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B Decays — Introduction and Overview

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B Decays — Introduction and Overview / CERN-TH.716e/94 February 1994 >¢~¤°5Lr/1/I B Decays — Introduction and Overview A. Ali*) Theory Division, CERN CH—1211 Geneva 23, Switzerland llllllilxillxnlilllll ¤\\\l\\\\\\ P QQBE To be published in B Decays (Q"'! Edition}, World Scientific Publishers, Singapore (editor: S. Stone} (1.994}. CERN-TH.7168/94 On leave of absence from DESY, Hamburg, FRG. OCR Output OCR OutputOCR OutputB Decays — lntroduction and Overview Ahmed Ali Theory Division, CERN CH-1211 Geneva 23, Switzerland Abstract This article gives an introduction and overview of B physics. It discusses the Kobayashi-Maskawa generalization of the Cabibbo—GIM matrix for flavour mixing to incorporate CP violation in the standard model (SM) of electroweak interactions, thereby postulating the existence of the b and t quarks. The dis covery of the T family of resonances by the Columbia-Fermilab-Stony Brook collaboration, in 1977, and its subsequent confirmation at DORIS II and later at CESR are reviewed. The bulk of the article is, however, devoted to the physics of B decays, which provide an almost ideal ground for testing QCD, involving both its perturbative and non—perturbative aspects. The rapport be tween current experiments and theoretical estimates obtained from frameworks embedded in QCD with varying degree of rigour is quantified. The main thrust of this review is in estimating the CKM matrix elements from B decays, which determine five of the nine matrix elements. This is then combined with the constraints from the CP-violation parameter \c|, in order to provide a profile of the CKM unitarity triangle. The interest in pursuing B physics at the ongoing and future experimental facilities is emphasized, in particular in rare B decays and CP violation, which will provide precision tests of the SM in the quark sector or perhaps indicate the existence of non-SM physics. 1. Weak-coupling Lagrangian for the b Quark and the CKM Matrix The Lagrangian density of the standard model for electroweak interactions (hence forth called SM) can be symbolically written asl C=£(f»W»B)+£(f,@)+£(WB»@)·V(‘I’) (I) OCR Output "On leave of absence from DESY, Hamburg, FRG. where the symbols f, W, B and <I> represent fermions (leptons and quarks), S U (2) L gauge bosons, WL, U (1)y gauge boson, Bu and the Higgs doublet field, respectively. The SM particle content together with the (weak) isospin properties of the basic quanta are given below, where we have assumed that there are three families of lep tons and quarks. Fermions L€pt¤¤S=(I/°) , (V") · , L(VT) L6 ifL, T <¤R,uR,m uarks:t <;)L(E); , b; uR,dR,cR,. <)L Gauge bosons WuZW,} z W,} BN Scalars .. + q»:,,q>+=,(j;) (j,) (2) The various terms in the SM Lagrangian can be written by demanding S U (2) L ®U(1) gauge invariance, lepton-quark universality, and family—independence of the elec troweak interactions. Since the SM Lagrangian is given in any standard textbook on electroweak interactions;) we shall not reproduce it here. The main interest in B physics lies in the study of the first two terms in (1) involving fermions, gauge bosons and the Higgs fields, in particular flavour-changing transitions. In order to appreciate how flavour-changing transitions emerge in the SM, it is worth while to write the first two terms in (1) explicitly. The interactions between the fermions and gauge bosons has the form: cw, W, B> = Z{?£10li+i§i1Z>’1§r+ ·z21pq2}+ Z @2210 nz, <3>OCR Output j=1 {:1 where j is the family index, li:( I;) llL ’*:€R’ qi: ¤‘U*¢:“R= q?¥=“R¤· L 10 E DMZ 1D' 5 DNS . Du = 8), —·— Zg '° Wu ·—Y (5Zg1Bu, DL Z Gb · i91frBu» (4) where gl and gg are, respectively, the U (1)y and SU(2)L coupling constants, 0** (cz = 1,2,3) are the (weak) isospin Pauli matrices, and the Gell—Mann — Nishijima formula Q = I3 + Y defines the (weak) hypercharge of the quarks and leptons. The interaction term L( f, gb) involving the fermions and the Higgs fields has the Yukawa form £(f7‘I’) = (UM), [ZW}; ]=1 + Z (*4,)<2‘i<1>¤’z+ (,, j,k=1 <hq>jk<2i<1>°d’;.