Cracking the Unitarity Triangle — A Quest in B Physics — Masahiro Morii Harvard University University of Arizona Physics Department Colloquium 7 October 2005

M. Morii, Harvard2 Outline Introduction to the Unitarity Triangle The Standard Model, the CKM matrix, and CP violation CP asymmetry in the B 0 meson decays Experiments at the B Factories Results from B A B AR and Belle Angles , ,  from CP asymmetries |V ub | from semileptonic decays |V td | from radiative-penguin decays Current status and outlook    Results presented in this talk are produced by the B A B AR, Belle, and CLEO Experiments, the Heavy Flavor Averaging Group, the CKMfitter Group, and the UTfit Collaboration The Unitarity Triangle

7 October 2005M. Morii, Harvard3 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” quarksleptons strongE&Mweak uYes d e−e− NoYes e No Yes u ud

7 October 2005M. Morii, Harvard4 Simplified Standard Model Strong force is transmitted by the gluon Electromagnetic force by the photon Weak force by the W  and Z 0 bosons u u g d d g u u  d d  e−e−  e−e− u u Z0Z0 d d Z0Z0 Z0Z0 e−e− e−e− Z0Z0 e e d u W+W+ e e−e− W−W− Note W ± can “convert” u ↔ d, e ↔

7 October 2005M. Morii, Harvard5 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? strongE&Mweak g  W ±W ± Z 0Z 0 −− c  s −− t  b leptonsquarks e−e− u e d 1st generation 2nd generation 3rd generation It turns out there are two “extra” copies of particles

7 October 2005M. Morii, Harvard6 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 Particle mass (eV/c 2 ) Q =  /3  1/3 The origin of mass is one of the most urgent questions in particle physics today

7 October 2005M. Morii, Harvard7 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 arbitrary 3  3 unitary matrices Weak interactions between u, c, t, and d, s, b are “mixed” by matrix V

7 October 2005M. Morii, Harvard8 Turn the masses back on Masses uniquely define 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 Cabibbo-Kobayashi-Maskawa matrix or CKM for short

7 October 2005M. Morii, Harvard9 Structure of the CKM matrix The CKM matrix looks like this  It’s not completely diagonal Off-diagonal components are small Transition across generations is allowed 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)

7 October 2005M. Morii, Harvard10 What are we made of, again? Dirac predicted existence of anti-matter in 1928 Positron (= anti-electron) discovered by Anderson 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 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 Are they?

7 October 2005M. Morii, Harvard11 C, P and T symmetries Three discrete symmetries of Nature Laws of physics are symmetric under C, P, and T Not true: weak interactions do not respect C and P Laws of physics are really symmetric under CP and T Wrong again: CP violation discovered in K L decays CP violation makes matter and anti-matter different The SM does this with the complex phase in the CKM matrix Ccharge conjugation particle  anti-particle Pparity x   x, y   y, z   z Ttime reversal t  tt  t Wu et al., 1957 Christenson et al. 1964

7 October 2005M. Morii, Harvard12 Truth, the whole truth CP violation must explain how much matter is in the Universe What’s predicted by the CKM mechanism is not enough... by several orders of magnitude The Standard Model runs into self-inconsistency at higher energies (1-10 TeV)  New Physics must exist to resolve this Almost all theories of New Physics introduce new sources of CP violation (e.g. 43 of them in SUSY) The CKM mechanism is almost certainly an incomplete explanation of CP violation Is the CKM mechanism the whole story of CP violation?

7 October 2005M. Morii, Harvard13 The Unitarity Triangle V † V = 1 gives us Experiments measure the angles , ,  and the sides This one has the 3 terms in the same order of magnitude A triangle on the complex plane

7 October 2005M. Morii, Harvard14 The UT 1998  % CL 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 Factories that produce and study B mesons in quantity

7 October 2005M. Morii, Harvard15 Anatomy of the B 0 system The B 0 meson is a bound state of b and d quarks They turn into each other spontaneously This is called the B 0 -B 0 mixing Particlechargemasslifetime GeV/c ps GeV/c ps Indistinguishable from the outside W+W+ W-W- b d d b

7 October 2005M. Morii, Harvard16 Time-dependent Interference Starting from a pure |B 0  state, we’d get Suppose B 0 and B 0 can decay into a same final state f CP Two paths can interfere Decay probability depends on: the decay time t the relative complex phase between the two paths mix Ignoring the lifetime f CP t = 0t = t

7 October 2005M. Morii, Harvard17 The Golden Mode Consider Phase difference is Direct path Mixing path

7 October 2005M. Morii, Harvard18 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 A CP (t)? Step 1: Produce and detect B 0  f CP events Step 2: Separate B 0 from B 0 Step 3: Measure the decay time t Solution: Asymmetric B Factory

7 October 2005M. Morii, Harvard19 B Factories Designed specifically for precision measurements of the CP violating phases in the CKM matrix SLAC PEP-II KEKB Produce ~10 8 B/year by colliding e + and e − with E CM = GeV

7 October 2005M. Morii, Harvard20 SLAC PEP-II site B A B AR PEP-II I-280 Linac

7 October 2005M. Morii, Harvard21 Step 2: Identify the flavor of the other B Decay products often allow us to distinguish B 0 vs. B 0 Asymmetric B Factory Collide e + and e − with E(e + ) ≠ E(e − ) PEP-II: 9 GeV e − vs. 3.1 GeV e +   = 0.56 Step 1: Reconstruct the signal B decay e−e− e+e+ Moving in the lab  (4S) Step 3: Measure  z   t

7 October 2005M. Morii, Harvard22 Detectors: B A B AR and Belle Layers of particle detectors surround the collision point We reconstruct how the B mesons decayed from their decay products B A B AR Belle

