Time-dependent and flavour-tagged angular observables for Bs -> phi mumu

flavio/data/config.yml

@@ -150,6 +150,9 @@ implementation:
   Lambdab->Lambdall subleading effects at low q2: Lambdab->Lambdall deltaC7 polynomial
   Lambdab->Lambdall subleading effects at high q2: Lambdab->Lambdall deltaC9 shift
 
+  # B->Vll angular coefficient amplitude
+  B->Vll amplitude formalism: Helicity Amplitudes
+
 # set the PDF set used for different processes (at the moment only dileptons)
 PDF set:
   dileptons:

flavio/data/parameters_metadata.yml

@@ -1128,6 +1128,9 @@ DeltaGamma/Gamma_B0:
 DeltaGamma/Gamma_Bs:
   tex: $\Delta \Gamma_s/\Gamma_s$
   description: Relative decay width difference in the $B_s$ system
+DeltaM/Gamma_Bs:
+  tex: $\Delta m_s/\Gamma_s$
+  description: Mass difference in the $B^0_s$ relative to the $B^0_s$ decay width
 
 tau_Bc_SM:
   tex: $\tau_{B_c}^\text{SM}$

flavio/data/parameters_uncorrelated.yml

@@ -169,6 +169,7 @@ Gamma12_B0_a: 11.7(1.3)
 # experimental decay width differences
 DeltaGamma/Gamma_B0: -0.002(10) # HFAG Summer 2016
 DeltaGamma/Gamma_Bs: 0.129(9) # HFAG Summer 2016
+DeltaM/Gamma_Bs: 26.79(0.08) # HFAG Summer 2014 - https://arxiv.org/abs/1412.7515
 
 
 # Meson lifetime bag parameters

flavio/physics/bdecays/bvll/__init__.py

@@ -9,3 +9,4 @@
 from . import lfv
 from . import nonfactorizable
 from . import subleading
+from . import auxiliary_quantities

flavio/physics/bdecays/bvll/amplitudes.py

@@ -69,20 +69,27 @@ def get_subleading(q2, wc_obj, par_dict, B, V, cp_conjugate):
     else:
         return {}
 
-def helicity_amps(q2, ff, wc_obj, par, B, V, lep):
+def helicity_amps(q2, ff, wc_obj, par, B, V, lep, corrections=True):
     if q2 >= 8.7 and q2 < 14:
         warnings.warn("The predictions in the region of narrow charmonium resonances are not meaningful")
-    return add_dict((
-        helicity_amps_ff(q2, ff, wc_obj, par, B, V, lep, cp_conjugate=False),
-        get_ss(q2, wc_obj, par, B, V, cp_conjugate=False),
-        get_subleading(q2, wc_obj, par, B, V, cp_conjugate=False)
-        ))
+    if corrections:
+        return add_dict((
+            helicity_amps_ff(q2, ff, wc_obj, par, B, V, lep, cp_conjugate=False),
+            get_ss(q2, wc_obj, par, B, V, cp_conjugate=False),
+            get_subleading(q2, wc_obj, par, B, V, cp_conjugate=False)
+            ))
+    return helicity_amps_ff(q2, ff, wc_obj, par, B, V, lep, cp_conjugate=False)
 
-def helicity_amps_bar(q2, ff, wc_obj, par, B, V, lep):
+def helicity_amps_bar(q2, ff, wc_obj, par, B, V, lep, corrections=True):
     if q2 >= 8.7 and q2 < 14:
         warnings.warn("The predictions in the region of narrow charmonium resonances are not meaningful")
-    return add_dict((
-        helicity_amps_ff(q2, ff, wc_obj, par, B, V, lep, cp_conjugate=True),
-        get_ss(q2, wc_obj, par, B, V, cp_conjugate=True),
-        get_subleading(q2, wc_obj, par, B, V, cp_conjugate=True)
-        ))
+    if corrections:
+        return add_dict((
+            helicity_amps_ff(q2, ff, wc_obj, par, B, V, lep, cp_conjugate=True),
+            get_ss(q2, wc_obj, par, B, V, cp_conjugate=True),
+            get_subleading(q2, wc_obj, par, B, V, cp_conjugate=True)
+            ))
+    return helicity_amps_ff(q2, ff, wc_obj, par, B, V, lep, cp_conjugate=True)
+
+def get_coefficients(q2, ff, wc_obj, par, B, V, lep, ml, mB, mV, mb):
+    return AuxiliaryQuantity['B->Vll amplitude formalism'].prediction(par_dict=par, wc_obj=wc_obj, q2=q2, ff=ff, B=B, V=V, lep=lep, ml=ml, mB=mB, mV=mV, mb=mb)

