EvtGen Models Documentation

SCALAR (S), VECTOR (V) and TENSOR (T) DECAYS

EvtPVVCPLH

This model decays a B⁰_s (pseudo)scalar to vector + vector, including CP-violation and different widths for the CP-even and CP-odd states. It is similar to the EvtSVVCP model, and it also uses for formulae from I. Dunietz et al, Phys.Rev. D43 2193 (1991) 2193. The model requires 8 parameters:

beta eta |G₁₊| argG₁₊ |G₀₊| argG₀₊ |G₁₋| argG₁₋;

The first argument is the relevant CKM angle in radians. The next argument is the parameter η, but is ignored in the model (i.e. assumed to be 1). The last six arguments are G₁₊, G₀₊ and G₁₋, and are expressed as their absolute values and phases. This model then uses these amplitudes together with the time evolution of the B − anti B system, and the flavour of the other B, to generate the time distributions. This example decays the B⁰_s meson to J/ψ φ:

Decay B0_s
  1.000 J/psi  phi  PVV_CPLH beta 1.0 1.0 0.0 1.0 0.0 1.0 0.0;
Enddecay

EvtSll

EvtSLN

Decay of a scalar to a lepton and a neutrino, e.g. D_s⁺ → μ⁺ ν_μ

Decay Ds+
  1.000 mu+ nu_mu SLN;
Enddecay

EvtSSDCP

This model simulates the decay of a B meson to a scalar and one other particle of arbitrary (integer) spin. It expects either 8, 12 or 14 model parameter arguments. An example of using this model is B → J/ψ K_S:

Decay B0
1.000 J/psi K0S    SSD_CP dm dgog |qop| arg(qop)
                          |Af| arg(Af) |Abarf| arg(Abarf)
                          |Afbar| arg(Afbar) |Abarfbar| arg(Abarfbar)
                          |z| arg(z);
Enddecay

where dm is the mass difference of the two mass eigenstates (in units of hbar/s), dgog is 2y ≡ 2(Γ_H−Γ_L)/(Γ_H+Γ_L). The value qop is q/p where |B_L,H〉 = p|B⁰〉 ± q|anti-B⁰〉. The values Af and Abarf are the amplitudes for the decay of a B⁰ and a anti-B⁰, respectively, to the final state f. The set of amplitudes Afbar and Abarfbar corresponds to the decay to the CP conjugate final state. These amplitudes are optional and are by default A_fbar = Abar^*_f and Abar_fbar =A^*_f, consistent with CPT for a common final state of the B⁰ and anti-B⁰. However, in modes such as B → D^* π it is useful to be able to specify these amplitudes separately.

The example below shows the decays B → J/ψ K_S and B → J/ψ K_L:

Define dm 0.472e12
Define minusTwoBeta -0.85

Decay B0
  0.5000 J/psi K0S   SSD_CP dm 0.0 1.0 minusTwoBeta 1.0 0.0 -1.0 0.0;
  0.5000 J/psi K0L   SSD_CP dm 0.0 1.0 minusTwoBeta 1.0 0.0  1.0 0.0;
Enddecay

Note that the sign of the amplitude for the anti-B⁰ decay have the oposite sign for the K_S since this final state is odd under parity.

To generate the final state π⁺ π⁻:

Define dm 0.472e12
Define minusTwoBeta -0.85
Define gamma 1.0

Decay B0
  1.0000 pi+ pi-   SSD_CP dm 0.0 1.0 minusTwoBeta 1.0 gamma 1.0 -gamma;
Enddecay

These examples have used |q/p|=1 and Δ Γ = 0. An example with non-trivial values for these parameters would be B_s → J/ψ η:

Define dms 14e12
Define dgog 0.1

Decay B_s0
  1.0000 J/psi eta  SSD_CP dms dgog 1.0 0.0 1.0 0.0 1.0 0.0;
Enddecay

This model can also be used for final states that are not CP eigenstates, such as B⁰ → D^*+ π⁻ and B⁰ → D^*− π⁺. We can generate these decays using

Define dms 14e12
Define minusTwoBeta -0.85
Define gamma 1.0

Decay B0
  1.0000 D*+ pi-  SSD_CP dm 0.0 1.0 minusTwoBeta 1.0 0.0 0.3 gamma;
Enddecay

where the Cabibbo-suppressed decay has a relative strong phase γ with respect to the Cabibbo-favoured decay.

EvtSSD_DirectCP

This model generates direct CP-violation for two-body B_u,d and B_s decays in an hadronic environment, where one of the decay daughters is a scalar and the other a scalar, vector or tensor particle. It requires one parameter, which defines the CP asymmetry between the branching fractions for the f and fbar states: [BR(fbar)−BR(f)]/[BR(fbar)+BR(f)].

