Cracking the Unitarity Triangle — A Quest in B Physics — Masahiro Morii Harvard University MIT Department of Physics Colloquium 20 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

20 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

20 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 ↔

20 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

20 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

20 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

20 October 2005M. Morii, Harvard8 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 Cabibbo-Kobayashi-Maskawa matrix or CKM for short

20 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)

20 October 2005M. Morii, Harvard10 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 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

20 October 2005M. Morii, Harvard11 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 it is a mirror image of our Universe To create a matter-dominant Universe, Ccharge conjugation particle  anti-particle Pparity x   x, y   y, z   z CP symmetry must be broken ee ee One of the three necessary conditions (Sakharov 1967)

20 October 2005M. Morii, Harvard12 CP violation CP violation was discovered in K L decays K L 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?

20 October 2005M. Morii, Harvard13 CP violation and New Physics 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/c 2 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 Are there additional (non-CKM) sources of CP violation?

20 October 2005M. Morii, Harvard14 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

20 October 2005M. Morii, Harvard15 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

20 October 2005M. Morii, Harvard16 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

20 October 2005M. Morii, Harvard17 Time-dependent Interference Starting from a pure |B 0  state, the wave function evolves as 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 Ignoring the lifetime f CP t = 0t = t time

20 October 2005M. Morii, Harvard18 The Golden Mode Consider Phase difference is Direct path Mixing path

20 October 2005M. Morii, Harvard19 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

20 October 2005M. Morii, Harvard20 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

20 October 2005M. Morii, Harvard21 SLAC PEP-II site B A B AR PEP-II I-280 Linac

20 October 2005M. Morii, Harvard22 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

20 October 2005M. Morii, Harvard23 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

20 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−

20 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

20 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 

20 October 2005M. Morii, Harvard27 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  as the reference    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

20 October 2005M. Morii, Harvard28 Angle  from 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

20 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

20 October 2005M. Morii, Harvard30 Strange hints Measured CP asymmetries 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! Penguin decays Penguin modes Golden mode

20 October 2005M. Morii, Harvard31 The sides To measure the lengths of the two sides, we must measure |V ub | ≈ and |V td | ≈ 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

20 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?

20 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!

20 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

20 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 v 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

20 October 2005M. Morii, Harvard36 Status of |V ub | |V ub | determined to  7.6% c.f. sin2  is  4.7% |V ub | world average as of Summer 2005 Measures the length of the left side of the UT

20 October 2005M. Morii, Harvard37 |V td | – 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  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

20 October 2005M. Morii, Harvard38 Radiative penguin decays Look for a different loop that does b  t  d Radiative-penguin decays New results from the B Factories: Translated to   (B  ) B A B AR (0.6  0.3)  10  6 Belle (1.3  0.3)  10  6 Average (1.0  0.2)  10  6

20 October 2005M. Morii, Harvard39 Impact on the UT We can now constrain the right side of the UT Comparable sensitivities to |V td | Promising alternative/crosscheck to the B 0 /B s mixing method B 0 /B s mixing Need more data!

20 October 2005M. Morii, Harvard40 The UT today Angles from CP asymmetries Sides + K L decaysCombined

20 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 New era of precision CKM measurements in search of NP The Standard Model is alive Some deviations observed  require further attention New Physics seems to be hiding quite skillfully

20 October 2005M. Morii, Harvard42 Constraining New Physics New Physics at ~TeV scale should affect low-energy physics 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 X s , X s  ,  D 0 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 H (GeV) tan  Allowed by B A B AR data B  B   b  sb  s Two Higgs doublet model

20 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