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From CKM to MNS and back

Physics of flavor. From CKM to MNS and back. …the physics of flavor is the flavor of physics…. Mario Campanelli NIKHEF colloqium Jan 16,2004. Introduction. Since the theory of Cabibbo angle in 1964, we know that eigenstates of mass and weak interactions do not coincide.

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From CKM to MNS and back

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  1. Physics of flavor From CKM to MNS and back …the physics of flavor is the flavor of physics… Mario Campanelli NIKHEF colloqium Jan 16,2004

  2. Introduction • Since the theory of Cabibbo angle in 1964, we know that eigenstates of mass and weak interactions do not coincide. • In the following 40 years, mixing of quarks and leptons has been one of the main subjects in particle physics, and this program is far from being over. • I will try to take you around in a trip to this field, with a personal look to what the future could be.

  3. weak mixing • In the SM, fermion fields can be rotated wrt mass eigenstates. This unitary rotation cancels out in NC and affects CC as Cabibbo-Kobayashi-Maskawa mixing matrix • Also for massless particles mixing can be rotated away. Now we know that neutrinos are massive, and a similar matrix (Maki, Nakagawa,Sakata) can be defined, with analogous formalism

  4. CKM mixing matrix • Mixing is expressed in terms of 3x3 unitary matrix operating on –e/3 quark mass eigenstates • After unitarity requirements, the matrix is expressed in terms of 3 mixing angles θ12θ23θ13 and a complex phase δ13 • Exploiting the hierarchy s12»s23»s13, • and setting λ≡ s12, the Wolfenstain parametrization expands in powers of λ

  5. Measurements of CKM elements (90% C.L., using constraints) Vus from Ke3 decays Vub from charmless decays b->ulν at Υ(4S) and LEP Vud comparing nuclear β decays and μ decays Vcd from charm production in ν interactions Vcb from decays B->D*lν Vcs from charm-tagged W decays in LEP, giving |Vcs|=0.97±0.09±0.07. No b are produced, so look for heavy-quark characteristics (displaced vertexes, heavy mass, leading effects, presence of D*) in jets from W decay, possibly using neural networks or likelihood functions. Tighter determination comes from ratio hadronic/leptonic W decays, leading to Σi,j|Vij|=2.039±0.025±0.001 (2 in a 3-generation CKM matrix), and using the other values as constraint, yielding |Vcs| = 0.996±0.013 Vtb from t->b observed events Vtb,Vts from B oscillations

  6. Unitarity triangle(s) Unitarity condition V+V=1 results in six independent costraints; three can be represented by triangles: • VudVus* + VcdVcs* + VtdVts*=0 λ-λ3-λ+λ3+A2λ5(1-ρ-iη)=0 • VusVub* + VcsVcb* + VtsVtb*=0 Aλ4(ρ+iη)+Aλ2-Aλ4-Aλ2=0 • VudVub* + VcdVcb* + VtdVtb*=0 Aλ3(ρ+iη)-Aλ3+Aλ3(1-ρ-iη)=0 The first (relative to K oscillations) and the second triangle are “smashed” into a segment, while the third one (relative to B physics) has sides of similar length. However, it was shown by C.Jarsklog that the area of all triangles, half the determinant J= |Im(VudVcbVub*Vcd*)| = |Im(VudVcsVcd*Vus*)| = … is the same, and proportional to direct CP violation.

  7. Representations of the b triangle We can align VcdVcb* on the x axis, and setting cos of small angles to 1, the relation becomes Vub* +Vtd=s12Vcb* and rescaling by s12Vcb*, the triangle will have base on (0,0)-(1,0) and apex on (Re(Vub)/|s12 Vcb|,-Im(Vub)/|s12 Vcb|) = (ρ(1- λ2/2),η(1- λ2/2)) (ρ,η) VtdVtb*/ VcdVcb* α VudVub*/ VcdVcb* β γ (0,0) (1,0)

  8. B oscillations and the side of the triangle The main constraints to the apex position (apart from direct CP) come from |Vub| and ε from K decays. Information on the VtdVtb*/VcdVcb* side comes from B oscillations (virtual t production) Vtb Vtd,ts t b d,s W W t d,s b Vtd,ts Vtb Bd osc. in dileptons in Belle: ΔMd=0.503± 0.08 ±0.10 ps-1

