## EvtGen Models

This section details the list of EvtGen decay models (in progress). Original documentation by Ryd et al is available here.

## EvtGen ModelsThis section details the list of EvtGen decay models (in progress). Original documentation by Ryd et al is available here. ## SCALAR (S), VECTOR (V) and TENSOR (T) DECAYS## EvtPVVCPLHThis model decays a B ^{0}_{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 |G _{1+},
G_{0+} and G_{1−}, 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 B^{0}_{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 ## EvtSLNDecay 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 ## EvtSSDCPThis 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); Enddecaywhere 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|B^{0} > ± q|anti-B^{0} >.
The values Af and Abarf are the amplitudes for the decay of a B^{0} and a
anti-B^{0}, 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 B^{0}
and anti-B^{0}. 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 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; EnddecayNote that the sign of the amplitude for the anti-B ^{0} 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; EnddecayThese 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; EnddecayThis model can also be used for final states that are not CP eigenstates, such as B ^{0} → D^{*+} π^{−}
and B^{0} → 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; Enddecaywhere the Cabibbo-suppressed decay has a relative strong phase γ with respect to the Cabibbo-favoured decay. ## EvtSSD_DirectCPThis 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 ## EvtSSSCPA 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 10^{12}), while
cp is the CP of the final state (± 1).
Next is the amplitude of a B^{0} 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-B^{0} 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 ## EvtSSSCPpngThis 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:
beta gamma delta dm cp |A ^{12}); cp is the CP of the final state (±
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 ## EvtSSSCPTThis model implements CPT violation for a scalar (B ^{0})
particle decaying into two scalars. It requires 8 parameters, which are:
angle dm |A| argA |barA| argbarA |D| argD; The amplitude for the B^{0} 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-B^{0} 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 10^{12}).
Next is the amplitude of a B^{0} 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-B^{0} 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 ## EvtSTSThis model decays a scalar meson to a tensor and a scalar. This example decays the B ^{+} meson to
D_{2}^{*0} π^{+}:
Decay B+ 1.000 D_2*0 pi+ STS; Enddecay ## EvtSTSCPA 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; The first argument is the relevant CKM angle in radians. The second argument is the mass difference in hbar/s (approx 0.5 x 10^{12}), while
cp is the CP of the final state (± 1).
Next is the amplitude of a B^{0} 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-B^{0} 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 B^{0} meson to a_{2}^{0} π^{0}:
Decay B0 1.000 a_20 pi0 STS_CP alpha dm 1 1.0 0.0 1.0 0.0; Enddecay ## EvtSVPA 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 ## EvtSVPHelAmpThe 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 ## EvtSVPCPThis 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 10^{12}), while
cp is the CP of the final state (± 1).
Next is the amplitude of a B^{0} 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-B^{0} 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 Decay B0 1.0 K*0 gamma SVP_CP beta dm 1 0.03 0.0 0.999 0.0; Enddecay ## EvtSVSModel for the decay of a scalar particle to a vector and scalar. Decay B0 1.00 rho+ pi0 SVS; Enddecay ## EvtSVSCPDecay 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 10^{12}), while
cp is the CP of the final state (± 1).
Next is the amplitude of a B^{0} 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-B^{0} 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 B^{0} 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 ## EvtSVSNONCPEIGENThis 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 B ^{0} -
anti-B^{0} 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 B^{0} and anti-B^{0} 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
a_{1}^{+} π^{−} and
a_{1}^{−} π^{+}
final states with the appropriate number of B^{0} and
anti-B^{0} 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 ## EvtSVSCPLHDecay of a neutral B meson to a scalar and a vector CP eigenstate, e.g. B ^{0} → J/ψ K_{S}. The first argument is the
B^{0} − anti-B^{0} 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 B^{0} and anti-B^{0} 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 ## EvtSVSCPisoThis 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 B ^{0} (or anti-B^{0})
modes B^{0} → V^{+} S^{−},
B^{0} → V^{−} S^{+} and
B^{0} → V^{0} S^{0},
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^{+} S^{0} and
B^{+} → V^{0} 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^{+} S^{0}) ≡
√2A^{+0} = T^{+0} + 2 P_{1}
A(B ^{+} → V^{0} S^{+}) ≡
√2A^{0+} = T^{0+} − 2 P_{1}
A(B ^{0} → V^{+} S^{−}) ≡
A^{+−} = T^{+−} + P_{1} + P_{0}
A(B ^{0} → V^{−} S^{+}) ≡
A^{−+} = T^{−+} − P_{1} + P_{0}
A(B ^{0} → V^{0} S^{0}) ≡
2 A^{00} = T^{0+} + T^{+0} −
T^{−+} − T^{+−} − 2 P_{0}
where the amplitudes T^{ij} contain no penguin contributions, P_{1} is
penguin amplitude for the final I = 1 state, and P_{0} for the final I = 0 state.
