and a given Particle instance. More...
 
void persistentOutput (PersistentOStream &os) const
 Function used to write out object persistently. More...
 
void persistentInput (PersistentIStream &is, int version)
 Function used to read in object persistently. More...
 
bool initialize () const
 Access to the initialize variable.
 
bool databaseOutput () const
 Access the database output variable.
 
virtual POWHEGType hasPOWHEGCorrection ()
 Has a POWHEG style correction.
 
virtual bool hasMECorrection ()
 Has an old fashioned ME correction.
 
virtual void initializeMECorrection (RealEmissionProcessPtr, double &, double &)
 Initialize the ME correction.
 
virtual RealEmissionProcessPtr applyHardMatrixElementCorrection (RealEmissionProcessPtr)
 Apply the hard matrix element correction to a given hard process or decay.
 
virtual bool softMatrixElementVeto (ShowerProgenitorPtr initial, ShowerParticlePtr parent, Branching br)
 Apply the soft matrix element correction. More...
 
virtual RealEmissionProcessPtr generateHardest (RealEmissionProcessPtr)
 Apply the POWHEG style correction.
 
- Public Member Functions inherited from ThePEG::Decayer
Ptr< Amplitude >::pointer amplitude () const
 
virtual bool needsFullStep () const
 
virtual ParticleVector decay (const DecayMode &dm, const Particle &p, Step &step) const
 
virtual double brat (const DecayMode &dm, const ParticleData &pd, double oldbrat) const
 
virtual double brat (const DecayMode &dm, const Particle &p, double oldbrat) const
 
virtual ParticleVector getChildren (const DecayMode &dm, const Particle &parent) const
 
virtual void finalBoost (const Particle &parent, const ParticleVector &children) const
 
virtual void setScales (const Particle &parent, const ParticleVector &children) const
 
void persistentOutput (PersistentOStream &os) const
 
void persistentInput (PersistentIStream &is, int version)
 
virtual bool needsFullStep () const
 
virtual ParticleVector decay (const DecayMode &dm, const Particle &p, Step &step) const
 
virtual double brat (const DecayMode &dm, const ParticleData &pd, double oldbrat) const
 
virtual double brat (const DecayMode &dm, const Particle &p, double oldbrat) const
 
virtual ParticleVector getChildren (const DecayMode &dm, const Particle &parent) const
 
virtual void finalBoost (const Particle &parent, const ParticleVector &children) const
 
virtual void setScales (const Particle &parent, const ParticleVector &children) const
 
void persistentOutput (PersistentOStream &os) const
 
void persistentInput (PersistentIStream &is, int version)
 
- Public Member Functions inherited from HandlerBaseT< UseRandom >
double rnd () const
 
double rnd (double xu) const
 
double rnd (double xl, double xu) const
 
bool rndbool () const
 
bool rndbool (double p) const
 
bool rndbool (double p1, double p2) const
 
int rndsign (double p1, double p2, double p3) const
 
int rnd2 (double p0, double p1) const
 
int rnd3 (double p0, double p1, double p2) const
 
int rnd4 (double p0, double p1, double p2, double p3) const
 
long irnd (long xu=2) const
 
long irnd (long xl, long xu) const
 
const StandardModelBase & SM () const
 
tSMPtr standardModel () const
 
- Public Member Functions inherited from ThePEG::Interfaced
virtual bool defaultInit ()
 
PPtr getParticle (PID) const
 
PDPtr getParticleData (PID) const
 
bool used () const
 
void useMe () const
 
tEGPtr generator () const
 
void persistentOutput (PersistentOStream &os) const
 
void persistentInput (PersistentIStream &is, int version)
 
PPtr getParticle (PID) const
 
PDPtr getParticleData (PID) const
 
bool used () const
 
void useMe () const
 
tEGPtr generator () const
 
void persistentOutput (PersistentOStream &os) const
 
void persistentInput (PersistentIStream &is, int version)
 
- Public Member Functions inherited from ThePEG::InterfacedBase
string fullName () const
 
string name () const
 
string path () const
 
string comment () const
 
void setup (istream &is)
 
virtual void debugme () const
 
void update ()
 
void init ()
 
virtual bool preInitialize () const
 
void initrun ()
 
void finish ()
 
void touch ()
 
void reset ()
 
void clear ()
 