  9. Bs mixing From Bd oscillations, using lattice QCD, we can derive the relation |Vtb*Vtd|=0.0079±0.0015; however, most of the uncertainties cancel out in the ratio So a measurement of the Bs mixingwould be the single largest improvement in the understanding of the CKM matrix. The present limit from LEP, SLD is ΔMs>14.4 ps-1 at 90% C.L. I will discuss in detail expected improvements at the Tevatron

  10. The angle β and CP violation ± 1 • In b decays, CP violation can occur in mixing, decay or interference between the two (decay into CP eigenstates) When tree decays are dominant, mixing and decay can result in a single weak phase, like in the golden channel J/Ψ Ks, where CDF RunI results Belle LP’03 sin2f1=0.733±0.057±0.028

  11. What about other channels? sin 2β can also be measured in other charmonium channels and channels with considerable penguin contribution. In that case the asymmetry gets more complicated: And rather than measuring directly sin 2β, constraints are put to the penguin contribution (the cosine term, zero in the no-penguin case). Still open (3.5% C.L.) sin2βeff (φ KS) : Babar: +0.45±0.43±0.07 Belle: -0.96 ±0.50

  12. Other angles • Penguin diagrams are unavoidable in measurement of the other angles, since no channels with dominant tree-level are present. • Es. without penguins B->π+π- equivalent to B->J/ΨK, but cosine term predicted (and measured) far from zero The separate measurements of sine and cosine term (together with knowledge of ρand η) can be interpreted in the complex plane of the ratio of tree to penguin contributions And used to get information on α using theoretical assumptions and the neutral B-> π0 π0 modes

  13. hadronic and leptonic mixing Hadronic mixing matrix has been studied for 40 years now, elements are measured with good precision. Hierarchic structure, allows perturbative expansion, expressed with a triangle whose nonzero area predicts CP violation in the b system, as observed. Still much to do, but a clear picture is emerging. • Experimental evidence of nonzero neutrino masses (therefore a measurable mixing matrix) only came in 1998 with atmospheric neutrino oscillations from SuperKamiokande.

  14. Neutrino oscillations • If leptons mix, interaction will have non-diagonal terms between weak eigenstates: In three families, the probability becomes Where the MSN mixing matrix U is normally expressed with exactly the same formalism as CKM

  15. Some differences with hadron mixing • Trivial: • do not bind into mesons, no hadronic effects, direct measurement of oscillation parameters • stable particles in relativistic motion, oscillate like sin2(Δm2L/E) instead of e-Γt cos(Δmt) • Not so trivial • can be antiparticle of itself (Majorana); in that case, two additional phases occur, non observable in oscillations (but in ν-less ββdecay) • In this case, a see-saw mechanism would explain the smallness of ν masses, being physical states mixing of a massless left-handed state and a right-handed state at the Plank scale; m1=MD2/MR,, m2≈MR • No hierarchical structure of mixing matrix is emerging, two angles are large, one is small • Propagation in matter can largely modify oscillation pattern

  16. The atmospheric neutrino region • νμand νe produced in cosmic rays (appr. ratio 2:1) reach detector after a baseline dependent on the angle. • angular dependence of νμdisappearance interpreted as oscillations; pattern not observed for νe, so leading oscillation must be νμ→ντor oscillation into a sterile state. However, matter propagation for neutrinos coming from below would be different; sterile fraction <19% at 90% C.L.

  17. The confirmation: long-baseline beams Oscillation observed also in the first terrestrial long-baseline experiment (K2K); other projects aim at precision parameter measurement (MINOS) and direct τ identification (CNGS) τ events in νμ→ντoscillation for a 3kton ICARUS in Gran Sasso, detected using kinematic techniques

  18. Solar neutrino region • Historical indication of neutrino oscillations, solar neutrinos always seen as “a problem”. • Final evidence from SNO, that can see not only νe disappearance from charge current events, but also the other flavors via neutral currents. Standard solar model finally tested after 30 years!