The model's 27 parameter arguments are:
- beta = corresponding CKM angle
- dm = B
^{0}− anti-B^{0}$ mass difference (≈ 0.5 x 10^{12}(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 - |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 - |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 - |P
_{0}|, φ(P_{0}) = magnitude and phase of the corresponding amplitude - |Pbar
_{0}|, φ(Pbar_{0}) = magnitude and phase of the corresponding amplitude for the CP-conjugate process - |P
_{2}|, φ(P_{2}) = magnitude and phase of the corresponding amplitude - |Pbar
_{2}|, φ(Pbar_{2}) = magnitude and phase of the corresponding amplitude for the CP-conjugate process.
^{0} meson to a_{1}^{−}
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 ## EvtSVVHelAmpA 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 _{+}, H_{0} 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 ## EvtSVVHelCPMixThis 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 _{+}, H_{0}, 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 ## EvtSVVNONCPEIGENThis 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 B ^{0} − anti-B^{0} 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 B^{0} and anti-B^{0} 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^{*±} ρ^{∓}
final states with the appropriate number of B^{0} and anti-B^{0} 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 ## EvtSVVCPThis 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 |G ^{0} − anti-B^{0} mass difference
in hbar/s (approximately 0.5 x 10^{12}).
The next argument is the parameter η and
is either +1 or −1. The last six arguments are G_{1+},
G_{0+} and G_{1−}, 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 B^{0} 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 ## EvtSVVCPLHPlease 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 10^{12}).
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 G_{1+},
G_{0+} and G_{1−}, 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 ## EvtTSSModel for the decay of a tensor particle to two scalars, e.g. D _{2}^{*0} → D^{0} π^{0}:
Decay D_2*0 1.000 D0 pi0 TSS; Enddecay ## EvtTVPA 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 ## EvtTVSPwaveThe 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 D_{2}^{*0} → D^{*0} π^{0},
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 ## EvtVSSDecays a vector particle into two scalars, generating the correct angular distributions. The amplitude is given by A = ε ^{μ}v_{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 ## EvtVSSMixDecays a vector particle into two scalars and generates the correct angular and time distributions for the particles in the decay Υ(4S) → B ^{0} anti-B^{0}.
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 B^{0} anti-B^{0} 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; EnddecayThe 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 B ^{0} anti-B^{0}-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) → B Define dm 0.474e12 Decay Upsilon(4S) 1.0 B0 anti-B0 VSS_BMIX dm; Enddecayto 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; Enddecayand 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; EnddecayFinally, 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; Enddecaygenerates 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. ## EvtVSPPwaveThe 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} →
D^{0} γ
Decay D*0 1.000 D0 gamma VSP_PWAVE; Enddecay ## EvtVVPVector → Vector photon, for example χ_{1} → 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; EnddecayThis model requires 8 parameters, which should be used to denote polarisation components for the daughters, but they are not actually used in the model! ## EvtVVSPwaveThe 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 a _{1}^{0} 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 ## SEMILEPTONIC DECAYS## EvtISGWThis 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 ## EvtISGW2This 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 ## EvtMelikhovSemileptonic 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; EnddecayThe last integer (1 to 4) specifies which form factor parameters are to be used (see table 4 in the paper). ## EvtSLPoleImplements semileptonic decays according to a pole-form parametrisation F = F(0)/[1 + a q ^{2}/M^{2} + b
q^{4}/M^{4}]^{p}
where M is the mass of the parent meson (in GeV/c ^{2}).
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; EnddecayThe 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 ## EvtPropSLPoleUses 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 ## EvtSLBKPoleImplements 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; EnddecayHere, 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/c ^{2}).
For vector (tensor) mesons, 8 (16) parameters are required.
## EvtHQETA 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 ρ^{2} (linear
form factor slope) and the form factor ratios R_{1} and R_{2},
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 ## EvtHQET2A description of the B → D^{*} l ν decay using the HQET dispersive relation
model.
The arguments are the form factor slope ρ^{2} and the form factor
ratios R_{1} and R_{2}.
