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Home , Toshihide Maskawa

PoS(FPCP2009)047 http://pos.sissa.it/ 2 rotations, to the × † ∗ — From B Factory to the Large Hadron Collider — Lecture about the Recent [email protected] Speaker. I thank the organizers for the invitation. This work is supported in part by the National Science Council of R.O.C. insight of Kobayashi and Maskawathere that exists a CP 3rd generation violation of . couldWe The arise end richness that from with followed a the defines perspective this charged on (FPCP) a conference. currents, (possible) if redux with a 4th generation of quarks. These are the transcriptions ofthe “a one talk who describing wasn’t) the and theoreticalcouple of insights how decades.” of this After prologue, those has we honored first led dealBreaking, (and to with which Nambu’s all insight is on the rooted Spontaneous Symmetry physics inresonates an we to analogy have this with been day, the as doing BCS we overLévy–Cabibbo theory await the the of theory, LHC last superconductivity. through era The to the insight dawn. GIM The mechanism second that half starts completed from the Gell-Mann– 2 ∗ † Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. c

Flavor Physics and CP Violation 2009, May 27 - June 1, 2009, Lake Placid, NY, USA grant NSC 97-2112-M-002-004-MY3, byTheoretical National Sciences Taiwan (North). University grant 97R0066-60, and the National Center of National Taiwan University E-mail: George Wei-Shu Hou PoS(FPCP2009)047 George Wei-Shu Hou prompted Heisenberg , and thus introducing p N m ] that maybe there is some ∼ = 1 n is a real difficulty. m N m 2  π m ? N m 2  π m for the discovery of the mechanism of spontaneous broken ” The B factory workers (this one included) feel as honored, ” (SSB) It is clear that SSB, the “Higgs” particle, the Origin of , but admitting immediately that ¯ N N U(1) is already verified experimentally, and that it does not require a physical × for the discovery of the origin of the broken symmetry which predicts the existence of at By 1956, Fermi had died, while Yang was busy with parity violation. It was of On September 30th, 2008, Ling-Fong Li gave a colloquium at NTU on the Higgs particle. Turning around to my colleague, Yeong-Chuan Kao, a Nambu fan, I said, “Could it be Nambu On October 2nd, I gave a seminar at the IPMU of Tokyo University, and stated after showing In the evening of October 7th, a little tired and bored, I recalled the date and went on-line, and So, 1/4 each of The 2008 goes to Kobayashi sensei and Maskawa I wonder whether the above can be called a “premonition,” but I certainly did not expect to be With Chadwick’s discovery of the neutron, the near equality of It was Fermi and Yang who, in 1949, put forward the suggestion [ is a bound state of University who followed up on the point. More particles have appeared since. Undaunted compositeness behind the scene. They pointedwhich out essentially that these means particles “structureless.” were assumedelementary But “elementary,” becomes then less they and state less that asπ “all their number such increases.” particles With ... this, they should suggest be that the pion At the end, I commented(SBGT) on of the SU(2) Higgs MechanismHiggs ..., that . Spontaneously Broken Then Gaugethe Theory I Prize said, this year, roughly becauseSecond, “There former BaBar should KEK shut be Director down enhanced in General,await April, the chance Totsuka LHC marking sensei, for era a passed to Japanese transition away dawn, receiving for Cabibbo, in Kobayashi the July. and B Maskawa Factory have good era.and chance Goldstone this Therefore, ?! year.” as Nambu certainly we wellwas deserves, over and 20 he’s years really ago. old Kao !” then After stated all, adamantly his that 65th Nambu birthday willthe get recent the CKM prize. fit, “Couldannouncement should this be be tomorrow.” He the got Year the of date CKM wrong, but ?” it Hitoshi didwas prompt Murayama exhilarated me responded to to that witness check the ... “the “predicting” announcement all ... three and Japanese names, the I geniusCommittee. was of certainly the astonished by Nobel the Committee. brutal cut-and-paste Though by the sensei, “ here to deliver this “lecture.” But here goes. 1. Introduction: the Trouble of Mass(es) Nobel 2008 0. Prologue: Predicting the 2008 Prize least three families of quarks in nature. by demonstrating the mechanismby of KM. CP Of Violation course, (CPV) by isPhysics implication indeed 2008 of as goes pointed the to out ordering, Nambusymmetry