time_dep

class FlavourTagLinearPDF(*args, eta_name='eta', eta_mean=[0.5, 0.5], tag_name='tag_value', true_tag='tag', tag_eff=[1.0, 1.0], prefix='', **kwargs)

Bases: BaseAmplitudeModel

init_params(*args, **kwargs)

model_name = 'flavour_tag_linear'

pdf(data)

class FlavourTagPDF(*args, eta_name='eta', tag_name='tag_value', true_tag='tag', tag_eff=None, **kwargs)

Bases: BaseAmplitudeModel

model_name = 'flavour_tag'

pdf(data)

class TimeDepAHelicityDecay(*args, has_barrier_factor=True, l_list=None, barrier_factor_mass=False, has_ql=True, has_bprime=True, aligned=False, allow_cc=True, ls_list=None, barrier_factor_norm=False, params_polar=None, below_threshold=False, force_min_l=False, params_head=None, no_q0=False, helicity_inner_full=False, ls_selector=None, add_covariant_term=False, **kwargs)

Bases: HelicityDecay

model with g_ls which dependent on the tag in data.

\[\delta_{tag,1}\sqrt{1-A_{p}} g_{+}(t) g_{ls} + \delta_{tag,-1} \sqrt{1+A_{p}}\frac{p}{q} g_{-}(t) g_{ls}\]

get_ls_amp(data, data_p, **kwargs)

init_params(*args, **kwargs)

model_name = 'time_dep_a'

class TimeDepAbarHelicityDecay(*args, has_barrier_factor=True, l_list=None, barrier_factor_mass=False, has_ql=True, has_bprime=True, aligned=False, allow_cc=True, ls_list=None, barrier_factor_norm=False, params_polar=None, below_threshold=False, force_min_l=False, params_head=None, no_q0=False, helicity_inner_full=False, ls_selector=None, add_covariant_term=False, **kwargs)

Bases: HelicityDecay

model with g_ls (which is g_lsb in other model) which dependent on the tag in data.

\[\delta_{tag,1}\sqrt{1-A_{p}} \frac{q}{p} g_{-}(t) g_{ls} + \delta_{tag,-1} \sqrt{1+A_{p}} g_{+}(t) g_{ls}\]

get_ls_amp(data, data_p, **kwargs)

init_params(*args, **kwargs)

model_name = 'time_dep_abar'

class TimeDepCpAmplitudeModel(decay_group, **kwargs)

Bases: TimeDepParamsAmplitudeModel

Time dependent amplitude with self-CP related process, the Abar will calculate through \(\bar{A}(p_{+}, p_{-}, p_{0}) = A(-p_{-}, -p_{+}, -p_{0})\)

eval_A_Abar(data)

init_params(*args, **kwargs)

model_name = 'time_dep_cp'

class TimeDepCpConvAmplitudeModel(*args, t_min=0.0, **kwargs)

Bases: TimeDepParamsConvAmplitudeModel

Time dependent amplitude with self-CP related process, the Abar will calculate through \(\bar{A}(p_{+}, p_{-}, p_{0}) = A(-p_{-}, -p_{+}, -p_{0})\)

eval_A_Abar(data)

init_params(*args, **kwargs)

model_name = 'time_dep_cp_conv'

class TimeDepCpFSAmplitudeModel(decay_group, **kwargs)

Bases: TimeDepParamsFSAmplitudeModel

Flavour specific version of time_dep_cp.

eval_A_Abar(data)

init_params(*args, **kwargs)

model_name = 'time_dep_cp_fs'

class TimeDepFTPDF(decay_group, base_model={'model': 'default'}, taggers=[{'model': 'flavour_tag'}], use_p_pbar_time=True, **kwargs)

Bases: BaseAmplitudeModel

init_params(*args, **kwargs)

model_name = 'flavour_tag_mix'

pdf(data)

class TimeDepHelicityDecay(*args, has_barrier_factor=True, l_list=None, barrier_factor_mass=False, has_ql=True, has_bprime=True, aligned=False, allow_cc=True, ls_list=None, barrier_factor_norm=False, params_polar=None, below_threshold=False, force_min_l=False, params_head=None, no_q0=False, helicity_inner_full=False, ls_selector=None, add_covariant_term=False, **kwargs)

Bases: TimeDepParamsHelicityDecay

Implement time effect arxiv:0904.1869

\[|M(t)\rangle=g_{+}(t)|M\rangle + \frac{q}{p} g_{-}(t)|\bar{M}\rangle, |\bar{M}(t)\rangle=\frac{p}{q}g_{-}(t)|M\rangle + g_{+}(t)|\bar{M}\rangle,\]

\(|M\rangle\) will use g_ls and \(|\bar{M}\rangle\) will use g_lsb.