  19. The confirmation: KamLAND • All reactors in Japan are a source for the first long-baseline reactor experiment, Kamland, that confirmed νe disappearance (towards the maximally-mixed νμντ combination) Solar angle is not maximal as the atmospheric one, but it is not small. Δm2 more than one order of magnitude smaller than the atmospherics

  20. The search for θ13 • The third angle, connecting νe to the others, has not been measured. The best limit comes from the reactor experiment CHOOZ. Finding this angle is the goal of most of the future experiments: • New reactors aim sin22θ<0.01 with: • 50 kton (10xCHOOZ) deep detector (less BG) • 2 detectors for syst. 3%->1% Conventional (NuMI) beam and super-beam (JHF) can extend by similar amount

  21. Conditions for CP violation • Nothing is known about the phase δ. Like in the hadronic system, it is connected to the amount of CP violation. In vacuum, the νe→νμoscillation probability is made of three terms: Independent of  P(e)=P(e)= 4c213[sin2 23s212s213+c212(sin213s213s223+ sin212s212(1-(1+s213)s223))] -1/2c213sin212s13sin223cos[cos213- cos223-2cos212sin212] +1/2c213sinsin212s13sin223[sin212-sin213+sin223] CP-even Campanelli CP-odd The last term changes sign under CP, so for δ>0 the oscillation probability does not conserve CP. To have an observable effect, however, θ13 cannot be so small otherwise the CP-violating term gets too small with respect to the constant solar term

  22. How to measure CP violation • Running an off-axis super-beam with νμand νμ • low energy, few events • systematics for cross section • marginal sensitivity • Coupling with a collimated β-beam from ion decay 6He++6Li+++e- νe 18Ne18F e+ νe to have a clean νe beam and search t-violation • feasible but challenging • not optimal for the low-θ13 region 40 kton 400 kton M.Mezzetto 2 years neutrino, 10 years antineutrino, CERN-Frejus superbeam

  23. Neutrino factories • The most lavish way to search for CP violation would be with high-energy beams of νe,νμ, νe,νμ produced in decay of stored muons. Large (O(50 kton)) detector with muon charge ID detect neutrinos after thousands of kilometers. -ee+ e eτ τ e +ee- e eτ τ e 8 oscillation modes simultaneously observable, strong signature from wrong-sign muons Bueno, Campanelli, Rubbia

  24. Remarks on a future leptonic CP observation • Observing difference in oscillation probability not sufficient to claim lepton CP discovery. Propagation in matter is not symmetric, a difference will be observed regardless of δ. Matter effects can be subtracted but sensitivity degrades above ~4000 km. • A simultaneous measurement of θ13 and δ can result in large correlations or degeneracy; they can be solved by using multiple baselines or combining neutrino factory and super-beams Bueno Campanelli Navas Rubbia A.Donini et al.

  25. Some theoretical speculations M.C.Gonzalez-Garcia • what to do with two different matrices we do not understand? Theorists proposed several kind of models. For instance (Fritzsch), writing Some approximate relations hold: According to the model, some specific relations can hold (like φ=π/2) allowing predictions on triangle angles

  26. More speculations Altarelli Feruglio Masina For lepton mixing, anarchical, semi-anarchical and hierarchical models predict in SU(5)xU(1) scenario a (unification scale) mass matrix for neutrinos of the kind with ε=1, λand λ2,respectively. Trasporting this matrix to our scale yields low-energy predictions “Anarchy” model successfully predicts large mixing angles and small mass ratios, and a value of θ13 close to present bounds. Similar exercises trying to unify both matrices require larger symmetries like SU(10)xU(2) Murayama

  27. sin22q Next big thing in lepton mixing: θ13 search in JHF Two phases (second not yet approved) 2008? Plan to start in 2007 ~1GeV n beam Super-K: 22.5 kt J-PARC (Tokai) Kamioka Hyper-K: 1000 kt 0.75MW 50 GeV PS at 4MW 50 GeV PS Off axis 2 deg, 5 years CHOOZ excluded JHF 0.75MW + Super-Kamiokande Future Super-JHF 4MW + Hyper-K(~1Mt) ~ JHF+SK 200 Sin22q13>0.006 sin22q13 p p n 0m 140m 280m 2 km 295 km

