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Recent Developments in Beauty and Charm Physics. Achille Stocchi . (LAL-Orsay/IN2P3-CNRS And Universit é de Paris Sud P11) stocchi@lal.in2p3.fr. Plan of the lectures :. ≤30’. Historical introduction to the CKM matrix and CP Violation. The Standard Model in the fermion sector :

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## Recent Developments in Beauty and Charm Physics

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**Recent Developments**in Beauty and Charm Physics Achille Stocchi (LAL-Orsay/IN2P3-CNRS And Université de Paris Sud P11) stocchi@lal.in2p3.fr**Plan of the lectures :**≤30’ Historical introduction to the CKM matrix and CP Violation The Standard Model in the fermion sector : the CKM matrix and the CP violation. The unitarity Triangle ≥30’ ~1h30’ Measurements related to CKM parameters and CP violation Extraction of the Unitarity triangle parameters ~30’ What next… and New Physics from B physics.**1**Historical introduction to the CKM matrix and CP Violation**Fundamental role of strange particles in the development of**flavour physics. I use them to introduce flavour physics ~1950 The concept of flavour : strangeness discovery ~1955 Parity Violation in weak decay 1963 DS=1 vs DS=0 Cabibbo theory ~1960 K0-K0 mixing 1964 KL pp CP violation in weak decays 1970 KL mm FCNC / GIM mechanism**The Strangeness : the begin of a new era…not ended yet**• ~1947 : discovery of new particles (on cosmic rays) • K (~500 MeV) L (~1100 MeV) • Why are these particles strange ? • They are produced (always in pair) as copiously as the as thep • Their lifetime is ~10-10 s ! Production through strong interaction Decay through weak interaction • There should be a reason to inhibit the decay through strong interactions….. • Introduction of a new quantum number • Conserved in strong interaction processes • Not conserved on weak interaction processes Pais intuition (1952) The strangeness (additive quantum number)**“V particle”: particles that are produced**in pairs and thus leaves a ‘v’ trial in a bubble chamber picture Details: create a new quantum number, “strangeness“ which is conserved by the production process (pair production) however, the decay must violate “strangeness” if only weak force is “strangeness violating” then it is responsible for the decay process hence (relatively) long lifetime… • Observations: • High production cross-section • Long lifetime • Conclusion: • must always be produced in pairs!**qc : the Cabibbo angle**Cabibbo Theory : The quarks d e sinvolved in weak processes are « rotated » by an angle Couplings : u d GFcosqcu s GF sinqc nm DS=1 m+ Purely leptonic decays (e.g. muon decay) do not contain the Cabibbo factor: cosqcor sinqc W+ u d, s 1.2 10-8 s (~0.63) (~1) 2.6 10-8 s 8.5 e ne W GF2 sin2qc K- p0e-ne s u u u**But the theory predicts flavour changing neutral transition**: sd 1970 : Glashow, Iliopoulos et Maiani (GIM) proposed the introduction of a fourth quark : the quark c (of charge 2/3) : Term added to the neutral coupling The neutral current does not change flavour : absence of FCNC - A strangeness changing neutral current would produce contributions larger by several order of magnitude to for instance KLmm ?