InitState state () const
 
bool locked () const
 
bool touched () const
 
void persistentOutput (PersistentOStream &os) const
 
void persistentInput (PersistentIStream &is, int version)
 
void update ()
 
void init ()
 
virtual bool preInitialize () const
 
void initrun ()
 
void finish ()
 
void touch ()
 
void reset ()
 
void clear ()
 
InitState state () const
 
bool locked () const
 
bool touched () const
 
void persistentOutput (PersistentOStream &os) const
 
void persistentInput (PersistentIStream &is, int version)
 
- Public Member Functions inherited from ThePEG::Base
void debug () const
 
- Public Member Functions inherited from ThePEG::Pointer::ReferenceCounted
CounterType referenceCount () const
 
- Public Member Functions inherited from ThePEG::Named
 Named (const string &newName=string())
 
const string & name () const
 
bool operator== (const Named &other) const
 
bool operator< (const Named &other) const
 

Static Public Member Functions

static void Init ()
 Standard Init function used to initialize the interfaces.
 
- Static Public Member Functions inherited from Herwig::DecayIntegrator
static void Init ()
 Standard Init function used to initialize the interfaces.
 
- Static Public Member Functions inherited from Herwig::HwDecayerBase
static void Init ()
 The standard Init function used to initialize the interfaces. More...
 
- Static Public Member Functions inherited from ThePEG::Decayer
static ParticleVector DecayParticle (tPPtr parent, Step &step, long maxtry=1000)
 
static void Init ()
 
- Static Public Member Functions inherited from ThePEG::HandlerBase
static void Init ()
 
- Static Public Member Functions inherited from ThePEG::Interfaced
static void Init ()
 
- Static Public Member Functions inherited from ThePEG::InterfacedBase
static void Init ()
 
- Static Public Member Functions inherited from ThePEG::Base
static void Init ()
 

Protected Member Functions

Clone Methods.
virtual IBPtr clone () const
 Make a simple clone of this object. More...
 
virtual IBPtr fullclone () const
 Make a clone of this object, possibly modifying the cloned object to make it sane. More...
 
Standard Interfaced functions.
virtual void doinit ()
 Initialize this object after the setup phase before saving and EventGenerator to disk. More...
 
virtual void doinitrun ()
 Initialize this object to the begining of the run phase.
 
- Protected Member Functions inherited from Herwig::DecayIntegrator
ParticleVector generate (bool inter, bool cc, const unsigned int &imode, const Particle &inpart) const
 Generate the momenta for the decay. More...
 
void imode (int in)
 Set the mode being use for this decay.
 
void ME (DecayMEPtr in) const
 Set the helicity matrix element for the decay.
 
void resetIntermediate (tcPDPtr part, Energy mass, Energy width)
 Reset the properities of all intermediates. More...
 
unsigned int numberModes () const
 Number of decay modes.
 
tDecayPhaseSpaceModePtr mode (unsigned int)
 Pointer to a mode.
 
tcDecayPhaseSpaceModePtr mode (unsigned int) const
 Pointer to a mode.
 
bool generateIntermediates () const
 Get whether or not the intermediates are included.
 
void generateIntermediates (bool in)
 Set whether or not the intermediates are included.
 
Energy initializePhaseSpaceMode (unsigned int imode, bool init, bool onShell=false) const
 Initialize the phase-space mode. More...
 
void hasOneLoopME (bool in)
 Whether or not the one loop matrix element is implemented.
 
void hasRealEmissionME (bool in)
 Whether or not the real emission matrix element is implemented.
 
- Protected Member Functions inherited from Herwig::HwDecayerBase
virtual void dofinish ()
 Finalize this object. More...
 