Decay B0
  1.00 pi+ pi- SSD_DirectCP 0.3;
Enddecay

EvtSSSCP

A model to decay a scalar particle into two scalars, which includes CP-violation. The 7 model parameters are:

angle dm cp |A| argA |barA| argbarA;

The first argument is the relevant CKM angle in radians. The second argument is the mass difference in hbar/s (approx 0.5 x 10¹²), while cp is the CP of the final state (&pm; 1). Next is the amplitude of a B⁰ to decay to the final state, which are given as the magnitude and phase of the amplitude. The last two arguments are the magnitude and phase of the amplitude for a decay of an anti-B⁰ to decay to the final state. This model then uses these amplitudes together with the time evolution of the B anti-B system and the flavour of the other B to generate the time distributions.

Decay B0
  1.000 pi+  pi-  SSS_CP alpha dm 1 1.0 0.0 1.0 0.0;
Enddecay

EvtSSSCPpng

This model takes into account penguin contributions in B → π π decays, as given by P. S. Marrocchesi and N. Paver, Int. J. Mod. Phys. A13 251 (1998). It assumes single (top) quark dominance for the penguin diagram. Parameters (7) for the model are:

The first two arguments are the relevant CKM angles in radians; the third argument is the relative strong phase in radians; dm is the mass difference in hbar/s (approx 0.5 x 10¹²); cp is the CP of the final state (&pm; 1); |A_tree| is the tree-level amplitude, and |A_tree/|A_penguin| is the ratio of the amplitudes for the tree and penguin diagrams (≈ 0.2 for this decay mode).

Decay B0
  1.000 pi+  pi- SSS_CP_PNG beta gamma 0.1 dm 1.0 1.0 0.2;
Enddecay

EvtSSSCPT

This model implements CPT violation for a scalar (B⁰) particle decaying into two scalars. It requires 8 parameters, which are:

The amplitude for the B⁰ state is given by

A cos(dm*t/2c) + i[(AQ/P) + 2D barA] sin(dm*t/2c)

where P = e^{−i angle}, Q = e^{i angle}, and D = |D|e^{i argD}. The amplitude for the anti-B⁰ state is

Abar cos(dm*t/2c) + i[(AP/Q) − 2D barA] sin(dm*t/2c)

The first argument is the relevant CKM angle in radians. The second argument is the mass difference in hbar/s (approx 0.5 x 10¹²). Next is the amplitude of a B⁰ to decay to the final state, which are given as the magnitude and phase of the amplitude. The next two arguments are the magnitude and phase of the amplitude for a decay of an anti-B⁰ to decay to the final state. The last two arguments specify the magnitude and phase of the D amplitude in the above expressions. This model then uses these amplitudes together with the time evolution of the B anti-B system and the flavour of the other B to generate the time distributions.

Decay B0
  1.000 pi+  pi-  SSS_CPT alpha dm 1.0 0.0 1.0 0.0 0.1 0.0;
Enddecay

EvtSTS

This model decays a scalar meson to a tensor and a scalar. This example decays the B⁺ meson to D₂^*0 π⁺:

Decay B+
  1.000 D_2*0  pi+  STS;
Enddecay

EvtSTSCP

A model to decay a scalar particle to a tensor and a scalar, which includes CP-violation. The 7 model parameters are:

angle dm cp |A| argA |barA| argbarA;

Decay B0
  1.000 a_20  pi0  STS_CP alpha dm 1 1.0 0.0 1.0 0.0;
Enddecay

EvtSVP

A routine to implement radiative decays of a scalar to a vector particle, such as χ_c0 → ψ γ; note that the photon needs to be the first daughter, the other vector particle the second daughter.

Decay chi_c0
  1.0 gamma psi SVP;
Enddecay

EvtSVPHelAmp

The decay of a scalar to a vector and a photon, which is parameterised by the helicity amplitudes (magnitude 1st, phase 2nd) H₊ and H₋.

Decay B0
  1.000 K*0  gamma  SVP_HELAMP 1.0 0.0 1.0 0.0;
Enddecay

EvtSVPCP

This specifies the decay of a scalar particle to a vector and a photon which includes CP-violation. The 7 model parameters are:

angle dm cp |A| argA |barA| argbarA;

The first daughter has to be the vector, the second must be the photon. The first argument is the relevant CKM angle in radians. The second argument is the mass difference in hbar/s (approx 0.5 x 10¹²), while cp is the CP of the final state (&pm; 1). Next is the amplitude of a B⁰ to decay to the final state, which are given as the magnitude and phase of the amplitude. The last two arguments are the magnitude and phase of the amplitude for a decay of an anti-B⁰ to decay to the final state. This model then uses these amplitudes together with the time evolution of the B anti-B system and the flavour of the other B to generate the time distributions.

Here, the helicity amplitudes of the decay are set to the following:

H₋ = difference of the CP even and odd amplitudes/√2
H₊ = sum of the CP even and odd amplitudes/√2
H₀ = zero

Decay B0
  1.0  K*0   gamma   SVP_CP  beta dm  1 0.03 0.0 0.999 0.0;
Enddecay

EvtSVS

Model for the decay of a scalar particle to a vector and scalar.

