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Cracking the Unitarity Triangle — A Quest in B Physics —

Cracking the Unitarity Triangle — A Quest in B Physics —. Masahiro Morii Harvard University Tohoku University Physics Colloquium 21 November 2005. Outline. Introduction to the Unitarity Triangle The Standard Model, the CKM matrix, and CP violation

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Cracking the Unitarity Triangle — A Quest in B Physics —

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  1. Cracking the Unitarity Triangle— A Quest in B Physics — Masahiro Morii Harvard University Tohoku University Physics Colloquium 21 November 2005

  2. Outline • Introduction to the Unitarity Triangle • The Standard Model, the CKM matrix, and CP violation • CP asymmetry in the B0meson decays • Experiments at the B Factories • Results from BABAR and Belle • Angles a, b, g from CP asymmetries • |Vub| from semileptonic decays • |Vtd| from radiative-penguin decays • Current status and outlook The Unitarity Triangle a g b Results presented in this talk are produced by the BABAR, Belle, and CLEO Experiments,the Heavy Flavor Averaging Group, the CKMfitter Group, and the UTfit Collaboration M. Morii, Harvard

  3. leptons quarks What are we made of? • Ordinary matter is made of electrons and up/down quarks • Add the neutrino and we have a complete “kit” • We also know how they interact with “forces” u u d M. Morii, Harvard

  4. g g d e− e− d Z0 Z0 Z0 Z0 Note W± can “convert”u↔ d, e↔ n ne e− u d ne u d e− Simplified Standard Model • Strong force is transmitted by the gluon • Electromagnetic force by the photon • Weak force by the Wand Z0bosons g g u d u d g u u W+ W− e− u ne d M. Morii, Harvard

  5. 1st generation 2nd generation 3rd generation Three generations • We’ve got a neat, clean, predictive theory of “everything” • Why 3 sets (= generations) of particles? • How do they differ? • How do they interact with each other? It turns out there are two “extra” copies of particles M. Morii, Harvard

  6. Particle mass (eV/c2) A spectrum of masses • The generations differ only by the masses  The structure is mysterious • The Standard Model has no explanation for the mass spectrum • All 12 masses are inputs to the theory • The masses come from the interaction with the Higgs particle • ... whose nature is unknown • We are looking for it with the Tevatron, and with the Large Hadron Collider (LHC) in the future The origin of mass is one of the most urgent questions in particle physics today Q = 1 0 +2/3 1/3 M. Morii, Harvard

  7. If there were no masses • Nothing would distinguish u from c from t • We could make a mixture of the wavefunctions and pretend it represents a physical particle • Suppose W connects u↔ d, c↔ s, t↔ b • That’s a poor choice of basis vectors M and N are arbitrary33 unitary matrices Weak interactions between u, c, t, and d, s, b are “mixed” by matrix V M. Morii, Harvard

  8. Turn the masses back on • Masses uniquely define the u, c, t, and d, s, b states • We don’t know what creates masses We don’t know how the eigenstates are chosen M and N are arbitrary • V is an arbitrary 33 unitary matrix • The Standard Model does not predict V • ... for the same reason it does not predict the particle masses or CKM for short Cabibbo-Kobayashi-Maskawa matrix M. Morii, Harvard

  9. Structure of the CKM matrix • The CKM matrix looks like this  • It’s not completely diagonal • Off-diagonal components are small • Transition across generations isallowed but suppressed • Matrix elements can be complex • Unitarity leaves 4 free parameters, one of which is a complex phase There seems to be a “structure”separating the generations This phase causes “CP violation” Kobayashi and Maskawa (1973) M. Morii, Harvard

  10. What are we made of, again? • Dirac predicted existence of anti-matter in 1928 • Positron (= anti-electron) discovered in 1932 • Our Universe contains (almost) only matter • Translation: he would like the laws of physics to be different for particles and anti-particles e e+ I do not believe in the hole theory, since I would like to have the asymmetry between positive and negative electricity in the laws of nature (it does not satisfy me to shift the empirically established asymmetry to one of the initial state) Pauli, 1933 letter to Heisenberg M. Morii, Harvard

  11. CP symmetry • C and P symmetries are broken in weak interactions • Lee, Yang (1956), Wu et al. (1957), Garwin, Lederman, Weinrich (1957) • Combined CP symmetry seemed to be good • Anti-Universe can exist as long as itis a mirror image of our Universe • To create a matter-dominant Universe, e e+ CP symmetry must be broken One of the three necessary conditions (Sakharov 1967) M. Morii, Harvard