- Protected Member Functions inherited from ThePEG::Interfaced
void reporeg (IBPtr object, string name) const
 
bool setDefaultReference (PtrT &ptr, string classname, string objectname)
 
 Interfaced (const string &newName)
 
 Interfaced (const Interfaced &i)
 
void setGenerator (tEGPtr generator)
 
- Protected Member Functions inherited from ThePEG::InterfacedBase
 InterfacedBase (string newName)
 
 InterfacedBase (const InterfacedBase &i)
 
virtual void readSetup (istream &is)
 
virtual void doupdate ()
 
virtual IVector getReferences ()
 
virtual void rebind (const TranslationMap &)
 
virtual void readSetup (istream &is)
 
virtual void doupdate ()
 
virtual IVector getReferences ()
 
virtual void rebind (const TranslationMap &)
 
- Protected Member Functions inherited from ThePEG::Pointer::ReferenceCounted
 ReferenceCounted (const ReferenceCounted &)
 
ReferenceCountedoperator= (const ReferenceCounted &)
 
 ReferenceCounted (const ReferenceCounted &)
 
ReferenceCountedoperator= (const ReferenceCounted &)
 
- Protected Member Functions inherited from ThePEG::Named
const Namedoperator= (const Named &other)
 
const string & name (const string &newName)
 

Private Member Functions

a1ThreePionCLEODecayeroperator= (const a1ThreePionCLEODecayer &)
 Private and non-existent assignment operator.
 
Complex rhoBreitWigner (int ires, Energy2 q2, int icharge) const
 Breit wigner for the $\rho$, $B^P_{\rho_k}(q^2)$. More...
 
Complex sigmaBreitWigner (Energy2 q2, int icharge) const
 Breit wigner for the $\sigma$, $B^S_\sigma(q^2)$. More...
 
Complex f0BreitWigner (Energy2 q2, int icharge) const
 Breit wigner for the $f_0(1370)$, $B^S_{f_0}(q^2)$. More...
 
Complex f2BreitWigner (Energy2 q2, int icharge) const
 Breit wigner for the $f_2$, $B^D_{f_2}(q^2)$. More...
 
void formFactors (int iopt, int ichan, Energy2 q2, Energy2 s1, Energy2 s2, Energy2 s3, complex< InvEnergy > &F1, complex< InvEnergy > &F2, complex< InvEnergy > &F3) const
 Calculate the form factors. More...
 

Private Attributes

vector< Energy > _rhomass
 Masses of the rho resonaces.
 
vector< Energy > _rhowidth
 Widths of the rho resonaces.
 
vector< Energy > _prhocc
 Momentum of the particles produced in charged rho decay.
 
vector< Energy > _prhoc0
 Momentum of the particles produced in neutral rho decay.
 
Energy _f2mass
 Mass of the $f_2$.
 
Energy _f2width
 Width of the $f_2$.
 
Energy _pf2cc
 Momentum for the decay of the $f_2$ to two charged pions.
 
Energy _pf200
 Momentum for the decay of the $f_2$ to two neutral pions.
 
Energy _f0mass
 Mass of the $f_0(1370)$.
 
Energy _f0width
 Width of the $f_0(1370)$.
 
Energy _pf0cc
 Momentum for the decay of the $f_0(1370)$ to two charged pions.
 
Energy _pf000
 Momentum for the decay of the $f_0(1370)$ to two neutral pions.
 
Energy _sigmamass
 Mass of the $\sigma$ meson.
 
Energy _sigmawidth
 Width of the $\sigma$ meson.
 
Energy _psigmacc
 Momentum for the decay of the $\sigma$ to two charged pions.
 
Energy _psigma00
 Momentum for the decay of the $\sigma$ to two neutral pions.
 
Energy _mpi0
 Mass of the neutral pion.
 
Energy _mpic
 Mass of the charged pion.
 
InvEnergy _coupling
 overall coupling for the decay
 
vector< double > _rhomagP
 Magnitude of the $p$-wave couplings of the rho resonance, $g^P_{\rho_k}$, ( $\beta_{1,2}$ in the CLEO paper.)
 
vector< double > _rhophaseP
 Phase of the $p$-wave couplings of the rho resonance, $g^P_{\rho_k}$, ( $\beta_{1,2}$ in the CLEO paper.)
 
vector< Complex_rhocoupP
 $p$-wave couplings of the rho resonance, $g^P_{\rho_k}$, ( $\beta_{1,2}$ in the CLEO paper.)
 
vector< InvEnergy2 > _rhomagD
 Magnitude of the $d$-wave couplings of the rho resonance, $g^D_{\rho_k}$, ( $\beta_{3,4}$ in the CLEO paper.)
 
vector< double > _rhophaseD
 Phase of the $d$-wave couplings of the rho resonance, $g^D_{\rho_k}$, ( $\beta_{3,4}$ in the CLEO paper.)
 
vector< complex< InvEnergy2 > > _rhocoupD
 $d$-wave couplings of the rho resonance, $g^D_{\rho_k}$, ( $\beta_{3,4}$ in the CLEO paper.)
 