**Absence of FCNC. The neutral current changing the strangness**(DS=1) not observed u d s s e+ coupling su coupling sd e+ e e- Z0 W+ u u u u • K++ e+ e- • K+0 e- e More formally. If we write the weak charged current**The interaction comes from a gauge group. From the previous**page it seems to be clear that for the weak interactions the group is the weak isospin. s+ - are the matrices which increase(decrease) of one unity the weak isospin. But to form an algebra we also need s3 FCNC Absenceof FCNC**In 1969-70 Glashow, Iliopoulos, and Maiani (GIM) proposed a**solution to the to the K0®m+ m- rate puzzle. More on The GIM Mechanism The branching fraction for K0®m+ m- was expected to be small as the first order diagram is forbidden (no allowed W coupling). nm m+ m- m+ K0 forbidden K+ allowed W+ ??0 not a Z0 u d s s The 2nd order diagram (“box”) was calculated & was found to give a rate higher than the experimental measurement! with only u quark there is a ultraviolet divergence with amplitude µ sinqccosqc GIM proposed that a 4th quark existed and its coupling to the s and d quark was: s’ = scosq - dsinq The new quark would produce a second “box” diagram amplitude µ -sinqccosqc These two diagrams cancel out the divergence**It remains a non zero contribution (which is infrared**divergent) for momentum lower than the mc, which does not cancel out. The amount of cancellation depends on the mass of the new quark For mc=mu It would be A quark mass of »1.5GeV is necessary to get good agreement with the experimental data. First “evidence” for Charm quark! and the fact that mc is such that was not yet observed…**neutrondecay**Strange particles Predictions ! Charm sector The charm discovery in 1974 and the verification of these predictions have been a tremendous triumph of this picture and these predictions have been verified : cd are Cabibbo suppressed wrt c s transitions**1977 : b quark Discovery**9.5-10.5 GeV : The series of Excess larger than the experimental resolution presence of more than one resonance Today….. more comments later on B-factories**The CKM matrix**CP Violation With 6 quarks REAL Cabibbo matrixCOMPLEX CKM (Cabibbo, Kobayashi,Maskawa) ci=cosqi et si=sinqi.qi are the three “rotation” angle instead of the single qc. The phase dintroduces the possibility of the CP violation Parametrization : We will discuss it in great details later**In fact the « strange » particles have been also**fundamental for pointing out for the first time the fact that the parity is not conserved in the weak interaction… Le puzzle t-q Experimentally The mass and the lifetime of la t and q are identical. • t + + - (J=0, P=+1) • q + 0 (J=0, P=-1) • The parity of t and of q are different • If t=q=K Parity Violation in weak interaction**Neutral Kaons**• Known: • K0 can decay to p+p- • Hypothesized: • K0 has a distinct anti-particle K0 • Claims: • K0 (K0) is a “particle mixture” with two distinct lifetimes • Each lifetime has its own set of decay modes • No more than 50% of K0 (K0) will decay to p+p- In terms of quarks: us vs. us**CP Violation in the Kaon sector - 1964**def :h=h’=1 • K0and K0are not CP eigenstates, but System with 2 p (p0 p0 , p+ p- ) P(pp)=+1 C=(-1)l+S P=(-1)lCP=(-1)2l=+1 p+ p- p0 System with 3 psi l=L=0 C=+1 P=(-1)3(-1)l=-1 CP = -1 l L Prod Decay t If CP is conserved Long lifetime because of the reduced space phase**If KL2there is CP violation.**Level of CP violation is : signal KL p+ p+ p0 2-body decay : the two p are back-to-back: |cosq|=1 q q p- cos q = 1 cos q 1 p-**2**The Standard Model in the fermion sector CKM matrix and CP Violation. The Unitarity Triangle**Flavour Physics in the Standard Model (SM) in the quark**sector: 10 free parameters ~ half of the Standard Model 6 quarks masses 4 CKM parameters In the Standard Model, charged weak interactions among quarks are codified in a 3 X 3 unitarity matrix : the CKM Matrix. The existence of this matrix conveys the fact that the quarks which participate to weak processes are a linear combination of mass eigenstates The fermion sector is poorly constrained by SM + Higgs Mechanism mass hierarchy and CKM parameters**Weak Isospin (symbol L because only the LEFT states are**involved ) Weak Hypercharge : (LEFT and RIGHT states ) I I3 Q Y Leptons doublet L e ½ ½ 