flavio/physics/bdecays/bvll/auxiliary_quantities.py

@@ -0,0 +1,67 @@
+import cmath
+from flavio.classes import AuxiliaryQuantity, Implementation
+from .. import angular
+from . import amplitudes
+from ... import mesonmixing
+from . import amplitudes_transversity
+
+
+def angular_coefficients_helicity(wc_obj, par, q2, ff, B, V, lep, ml, mB, mV, mb, corrections=True):
+    """
+    Returns the angular coefficients J, J_bar, J_h, J_s for the B->Vll decay
+    in the helicity amplitude formalism.
+    """
+    h = amplitudes.helicity_amps(q2, ff, wc_obj, par, B, V, lep, corrections=corrections)
+    h_bar = amplitudes.helicity_amps_bar(q2, ff, wc_obj, par, B, V, lep, corrections=corrections)
+    J = angular.angularcoeffs_general_v(h, q2, mB, mV, mb, 0, ml, ml)
+    J_bar = angular.angularcoeffs_general_v(h_bar, q2, mB, mV, mb, 0, ml, ml)
+    h_tilde = h_bar.copy()
+    h_tilde[('pl', 'V')] = h_bar[('mi', 'V')]
+    h_tilde[('pl', 'A')] = h_bar[('mi', 'A')]
+    h_tilde[('mi', 'V')] = h_bar[('pl', 'V')]
+    h_tilde[('mi', 'A')] = h_bar[('pl', 'A')]
+    h_tilde['S'] = -h_bar['S']
+    q_over_p = mesonmixing.observables.q_over_p(wc_obj, par, B)
+    phi = cmath.phase(-q_over_p) # the phase of -q/p
+    J_h = angular.angularcoeffs_h_v(phi, h, h_tilde, q2, mB, mV, mb, 0, ml, ml)
+    J_s = angular.angularcoeffs_s_v(phi, h, h_tilde, q2, mB, mV, mb, 0, ml, ml)
+    return J, J_bar, J_h, J_s
+
+
+def angular_coefficients_transversity(wc_obj, par, q2, ff, B, V, lep, ml, mB, mV, mb):
+    """ 
+    Returns the angular coefficients J, J_bar, J_h, J_s for the B->Vll decay
+    in the transversity amplitude formalism.
+    """
+    A = amplitudes_transversity.transversity_amps(q2, ff, wc_obj, par, B, V, lep)
+    A_bar = amplitudes_transversity.transversity_amps_bar(q2, ff, wc_obj, par, B, V, lep)
+    J = amplitudes_transversity.angularcoeffs_general_transversity(A, q2, ml)
+    J_bar = amplitudes_transversity.angularcoeffs_general_transversity(A_bar, q2, ml)
+    A_tilde = A_bar.copy()
+    A_tilde['perp_L'] = -1 * A_bar['perp_L']
+    A_tilde['perp_R'] = -1 * A_bar['perp_R']
+    A_tilde['S'] = -1 * A_bar['S']  # Table 3 of https://arxiv.org/pdf/1502.05509
+    q_over_p = mesonmixing.observables.q_over_p(wc_obj, par, B)
+    J_h: dict[str | int, float] = amplitudes_transversity.angularcoeffs_h_transversity(A, A_tilde, q2, ml, q_over_p)
+    J_s: dict[str | int, float] = amplitudes_transversity.angularcoeffs_s_transversity(A, A_tilde, q2, ml, q_over_p)
+    return J, J_bar, J_h, J_s
+
+
+quantity = 'B->Vll amplitude formalism'
+a = AuxiliaryQuantity(name=quantity, arguments=['q2', 'ff', 'B', 'V', 'lep', 'ml', 'mB', 'mV', 'mb'])
+a.set_description('J, J_bar, J_h, J_s coefficients for the B->Vll decay amplitude.')
+
+iname = 'Helicity Amplitudes'
+i = Implementation(name=iname, quantity=quantity,
+                   function=lambda wc_obj, par, q2, ff, B, V, lep, ml, mB, mV, mb: angular_coefficients_helicity(wc_obj, par, q2, ff, B, V, lep, ml, mB, mV, mb, corrections=True))
+i.set_description("Angular coefficients from the helicity amplitude formalism, including all corrections from subleading effects and QCDF.")
+
+iname = 'Helicity Amplitudes (no corrections)'
+i = Implementation(name=iname, quantity=quantity,
+                   function=lambda wc_obj, par, q2, ff, B, V, lep, ml, mB, mV, mb: angular_coefficients_helicity(wc_obj, par, q2, ff, B, V, lep, ml, mB, mV, mb, corrections=False))
+i.set_description("Angular coefficients from the helicity amplitude formalism, without corrections from subleading effects and QCDF.")
+
+iname = 'Transversity Amplitudes (no corrections)'
+i = Implementation(name=iname, quantity=quantity,
+                   function=angular_coefficients_transversity)
+i.set_description("Angular coefficients from the transversity amplitude formalism, without corrections from subleading effects and QCDF.")