Working Group 6 Subtopic: Monte Carlo Event Generators

- B decays - general CP asymmetry - tables - other generators -

List of Questions

1. Semileptonic B Decays

Which Monte Carlo generator faithfully reproduces primary and secondary lepton spectra?

Which models describe best the dominant exclusive b -> c decays (D l nu, D* l nu, ...)?

Which models describe best the dominant exclusive b -> u decays (pi l nu, rho l nu, eta l nu, omega l nu, ...)?

What is known on higher resonances, which feed down into rho l nu, pi l nu...?

2. Inclusive and Exclusive Hadronic Decays

How are inclusive B decays described?

Are fragmentation models adequate to predict multiplicities and spectra?

How should b -> s g be simulated?

Are multiplicities of charged particles, photons, pions, kaons, protons, Lambdas... ok?

Are inclusive spectra of stable final particles faithfully reproduced?

Are strangeness-flavour correlations (K, Lambda) ok?

Are D and D_s meson properties ok: spectra, flavour correlation?

What branching ratios should be used (from experiment/theory)?

3. Models for Rare B Decays

Optimization of Monte Carlo Event Generators

1. Parameters for Event Generators

The particle data table will be used in future to generate specific tables for event generators EvtGen and JETSET. It is also the input to the PDT class used in BABAR reconstruction and analysis.

The (not-yet-existing) decay table will be used for event generators EvtGen and JETSET, and derived from the present one for JETSET.

The table from the JETSET tuning (note 174, 1994) used for the BABAR TDR is this. The comparison with data can be seen from this postscript file.

The table corresponding to a unmodified JETSET depends on the subversion, so always feed it a table! That is what I got from JETSET 7.408, and it corresponds to these performance plots.

The most recent update for JETSET is here. Both tables allow only one B to decay (The "3"s in the table, to study tagging properties). The comparison with data can be seen from this postscript file.

The same comparison has been made with EvtGen V00-03-04 (corresponding to the current production version) with a decay table updated to the CLEO tuning by Peter Kim and the modified JETSET tables "new2" in this postscript file.

This is EvtGen V00-04-67.

This is EvtGen V00-04-71? to be tagged.

For details on the models for B decays see (3) below.

2. Oscillation and CP asymmetries

are covered by the BABAR MC generator interface beget

Note, that most studies can be comfortably split into separate

MC acceptance studies,
MC background studies,
tagging studies, and
CP fitting tests.

without the need to impose time-dependent asymmetries for the first three steps.

A general formalism can be implemented using the following amplitude:

A = Ph1 * exp(-1/2(T1+T2) * [C cos( x(T1-T2)/2 ) 
    + i * S * sin( x(T1-T2)/2 )]

with 

 Ph1 = a common phase, 

 T1 = t1/tau, T2 = t2/tau the scaled lifetimes of the two B mesons

 x = 0.70 (B0 mixing parameter)

 C = A1 Abar2 - Abar1 A2
 S = q/p * Abar1 Abar2 - p/q * A1 A2 

 q/p = phase of(V_td^2 V*_tb^2)

 A1 = amplitude for B0 -> final state 1
 Abar1 = amplitude for anti-B0 -> final state 1
 A2 = amplitude for B0 -> final state 2
 Abar2 = amplitude for anti-B0 -> final state 2

These amplitudes may be in any formalism, i.e. Zemach, helicity etc. It is essential, however, that the correct CP sign is applied going from Ai to Abari.

The complex amplitude A (using |A|^2 as probability) will produce the correct behaviour for all cases, especially

mixing, cos(x Delta T) behaviour: both B decay into a flavour eigenstate, and two of the four decay amplitudes are just 0.
interference-of-oscillation-and-decay-CP-violation, sin(x Delta T) behaviour: on the tag side, one amplitude is 0, on the signal side, A and Abar are related by a sign, representing the eigenvalue of the CP eigenstate, and the interchange of V_xy <-> V*_xy for the CKM elements.
decay to two CP eigenstates (or B/Bbar common states): on both sides, A and Abar are related by a sign, representing the eigenvalue of the CP eigenstate, and the interchange of V_xy <-> V*_xy for the CKM elements.

more complicated cases, with sums of amplitudes (as used for gamma determination via direct CP violation) fit also into this scheme.

The EVTGEN amplitude formalism might be best suited to implement the general formalism.

Remarks:

the formula above uses two approximations: Delta Gamma = 0 and |q/p|=1. Both are good for B0 at the 1% level, but not for B_s.

we may not want to simulate all the details contained in the above formula, since it will become soon very time consuming, walking through several generations of a decay chain until the amplitude can finally be computed! Cases like (3) are certainly rare enough to make the difference between incoherent and coherent treatment invisible in tagging and background studies, and we may want to simulate the full coherence only in studies associated with searching for such effects.

3. B decays

As default event generator for Y(4S) and B decays, we use the Lund program JETSET version 7.4.

A tuned decay table for this program is the beget default. An update is in progress (download it for testing; see section (1) above).

References:
BABAR note 174.

A new generator EvtGen specialized for B decays has been developed in C++ and is currently improved by Anders Ryd.

Quoting Anders: "This project was originated as an attempt to generate semileptonic decays of B-mesons to P-wave charm mesons with the correct angular distributions of the decay of the charm meson. The project grew with the implementation of the ISGW2 model for semileptonic decay.

The first goal of this project is to provide a generator of semileptonic decays of B-mesons for physics studies in BaBar. However, the generator has convenient tools for generating other decays as well and in the area of CP violation the decays of B->pi pi and B->Psi K* has been implemented."

Documentation: README file, EvtGen page.

A decay table for the EvtGen/JETSET combo can soon be found here.

3.1 Matrix elements for semileptonic decays

the Lund default may be used for a "first look"

better event generators will be implemented in cooperation with group 4
ISGW is implemented in EvtGen.

radiative photons (for e): Photos may be used, not yet implemented.

3.2 Multihadron production from spectator, annihilation and penguin processes

multi-hadron final states are produced via "fragmentation" of 4 initial quarks, using increased multiplicity parameters.

missing fractions of two-body decays are in the decay table. In future, we will use the EvtGen strategy to have the total two-body BR in the decay table, and reject two-body channels if they are produced via inclusive quark modes.