Decay B0
  1.00 rho+ pi0 SVS;
Enddecay

EvtSVSCP

Decay of a scalar to a vector and a scalar, allowing for CP-violating asymmetries. The 7 model parameters are:

angle dm cp |A| argA |barA| argbarA;

The first daughter has to be the vector. The first argument is the relevant CKM angle in radians. The second argument is the mass difference in hbar/s (approx 0.5 x 10¹²), while cp is the CP of the final state (&pm; 1). Next is the amplitude of a B⁰ to decay to the final state, which are given as the magnitude and phase of the amplitude. The last two arguments are the magnitude and phase of the amplitude for a decay of an anti-B⁰ to decay to the final state. This model then uses these amplitudes together with the time evolution of the B anti-B system and the flavour of the other B to generate the time distributions.

This example decays the B⁰ meson to J/ψ K_S:

Decay B0
  1.000 J/psi  K_S0  SVS_CP beta dm -1 1.0 0.0 1.0 0.0;
Enddecay

EvtSVSNONCPEIGEN

This model allows us to generate scalar to vector + scalar decays, where the final state is not a CP-eigenstate. It requires 7 to 11 arguments. The first parameter is the weak phase angle for the decay amplitude. The second parameter is the B⁰ - anti-B⁰ mass difference (in hbar/s). The next parameter is the "flip" variable, which sets the fraction of f to fbar decays, where the state specified in the decay table is considered the "f" state. Set it to 0 to always get the final f case, and to 1 to always get the fbar final state. Otherwise, set it to 0.5 to get the physical situation. This model automatically generates the correct number of B⁰ and anti-B⁰ tags, depending on the specified amplitudes. The remaining parameters specify the magnitude and phase of the four decay amplitudes A_f, Abar_f, A_fbar and Abar_fbar. Note that the last four parameters are optional. If they are not specified, then they are evaluated from the following relations between the complex amplitudes: A_fbar = Abar_f, Abar_fbar = A_f.

The following example will generate a mixture of a₁⁺ π⁻ and a₁⁻ π⁺ final states with the appropriate number of B⁰ and anti-B⁰ tags.

Alias MYB B0

Decay Upsilon(4S)
  1.00  MYB B0
Enddecay

Decay MYB
  1.000 a_1- pi+ SVS_NONCPEIGEN alpha dm 0.5 1.0 0.0 3.0 0.0 3.0 0.0 1.0 0.0;
Enddecay

EvtSVSCPLH

Decay of a neutral B meson to a scalar and a vector CP eigenstate, e.g. B⁰ → J/ψ K_S. The first argument is the B⁰ − anti-B⁰ mass difference (hbar/s). The second argument is Δ Γ/Γ. The third and fourth arguments are the magnitude and phase of q/p, and the last four arguments are the magnitude and phases of the amplitude for B⁰ and anti-B⁰ to decay to the final state f.

Decay B0
  1.000   J/psi  K_S0   SVS_CPLH  0.472e12 0.1  1.0  0.7  1.0 0.0 1.0 0.0;
Enddecay

EvtSVSCPiso

This model considers B decays into a vector and a scalar from the point of view of isospin analysis. The vector should always be listed first. For the three B⁰ (or anti-B⁰) modes B⁰ → V⁺ S⁻, B⁰ → V⁻ S⁺ and B⁰ → V⁰ S⁰, it takes into account mixing, and generates the corresponding CP-violating asymmetries. It can also }be used for the two isospin-related B⁺ (B⁻) modes, B⁺ → V⁺ S⁰ and B⁺ → V⁰ S⁺, as all five modes should be treated together in this approach. Following the conventions of Lipkin, Nir, Quinn, and Snyder (Phys. Rev. D44, 1454 (1991)), the various decay amplitudes can be written as follows:

A(B⁺ → V⁺ S⁰) ≡ √2A⁺⁰ = T⁺⁰ + 2 P₁
A(B⁺ → V⁰ S⁺) ≡ √2A⁰⁺ = T⁰⁺ − 2 P₁
A(B⁰ → V⁺ S⁻) ≡ A⁺⁻ = T⁺⁻ + P₁ + P₀
A(B⁰ → V⁻ S⁺) ≡ A⁻⁺ = T⁻⁺ − P₁ + P₀
A(B⁰ → V⁰ S⁰) ≡ 2 A⁰⁰ = T⁰⁺ + T⁺⁰ − T⁻⁺ − T⁺⁻ − 2 P₀

where the amplitudes T^ij contain no penguin contributions, P₁ is penguin amplitude for the final I = 1 state, and P₀ for the final I = 0 state.

The model's 27 parameter arguments are:

beta = corresponding CKM angle
dm = B⁰ − anti-B⁰$ mass difference (≈ 0.5 x 10¹² (hbar/s))
"flip" sets the fraction of B → f to B → fbar decays, where the state specified in the decaytable is considered the "f" state. Set it to 0 to always get the B → f case, and to 1 to always get the B → fbar case.
|T⁺⁰|, φ(T⁺⁰) = magnitude and phase of the corresponding amplitude
|Tbar⁺⁰|, φ(Tbar⁺⁰) = magnitude and phase of the corresponding amplitude for the CP-conjugate process
|T⁰⁺|, φ(T⁰⁺) = magnitude and phase of the corresponding amplitude
|Tbar⁰⁺|, φ(Tbar⁰⁺) = magnitude and phase of the corresponding amplitude for the CP-conjugate process
|T⁺⁻|, φ(T⁺⁻) = magnitude and phase of the corresponding amplitude
|Tbar⁺⁻|, φ(Tbar⁺⁻) = magnitude and phase of the corresponding amplitude for the CP-conjugate process
|T⁻⁺|, φT⁻⁺ = magnitude and phase of the corresponding amplitude
|Tbar⁻⁺|, φ(Tbar⁻⁺) = magnitude and phase of the corresponding amplitude for the CP-conjugate process
|P₀|, φ(P₀) = magnitude and phase of the corresponding amplitude
|Pbar₀|, φ(Pbar₀) = magnitude and phase of the corresponding amplitude for the CP-conjugate process
|P₂|, φ(P₂) = magnitude and phase of the corresponding amplitude
|Pbar₂|, φ(Pbar₂) = magnitude and phase of the corresponding amplitude for the CP-conjugate process.

This example decays the B⁰ meson to a₁⁻ π⁺, assuming no penguin contributions:

Decay B0
1.000 a_1-  pi+      SVS_CP_ISO beta dm 0.0 1.0 0.0 1.0 0.0
                                              1.0 0.0 1.0 0.0
                                              1.0 gamma 3.0 -gamma
                                              3.0 gamma 1.0 -gamma
                                              0.0  0.0  0.0 0.0;

Enddecay

EvtSVVHelAmp

A routine to decay a scalar particle to two vector particles by specifying their helicity amplitudes. There are 6 arguments, ordered as amplitude then phase, for H₊, H₀ and H₋ (Jacob and Wick convention).

Decay B0
  1.00 D_s*- rho+ SVV_HELAMP 1.0 0.0 1.0 0.0 1.0 0.0;
Enddecay

EvtSVVHelCPMix

This is a model to decay a scalar particle to two vectors, taking appropriate weak phases into account to get mixing and CP violation through interference. The decay amplitudes are based on EvtSVVHelAmp, and is appropriate for decays such as B_s → J/ψ φ. See I. Dunietz and J. L. Rosner, Phys. Rev. D 34, 1404 (1986). It requires 12 model parameters, which are

|H₊| argH₊ |H₀| argH₀ |H₋| argH₋; m0 dm gamma dGamma mixPhase directPhase;

where H₊, H₀, H₋ are the helicity amplitude terms, m0 and dm are the average mass and mass difference of the light and heavy mass eigenstates (hbar/s), gamma and dGamma are the average width and width difference of these same eigenstates, while mixPhase and directPhase are the weak mixing and direct phases, respectively. For B_s → J/ψ φ, mixPhase = 2*arg(V_ts V_tb), directPhase = 0:

Decay B0s
  1.00 J/psi phi SVVHELCPMIX dm m gamma dGamma delta1 delta2 mixPhase 0.0;
Enddecay

EvtSVVNONCPEIGEN

This model is based on the SVS_NONCPEIGEN model and allows the generation of CP violation in scalar to vector + vector decays, where the final state is not a CP-eigenstate. It expects between 15 and 27 parameter arguments. The first argument is the B⁰ − anti-B⁰ mass difference (in hbar/s). The second argument is the CKM angle beta, while the third argument is the weak angle relevant to the decay mode being generated. In the example below it is CKM gamma. The next 24 arguments are the magnitudes and phases of the amplitudes for the four types of decay, A_f, Abar_f, A_fbar and Abar_fbar, which are split into the three different helicity states +, 0 and −. Depending on the specified amplitudes, the final state will be charge conjugated and the correct number of B⁰ and anti-B⁰ tags are generated. Note that the last 12 parameters are optional. If they are not specified, then they are evaluated according to the following relation between the complex amplitudes (with i=+,0,−): A_ifbar = Abar_if, Abar_ifbar = A_if.

This example will generate B → D^*&pm; ρ^&mp; final states with the appropriate number of B⁰ and anti-B⁰ tags. The chosen helicity amplitude parameters are those measured by CLEO.

Alias MYB B0

Decay Upsilon(4S)
  1.00  MYB anti-B0
Enddecay

Decay MYB
  1.000 rho+ D*- SVV_NONCPEIGEN dm beta gamma 0.322 0.31 0.941 0
                                             0.107 1.42 0.02  0
                                             0.02  0    0.02  0;
Enddecay

EvtSVVCP

This model decays a scalar particle to two vector mesons, allowing for CP-violating asymmetries. It is based on the work from I. Dunietz et al, Phys.Rev. D43 2193 (1991) 2193, and requires 9 parameters:

beta dm eta |G₁₊| argG₁₊ |G₀₊| argG₀₊ |G₁₋| argG₁₋;

The first argument is the relevant CKM angle in radians. The second argument is the B⁰ − anti-B⁰ mass difference in hbar/s (approximately 0.5 x 10¹²). The next argument is the parameter η and is either +1 or −1. The last six arguments are G₁₊, G₀₊ and G₁₋, and are expressed as their absolute values and phases. This model then uses these amplitudes together with the time evolution of the B − anti B system, and the flavour of the other B, to generate the time distributions.

