CKM Status In this lecture, we study the results summarized in this plot. February 3, 2020 Sridhara Dasu, CKM Status 1 Quark Mixing : Unitarity Mass eigen states Weak eigen states Quark Mixing In Standard Model CP violation is due to single non-zero complex phase of this matrix Cabibbo - Kobayashi - Maskawa (CKM) d Vud Vus Vub d s = V V V
cs cb s cd b V V V td ts tb b * ub ud * cd Agreement amongst various measurements of angles and sides is crucial test of the Standard Model * td Unitary matrix V V + VcbV + VtbV = 0 |Vub / Vcb|
bul/bcl February 3, 2020 All but Ms (CDF/D0) are accessible to BaBar |Vtd / Vts| Bd,s mixing: Md / Ms BK Sridhara Dasu, CKM Status Clean experiment/theory 2 The Standard Model CKM Matrix Mass Eigenstate s Weak Eigenstate s Quark Mixing VCKM Vud = Vcd Vtd
Vus Vcs Vts Vub Vcb Vtb CKM Matrix Complex matrix described by 3 real parameters + 1 complex phase Wolfenstein parameterization: Exploit hierarchy in magnitudes by using Cabibbo angle, =sinsinc VCKM 1 2 / 2 1 2 / 2 A 3 (1 i ) A 2 A 3 ( i ) A 2
1 A, , are O(1) CP Violation: February 3, 2020 =0 no CPV from SM Sridhara Dasu, CKM Status 3 Unitarity Triangle Choice of parameters: =( 1 2 / 2 ) , A, and = (1 2 / 2 ) Unitarity : 1 + R t + R u =0 At the 1% level: Vus = V us =si c =0.2205 0.0018 At te 2% eve: V c
A = V c / 2 A =0.83 0.06 |V u | d |V td | - pe (, ) Ru Rt (0, 0) (1, 0) Vud Vub 2 2 i Ru = + e
Vcd Vcb Vtd Vtb 2 2 i Rt = ( 1 ) + e Vcd Vcb * =arg Vub , =p February 3, 2020 Sridhara Dasu, CKM Status 4 Weak B Decays Access to CKM Parameters b
Wt Rare Effective February 3, 2020 s,d Sridhara Dasu, CKM Status 5 B Mixing Neutral B mesons can turn into their anti-particle BsH = 12 (| Bs + | Bs ) =CP odd BsL = 12 (| Bs | Bs ) =CP even February 3, 2020 Sridhara Dasu, CKM Status 6 B Mass & Lifetime Difference Second order weak diagram gives non-zero matrix element In basis have a non-diagonal Hamiltonian B H B
B B M H = * M 12 Recall Eigenstates are: M 12 i * M 2 12 12 | BsH = 12 (| Bs+ | Bs ) Vt VW*tsb s b0s Buc, t,uc0sB + W b
Vts Vtbs* | BsL = 12 (| Bs| Bs ) 64 7 48 m / 2 M H , L =M Re( M12 2i 12 ) H , L = 2 Im( M12 2i 12 ) 14 2 43 / 2 February 3, 2020 1 = 12 ( L + H ) t = L H Unlike the case of neutral K mesons, for B mesons M is significant but is negligible. Sridhara Dasu, CKM Status 7 B Mixing Neutral B mesons can turn into their anti-particle
In SM described by box diagrams measure |Vts(d)| ms(d) =sin [GF2mt2 F(mt2/mW2)/6p2] mBs(d)f2Bs(d)BBs(d)|Vts(d)V*tb|2 Oscill. Freq. February 3, 2020 From lattice O(30%) error Sridhara Dasu, CKM Status ~1 8 Bd & Bs Mixing Measurement of UT side yields measurement of with O(5%) theory error February 3, 2020 Sridhara Dasu, CKM Status
9 The Golden Channel February 3, 2020 Sridhara Dasu, CKM Status 10 Time Dependent Measurements February 3, 2020 Sridhara Dasu, CKM Status 11 The SLAC B-Factory Design Luminosity: 3 x 1033 cm-2 s-1 (Reached in 2001) Peak Luminosity: 9 x 1033 cm-2 s-1 (Reached in 2004) February 3, 2020 Sridhara Dasu, CKM Status
12 e+ e b b + e Signal: e (4S ) B B Continuum background: e+ e uu, dd , ss, cc, t +t February 3, 2020 Sridhara Dasu, CKM Status scont : sB ~ 4.3 : 1 13 BaBar , p0 and e ID p/K/p ID and KL ID RPC problems overcome Forward RPCs replaced (2002) Barrel RPCs LSTs (2004/6) February 3, 2020 Sridhara Dasu, CKM Status Charged Particle Tracking,
