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The CKM matrix and the determination of Vcd with the Chorus detector CP3 meeting, Louvain-la-Neuve 27th of January, 2004 Sergey Kalinin, FYNU, UCL

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Electroweak interactions History: 1930 ’ s: Fermi ’ s theory described b decay. 1950 ’ s: V-A (vector-axial vector) Theory: Yang & Lee describe parity violation Feynman and Gell-Mann describe muon decay and decay of strange mesons 1960 ’ s: Cabibbo Theory N. Cabibbo proposes “ quark mixing ” (1963) "explains" why rates for decays with S =0 > S=1 Quarks in strong interaction are not the same as the ones in the weak interaction: weak interaction basis different than strong interaction basis

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TypeCommentExamples Leptonicinvolves only leptonsmuon decay ( evv) e e - e e - Semileptonicleptons and quarksneutron decay ( s=0) K + + ( s=1) Non-Leptonicinvolves only quarks - p & K + + o Some details of Weak Interactions quarks and leptons are grouped into doublets (SU(2)) (sometimes called families or generations) For every quark doublet there is a lepton doublet e W-W- , e-e- W-W- Allowed NOT Allowed e-e- Classification of weak interactions

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Origin of CKM matrix Charged current in general form : is 3x3 matrix And s- and b-quarks are stable. We know it’s not the case!

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Cabibbo’s conjecture was that the quarks that participate in the weak interaction are a mixture of the quarks that participate in the strong interaction. This mixing was originally postulated by Cabibbo (1963) to explain certain decay patterns in the weak interactions and originally had only to do with the d and s quarks. d’ = d cos + s sin Thus the form of the interaction (charged current) has an extra factor for d and s quarks d quark: J u u (1- 5 )cos c s quark: J u u (1- 5 )sin c u W-W- u W-W- cos c sin c ds Cabibbo Model

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The Cabibbo angle is important for determining the rate of many reactions: The Cabibbo angle can measured using data from the following reactions: From the above branching ratio’s we find: c = 0.27 radians ++ u W+W+ cos c or sin c d, s Purely leptonic decays (e.g. muon decay) do not contain the Cabibbo factor:

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CKM matrix x y z The matrix has 4 real parameters : 3 angles and 1 phase Lets confront (d,s,b) with (z,y,x). Then we make three rotations around Z-, around X- and around Y-axis.

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CKM matrix Thus we obtain for Kabayashi-Maskava representation: Wolfenstein representation : Here =sin and A, , are real

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CKM matrix The matrix is supposed to be unitary 4th generation?

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CKM matrix Current measured values (PDG 2002): Several important points here : The matrix is almost diagonal The further away from a family, the smaller matrix element Since the matrix is unitary there are lot of constraints on elements So far experimental results are consistent with expectations from a Unitary matrix

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No one knows how to calculate the values of the CKM matrix. Experimentally, the cleanest way to measure the CKM elements is by using interactions or decays involving leptons. CKM factors are only present at one vertex in decays with leptons. V ud : neutron decay: n pev d uev V us : kaon decay: K 0 + e - v e s uev V bu : B-meson decay: B - ( or + )e - v e b uev V bc : B-meson decay: B - D 0 e - v e b cev V cs : charm decay: D 0 K - e + v e c sev V cd : neutrino interactions: d - c d c Measuring the CKM Matrix “Spectator” Model decay of D 0 K - e + v e c u s u e, W K-K- D0D0 V cs

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Chorus beam : : e : e 1.00 : 0.05 : 0.017 : 0.007 ~ 27 GeV CC ~3.3. 10 -6 CC (0.1 background event) CHORUS NOMAD 124 m290 m408 m 450 GeV SPS protons Beryllium target hornreflectorvacuum tunnel earth/iron shielding

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CHORUS detector overview h+ is hadronic system with positive electric charge

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Automatic scanning of emulsion

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Charm tagging D+

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Charm physics in CHORUS

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Advantages and difficulties More than 3000 manually confirmed charm events (zero background) New MC generator (NuTeV) allows NLO analysis Anti-neutrino sample is not big(~50events) No invariant mass reconstruction or particle ID

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d(x) |V cd | 2 +s(x) |V cs | 2 d(x)+s(x) CC charm CC all had had charm ~ |V cd | 2 s 0 for large x Bjorken Sea quarks Valence quarks Measuring Vcd

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Why it’s not that easy Cross-section depends on energy electronic detectors were not designed for charm physics geometrical acceptance of the detector NLO effects Poor anti-neutrino sample Diffractive and quasi-elastic ingredients in charm cross-section

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Charm over charged-current ratio ‘corrected’ means corrected for neutral decays and charm selection efficiencies(to be done more accurately)

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Outlook First rough result is not very different from other experiments. A lot of work still to be done : selection efficiencies, proper contribution from quasi-elastic and diffractive charm production, low energies, etc

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x-distibution of neutrino charged-current interactions in CHORUS x-distribution of anti-neutrino charged-current interactions in CHORUS x-distribution

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Constraints on unitarity triangle http://ckmfitter.in2p3.fr

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