InvEnergy2 _f2mag
 Magntiude of the coupling of the $f_2$ resonance, $g_{f_2}$, ( $\beta_5$ in the CLEO paper.)
 
double _f2phase
 Phase of the coupling of the $f_2$ resonance, $g_{f_2}$, ( $\beta_5$ in the CLEO paper.)
 
complex< InvEnergy2 > _f2coup
 Coupling of the $f_2$ resonance, $g_{f_2}$, ( $\beta_5$ in the CLEO paper.)
 
double _f0mag
 Magntiude of the coupling of the $f_0(1370)$ resonance, $g_{f_0}$, ( $\beta_6$ in the CLEO paper.)
 
double _f0phase
 Phase of the coupling of the $f_0(1370)$ resonance, $g_{f_0}$, ( $\beta_6$ in the CLEO paper.)
 
Complex _f0coup
 Coupling of the $f_0(1370)$ resonance, $g_{f_0}$, ( $\beta_6$ in the CLEO paper.)
 
double _sigmamag
 Magntiude of the coupling of the $\sigma$ resonance, $g_\sigma$, ( $\beta_7$ in the CLEO paper.)
 
double _sigmaphase
 Phase of the coupling of the $\sigma$ resonance, $g_\sigma$, ( $\beta_7$ in the CLEO paper.)
 
Complex _sigmacoup
 Coupling of the $\sigma$ resonance, $g_\sigma$, ( $\beta_7$ in the CLEO paper.)
 
bool _localparameters
 Use local values of the mass parameters.
 
vector< double > _zerowgts
 Weights for the channels for the zero charged pion channel.
 
vector< double > _onewgts
 Weights for the channels for the one charged pion channel.
 
vector< double > _twowgts
 Weights for the channels for the two charged pion channel.
 
vector< double > _threewgts
 Weights for the channels for the three charged pion channel.
 
double _zeromax
 Maximum weight for the zero charged pion channel.
 
double _onemax
 Maximum weight for the one charged pion channel.
 
double _twomax
 Maximum weight for the two charged pion channel.
 
double _threemax
 Maximum weight for the three charged pion channel.
 
RhoDMatrix _rho
 Spin density matrix.
 
vector< Helicity::LorentzPolarizationVector_vectors
 Polarization vectors.
 

Static Private Attributes

static ClassDescription< a1ThreePionCLEODecayerinita1ThreePionCLEODecayer
 Describe a concrete class with persistent data.
 

Additional Inherited Members

- Public Types inherited from Herwig::DecayIntegrator
enum  MEOption { Initialize, Calculate, Terminate }
 Enum for the matrix element option.
 
- Public Types inherited from Herwig::HwDecayerBase
enum  POWHEGType { No, ISR, FSR, Both }
 Virtual members to be overridden by inheriting classes which implement hard corrections. More...
 
- Public Types inherited from ThePEG::InterfacedBase
enum  InitState
 
- Public Types inherited from ThePEG::Pointer::ReferenceCounted
typedef unsigned int CounterType
 
- Public Attributes inherited from ThePEG::InterfacedBase
 initializing
 
 uninitialized
 
 initialized
 
 runready
 
- Public Attributes inherited from ThePEG::Pointer::ReferenceCounted
const unsigned long uniqueId
 
- Static Protected Member Functions inherited from ThePEG::Interfaced
static void registerRepository (IBPtr)
 
static void registerRepository (IBPtr, string newName)
 

Detailed Description

The a1ThreePionCLEODecayer class is designed to implement the decay of the $a_1$ to three pions using the model of Phys.Rev.D61:012002,2000, (hep-ex/9902022) (CLEO) which was fitted to the one charged and two neutral pion channel for the charged $a_1$ decay in $\tau \to a_1 -> \pi\pi\pi$.

The other modes are infered from this using isospin. This is a sophisticated model including the coupling of the $a_1$ to the $\rho$, $\rho(1450)$, $f(1370)$ and $\sigma$ sigma mesons.