Vertex Reconstruction (t), Low momentum particle ID dE/dx 14 Four Main Themes in B Physics CP Violation in B decays Due to interference of mixing and decay amplitudes (indirect) Due to decay amplitude interference (direct) Searches for and studies of rare decays Sensitive to physics beyond the Standard Model B decay rate to rare final states CP violation of rare decays - can be very sensitive Precision determination of CKM matrix elements Need to significantly improve in order to determine whether observed CP violation is consistent with SM predictions Improving our understanding of B decays Feeds back into precision SM tests and measurements February 3, 2020 Sridhara Dasu, CKM Status 15 Sin2 Measurement (cc )KS0 (CP odd) modes (cc )KL0 (CP even) modes
B BA AB BAR AR Update for ICHEP04 B BA AB BAR AR BABAR PUB-04/038 sin2 =+0.722 0.040 0.023 (cc)K 0 +(cc)K 0 S L = A / A =0.950 0.0310.013 205f b 1 o pe k o 2 2 7 M BB pis 7 7 3 0 CPe ve ts (te d si) February 3, 2020 Sridhara Dasu, CKM Status 16 sin2 Comparison CP violation in B system is almost
consistent with Standard Model expectations Comparison of Tree and Gluonic penguin dominated decays provide new physics sensitivity Curiously gluonic penguin results are systematically low More data is needed to resolve experimental discrepancies Do electroweak penguin modes have anything to say? February 3, 2020 Sridhara Dasu, CKM Status 17 Electromagnetic Penguin Penguins used for understanding the B-mesons: Improves precision of Vub u,d b Wt
s,d Vts,Vtd B-meson mass Penguins used for measuring Vtd B[ B ( / )] Vtd * B[ B K ] Vts February 3, 2020 2 B-quark mass L( ) =M B ( ) 1 ( ) =p2 ( ) b-quark Fermi momentum Sridhara Dasu, CKM Status 18 Photon Spectrum Sum of exclusive method
Lepton tagged inclusive preliminary K* K* (4s) frame B rest frame February 3, 2020 Sridhara Dasu, CKM Status 19 Moments of Spectrum Penguins used for understanding the B-mesons: Improves precision of Vub First, Second moments of E hep-ex/0506043 B-meson mass
B-quark mass 88 M B B L( ) =M B ( ) 1 ( ) =p2 ( ) b-quark Fermi momentum First and second moments of the photon spectrum are used in heavy quark effective theory models. February 3, 2020 Sridhara Dasu, CKM Status 20 Shape Function HQ parametersdetermine shape function for Vub extraction Fit to the E spectrum in bs Belle+Babar Fit to the E moments of E spectrum - Babar Had and lept. moments in bcl Babar+others Fit to all moments Fit to bcl moments Fit to bs moments
CKM-05 |Vcb| : moments analyses have 1.52% precision! Vcb inclusive =(42.0 0.6exp 0.8 theo ) 10 3 Vcb exclusive =(40.2 2.1exp 1.8theo ) 103 February 3, 2020 Sridhara Dasu, CKM Status Belle bs spectrum fit 21 |Vub | The extraction of |Vub|from the measured partial BFs is not trivial Inclusive decays depend on measured shape function and OPE nonperturbative corrections free quark decay 2 d ~ V[u ,c ] b quark model + d (PS)
Method Cn n ( ) QCD mb 4.39 0.20 0.27 Inclusive, Belle only bs spectrum 5.08 0.47 0.48 February 3, 2020 n Vub(10-3) Inclusive, bcl & bs moments Indirectly, from CKM fit Average of Inclusive Determinations of |Vub|
3.53+00..22 21 Sridhara Dasu, CKM Status More work needed to resolve discrepancies 22 Standard Model Unitarity Tree Level sin2 Consistent with SM Progress requires Measurements of , Penguin pollution Further checks of sin2 Measure in penguins Measurement of sides Vub, Vtd Rare processes Hadronic uncertainty HeavyLight form factor calculation Radiative penguins are beginning to play an important role in constraining SM unitarity February 3, 2020
Sridhara Dasu, CKM Status 23 Two Lifetimes CP-odd fraction (t H) ~ 22% -1 s =0.47 +0.19 0.01 ps 0.24 t L =1.05+0.16 0.13 0.02 ps t H =2.07 +0.58 0.46 0.03ps + Recent D0: February 3, 2020 s =0.65+0.25 0.33 0.01 s t L =1.23+0.14 0.11 ps t H =1.52
+0.39 0.43 ps s =0.21+0.27 0.40 s Sridhara Dasu, CKM Status t SL =1.420.040.06 ps 24
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