0 -1 eL- ½ -½ -1 -1 singlet R eR- 0 0 -1 -2 quarks doublet L uL ½ ½ 2/3 1/3 dL ½ -½ -1/3 1/3 singlet R uR 0 0 2/3 4/3 singlet R dR 0 0 -1/3 -2/3 The Standard Model is based on the following gauge symmetry SU(2)LU(1)Y Idem for the other families**The mass should appear in a LEFT-RIGHT coupling**Short digression on the mass R : SU(2) singlet L : SU(2) doublet The mass terms are not gauge invariant under SU(2)LU(1)Y R (I=0,Y=-2) leptoniR (I=0,Y=-2/3) quark dR (I=0,Y=4/3) quark uR Adding a doublet L (I=1,Y=-1) leptoniL (I=1,Y=1/3) quark dL (I=1,Y=1/3) quark uL h (I=1/2,Y=1) Yukawa interaction :**** u d c s t b e e W uL uR dL dR eL eR H The SM quantum numbers are I3and Y The gauge interactions are Flavour blind In this basis the Yukawa interactions has the following form : With: To be manifestly invariant under SU(2) complex Two matrices are needed to give a mass term to the u-type and d-typequarks ………. We made the choice of having the Mass Interaction diagonal ……. ……. * SSB=Spontaneous Symmetry Breaking**The coupling is not**anymore universal u d u s u b c d c s c b t d t s t b W To have mass matrices diagonal and real, we have defined: The mass eigenstates are: In this basis the Lagrangian for the gauge interaction is: Unitary matrix**The mass is a LEFT-RIGHT coupling and has to**respect the gauge invarianceSU(2)LU(1)Y u d c s t b e e W To have mass matrices diagonal and real, we have defined: The mass eigenstates are: The Lagrangian for the gauge interaction is: SUMMARY h (I=1/2,Y=1)**M(diag) is unchanged if**Pf = phase matrix I cannot play the same game with all four fields but only with 3 over 4 (2n-1) irreducible phases**Generally for a rotation matrix in complex plane**Quark families # Angles # Phases # Irreducible Phases n n(n-1)/2 n(n+1)/2 n(n+1)/2-(2n-1)=(n-1)(n-2)/2 2 3 4 1 3 6 3 6 10 0 1 3 If V complex CPT T is an anti-linear operator T(V)=V* T violated CP violated CP Violation 3 families Original idea in : M.Kobayashi and T.Maskawa, Prog Theor. Phys 49, 652 (1973) 3 family flavour mixing in quark sector needed for CP violation. Note the date …1973 even before the discovery of the charm quark ! We can also simply say, that the CP transformation rules imply that each combinations of fields and derivatives that appear in a Lagrangian transform under CP to its hermitian conjugate. The coefficient (mass/coupling…), if there are complex, transform in their complex conjugate**Product of three rotation matrix (3 angles + 1 phase with**3families) There are 36 possibilities [ (32)perm. 3d=0 2 d=1 ] Standard Parametrization c13 = c23 = 1 Now experimentally : s13 and s23 are of order : 10-3 and 10-2 With an excellent accuracy Consequently, with an excellent accuracy four independent parameters are given as**The expected B meson lifetime**Surprise: the B meson lifetime Both MAC and MARK-II were detectors at PEP, a 30 GeV e+e- collider at SLAC (Stanford)**Surprise: Vcb**is very small! Mark-II paper MAC paper Vus ~0.22 Vcb ~0.04 t(B)~1.6ps ct ~450mm L~2mm This fact is also very important and allow to perform B physics, since the B mesons can be identified (their lifetime measured) L=gb ct gb~5 not measurable ! t(B)~0.05ps ct ~15mm L~75mm**CLEO collaboration**at CESR (Cornell):s=M(4S) bu versus b c From a sample of 42.2K BB events (40.6/pb) |Vub| << |Vcb| << |Vus|**L. Wolfenstein, Phys. Rev. Lett. 51 (1983) 1945.**• Parametrization of the Kobayashi-Maskawa Matrix • Lincoln Wolfenstein • Department of Physics, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213 • Received 22 August 1983 • The quark mixing matrix (Kobayashi-Maskawa matrix) is expanded in powers of a small parameter λ equal • to sinθc=0.22. The term of order λ2 is determined from the recently measured B lifetime. Two remaining • parameters, including the CP-non conservation effects, enter only the term of order λ3 and are poorly • constrained. A significant reduction in the limit on ε′/ε possible in an ongoing experiment would tightly • constrain the CP-non conservation parameter and could rule out the hypothesis that the only source of CP • non conservation is the Kobayashi-Maskawa mechanism.