In this case the current is given by

\[\mathcal{M} = \epsilon_\mu \left[F_1(p_2-p_3)^\mu+F_2(p_3-p_1)^\mu+F_3(p_1-p_2)^\mu\right].\]

The form factors for the $a_1^0 \to \pi^0 \pi^0 \pi^0$ mode are

\[F_1= \phantom{-}\frac23\left(g_\sigma B^S_\sigma(s_3)+g_{f_0}B^S_{f_0}(s_3)\right) -\frac23\left(g_\sigma B^S_\sigma(s_2)+g_{f_0}B^S_{f_0}(s_2)\right) +g_{f_2}\left(\frac12(s_3-s_2)B^D_{f_2}(s_1) -\frac1{18}\frac{(4m_{\pi^0}^2-s_2)(q^2+s_2-m_{\pi^0}^2)}{s_2}B^D_{f_2}(s_2) +\frac1{18}\frac{(4m_{\pi^0}^2-s_3)(q^2-m_{\pi^0}^2+s_3)}{s_3}B^D_{f_2}(s_3)\right) *\]

\[F_2=\phantom{-}\frac23(g_\sigma B^S_\sigma(s_3)+g_{f_0}B^S_{f_0}(s_3)) -\frac23(g_\sigma B^S_\sigma(s_1)+g_{f_0}B^S_{f_0}(s_1)) +g_{f_2}\left( \frac12(s_3-s1)B^D_{f_2}(s_2) -\frac1{18}\frac{(4m_{\pi^0}^2-s_1)(q^2+s_1-m_{\pi^0}^2)}{s_1}B^D_{f_2}(s_1) +\frac1{18}\frac{(4m_{\pi^0}^2-s_3)(q^2-m_{\pi^0}^2+s_3)}{s_3}B^D_{f_2}(s_3)\right) *\]

\[F_3=-\frac23(g_\sigma B^S_\sigma(s_1)+g_{f_0}B^S_{f_0}(s_1)) +\frac23(g_\sigma B^S_\sigma(s_2)+g_{f_0}B^S_{f_0}(s_2)) +g_{f_2}\left( \frac12(s_1-s_2)B^D_{f_2}(s_3) -\frac1{18}\frac{(4m_{\pi^0}^2-s_1)(q^2+s_1-m_{\pi^0}^2)}{s_1}B^D_{f_2}(s_1) +\frac1{18}\frac{(4m_{\pi^0}^2-s_2)(q^2+s_2-m_{\pi^0}^2)}{s_2}B^D_{f_2}(s_2)\right) *\]

The form factors for the $a_1^+ \to \pi^0 \pi^0 \pi^+$ mode are

\[F_1=\sum_k\left\{-\frac{g^P_{\rho_k}}3B_{\rho_k}^P(s_1) -g^D_{\rho_k}B_{\rho_k}^P(s_2) \left((s_3-m_{\pi^+}^2)-(s_1-m_{\pi^0}^2)\right)\right\} +\frac23\left(g_\sigma B^S_\sigma(s_3)+g_{f_0}B^S_{f_0}(s_3)\right) +\frac{g_{f_2}}{18s_3}(q^2-m_{\pi^+}^2+s_3)(4m_{\pi^0}^2-s_3)B^D_{f_2}(s_3) *\]

\[F_2=\sum_k\left\{-\frac13g^P_{\rho_k}B_{\rho_k}^P(s_2) -g^D_{\rho_k}B_{\rho_k}^P(s_1) \left((s_3-m_{\pi^+}^2)-(s_2-m_{\pi^0}^2)\right)\right\} +\frac23\left(g_\sigma B^S_\sigma(s_3)+g_{f_0}B^S_{f_0}(s_3)\right) +\frac1{18s_3}g_{f_2}(q^2-m_{\pi^+}^2+s_3)(4m_{\pi^0}^2-s_3)B^D_{f_2}(s_3) *\]

\[F_3=\sum_k g^D_{\rho_k}\left\{ -\frac13B_{\rho_k}^P(s_1)\left((s_3-m_{\pi^+}^2)-(s_2-m_{\pi^0}^2)\right) +\frac13B_{\rho_k}^P(s_2)\left((s_3-m_{\pi^+}^2)-(s_1-m_{\pi^0}^2)\right)\right\} -\frac{g_{f_2}}2(s_1-s_2)B^D_{f_2}(s_3)\]

