[mesonmixing] Changed the sign convention for S_psiphi!

This is to better agree with the theory literature. Note that now
S_psiphi^flavio = -sin(phi_s)^LHCb,ATLAS,CMS
so that S_psiphi is positive in the SM.

flavio/physics/mesonmixing/observables.py

@@ -53,19 +53,19 @@ def amplitude_Bspsiphi(par):
     xi_c = ckm.xi('c', 'bs')(par) # V_cb V_cs*
     return xi_c
 
-def S(wc_obj, par, meson, amplitude):
+def S(wc_obj, par, meson, amplitude, etaCP):
     M12, G12 = get_M12_G12(wc_obj, par, meson)
     qp = common.q_over_p(M12, G12)
     A = amplitude(par)
     A_bar = amplitude(conjugate_par(par))
-    xi = qp * A / A_bar
-    return 2*xi.imag / ( 1 + abs(xi)**2 )
+    xi = etaCP * qp * A / A_bar
+    return -2*xi.imag / ( 1 + abs(xi)**2 )
 
 def S_BJpsiK(wc_obj, par):
-    return S(wc_obj, par, 'B0', amplitude_BJpsiK)
+    return S(wc_obj, par, 'B0', amplitude_BJpsiK, etaCP=-1)
 
 def S_Bspsiphi(wc_obj, par):
-    return S(wc_obj, par, 'Bs', amplitude_Bspsiphi)
+    return S(wc_obj, par, 'Bs', amplitude_Bspsiphi, etaCP=+1)
 
 
 # Observable and Prediction instances

flavio/physics/mesonmixing/test_mesonmixing.py

@@ -55,7 +55,7 @@ def test_bmixing(self):
         self.assertAlmostEqual(observables.a_fs(wc_obj, par, 'B0')/-4.7e-4, 1, places=0)
         self.assertAlmostEqual(observables.a_fs(wc_obj, par, 'Bs')/2.22e-5, 1, places=0)
         self.assertAlmostEqual(observables.S_BJpsiK(wc_obj, par), 0.73, places=1)
-        self.assertAlmostEqual(observables.S_Bspsiphi(wc_obj, par), asin(-0.038), places=2)
+        self.assertAlmostEqual(observables.S_Bspsiphi(wc_obj, par), asin(+0.038), places=2)
 
     def test_bmixing_classes(self):
         ps = 1e-12*s
@@ -66,7 +66,7 @@ def test_bmixing_classes(self):
         self.assertAlmostEqual(Observable.get_instance('a_fs_d').prediction_central(c, wc_obj)/-4.7e-4, 1, places=-1)
         self.assertAlmostEqual(Observable.get_instance('a_fs_s').prediction_central(c, wc_obj)/2.22e-5, 1, places=-1)
         self.assertAlmostEqual(Observable.get_instance('S_psiK').prediction_central(c, wc_obj), 0.73, places=-1)
-        self.assertAlmostEqual(Observable.get_instance('S_psiphi').prediction_central(c, wc_obj), asin(-0.038), places=-1)
+        self.assertAlmostEqual(Observable.get_instance('S_psiphi').prediction_central(c, wc_obj), asin(+0.038), places=-1)
 
     def test_running(self):
         c_in = np.array([ 0.20910694,  0.77740198,  0.54696337,  0.46407456,  0.42482153,