  12. CP violation • CP violation was discovered in KL decays • KL decays into either 2 or 3 pions • Couldn’t happen if CP was a good symmetry of Nature  Laws of physics apply differently to matter and antimatter • The complex phase in the CKM matrix causes CP violation • It is the only source of CP violation in the Standard Model Christenson et al. (1964) Final states have different CP eigenvalues Nothing else? M. Morii, Harvard

  13. CP violation and New Physics Are there additional (non-CKM) sources of CP violation? • The CKM mechanism fails to explain the amount of matter-antimatter imbalance in the Universe • ... by several orders of magnitude • New Physics beyond the SM is expected at 1-10 TeV scale • e.g. to keep the Higgs mass < 1 TeV/c2 • Almost all theories of New Physics introduce new sources of CP violation (e.g. 43 of them in supersymmetry) • Precision studies of the CKM matrix may uncover them New sources of CP violation almost certainly exist M. Morii, Harvard

  14. The Unitarity Triangle • V†V = 1 gives us • Experiments measure the angles a, b, g and the sides This one has the 3 terms in the same order of magnitude A triangle on the complex plane M. Morii, Harvard

  15. 95% CL The UT 1998 2005 • We did know something about how the UT looked in the last century • By 2005, the allowed region for the apex has shrunk to about 1/10 in area The improvements are due largely to the B Factoriesthat produce and study B mesonsin quantity M. Morii, Harvard

  16. W+ b d W- d b Anatomy of the B0 system • The B0 meson is a bound state of b and d quarks • They turn into each other spontaneously • This is called the B0-B0 mixing Indistinguishable from the outside M. Morii, Harvard

  17. Time-dependent Interference • Starting from a pure |B0 state, the wave function evolves as • Suppose B0 and B0 can decay into a same final state fCP • Two paths can interfere • Decay probability depends on: • the decay time t • the relative complex phase between the two paths Ignoring the lifetime time fCP t = 0 t = t M. Morii, Harvard

  18. The Golden Mode • Consider • Phase difference is Direct path Mixing path M. Morii, Harvard

  19. Time-dependent CP Asymmetry • Quantum interference between the direct and mixed paths makes and different • Define time-dependent CP asymmetry: • We can measure the angle of the UT • What do we have to do to measure ACP(t)? • Step 1: Produce and detect B0 fCP events • Step 2: Separate B0 from B0 • Step 3: Measure the decay time t Solution: Asymmetric B Factory M. Morii, Harvard

  20. B Factories • Designed specifically for precision measurements of the CP violating phases in the CKM matrix SLAC PEP-II KEKB Produce ~108B/year by colliding e+ and e− with ECM = 10.58 GeV M. Morii, Harvard

  21. SLAC PEP-II site Linac I-280 BABAR PEP-II M. Morii, Harvard

  22. Step 1: Reconstruct the signal B decay Step 2: Identify the flavorof the other B Decay products often allow us to distinguishB0 vs. B0 Step 3:Measure Dz Dt Asymmetric B Factory • Collide e+ and e− withE(e+) ≠ E(e−) • PEP-II: 9 GeV e− vs. 3.1 GeVe+ bg = 0.56 Moving in the lab U(4S) e+ e− M. Morii, Harvard

  23. Detectors: BABAR and Belle • Layers of particle detectors surround the collision point • We reconstruct how the B mesons decayed from their decay products BABAR Belle M. Morii, Harvard

  24. J/y KS event A B0 → J/yKS candidate (r-fview) p − p − m+ p + Pions from p + K− p + m− Muons from Red tracks are from the other B,which was probably B0 M. Morii, Harvard

  25. CPV in the Golden Channel • BABAR measured in B0 J/y+ KS and related decays 227 million events J/yKS J/yKL M. Morii, Harvard

  26. Three angles of the UT • CP violation measurements at the B Factories give Precision of b is 10 times better than a and g M. Morii, Harvard

  27. CKM precision tests • Measured angles agree with what we knew before 1999 • But is it all? • We look for small deviation from the CKM-only hypothesis by using the precise measurement of angle b as the reference The CKM mechanism is responsible for the bulk of the CP violation in the quark sector Next steps • Measure b with different methods that have different sensitivity to New Physics • Measure the sides a g b M. Morii, Harvard

  28. Angle b from penguin decays • The Golden mode is • Consider a different decaye.g., • b cannot decay directly to s • The main diagram has a loop • The phase from the CKM matrix is identical to the Golden Mode • We can measure angle b in e.g.B0 f + KS Tree Penguin top is the main contributor M. Morii, Harvard