The form factors for $a_1^0\to\pi^+\pi^-\pi^0$.

\[F_1=\sum_k\left\{g^P_{\rho_k}B_{\rho_k}^P(s_1) -\frac{g^D_{\rho_k}}3B_{\rho_k}^P(s_2)(s_3-m_{\pi^0}^2-s_1+m_{\pi^+}^2)\right\} +\frac23\left(g_\sigma B^S_\sigma(s_3)+g_{f_0}B^S_{f_0}(s_3)\right) +\frac{g_{f_2}}{18s_3}(q^2-m_{\pi^0}^2+s_3)(4m_{\pi^+}^2-s_3)B^D_{f_2}(s_3)\]

\[F_2=\sum_k\left\{g^P_{\rho_k}B_{\rho_k}^P(s_2) -\frac{g^D_{\rho_k}}3B_{\rho_k}^P(s_1)(s_3-m_{\pi^0}^2-s_2+m_{\pi^+}^2)\right\} +\frac23\left(g_\sigma B^S_\sigma(s_3)+g_{f_0}B^S_{f_0}(s_3)\right) +\frac{g_{f_2}}{18s_3}(q^2-m_{\pi^0}^2+s_3)(4m_{\pi^+}^2-s_3)B^D_{f_2}(s_3)\]

\[F_3=\sum_k g^D_{\rho_k}\left\{-\frac13B_{\rho_k}^P(s_1)(s_3-m_{\pi^0}^2-s_2+m_{\pi^+}^2) +\frac13B_{\rho_k}^P(s_2)(s_3-m_{\pi^0}^2-s_1+m_{\pi^+}^2) \right\} -\frac{g_{f_2}}2(s_1-s_2)B^D_{f_2}(s_3)\]

The form factors for $a_1^+\to \pi^+ \pi^+ \pi^-$ mode

\[F_1=\sum_k\left\{-g^P_{\rho_k}B_{\rho_k}^P(s_1) -\frac{g^D_{\rho_k}}3B_{\rho_k}^P(s_2)(s_1-s_3)\right\} -\frac23\left(g_\sigma B^S_\sigma(s_2)+g_{f_0} B^S_{f_0}(s_2)\right) +g_{f_2}\left(\frac12(s_3-s_2)B^D_{f_2}(s_1) -\frac1{18s_2}(4m_{\pi^+}^2-s_2)(q^2+s_2-m_{\pi^+}^2)B^D_{f_2}(s_2)\right)\]

\[F_2=\sum_k\left\{-g^P_{\rho_k}B_{\rho_k}^P(s_2) -\frac{g^D_{\rho_k}}3B_{\rho_k}^P(s_1)(s_2-s_3)\right\} -\frac23\left(g_\sigma B^S_\sigma(s_1)+g_{f_0} B^S_{f_0}(s_1)\right) +g_{f_2}\left(\frac12(s_3-s_1)B^D_{f_2}(s_2) -\frac1{18s_1}(4m_{\pi^+}^2-s_1)(q^2+s_1-m_{\pi^+}^2)B^D_{f_2}(s_1)\right)\]

\[F_3=\sum_k -g^D_{\rho_k}\left( \frac13(s_2-s_3)B_{\rho_k}^P(s_1) -\frac13(s_1-s_3)B_{\rho_k}^P(s_2)\right) -\frac23\left(g_\sigma B^S_\sigma(s_1)+g_{f_0}B^S_{f_0}(s_1)\right) +\frac23\left(g_\sigma B^S_\sigma(s_2)+g_{f_0}B^S_{f_0}(s_2)\right)\]

\[ +g_{f_2}\left(-\frac1{18s_1}(4m_{\pi^+}^2-s_1)(q^2+s_1-m_{\pi^+}^2)B^D_{f_2}(s_1) +\frac1{18s_2}(4m_{\pi^+}^2-s_2)(q^2+s_2-m_{\pi^+}^2)B^D_{f_2}(s_2)\right)\]

where

  • $g_{f_2}$ is the coupling of the $f_2$ to the $a_1$
  • $g_{f_0}$ is the coupling of the $f_0(1370)$ to the $a_1$
  • $g_{\sigma}$ is the coupling of the $\sigma$ to the $a_1$
  • $g^P_{\rho_k}$ is the $p$-wave coupling of the $\rho_k$ multiplet to the $a_1$.
  • $g^D_{\rho_k}$ is the $d$-wave coupling of the $\rho_k$ multiplet to the $a_1$.
  • $s_3=m^2_{12}$ is the invariant mass squared of particles 1 and 2.
  • $s_2=m^2_{13}$ is the invariant mass squared of particles 1 and 3.
  • $s_1=m^2_{23}$ is the invariant mass squared of particles 2 and 3.

