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Laura++  v1r2
A maximum likelihood fitting package for performing Dalitz-plot analysis.
LauRelBreitWignerRes.cc
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1 
2 // Copyright University of Warwick 2004 - 2013.
3 // Distributed under the Boost Software License, Version 1.0.
4 // (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
5 
6 // Authors:
7 // Thomas Latham
8 // John Back
9 // Paul Harrison
10 
15 #include <iostream>
16 
17 #include "LauConstants.hh"
18 #include "LauRelBreitWignerRes.hh"
19 
20 ClassImp(LauRelBreitWignerRes)
21 
22 
23 LauRelBreitWignerRes::LauRelBreitWignerRes(TString resName, Double_t resMass, Double_t resWidth, Int_t resSpin,
24  Int_t resCharge, Int_t resPairAmpInt, const LauDaughters* daughters) :
25  LauAbsResonance(resName, resMass, resWidth, resSpin, resCharge, resPairAmpInt, daughters),
26  q0_(0.0),
27  p0_(0.0),
28  pstar0_(0.0),
29  resMassSq_(0.0),
30  mDaugSum_(0.0),
31  mDaugSumSq_(0.0),
32  mDaugDiff_(0.0),
33  mDaugDiffSq_(0.0),
34  mParentSq_(0.0),
35  mBachSq_(0.0),
36  resR_(4.0),
37  parR_(4.0),
38  resRSq_(16.0),
39  parRSq_(16.0),
40  FR0_(1.0),
41  FB0_(1.0),
42  barrierType_(LauAbsResonance::BWPrimeBarrier)
43 {
44 }
45 
47 {
48 }
49 
51 {
52  // Set-up various constants. This must be called again if the mass/width/spin
53  // of a resonance changes...
54 
55  Int_t resSpin = this->getSpin();
56  Double_t resMass = this->getMass();
57  Double_t massDaug1 = this->getMassDaug1();
58  Double_t massDaug2 = this->getMassDaug2();
59  Double_t massBachelor = this->getMassBachelor();
60  Double_t massParent = this->getMassParent();
61 
62  // Create the mass squares, sums, differences etc.
63  resMassSq_ = resMass*resMass;
64  mDaugSum_ = massDaug1 + massDaug2;
66  mDaugDiff_ = massDaug1 - massDaug2;
68  mParentSq_ = massParent*massParent;
69  mBachSq_ = massBachelor*massBachelor;
70 
71  // Create an effective resonance pole mass to protect against resonances
72  // that are below threshold
73  Double_t effResMass = resMass;
74  if (resMassSq_ - mDaugSumSq_ < 0.0 ){
75  Double_t minMass = mDaugSum_;
76  Double_t maxMass = massParent - massBachelor;
77  Double_t tanhTerm = std::tanh( (resMass - ((minMass + maxMass)/2))/(maxMass-minMass));
78  effResMass = minMass + (maxMass-minMass)*(1+tanhTerm)/2;
79  }
80  Double_t effResMassSq = effResMass*effResMass;
81 
82  // Decay momentum of either daughter in the resonance rest frame
83  // when resonance mass = rest-mass value, m_0 (PDG value)
84  Double_t term1 = effResMassSq - mDaugSumSq_;
85  Double_t term2 = effResMassSq - mDaugDiffSq_;
86  Double_t term12 = term1*term2;
87  if (term12 > 0.0) {
88  q0_ = TMath::Sqrt(term12)/(2.0*effResMass);
89  } else {
90  q0_ = 0.0;
91  }
92 
93  // Momentum of the bachelor particle in the resonance rest frame
94  // when resonance mass = rest-mass value, m_0 (PDG value)
95  Double_t eBach = (mParentSq_ - effResMassSq - mBachSq_)/(2.0*effResMass);
96  Double_t termBach = eBach*eBach - mBachSq_;
97  if ( eBach<0.0 || termBach<0.0 ) {
98  p0_ = 0.0;
99  } else {
100  p0_ = TMath::Sqrt( termBach );
101  }
102 
103  // Momentum of the bachelor particle in the parent rest frame
104  // when resonance mass = rest-mass value, m_0 (PDG value)
105  Double_t eStarBach = (mParentSq_ + mBachSq_ - effResMassSq)/(2.0*massParent);
106  Double_t termStarBach = eStarBach*eStarBach - mBachSq_;