}, <5> where QC _ ' * _ " ZU2¢¢0* _¢" - s with both <I> and <1>° transforming as a (weak) isospin doublet. The hypercharge of the Higgs fields can be written by inspection. The Yukawa coupling constants (h;)j, (hq) jk and (h'q),k are arbitrary complex numbers and each term in (5) is independently SU(2)L ® U(1)y invariant due to the fact that the SU(2)L acts only on ZL and QL and on the Higgs doublet <I> and <I>°, whose products are S U (2) scalars. After spontaneous symmetry breaking S U (2) L ® U (1)y —> U (1)EM, which pre serves the symmetry under U (1) electromagnetism, the gauge bosons, fermions and the neutral scalar field gb acquire non-zero masses through the Higgs mechanism V(¢) = M2I¢|2 + »\|¢|4; #2 < 0 ig) > 0, (6) with V(cb)m,,, at |<b| = v/(/5 = (/—p2/2/\, where v is the neutral—Higgs vacuum expectation value. Making the Higgs transformation gb —> gb + v in (5), one finds (¢ is the physical Higgs scalar with mi = 2}\v2): - 5(f,SSB ¢)= E:(mj)zZi]iq1 1 (y)+ i J=1 · -· Z {(mjk)U ituiiz + (mjk)1;1 ) (g)didfz1+ OCR Output b+ h- ¢·» (7) j,k=1 (mj); (hi): +1, (m1k)U (h'1)jk #3, (m1k)p (h’q)jk (8) Since in the SM there are no right—handed fields ui? = 1,2,3), the neutrinos ui remain massless and the charged lepton mass matrix is diagonal. Hence, in the SM there are no family—changing leptonic interactions — an aspect that will soon come under experimental scrutiny from the ongoing and planned experiments dedicated to the neutrino mass and oscillation measurements. In (8), (mjk)U and (mjk)D are the (3 >< 3) quark mass matrices for the up- and down—type quarks, respectively. In order to write the Lagrangian in terms of the quark mass eigenstates one has to diagonalize the mass matrices (mjk)U and (m,k)D. This can be done with the help of two unitary matrices. It is customary to denote them by Vfp and VI? l (likewise for the down type quarks): Vf°'°mUV§p` E (md,,,g_)U E Diag. (mu ,mc ,mt), (9) _ _um ·down VgmDVR ° li : (md,ag_)D : Dzag. (md ,m, ,mb), with Vfpl Vfp = 1, etc. Concentrating on the up—type quarks in (7) one can do the following manipulation : T "’”pl i2LmUuR = GLVITPV£mUV,QV,§‘puR (10) = ULVE" (md¢¤g.)U (V£"~R)» which shows that the physical quark fields (mass eigenstates) are: tim : vg~¤uL : vg? CLUL it qu) Ph dL U5 : VId0wndL = Vrdcwn dLSL br Likewise, ugysh = Vffpug, d};”’}h = V}§°"’"dR. Onecan now rewrite the term £( f, (D) hin the SM Lagrangian in terms of (u},)Phy’ and (di)Phy’, obtaining SSB - · Elf, Q) Z _ Q51+ 6 ZE {:1mqaqiqi + ZJ j=1 OCRmlaljlj Output v (12) where it is now understood that q1 = g (uliy+hs ulgys)h = u ctc., and we have dropped the superscript on the quark fields. The identification of the parameters mh, mm with the lepton and quark masses is now evident. In addition, the SM Lagrangian has speciiied the Higgs-fermion (Q5 f f ) Yukawa couplings and their Lorentz structure, as well as their C, P, and CP properties. All these symmetries are separately conserved in .C( f, SSBq$)and the Higgs-fermion Yukawa couplings are manifestly diagonal in flavour space. It should be emphasized that this is a consequence of the SM choice of a single doublet Higgs field since, otherwise, flavour-changing neutral—current (FCNC) transitions in the Higgs sector would be allowed. In general, generating fermion masses with their known values and keeping the FCNC transitions at an acceptable phenomenological level is a highly non—trivial problem. Finally, one can carry through the transformation (10) in the part of the SM Lagrangian describing the fermion-gauge boson couplings, L( f, W,B). Written in terms of the physical boson (W}, ZE, Au) and fermion fields, it is easy to show that the neutral current (NC) part of £( f, W, B) is manifestly flavour-diagonal. Thus, all flavour—changing transitions in the SM are confined to the the charged current (CC) sector. Denoting the quarks and leptons by f,(i : 1...6), the neutral current in the SM is given by: J:/YC ([3L —QS1H20w)i+€AuQg]fg. The electroweak mixing angle in Jivc, denoted by OW, has its origin in the diag onalization of the gauge boson mass matrix, and it has the the usual definition cos HW = g2/\/gf + gg, with the electric charge defined as e E gz sin OW. It is easy to check that the neutral current interaction induced by the Z exchange violates P and C but conserves CP. The electromagnetic interaction conserves, of course, all three C, P, and CP separately. We now proceed to discuss the texture of the charged current JEC, which is to be derived from the .C( f, W,B) part of the SM Lagrangian using the mass eigen states. The CC couplings in the SM involve only the left-handed fermions qi and I},. Concentrating on the hadronic (quark) part of LCC, one can now do the following manipulations: LCC : —-——°·* ~w+d* ii. 2\/§SlD26W ULSY ut L + C uv‘piv‘wv°“"lv¤~md+gggw,j§gg h.c. y M .._.._...C 3 -PhiW+ Vu? I _-’ 2x/Zsinww (UL l il down?” i L )VL Ph (dLij +11j us>C (14) OCR Output Thus, the charged current JS,C which couples to the W*, is JS=C (&»E»{)L'7uVCKMd ( ) b8» L (15) where we have again dropped the superscript and VCKM E V£LpV1;isl0wnl a (3 >< 3) unitary matrix in the flavour space, first written down by Kobayashi and Maskawa in 19733.
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