The Breit-Wigner factors are given by $B^L_Y(s_i) = \frac{m^2_Y}{m^2_Y-s_i)+im_Y\Gamma^{Y,L}(s_i)}$ where $\Gamma^{Y,L}(s_i) = \Gamma^Y\left(\frac{p(s_i)}{p(M_Y}\right)^{2L+1}\frac{m_Y}{\sqrt{s_i}}$ $m_Y$ and $\Gamma^Y$ are the mass and width of the particle $Y$ respectively. $p(s_i)$ is the momentum of the outgoing pion in the rest frame of the resonanc $Y$.

See also
ThreePionCLEOCurrent
DecayIntegrator

Definition at line 146 of file a1ThreePionCLEODecayer.h.

Member Function Documentation

◆ clone()

virtual IBPtr Herwig::a1ThreePionCLEODecayer::clone ( ) const
inlineprotectedvirtual

Make a simple clone of this object.

Returns
a pointer to the new object.

Implements ThePEG::InterfacedBase.

Definition at line 238 of file a1ThreePionCLEODecayer.h.

◆ dataBaseOutput()

virtual void Herwig::a1ThreePionCLEODecayer::dataBaseOutput ( ofstream &  os,
bool  header 
) const
virtual

Output the setup information for the particle database.

Parameters
osThe stream to output the information to
headerWhether or not to output the information for MySQL

Reimplemented from Herwig::DecayIntegrator.

◆ doinit()

virtual void Herwig::a1ThreePionCLEODecayer::doinit ( )
protectedvirtual

Initialize this object after the setup phase before saving and EventGenerator to disk.

Exceptions
InitExceptionif object could not be initialized properly.

Reimplemented from ThePEG::InterfacedBase.

◆ f0BreitWigner()

Complex Herwig::a1ThreePionCLEODecayer::f0BreitWigner ( Energy2  q2,
int  icharge 
) const
inlineprivate

Breit wigner for the $f_0(1370)$, $B^S_{f_0}(q^2)$.

Parameters
q2The scale, $q^2$.
ichargeWhich pion masses to use for the momentum calculation
Returns
The Breit-Wigner

Definition at line 318 of file a1ThreePionCLEODecayer.h.

References Herwig::Kinematics::pstarTwoBodyDecay(), sqr(), and sqrt().

◆ f2BreitWigner()

Complex Herwig::a1ThreePionCLEODecayer::f2BreitWigner ( Energy2  q2,
int  icharge 
) const
inlineprivate

Breit wigner for the $f_2$, $B^D_{f_2}(q^2)$.

Parameters
q2The scale, $q^2$.
ichargeWhich pion masses to use for the momentum calculation
Returns
The Breit-Wigner

Definition at line 334 of file a1ThreePionCLEODecayer.h.

References pow(), Herwig::Kinematics::pstarTwoBodyDecay(), sqr(), and sqrt().

◆ formFactors()

void Herwig::a1ThreePionCLEODecayer::formFactors ( int  iopt,
int  ichan,
Energy2  q2,
Energy2  s1,
Energy2  s2,
Energy2  s3,
complex< InvEnergy > &  F1,
complex< InvEnergy > &  F2,
complex< InvEnergy > &  F3 
) const
private

Calculate the form factors.

Parameters
ioptThe mode being calculated in the order given above
ichanThe phase space channel in the order given in the doinit member.
q2The sacale $q^2$.
s1The invariant mass squared of particles 2 and 3, $s_1=m^2_{23}$.
s2The invariant mass squared of particles 1 and 3, $s_2=m^2_{13}$.
s3The invariant mass squared of particles 1 and 2, $s_3=m^2_{12}$.
F1The form factor $F_1$.
F2The form factor $F_2$.
F3The form factor $F_3$.