**CKM Matrix**in «3-D» b 1 1 0.01 1 0.22 0.04 0.01 0.04 d s u c t md ms**Wolfenstein parametrization**Parameters and We observe that : Approximate Parametrization Diagonal elements ~ 1 Vus , Vcd ~ 0.2 Each element of the CKM matrix is expanded as a power series in the small parameter l=|Vus|~0.22 Vcb , Vts ~ 4 10-2 Vub , Vtd ~ 4 10-3 u c t 1 same 1-2 2-3 1-3 familiy d s b**b**c,u A l3(r-ih) Vub,Vcb Al2 B decays t A l3(1-r-ih) -Al2 1 Vtb B Oscillations d, s b d, s b Vtd,Vts Wolfenstein parametrization 4 parameters : l ,A, r, h The CKM Matrix d s b u 1-l2/2 l c -l 1-l2/2 h complex, responsible of CP violation in SM The b-Physics plays a very important role in the determination of those parameters**To have a CKM matrix expressed with Wolfenstein parameters**valid up to l6 We define : the corrections to Vus are at l7 to Vcb are at l8 In particular Which we will see will allow a generalization of the unitarity triangle in r and h plane**The Unitarity Triangle**The CKM is unitary The non-diagonal elements of the matrix products correspond to 6 triangle equations Remember that :**Each of the angles of the unitarity triangle is the relative**phase of two adjacent sides (a part for possible extra p and minus sign) a + b + g = p The reason of making the arg of the ratio of two legs is simple So the relative phase**APPENDIX**Part I**1974 : cquark Discovery : J/**m(J/)<2 m(D0) c c Seen as a resonancem~3.1 GeV G~10-100KeV D u J/ u • Brookhaven(p on Be target) D c c e+ m+ c c hadrons c e- m- c G~70 KeV G(ee)~5 KeV G(mm)~5 KeV e+e-finalstate SLAC (e+e-) 3.10 3.12 3.14 The decay through strong interaction is so suppressed that the electromagnetic interaction becomes important hadronic final state**Phys Rev 103,1901 (1956)**There is a HUGE difference between K0pp and K0 ppp in phasespace (~600x!). The huge difference is because mK0 – 3mp = 75 MeV/c2**APPENDIX**Part II 1) CKM mechanism in the lepton sector and for the neutral currents (Z0)**** e e W If a similar procedure is applied to the lepton sector Since the neutrino are (were) massless the matrix which change the basis from int-> mass is in principle arbitary We can always choose Now the neutrino have a mass, it exists a similar matrix in the lepton sector with mixing a CP violation**Facultatif**u u d d s s c c b b t t l l n Z0 For the Z0 The neutral currents stay universal, in the mass basis : we do not need extra parameters for their complete description n**The area of the UT**The standard representation of the CKM matrix is: However, many representations are possible. What are the invariants under re-phasing? • Simplest: Uai = |Vai|2 is independent of quark re-phasing • Next simplest: Quartets: Qaibj = Vai Vbj Vaj* Vbi*witha≠band i≠j • “Each quark phase appears with and without *” • V†V=1: Unitarity triangle: Vud Vcd* + Vus Vcs* + Vub Vcb* = 0 • Multiply the equation by Vus* Vcs and take the imaginary part: • Im (Vus* Vcs Vud Vcd*) = - Im (Vus* Vcs Vub Vcb*) • J = Im Qudcs = - Im Qubcs • The imaginary part of each Quartet combination is the same (up to a sign) • In fact it is equal to 2x the surface of the unitarity triangle • Area = ½ |Vcd||Vcb| h ; h=|Vud||Vub|sin arg(-VudVcbVub*Vcb*)| • =1/2 |Im(VudVcbVub*Vcb*)|)| • Im[Vai Vbj Vaj* Vbi*] = J ∑eabgeijk where J is the universal Jarlskog invariant • Amount of CP Violation is proportional to J

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