  29. New Physics in the loop • The loop is entirely virtual • W and t are much heavier than b • It could be made of heavier particlesunknown to us • Most New Physics scenarios predictmultiple new particles in 100-1000 GeV • Lightest ones close to mtop = 174 GeV • Their effect on the loop can be as big as the SM loop • Their complex phases are generally different Comparing penguins with trees is a sensitive probe for New Physics M. Morii, Harvard

  30. Strange hints • Measured CP asymmetries show a suspicious trend • Naive average of penguins give sin2b = 0.50  0.06 • Marginal consistency from the Golden Mode(2.6s deviation) Penguin decays Penguin modes Golden mode Need more data! M. Morii, Harvard

  31. To measure the lengths of thetwo sides, we must measure|Vub| ≈ 0.004 and |Vtd| ≈ 0.008 The smallest elements – not easy! Main difficulty: Controlling theoretical errors due to hadronic physics Collaboration between theory and experiment plays key role The sides a g b Vub Vtd M. Morii, Harvard

  32. |Vub| – the left side • |Vub| determines the rate of the b utransition • Measure the rate of b uvdecay ( = e or m) • The problem: b cv decay is much faster • Can we overcome a 50 larger background? M. Morii, Harvard

  33. Detecting b → uℓv • Use mu << mc difference in kinematics • Signal events have smaller mX  Larger E and q2 E = lepton energy q2 = lepton-neutrino mass squared u quark turns into 1 or more hardons mX = hadron system mass Not to scale! M. Morii, Harvard

  34. Figuring out what we see • Cut away b cv  Lose a part of the b uvsignal • We measure • Predicting fC requires the knowledge of the b quark’s motion inside the B meson  Theoretical uncertainty • Theoretical error on |Vub| was ~15% in 2003 • Summer 2005: • What happened in the last 2 years? Cut-dependentconstant predictedby theory Total buv rate Fraction of the signal that pass the cut HFAG EPS 2005 average M. Morii, Harvard

  35. Progress since 2003 • Experiments combine E, q2, mX to maximize fC • Recoil-B technique improves precisions • Loosen cuts by understanding background better • Theorists understand the b-quark motion better • Use information from b sg and b  cv decays • Theory error has shrunk from ~15% to ~5% in the process Fully reconstructedB hadrons BABARpreliminary b  cvbackground v X  M. Morii, Harvard

  36. Status of |Vub| |Vub| world average as of Summer 2005 • |Vub| determined to 7.6% • c.f. sin2b is 4.7% Measures the length of the left side of the UT M. Morii, Harvard

  37. |Vtd| – the right side • Why can’t we just measure the t d decay rates? • Top quarks are hard to make • Must use loop processes where b  t d • Best known example: mixing combined with mixing • Dmd= (0.509  0.004) ps−1 • mixing is being searched for at Tevatron (and LEP+SLD) • Dms > 14.5 ps-1 at 95 C.L. (Lepton-Photon 2005) B0 oscillation frequency Bs oscillation frequency M. Morii, Harvard

  38. Radiative penguin decays • Look for a different loop that does b  t d • Radiative-penguin decays • New results from the B Factories: • Translated to  M. Morii, Harvard

  39. Impact on the UT • We can now constrain the right side of the UT • Comparable sensitivities to |Vtd| • Promising alternative/crosscheck to the B0/Bs mixing method B0/Bs mixing Need more data! M. Morii, Harvard

  40. The UT today Sides + KL decays Combined Angles from CP asymmetries M. Morii, Harvard

  41. The UT today • The B Factories have dramaticallyimproved our knowledge of theCKM matrix • All angles and sides measuredwith multiple techniques • New era of precision CKMmeasurements in search of NP • The Standard Model is alive • Some deviations observed require further attention New Physics seems to be hidingquite skillfully M. Morii, Harvard

  42. Two Higgs doublet model Allowed byBABAR data mH (GeV) b sg B tn tanb Constraining New Physics • New Physics at ~TeV scale should affect low-energyphysics • Effects may be subtle, but we have precision • Even absence of significant effects helps to identify NP • In addition to the UT, we explore: • rare B decays into Xsg, Xs+-, tn • D0 mixing and rare D decays • lepton-number violating decays Precision measurements at the B Factories place strong constraints on the nature of New Physics M. Morii, Harvard

  43. Outlook • The B Factories will pursue increasingly precise measurements of the UT and other observables over the next few years • Will the SM hold up? • Who knows? • At the same time,we are setting a tightweb of constraints on what New Physics can or cannot be What the B Factories achieve in the coming years will provide a foundation for future New Physics discoveries M. Morii, Harvard

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