107  if ( eStarBach<0.0 || termStarBach<0.0 ) {
108  pstar0_ = 0.0;
109  } else {
110  pstar0_ = TMath::Sqrt( termStarBach );
111  }
112 
113  // Blatt-Weisskopf barrier factor constant: z = q^2*radius^2
114  // Calculate the Blatt-Weisskopf form factor for the case when m = m_0
116 
117  if (resSpin > 3) {
118  std::cerr << "WARNING in LauRelBreitWignerRes::initialise : Resonances spin is > 3. Blatt-Weisskopf form factors will be set to 1.0" << std::endl;
119  }
120 }
121 
122 void LauRelBreitWignerRes::setBarrierRadii(Double_t resRadius, Double_t parRadius, LauAbsResonance::BarrierType type)
123 {
124  // Reset the Blatt-Weisskopf barrier radius for the resonance and its parent
125  resR_ = resRadius;
126  parR_ = parRadius;
127 
128  resRSq_ = resRadius*resRadius;
129  parRSq_ = parRadius*parRadius;
130 
131  barrierType_ = type;
132 
133  // Recalculate the Blatt-Weisskopf form factor for the case when m = m_0
134  Double_t zR0 = q0_*q0_*resRSq_;
135  Double_t zB0 = p0_*p0_*parRSq_;
136  if ( ( type == LauAbsResonance::BWPrimeBarrier ) || ( type == LauAbsResonance::ExpBarrier ) ) {
137  FR0_ = (resR_==0.0) ? 1.0 : this->calcFFactor(zR0);
138  FB0_ = (parR_==0.0) ? 1.0 : this->calcFFactor(zB0);
139  }
140 }
141 
143 {
144  // Calculate the requested form factor for the resonance, given the z value
145  Double_t fFactor(1.0);
146 
147  // For scalars the form factor is always unity
148  // TODO: and we currently don't have formulae for spin > 3
149  Int_t resSpin = this->getSpin();
150  if ( (resSpin == 0) || (resSpin>3) ) {
151  return fFactor;
152  }
153 
155  if (resSpin == 1) {
156  fFactor = TMath::Sqrt(2.0*z/(z + 1.0));
157  } else if (resSpin == 2) {
158  fFactor = TMath::Sqrt(13.0*z*z/(z*z + 3.0*z + 9.0));
159  } else if (resSpin == 3) {
160  fFactor = TMath::Sqrt(277.0*z*z*z/(z*z*z + 6.0*z*z + 45.0*z + 225.0));
161  }
163  if (resSpin == 1) {
164  fFactor = TMath::Sqrt(1.0/(z + 1.0));
165  } else if (resSpin == 2) {
166  fFactor = TMath::Sqrt(1.0/(z*z + 3.0*z + 9.0));
167  } else if (resSpin == 3) {
168  fFactor = TMath::Sqrt(1.0/(z*z*z + 6.0*z*z + 45.0*z + 225.0));
169  }
170  } else if ( barrierType_ == LauAbsResonance::ExpBarrier ) {
171  if (resSpin == 1) {
172  fFactor = TMath::Exp( -TMath::Sqrt(z) );
173  } else if (resSpin == 2) {
174  fFactor = TMath::Exp( -z );
175  } else if (resSpin == 3) {
176  fFactor = TMath::Exp( -TMath::Sqrt(z*z*z) );
177  }
178  }
179 
180  return fFactor;
181 
182 }
183 
184 LauComplex LauRelBreitWignerRes::resAmp(Double_t mass, Double_t spinTerm)
185 {
186  // This function returns the complex dynamical amplitude for a Breit-Wigner resonance,
187  // given the invariant mass and cos(helicity) values.
188 
189  LauComplex resAmplitude(0.0, 0.0);
190 
191  if (mass < 1e-10) {
192  std::cerr << "WARNING in LauRelBreitWignerRes::amplitude : mass < 1e-10." << std::endl;
193  return LauComplex(0.0, 0.0);
194  } else if (q0_ < 1e-30) {
195  return LauComplex(0.0, 0.0);
196  }
197 
198  // Calculate the width of the resonance (as a function of mass)
199  // First, calculate the various form factors.
200  // NB
201  // q is the momentum of either daughter in the resonance rest-frame,
202  // p is the momentum of the bachelor in the resonance rest-frame,
203  // pstar is the momentum of the bachelor in the parent rest-frame.
204  // These quantities have been calculate in LauAbsResonance::amplitude(...)