7 October 2005M. Morii, Harvard23 B A B AR picture “Rear” view of B A B AR near completion.

7 October 2005M. Morii, Harvard24 J/y KS event A B 0 → J/  K S candidate (r-  view) Muons from Pions from Red tracks are from the other B, which was probably B 0  −  + ++ −−  −  + K−K−

7 October 2005M. Morii, Harvard25 CPV in the Golden Channel B A B AR measured in B 0  J/  + K S and related decays J/  K S 227 million events J/  K L

7 October 2005M. Morii, Harvard26 Three angles of the UT CP violation measurements at the B Factories give Angle (degree)Decay channels  B    B   cc  K   B   D (*) K (*) Precision of  is 10 times better than  and 

7 October 2005M. Morii, Harvard27 CKM precision tests Angle measurements agree with the Standard Model But is it all? We’ve measured  precisely, but  and  are much harder One good measurement doesn’t test consistency    Next steps Measure  with different methods that have different sensitivity to New Physics Measure the sides Next steps Measure  with different methods that have different sensitivity to New Physics Measure the sides The CKM mechanism is responsible for the bulk of the CP violation in the quark sector

7 October 2005M. Morii, Harvard28 Penguin decays The Golden mode is Consider a different decay e.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  in e.g. B 0   K S Tree Penguin top is the main contributor

7 October 2005M. Morii, Harvard29 New Physics in the loop The loop is entirely virtual W and t are much heavier than b It could be made of heavier particles unknown to us Most New Physics scenarios predict multiple new particles in GeV Lightest ones close to m top = 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

7 October 2005M. Morii, Harvard30 Strange hints Measurements show a suspicious trend Naive average of penguins give sin2  = 0.50  0.06 Marginal consistency from the Golden Mode (2.6  deviation) Need more data! Golden Mode Penguin decays

7 October 2005M. Morii, Harvard31 The sides To measure the lengths of the two sides, we must measure |V ub | ≈ 0.04 and |V td | ≈ 0.08 The smallest elements – not easy! Main difficulty: Controlling theoretical errors due to hadronic physics Collaboration between theory and experiment plays key role    V td V ub

7 October 2005M. Morii, Harvard32 |V ub | – the left side |V ub | determines the rate of the b  u transition Measure the rate of b  u v decay ( = e or  ) The problem: b  c v decay is much faster Can we overcome a 50  larger background?

7 October 2005M. Morii, Harvard33 Use m u << m c  difference in kinematics Signal events have smaller m X  Larger E and q 2 Detecting b → uℓv u quark turns into 1 or more hardons q 2 = lepton-neutrino mass squared m X = hadron system mass E = lepton energy Not to scale!

7 October 2005M. Morii, Harvard34 Figuring out what we see Cut away b  c v  Lose a part of the b  u v signal We measure Predicting f C requires the knowledge of the b quark’s motion inside the B meson  Theoretical uncertainty Theoretical error on |V ub | was ~15% in 2003 Summer 2005: What happened in the last 2 years? Total b  u v rate Fraction of the signal that pass the cut Cut-dependent constant predicted by theory HFAG EPS 2005 average

7 October 2005M. Morii, Harvard35 Progress since 2003 Experiments combine E, q 2, m X to maximize f C Recoil-B technique improves precisions Loosen cuts by understanding background better Theorists understand the b-quark motion better Use information from b  s  and b  c decays Theory error has shrunk from ~15% to ~5% in the process Fully reconstructed B  hadrons v X B A B AR preliminary b  c v background

7 October 2005M. Morii, Harvard36 Status of |V ub | |V ub | has been measured to  7.6% c.f. sin2  is  4.7% Fruit of collaboration between theory and experiment

7 October 2005M. Morii, Harvard37 |V td | – the right side Why can’t we just measure the t  d decay rates? Top is hard to make Must use loop processes where b  t  d Best known example: mixing combined with mixing  m d  = (0.509  0.004) ps −1 mixing is being searched for at Tevatron (and LEP+SLD)  m s > 14.5 ps -1 at 95 C.L. (Lepton-Photon 2005) B 0 oscillation frequency B s oscillation frequency

7 October 2005M. Morii, Harvard38 Radiative penguin decays Look for a different loop that does b  t  d Radiative-penguin decays New results from B Factories: ModeB A B AR Belle B+  +B+  + < 1.8  (0.6  0.4)  B0  0B0  0 < 0.4  (1.2  0.3)  B 0   < 1.0  (0.6  0.3)  B  [   /  ]  < 1.2  (1.3  0.3)  % C.L. Average

7 October 2005M. Morii, Harvard39 Impact on the UT From the radiative-penguin measurements Comparable sensitivities to |V td | Promising alternative/crosscheck to the B 0 /B s mixing method limits from the B 0 /B s mixing Need more data!

7 October 2005M. Morii, Harvard40 The UT today

7 October 2005M. Morii, Harvard41 The UT today The B Factories have dramatically improved our knowledge of the CKM matrix All angles and sides measured with multiple techniques Bad news: the Standard Model lives Some deviations observed  require further attention New Physics seems to be hiding quite skillfully Good news: the Standard Model lives! New Physics at ~TeV scale affect physics at low energies Precision measurements at the B Factories place strong constraints on the nature of New Physics

7 October 2005M. Morii, Harvard42 B Factories and New Physics m H (GeV) tan  Allowed by B A B AR data B  B   b  sb  s Two Higgs doublet model In addition to the angles and the sides of the UT, we explore: rare B decays into X s , X s  ,  D 0 mixing and rare D decays lepton-number violating decays Even absence of significant effects contributes to identifying NP If we measure them precisely enough Some of the best limits on NP come from rare B decays

7 October 2005M. Morii, Harvard43 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 tight web 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