This example decays the B⁰ meson to J/ψ K^*0:

Decay B0
  1.000 J/psi  K*0  SVV_CP beta dm 1.0 1.0 0.0 1.0 0.0 1.0 0.0;
Enddecay

EvtSVVCPLH

Please be aware that there can be serious mistakes in this model, since it has not been thoroughly tested.

Decay of a scalar to two vector mesons and allows for CP violating time asymmetries including different lifetimes for the different mass eigenstates, the light and heavy states. This model is only intended for B_s decays, like B_s → J/ψ φ, and requires 9 parameter arguments. The first argument is the relevant CKM angle in radians. The second argument is the B_s − anti-B_s mass difference in hbar/s (>1.8 x 10¹²). The width difference is not an input parameter to the model since it is determined via the definition of B_s0L and B_s0H in the "evt.pdl" file. The third argument is the parameter η defined in I. Dunietz et al, Phys.Rev. D43 2193 (1991) 2193, and is either +1 or −1. The last six arguments are G₁₊, G₀₊ and G₁₋, and are expressed as their absolute values and phases. This model then uses these amplitudes together with the time evolution of the B_s to generate the time dependent angular distributions.

This example decays the B_s meson to J/ψ φ:

Decay B_s0
  1.000   J/psi  phi   SVV_CPLH  0.4 3.0e12 1 1.0 0.0 1.0 0.0 1.0 0.0;
Enddecay

EvtTSS

Model for the decay of a tensor particle to two scalars, e.g. D₂^*0 → D⁰ π⁰:

Decay D_2*0
  1.000 D0  pi0  TSS;
Enddecay

EvtTVP

A routine to implement radiative decays of a tensor to a vector particle, such as χ_c2 → ψ γ, using the matrix element from S. P. Baranov et al, Phys. Rev. D 85, 014034 (2012). When using this decay mode, the photon needs to be defined first, the other vector particle second.

Decay chi_c2
  1.0 gamma psi TVP;
Enddecay

EvtTVSPwave

The decay of a tensor particle to a vector and a scalar. The decay takes six arguments, which parameterizes the P, D, and F wave amplitudes. The first two arguments are the magnitude and the phase of the P-wave amplitude, the third and forth are the D-wave amplitude and the last two are the F-wave amplitude:

|P| argP |D| argD |F| argF;

This model has only been used yet for D-wave, so further tests are needed before it is safe to use for nonzero P- and F-wave amplitudes. Here is the example decay D₂^*0 → D^*0 π⁰, which is expected (by HQET) to be dominated by the D-wave component:

Decay D_2*0
  1.000 D*0 pi0  TVS_PWAVE 0.0 0.0 1.0 0.0 0.0 0.0;
Enddecay

EvtVll

EvtVSS

Decays a vector particle into two scalars, generating the correct angular distributions. The amplitude is given by A = ε^μv_μ, where ε is the polarisation vector of the parent particle and v is the 4-velocity of the first daughter.

Decay D*+
  1.0  D0 pi+ VSS;
Enddecay

EvtVSSMix

Decays a vector particle into two scalars and generates the correct angular and time distributions for the particles in the decay Υ(4S) → B⁰ anti-B⁰. The mass difference is supplied as an argument to the model, in units of hbar/s. The example below shows how to generate the mixture of mixed and unmixed B⁰ anti-B⁰ events:

Define dm 0.474e12

Decay Upsilon(4S)
  0.420 B0      anti-B0                         VSS_MIX dm;
  0.040 anti-B0 anti-B0                         VSS_MIX dm;
  0.040 B0      B0                              VSS_MIX dm;
Enddecay

The user has to manually specify the fractions of mixed and un-mixed events through the branching fractions. This means that all this model does is to generate the right time distribution for the given final state. Use the new EvtVSSBMix model to generate mixing in the correct proportions using a single decay channel.

EvtVSSBMix(CPT)

Decays a C=−1 vector particle into two scalar particles using B⁰ anti-B⁰-like coherent mixing. The two possible daughter particles must be charge conjugates and have the same lifetime. Their mass difference is supplied as an argument to the model, in units of hbar/s.

While the mass difference is a required argument, Δ Γ/Γ and |q/p| can be supplied as optional arguments, with defaults of 0 and 1, respectively. The examples below illustrate how this model accomodates aliased daughters.

The example shows how to generate Υ(4S) → B⁰ anti-B⁰ decays with coherent mixing (but without CP violating effects).

Define dm 0.474e12

Decay Upsilon(4S)
  1.0 B0  anti-B0  VSS_BMIX dm;
Enddecay

to include a non-zero Δ Γ/Γ:

Define dm 0.474e12
Define dgog 0.5

Decay Upsilon(4S)
  1.0 B0  anti-B0  VSS_BMIX dm dgog;
Enddecay

and to specify |q/p|:

Define dm 0.474e12
Define dgog 0.5
Define qoverp 1.2

Decay Upsilon(4S)
  1.0 B0  anti-B0  VSS_BMIX dm dgog qoverp;
Enddecay

Finally, aliased particles can be generated using this model

Define dm 0.474e12
alias myB0 B0
alias myanti-B0 anti-B0

Decay Upsilon(4S)
  1.0 B0  anti-B0 myB0 myanti-B0 VSS_BMIX dm;
Enddecay

generates either B0 myanti-B0, anti-B0 myanti-B0, myB0 anti-B0, or myB0 B0.