205 
206  Int_t resSpin = this->getSpin();
207  Double_t resMass = this->getMass();
208  Double_t resWidth = this->getWidth();
209  Double_t q = this->getQ();
210  Double_t p = this->getP();
211  //Double_t pstar = this->getPstar();
212 
213  Double_t zR = q*q*resRSq_;
214  Double_t zB = p*p*parRSq_;
215  Double_t fFactorR = (resR_==0.0) ? 1.0 : this->calcFFactor(zR);
216  Double_t fFactorB = (parR_==0.0) ? 1.0 : this->calcFFactor(zB);
217  Double_t fFactorRRatio = fFactorR/FR0_;
218  Double_t fFactorBRatio = fFactorB/FB0_;
219 
220  Double_t qRatio = q/q0_;
221  Double_t qTerm(0.0);
222  if (resSpin == 0) {
223  qTerm = qRatio;
224  } else if (resSpin == 1) {
225  qTerm = qRatio*qRatio*qRatio;
226  } else if (resSpin == 2) {
227  qTerm = TMath::Power(qRatio, 5.0);
228  } else {
229  qTerm = TMath::Power(qRatio, 2*resSpin + 1);
230  }
231 
232  Double_t totWidth = resWidth*qTerm*(resMass/mass)*fFactorRRatio*fFactorRRatio;
233 
234  Double_t massSq = mass*mass;
235  Double_t massSqTerm = resMassSq_ - massSq;
236 
237  // Compute the complex amplitude
238  resAmplitude = LauComplex(massSqTerm, resMass*totWidth);
239 
240  // Scale by the denominator factor, as well as the spin term and Blatt-Weisskopf factors
241  resAmplitude.rescale((fFactorRRatio*fFactorBRatio*spinTerm)/(massSqTerm*massSqTerm + resMassSq_*totWidth*totWidth));
242 
243  return resAmplitude;
244 }
245 
Double_t getQ() const
Get the current value of the daughter momentum in the resonance rest frame.
Double_t resR_
Radius of the barrier for resonance decay.
Double_t getMassBachelor() const
Get the mass of the bachelor daughter.
Double_t getMass() const
Get the mass of the resonance.
void setBarrierRadii(Double_t resRadius, Double_t parRadius, LauAbsResonance::BarrierType type)
Set the form factor model and parameters.
Double_t FB0_
Value of the form factor for parent decay (at pole mass)
Double_t q0_
Momentum of the daughters in the resonance rest frame (at pole mass)
Double_t getMassParent() const
Get the parent particle mass.
Double_t resRSq_
Square of the radius of the barrier for resonance decay.
Double_t resMassSq_
Square of the resonance mass.
Class that defines the particular 3-body decay under study.
Definition: LauDaughters.hh:33
Double_t calcFFactor(Double_t z)
Calculate the form factor for the resonance.
virtual ~LauRelBreitWignerRes()
Destructor.
Double_t getP() const
Get the current value of the bachelor momentum in the resonance rest frame.
virtual LauComplex resAmp(Double_t mass, Double_t spinTerm)
Complex resonant amplitude.
Double_t mDaugSum_
Sum of the two daughter masses.
LauAbsResonance::BarrierType barrierType_
Model to be used for the form factor.
Double_t getMassDaug1() const
Get the mass of daughter 1.
File containing declaration of LauRelBreitWignerRes class.
Double_t getMassDaug2() const
Get the mass of daughter 2.
Double_t FR0_
Value of the form factor for resonance decay (at pole mass)
Double_t parR_
Radius of the barrier for parent decay.
Double_t mParentSq_
Square of the parent mass.
Double_t mBachSq_
Square of the bachelor mass.
Double_t p0_
Momentum of the bachelor in the resonance rest frame (at pole mass)
Double_t pstar0_
Momentum of the bachelor in the parent rest frame (at pole mass)
Class for defining the relativistic Breit-Wigner resonance model.
Double_t mDaugDiff_
Difference of the two daughter masses.
Double_t mDaugDiffSq_
Square of the difference of the two daughter masses.
Double_t parRSq_
Square of the radius of the barrier for parent decay.
Double_t getWidth() const
Get the width of the resonance.
Abstract class for defining type for resonance amplitude models (Breit-Wigner, Flatte etc...
void rescale(Double_t scaleVal)
Scale this by a factor.
Definition: LauComplex.hh:282
File containing LauConstants namespace.
Double_t mDaugSumSq_
Square of the sum of the two daughter masses.
virtual void initialise()
Initialise the model.
Class for defining a complex number.
Definition: LauComplex.hh:47
BarrierType
Define the allowed types of barrier factors.
Int_t getSpin() const
Get the spin of the resonance.