Decay B0 1.0 D*- e+ nu_e HQET2 1.35 1.3 0.8; Enddecay ## EvtGoityRobertsModel 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 ## EvtFlatQ2B → X _{u} l ν with flat q^{2} distribution
Decay B- 0.5000 eta e- anti-nu_e FLATQ2; 0.5000 eta mu- anti-nu_mu FLATQ2; Enddecay ## LEPTONIC DECAYS## EvtTauHadnuImplementation 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; EnddecayModel 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/c ^{2}.
## EvtTauVectornuVector 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 ## DALTZ PLOT/TWO BODY/MULTI-BODY DECAYS## EvtGenericDalitzImplements 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> ## EvtDDalitzModels 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
^{+}→K^{0}π^{+}π^{0}with ρ^{+}and K^{*0}resonances using data from the MarkIII experiment. (Phys.Lett. B196, 107 (1987)) -
D
^{0}→K^{0}π^{+}π^{-}with K^{*}(892), K_{0}^{*}(1430), K_{2}^{*}(1430), K^{*}(1680), ρ(892), ω(782), f_{0}(980), f_{0}(1370) and f_{2}(1270) resonances using data from the E691 experiment. (Phys.Rev. D48 56 (1993)) -
D
^{0}→K^{-}π^{+}π^{0}with ρ, K^{*0}, K^{*-}, K_{0}(1430)^{-}, K_{0}(1430), ρ(1700) and K^{*}(1680)^{-}using data from the E691 experiment. (Phys.Rev. D48 56 (1993)) -
D
^{0}→K^{0}K^{+}K^{-}with φ, a_{0}(980) and f_{0}(980) resonances using data from the BaBar experiment. (arXiv:hep-ex/0207089) -
D
_{s}^{+}→K^{-}K^{+}π^{+}with K^{*}(892), K_{0}^{*}(1430), f_{0}(980), φ(1020), f_{0}(1370) and f_{0}(1710) resonances using data from the BaBar experiment. (arXiv:1011.4190) -
D
^{+}→K^{-}K^{+}π^{+}with K^{*}(892), K_{0}^{*}(1430), φ(1020), a_{0}(1450), φ(1680) and K_{2}^{*}(1430) resonances using data from the CLEO experiment. (Phys.Rev. D78 e072003 (2008)) -
D
^{+}→π^{-}π^{+}K^{+}with ρ(770), K^{*}(890), f_{0}(980) and K_{2}^{*}(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), K_{0}^{*}(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), f_{0}(980), f_{2}(1270), f_{0}(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), f_{0}(980), f_{2}(1270), f_{0}(1370) and ρ(1450) resonances using data from the E791 experiment. (Phys.Rev.Lett. 86 765 (2001)) -
D
^{0}→π^{+}π^{-}π^{0}with ρ(770), ρ(1450), ρ(1700), f_{0}(980), f_{0}(1370), f_{0}(1500), f_{0}(1720), f_{2}(1270) and σ(400) resonances using data from the BaBar experiment. (Phys.Rev.Lett. 99 251801 (2007))
^{+}→K^{-}π^{+}π^{+}:
Decay D+ 1.000 K- pi+ pi+ D_DALITZ; Enddecay ## EvtOmegaDalitzThe Dalitz plot amplitude for the decay ω→π ^{+}π^{-}π^{0}.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 ## EvtPhspGeneric phase space to n-bodies. All spins of particles in the initial and final state are averaged. The example below shows the decay D ^{0}→K^{*-}π^{+}π^{0}π^{0}:
Decay D0 1.000 K*- pi+ pi0 pi0 PHSP; Enddecay ## EvtPartWaveThis 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^{*0}ρ^{+}; 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 ## EvtBto2piCPisoThis model approaches the three B→ππ modes from the point of view of isospin analysis. It is applicable to both the two B ^{0} (B^{0}) 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^{+}π^{0})≡A^{+0}=3 A_{2}A(B ^{0}→π^{+}π^{-})≡√1/2 A^{+-}=A_{2} - A_{0}A(B ^{0}→π^{0}π^{0})≡A^{00}=2 A_{2} + A_{0}where A _{2} is the amplitude for I_{f} = 2 states (tree only), and A_{0}, for I_{f} = 0 states (where both tree and penguin contribute).
The model requires 10 parameters:
beta dm |A ^{0}B^{0} mass difference (≈0.5×10^{12}s^{-1}). The remaining 8 arguments are A_{2}, A_{2}, A_{0} and A_{0} 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; EnddecayNote that precise numerical estimates for the amplitudes are not available at the moment. ## BARYONIC DECAYS## EvtBBScalarB → 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_BarGammaB‾ → 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 ## EvtBHadronicThis 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 |