This model is similar to the EvtVSSMix model, but it eliminates the need to manually specify the fractions of mixed and un-mixed events through branching fractions. This approach has the effect that the resulting mixing distributions are necessarily self consistent, which is not true for the VSS_MIX model when using the wrong branching fractions.

EvtVSPPwave

The P-wave decay of a vector to a scalar meson and a photon. The first daughter is the scalar meson and the second daughter is the photon. This decay is useful, for example, in the decay D^*0 → D⁰ γ

Decay D*0
  1.000 D0  gamma  VSP_PWAVE;
Enddecay

EvtVVP

Vector → Vector photon, for example χ₁ → ψ γ

Decay chi_c1
1.000  J/psi  gamma                VVP 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0;
Enddecay

This model requires 8 parameters, which should be used to denote polarisation components for the daughters, but they are not actually used in the model!

EvtVVSPwave

The decay of a vector particle to a vector and a scalar. The decay takes six arguments, which parameterizes the S-, P- and D-wave amplitudes. The first two arguments are the magnitude and the phase of the S-wave amplitude, the third and forth are the P-wave amplitude and the last two are the D-wave amplitude. This model has only been used yet for P-wave decays, so further tests are needed before it is safe to use use for nonzero S- and D-wave amplitudes. The example below shows how to decay the a₁⁰ in pure P-wave to ρ π:

Decay a_10
  1.000 rho0 pi0  VVS_PWAVE 0.0 0.0 1.0 0.0 0.0 0.0;
Enddecay

EvtVVpipi

EvtVVPIPI_WEIGHTED

SEMILEPTONIC DECAYS

EvtISGW

This is a model for semileptonic decays of B, D, and D_s mesons according to the ISGW model from Isgur, Scora, Grinstein and Wise, Phys. Rev. D 39, 799 (1989). The first daughter is the meson produced in the semileptonic decay. The second and third arguments are the lepton and the neutrino, respectively.

Decay anti-B0
  1.000 D*+ e- anti-nu_e     ISGW;
Enddecay

EvtISGW2

This is a model for semileptonic decays of B, D, and D_s mesons according to an update to the EvtISGW model from D. Scora and N. Isgur, Phys. Rev. D52, 2783 (1995). The first daughter is the meson produced in the semileptonic decay. The second and third arguments are the lepton and the neutrino, respectively.

Decay anti-B0
  1.000 D*+ e- anti-nu_e     ISGW2;
Enddecay

EvtMelikhov

Semileptonic decays B → (π,ρ) e anti-ν_e, using HQET form factors from Melikhov.

Decay anti-B0
  1.000 D*+ e- anti-nu_e     MELIKHOV 1;
Enddecay

The last integer (1 to 4) specifies which form factor parameters are to be used (see table 4 in the paper).

EvtSLPole

Implements semileptonic decays according to a pole-form parametrisation F = F(0)/[1 + a q²/M² + b q⁴/M⁴]^p
where M is the mass of the parent meson (in GeV/c²).

Decay B0
  1.000 rho- mu+ nu_mu SLPOLE 0.27 -0.11 -0.75 1.0 0.23 -0.77 
             -0.40 1.0 0.34 -1.32 0.19 1.0 0.37 -1.42 0.50 1.0;

Enddecay

The first daughter needs to be the meson produced in the semileptonic decay. The second and third arguments are the lepton and the neutrino, respectively. For each form factor, there are four arguments: F(0), a, b and p. The number of parameters depends on the type of the meson.

For scalar mesons, 8 parameters are required: two 4-parameter sets for the f₊ and f₀ factors
For vector mesons, 16 parameters are required: four 4-parameter sets for the A₁, A₂, V and A₀ factors
For tensor mesons, 16 parameters are required: four 4-parameter sets for the k, h, b₊ and b₋ factors

EvtPropSLPole

Uses the EvtSLPole form-factors and parameters for describing semileptonic decays, but also implements a Breit-Wigner resonance amplitude for the meson.

Decay B0
  1.000 rho- mu+ nu_mu PROPSLPOLE list_of_parameters;
Enddecay

EvtSLBKPole

Implements B (D) → meson (π) l ν semileptonic decays using the form factor parameterisation from Becirevic and Kaidalov, Phys. Lett. B 478, 417 (2000)

Decay B0
  1.00 pi- mu+ nu_mu SLBKPOLE list_of_parameters;
Enddecay

Here, the list of parameters depends on the spin of the meson produced in the semileptonic decay. For scalar mesons, 4 parameters are required: f0, α, β and the mass of the parent (in GeV/c²). For vector (tensor) mesons, 8 (16) parameters are required.

EvtHQET

A simple implementation of form factors within the Heavy Quark Effective Theory (HQET) model of semileptonic B → D^* l ν decays, where l denotes either e or μ. The model parameters are ρ² (linear form factor slope) and the form factor ratios R₁ and R₂, as defined in this paper. Any pseudoscalar semileptonic decay to a vector meson can use this model.