  28. Next big thing in hadron mixing: ΔΓs in CDF Minimise error on pT with fully reconstructed decays Bs→Ds π CDF ~ 65 fs (50 fs with L00) D0 ~ 75 fs Flavour tagging Need everything for εD2~5% ε = tag efficiency D = tag correct (dilution) Yield – need >O(1000) events So far, seen ~0.7 ev/pb-1 With improved trigger and detector almost factor 2 gain Add more decay modes • At least 30 times faster than Bd mixing Δmd=0.502 ± 0.006 ps-1 • Needs exquisite proper time resolution Bs Ds, Ds  Ds  , K*K, 

  29. Triggering on heavy flavors in hadronic environment • CDF can have such an ambitious program in b physics thanks to its unique trigger system. At level 1, the XFT can measure tracks in the chamber with eff.=96% σ(Φ)=5mr σ(pT)=(1.74 pT)%. • Information is combined with silicon hits and compared to predefined roads stored into an associative memory 35μm  33 μm resol  beam  σ = 48 μm Displaced two track trigger Tracks: pT>2 GeV, d0>120 μm ΣpT>5.5 GeV Fully hadronic B decays (B→hh’, Bs→Dsπ, D→Kπ …) SVT impact parameter (μm)

  30. First measurements on Bs • Not enough luminosity to see oscillations: measurement of relative Bs and Bd yields

  31. Bs mixing sensitivity • S=signal events • B=background events • σtproper time resolution • εD2 effettive tagging efficiency currently: s=1600 ev/fb-1, S/B=2/1, εD2=4%, σt=0.0067 ps  2σ measurement of Δms=15ps-1 from 500 pb-1 data improvements: s=2000 ev/fb-1 with additional channels, εD2=5% with TOF, σt=0.005 ps with L00 and event beamline 2.11 fb-1 (baseline) and 3.78 fb-1 (design) by 2007

  32. ΔΓs/Γs CKM-independent QCD factors • ΔΓs/Δms =-3π/2 mb2/mt2η(ΔΓs)/η(Δms) • SM: ΔΓs/Δms =3.7+0.8-1.5 10-3 • LQCD: ΔΓs/Γs=0.12±0.06 • Present 95% C.L. limit: ΔΓs/Γs<0.54 Disentangle on a statistical basis contributions to the B->hh peak, then fit lifetimes for the different charges • Expected sensitivity: • 0.29 at 500 pb-1 • 0.10 at 2 fb-1

  33. B physics in the LHC era • Dominated by dedicated hadron experiment(s) LHCb (and BTeV) • Multiple channels allow measurement of angles αand γ • Es. measure Φs from Bs->J/ΨΦ (5s discovery possible in 1 year) and γ+Φs from asymmetry of Bs->DS+K- Using the four B->hh channels precision can go to 40-60 with contributions from penguins or new physics Dalitz-plot analysis of B->π+π-π0 can give sin(2α)and cos(2α)for δ(α) = 40 all this will lead to stronger constraints on new physics

  34. What can ATLAS and CMS do? • In principle complementary to dedicated experiments in η coverage and larger statistics for leptonic channels, in practice limited by bandwidth and PID. Competitive in rare leptonic decays like B->μμ(X) and Bc->J/Ψ(X) Some b-physics capability could be recovered using a similar system to the CDF SVT, a dedicated processor (FastTrack) for on-line track recognition. Without interfering with the rest of the DAQ, it “sniffs” tracker data going to the memory buffer and stores good quality tracks to another buffer accessible by higher-level triggers. Presently proposed to ATLAS as an upgrade, for low-luminosity running as well as high-pt b physics

  35. Summary • We made a quick tour in the world of flavors, trying to stress differences and similarities between leptons and hadrons. • Both sectors saw in the recent past important discoveries, and more are announced for the next future • Big expectations from b-factories, neutrino beams, hadron colliders • Although techniques are very different, the underlying physics is the same

  36. Three reasons to expect something new • Both neutrino oscillations and CP-violation in b physics are recent discoveries: much more has to be dug • Historically, new phenomena have been seen first in low-energy data (neutral currents, top at LEP; GUT from see-saw? SUSY in b decays?) • Reductionism (driving force of physics since Kepler and Newton): there are too many free parameters over there. There must be some underlying structure!

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