Module flavio.physics.bdecays.formfactors.b_v.sse

Functions

def ff(process, q2, par, n=2)

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def ff(process, q2, par, n=2):
    r"""Central value of $B\to V$ form factors in the lattice convention
    and simplified series expansion (SSE) parametrization.

    The lattice convention defines the form factors
    $A_0$, $A_1$, $A_{12}$, $V$, $T_1$, $T_2$, $T_{23}$.

    The SSE defines
    $$F_i(q^2) = P_i(q^2) \sum_k a_k^i \,z(q^2)^k$$
    where $P_i(q^2)=(1-q^2/m_{R,i}^2)^{-1}$ is a simple pole.
    """
    pd = process_dict[process]
    mres = mres_bsz[pd['q']]
    mB = par['m_'+pd['B']]
    mV = par['m_'+pd['V']]
    ff = {}
    for i in ["A0","A1","A12","V","T1","T2","T23"]:
        a = [ par[process + ' SSE ' + i.lower() + '_' + 'a' + str(j)] for j in range(n) ]
        ff[i] = pole(i, mres, q2)*np.dot(a, zs(mB, mV, q2, t0=12.)[:n])
    return ff

Central value of $B\to V$ form factors in the lattice convention and simplified series expansion (SSE) parametrization.

The lattice convention defines the form factors $A_0$, $A_1$, $A_{12}$, $V$, $T_1$, $T_2$, $T_{23}$.

The SSE defines $$F_i(q^2) = P_i(q^2) \sum_k a_k^i \,z(q^2)^k$$ where $P_i(q^2)=(1-q^2/m_{R,i}^2)^{-1}$ is a simple pole.

def pole(ff, mres, q2)

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def pole(ff,mres,q2):
    mresdict = {'A0': 0,'A1': 2,'A12': 2,'V': 1,'T1': 1,'T2': 2,'T23': 2}
    m = mres[mresdict[ff]]
    return 1/(1-q2/m**2)

def zs(mB, mV, q2, t0)

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def zs(mB, mV, q2, t0):
    zq2 = z(mB, mV, q2, t0)
    return np.array([1, zq2, zq2**2])