Decay B-
  1.0   D*0   mu-  anti-nu_mu    HQET 0.92 1.18 0.72;
Enddecay

EvtHQET2

A description of the B → D^* l ν decay using the HQET dispersive relation model. The arguments are the form factor slope ρ² and the form factor ratios R₁ and R₂.

Decay B0
  1.0   D*-   e+  nu_e   HQET2 1.35 1.3 0.8;
Enddecay

EvtGoityRoberts

Model for the non-resonant D^(*) π l ν decays of B mesons. The daughters are in the order: D-meson, pion, lepton and the neutrino. This is not exactly what was published by J. L. Goity and W. Roberts, Phys. Rev. D51, 3459 (1995), partly due to errors in the paper, and because the D^* had to be removed from the D π non-resonant component.

Decay B0
  1.000 D0B  pi- e+ nu_e  GOITY_ROBERTS;
Enddecay

EvtFlatQ2

B → X_u l ν with flat q² distribution

Decay B-
  0.5000 eta   e-    anti-nu_e         FLATQ2;
  0.5000 eta   mu-   anti-nu_mu        FLATQ2;
Enddecay

EvtBToVlnuBall

EvtBToPlnuBK

EvtKKLambdaC

EvtVub

EvtVubHybrid

EvtVubNLO

EvtVubBLNP

EvtVubBLNPHybrid

LEPTONIC DECAYS

EvtTauHadnu

Implementation of the τ → π π ν_τ decay, using the theoretical model from Kuhn, Mirkes and Santamaria, together with parameters from the CLEO collaboration paper (see table 1 therein).

Decay tau-
  1.000 pi- pi- pi+  nu_tau   TAUHADNU -0.108 0.7749 0.149 1.364 0.400 1.23 0.4;
Enddecay

Model parameters are: β (ρ' amplitude contribution), mass of ρ, width of ρ, mass of ρ', width of ρ', mass of a1, width of a1. Masses and widths are in GeV/c².

EvtTauVectornu

Vector decay of the τ, for example τ⁻ → ρ⁻ ν_τ

Decay tau+
  0.50         rho+ anti-nu_tau                     TAUVECTORNU;
  0.25         a_1+ anti-nu_tau                     TAUVECTORNU;
  0.25         K*+  anti-nu_tau                     TAUVECTORNU;
Enddecay

EvtTaulnunu

EvtTauScalarnu

EvtLNuGamma

DALTZ PLOT/TWO BODY/MULTI-BODY DECAYS

EvtGenericDalitz

Implements a generic Dalitz plot decay. The resonance structure of each Dalitz plot is defined in XML. The model takes a single parameter xmlFile which specifies the XML file containing the resonance structure for that decay.

Decay D0
  1.00         KS pi+ pi-        GENERIC_DALITZ xml/KSpipiDalitz.xml
Enddecay

<decay name="D0" >
  <channel br="1.00" daughters="KS pi+ pi-" model="GENERIC_DALITZ" 
           xmlFile="xml/KSpipiDalitz.xml"/>
</decay>

EvtDDalitz

Models the Dalitz plot amplitude for three-body D decays; namely for decays:

D⁺→K^-π⁺π⁺ with K^*(892), K^*(1430), K^*₂(1430), K^*(1680) and κ(800) resonances using data from the CLEO-c experiment. (arXiv:0802.4214)
D⁺→K⁰π⁺π⁰ with ρ⁺ and K^*0 resonances using data from the MarkIII experiment. (Phys.Lett. B196, 107 (1987))
D⁰→K⁰π⁺π^- with K^*(892), K₀^*(1430), K₂^*(1430), K^*(1680), ρ(892), ω(782), f₀(980), f₀(1370) and f₂(1270) resonances using data from the E691 experiment. (Phys.Rev. D48 56 (1993))
D⁰→K^-π⁺π⁰ with ρ, K^*0, K^*-, K₀(1430)^-, K₀(1430), ρ(1700) and K^*(1680)^- using data from the E691 experiment. (Phys.Rev. D48 56 (1993))
D⁰→K⁰K⁺K^- with φ, a₀(980) and f₀(980) resonances using data from the BaBar experiment. (arXiv:hep-ex/0207089)
D_s⁺→K^-K⁺π⁺ with K^*(892), K₀^*(1430), f₀(980), φ(1020), f₀(1370) and f₀(1710) resonances using data from the BaBar experiment. (arXiv:1011.4190)
D⁺→K^-K⁺π⁺ with K^*(892), K₀^*(1430), φ(1020), a₀(1450), φ(1680) and K₂^*(1430) resonances using data from the CLEO experiment. (Phys.Rev. D78 e072003 (2008))
D⁺→π^-π⁺K⁺ with ρ(770), K^*(890), f₀(980) and K₂^*(1430) resonances using data from the FOCUS experiment. (Phys.Lett. B601 10 (2004))
D_s⁺→π^-π⁺K⁺ with ρ(770), K^*(890), K^*(1410), K₀^*(1430) and ρ(1450) resonances using data from the FOCUS experiment. (Phys.Lett. B601 10 (2004))
D⁺→π^-π⁺π⁺ with ρ(770), σ(500), f₀(980), f₂(1270), f₀(1370) and ρ(1450) resonances using data from the E791 experiment. (Phys.Rev.Lett. 86 770 (2001))
D_s⁺→π^-π⁺π⁺ with ρ(770), f₀(980), f₂(1270), f₀(1370) and ρ(1450) resonances using data from the E791 experiment. (Phys.Rev.Lett. 86 765 (2001))
D⁰→π⁺π^-π⁰ with ρ(770), ρ(1450), ρ(1700), f₀(980), f₀(1370), f₀(1500), f₀(1720), f₂(1270) and σ(400) resonances using data from the BaBar experiment. (Phys.Rev.Lett. 99 251801 (2007))