◆ fullclone()

virtual IBPtr Herwig::a1ThreePionCLEODecayer::fullclone ( ) const
inlineprotectedvirtual

Make a clone of this object, possibly modifying the cloned object to make it sane.

Returns
a pointer to the new object.

Reimplemented from ThePEG::InterfacedBase.

Definition at line 244 of file a1ThreePionCLEODecayer.h.

◆ me2()

double Herwig::a1ThreePionCLEODecayer::me2 ( const int  ichan,
const Particle part,
const ParticleVector decay,
MEOption  meopt 
) const
virtual

Return the matrix element squared for a given mode and phase-space channel.

Parameters
ichanThe channel we are calculating the matrix element for.
partThe decaying Particle.
decayThe particles produced in the decay.
meoptOption for the calculation of the matrix element
Returns
The matrix element squared for the phase-space configuration.

Implements Herwig::DecayIntegrator.

◆ modeNumber()

virtual int Herwig::a1ThreePionCLEODecayer::modeNumber ( bool &  cc,
tcPDPtr  parent,
const tPDVector children 
) const
virtual

Which of the possible decays is required.

Parameters
ccIs this mode the charge conjugate
parentThe decaying particle
childrenThe decay products

Implements Herwig::DecayIntegrator.

◆ persistentInput()

void Herwig::a1ThreePionCLEODecayer::persistentInput ( PersistentIStream is,
int  version 
)

Function used to read in object persistently.

Parameters
isthe persistent input stream read from.
versionthe version number of the object when written.

◆ persistentOutput()

void Herwig::a1ThreePionCLEODecayer::persistentOutput ( PersistentOStream os) const

Function used to write out object persistently.

Parameters
osthe persistent output stream written to.

◆ rhoBreitWigner()

Complex Herwig::a1ThreePionCLEODecayer::rhoBreitWigner ( int  ires,
Energy2  q2,
int  icharge 
) const
inlineprivate

Breit wigner for the $\rho$, $B^P_{\rho_k}(q^2)$.

Parameters
iresThe $\rho$ multiplet to used.
q2The scale, $q^2$.
ichargeWhich pion masses to use for the momentum calculation
Returns
The Breit-Wigner

Definition at line 285 of file a1ThreePionCLEODecayer.h.

References pow(), Herwig::Kinematics::pstarTwoBodyDecay(), sqr(), and sqrt().

◆ sigmaBreitWigner()

Complex Herwig::a1ThreePionCLEODecayer::sigmaBreitWigner ( Energy2  q2,
int  icharge 
) const
inlineprivate

Breit wigner for the $\sigma$, $B^S_\sigma(q^2)$.

Parameters
q2The scale, $q^2$.
ichargeWhich pion masses to use for the momentum calculation
Returns
The Breit-Wigner

Definition at line 302 of file a1ThreePionCLEODecayer.h.

References Herwig::Kinematics::pstarTwoBodyDecay(), sqr(), and sqrt().

◆ threeBodyMatrixElement()

virtual double Herwig::a1ThreePionCLEODecayer::threeBodyMatrixElement ( const int  imode,
const Energy2  q2,
const Energy2  s3,
const Energy2  s2,
const Energy2  s1,
const Energy  m1,
const Energy  m2,
const Energy  m3 
) const
virtual

The matrix element to be integrated for the three-body decays as a function of the invariant masses of pairs of the outgoing particles.

Parameters
imodeThe mode for which the matrix element is needed.
q2The scale, i.e. the mass squared of the decaying particle.
s3The invariant mass squared of particles 1 and 2, $s_3=m^2_{12}$.
s2The invariant mass squared of particles 1 and 3, $s_2=m^2_{13}$.
s1The invariant mass squared of particles 2 and 3, $s_1=m^2_{23}$.
m1The mass of the first outgoing particle.
m2The mass of the second outgoing particle.
m3The mass of the third outgoing particle.
Returns
The matrix element

Reimplemented from Herwig::DecayIntegrator.

◆ threeBodyMEIntegrator()

virtual WidthCalculatorBasePtr Herwig::a1ThreePionCLEODecayer::threeBodyMEIntegrator ( const DecayMode dm) const
virtual

Method to return an object to calculate the 3 body partial width.

Parameters
dmThe DecayMode
Returns
A pointer to a WidthCalculatorBase object capable of calculating the width

Reimplemented from Herwig::DecayIntegrator.


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