A factor \(\sqrt{1\\pm A_{p}}\) is add to include production asymmetry.

get_mix_g_ls(data, data_p, **kwargs)

init_params(*args, **kwargs)

model_name = 'time_dep_gls'

class TimeDepParamsAmplitudeModel(decay_group, **kwargs)

Bases: BaseAmplitudeModel

Implement time effect arxiv:0904.1869 Require to use decay model time_dep_params.

eval_A_Abar(data)

eval_A_Abar_time(data)

eval_P_Pbar_time(data)

init_params(*args, **kwargs)

model_name = 'time_dep_params'

pdf(data)

class TimeDepParamsConvAmplitudeModel(*args, t_min=0.0, **kwargs)

Bases: TimeDepParamsAmplitudeModel

\[|A(t)| = \int | A(\tau)|^2 \frac{1}{\sqrt{2\pi}\sigma} \exp(-\frac{(t-\tau)^2}{2\sigma^2}) d\tau\]

Convolve with a Gaussian function

eval_P_Pbar_time(data)

model_name = 'time_dep_params_conv'

class TimeDepParamsFSAmplitudeModel(decay_group, **kwargs)

Bases: TimeDepParamsAmplitudeModel

Flavour specific version of time_dep_params.

eval_A2_Abar2_time(data)

eval_P_Pbar_time(data)

model_name = 'time_dep_params_fs'

class TimeDepParamsHelicityDecay(*args, has_barrier_factor=True, l_list=None, barrier_factor_mass=False, has_ql=True, has_bprime=True, aligned=False, allow_cc=True, ls_list=None, barrier_factor_norm=False, params_polar=None, below_threshold=False, force_min_l=False, params_head=None, no_q0=False, helicity_inner_full=False, ls_selector=None, add_covariant_term=False, **kwargs)

Bases: HelicityDecay

model with g_ls and g_lsb which dependent on the tag in data.

get_g_ls_bar()

get_ls_amp(data, data_p, **kwargs)

get_mix_g_ls(data, data_p, **kwargs)

init_params()

model_name = 'time_dep_params'

cal_gp_gm(t, gamma, delta_m, delta_gamma)

\[g_{+}(t) = \left[\cosh\frac{\Delta\Gamma t}{4}\cos\frac{\Delta mt}{2}-i\sinh\frac{\Delta\Gamma t}{4}\sin\frac{\Delta mt}{2}\right]\exp\left[-\frac{\Gamma t}{2}\right],\]

\[g_{-}(t) = \left[-\sinh\frac{\Delta\Gamma t}{4}\cos\frac{\Delta mt}{2}+i\cosh\frac{\Delta\Gamma t}{4}\sin\frac{\Delta mt}{2}\right]\exp\left[-\frac{\Gamma t}{2}\right].\]

\(\exp\left[-i mt\right]\) is not included, since its has \(|A|=1\).

conv_exp_gaussian(t, sigma, a, left=0.0)

\[\int_{l}^{\infty} \exp(-a\tau) \frac{1}{\sqrt{2\pi}\sigma} \exp(-\frac{(t - \tau)^2}{2\sigma^2}) d \tau = \frac{\exp[- ax + \frac{a^2\sigma^2}{2}]}{2}\text{erfc}\frac{a\sigma^2 + l - x}{\sqrt{2}\sigma}\]

conv_exp_gaussian_complex(t, sigma, a, b, left=0.0)

\[\int_{l}^{\infty} \exp(-(a+bi) \tau) \frac{1}{\sqrt{2\pi}\sigma} \exp(-\frac{(t - \tau)^2}{2\sigma^2}) d \tau = \frac{\exp[- (a+bi)x + \frac{(a+bi)^2 \sigma^2}{2}]}{2}\text{erfc}\frac{(a+bi)\sigma^2 + l - x}{\sqrt{2}\sigma} = \exp(-\frac{x^2}{2s^2}) \text{Faddeeva}(i\frac{(a+bi)\sigma^2 + l - x}{\sqrt{2}\sigma} )\]

erfc(z)

erfc_xy(x, y)

fix_cp_params(config, r1, r2)

using the same paramters for A and Abar

only work for dalitz plot (all J=0 for initial and final particles)

fix_cp_params_aabar(config, r1, r2)

using the same paramters for A and Abar of time_dep_a and time_dep_abar

only work for dalitz plot (all J=0 for initial and final particles)