The example below shows the decay D⁺→K^-π⁺π⁺:

Decay D+
  1.000    K- pi+ pi+     D_DALITZ;
Enddecay

EvtOmegaDalitz

The Dalitz plot amplitude for the decay ω→π⁺π^-π⁰.
The amplitude for this process is given by A = ε_μναβ p^μ_π⁺ p^ν_π^- p^α_π⁰ ε^β.

Decay omega
  1.000    pi+ pi- pi0    OMEGA_DALITZ;
Enddecay

EvtEtaDalitz

EvtPhsp

Generic phase space to n-bodies. All spins of particles in the initial and final state are averaged.

The example below shows the decay D⁰→K^*-π⁺π⁰π⁰:

Decay D0
  1.000    K*- pi+ pi0 pi0   PHSP;
Enddecay

EvtPi0Dalitz

EvtD0mixDalitz

EvtD0gammaDalitz

EvtPartWave

This model is similar to the EvtHelAmp model in that it allows any tow-body decay specified by the partial wave amplitudes. This model translates the partial wave amplitudes to helicity amplitudes using the Jacob Wick transformation. The partial wave amplitudes are complex numbers, specified as a magnitude and a phase. The amplitudes M_LS are sorted on the highest values of L and then on the highest value of S.

The example shows the decay B⁺→D^*0ρ⁺; occuring via a pure P-wave.

Decay B+
  1.000    anti-D*0 rho+     PARTWAVE 0.0 0.0 1.0 0.0 0.0 0.0;
Enddecay

EvtBToDDalitzCPK

EvtPhiDalitz

EvtBTo4piCP

EvtBTo3piCP

EvtBto2piCPiso

This model approaches the three B→ππ modes from the point of view of isospin analysis. It is applicable to both the two B⁰ (B⁰) modes, in which case it takes into account mixing, and to the B⁺ (B^-) mode, as all three modes should indeed be treated together in this approach. Following the conventions of Lipkin, Nir, Quinn, and Snyder (Phys. Rev. D44, 1454 (1991)), the various decay amplitudes can be written as follows:
A(B⁺→π⁺π⁰)≡A⁺⁰=3 A₂
A(B⁰→π⁺π^-)≡√1/2 A^+-=A₂ - A₀
A(B⁰→π⁰π⁰)≡A⁰⁰=2 A₂ + A₀
where A₂ is the amplitude for I_f = 2 states (tree only), and A₀, for I_f = 0 states (where both tree and penguin contribute). The model requires 10 parameters:

beta dm |A₂| argA₂ |A₂| argA₂ |A₀| argA₀ |A₀| argA₀

The first argument is the relevant CKM angle in radians. The next argument is the B⁰B⁰ mass difference (≈0.5×10¹²s^-1). The remaining 8 arguments are A₂, A₂, A₀ and A₀ expressed as their absolute values and phases.

Decay B0
  1.000 pi+ pi-  BT02PI_CP_ISO  beta dm 1.0 gamma 1.0 -gamma;
                                        1.0 gamma 1.0 -gamma;
Enddecay

Note that precise numerical estimates for the amplitudes are not available at the moment.

EvtCBTo3piP00

EvtCBTo3piMPP

EvtBToKpipiCP

EvtPto3P

EvtBtoKD3P

EvtMultibody

BARYONIC DECAYS

EvtBBScalar

B → baryon baryon scalar model based on the charmless three-body baryonic models, such as B → Λ p π, from Chua, Hou and Tsai: Phys. Rev. D66, 054004 (2002) and Eur. Phys. J. C29, 27 (2003)

Decay B-
  1.000 Sigma0 anti-p- pi0 B_TO_2BARYON_SCALAR;
Enddecay

EvtLambdaP_BarGamma

B‾ → Λ p γ according to Cheng and Yang, Phys Lett B 533, 271 (2002)

Decay B-
  1.000 Lambda0 anti-p- gamma B_TO_LAMBDA_PBAR_GAMMA;
Enddecay

EvtBHadronic

This is an (experimental) model for hadronic B decays using naive factorisation with form factors implemented in the EvtISGW2 model . It takes a list of baryons, with 2 integer parameters (JH and JW) to specify the number of vector currents. Not recommended for general use.

Decay B0
  1.0 P1 P2 ... PN BHADRONIC JH JW;
Enddecay