the sensei, more in “ important subatomic 1/2 physics. ofMass, The is Nobel the main Prize goal in at the Large Hadron Collider. to propose isospin symmetry, that the two form an isodoublet, the nucleon “internal symmetries.” From Yukawa’s proposal to Powell’salso discovery, as came the in dust as settled, an the isotriplet. pion But why, then, PoS(FPCP2009)047 ” , turned ) ] “Quasi- Everyone n ], however, , 1 11 4 ” With these p , Λ ( George Wei-Shu Hou with compositeness? One day before publi- -beams. N ), an isodoublet and an e m Λ ]. The rest is history. The 2 9 Give it another month, or a ” at the conference, recalls  and π n m , p ” Sound like all praises. However, ], a triumph of Squalid State Physics! (or People don’t understand him, because 10 Λ ], Nambu writes, “ In a pig’s eye! 5 ] in “Broken Symmetry,” which is also the 5 and Over the years, you could rely on Yoichiro to N 3 ” Schrieffer soon joined the Chicago faculty, and ], it was shown, ingeniously, how 3 ] that it is ] “Strings and — The seer, this year’s physics Nobel 2 7 , the quarks of Gell-Mann. In the latter seminal paper [ ) s , d , u ( ] “my early exposure to condensed matter physics has been quite beneficial to 6 ” And Murray Gell-Mann says “ ]. The omega was discovered the next year. ” mesons of the day, were composites à la the Fermi–Yang suggestion. 8 τ ” or “ θ In his autobiography notes in Broken Symmetry [ Early indication of nucleon structure is the measurement of anomalous magnetic moment of proton by . But this was a momentous time, both at Chicago, and at Illinois. “ Scientific American reran their “Profile: ” of 1995, immediately after the Still, where does the proton mass come from? [In fact, where does “Mass” come from? This is It was Gell-Mann who quipped the words “Squalid State Physics,” but it was Squalid State This was one step away from quarks. In the poster of “The Jubilee of the Sakata Model” 1 At time of the Sakata paper, Hofstadter was uncovering nucleon structure at Stanford with in Nambu’s own words, thatseemed he smarter wrote than decades I. I laterHe could to was not encourage referring accomplish a to what junior the Iwhen colleague: Institute wanted he of was to “ already Advanced and an Study, had associate thehe a professor place was nervous at he met breakdown. Chicago, went with when after he ridicule. proposed his a Richard doctorate. new Feynman particle Even shouted in “ 1957, BCS theory of superconductivity was published in 1957 [ particles and Gauge Invariance in the Theory of Superconductivity.” He obtained Ward identities provide deep and penetrating insights on very many questions. Nambu could discuss with him in depth. In July 1959, Nambu submitted the paper [ Nobel announcement, with the title [ me.” And (and physics as a whole) is forever grateful. laureate, saw them all.”he is Ed so Witten farsighted. is quoted as saying “ Laurie Brown [ month and a half. Wait ’tilparting I words get to back Bob and Schrieffer, John keepthe Bardeen working. Nobel left Maybe for Prize something’ll Sweden in happen. in Physics, late his November first, of for 1956 the to discovery accept of the transistor [ cation of the BCS paper, BobBCS Schrieffer, theory still in a progress student, ... cameconserve to I electron Chicago was number. to very give much It a disturbedboldness did seminar by and on not the tried the make fact to that sense understand their ... the wave problem. function At did the not same time I was impressed by their still the prevailing question of the day.] And, can one understand Physics that came to theacknowledges that rescue. [ Nambu, who received a Sc.D. from Tokyo University in 1952, Nobel 2008 by the mass issue, Sakata proposed [ upside down, became Gell-Mann refers to “the old Sakata model” but without giving a citation. namesake of the 2008 Nobel Prize in Physics. 2. Squalid State to the Rescue — Nambu’s Insight It was Nambu who guided the way, as documented [ held at in October 2006 [ isosinglet, respectively, that are “elementary,” and all otheror particles, the whether “ the heavier , PoS(FPCP2009)047 ]: 13 On other 3 ” ], made rigor- 14 George Wei-Shu Hou 2 ]. 16 ] the term Ginzburg–Landau– my biased opinion, there being 12 ]: “ 6 ], the precursor to the BCS theory of as “collective excitation” 17 π .” Let me now return to Nambu’s prize. ], and published in the CERN Courier [ 9 . I also should have paid more attention to the 4 In hindsight I regret that I should have explored in ]: “ 6 He superfluidity and nucleon pairing in nuclei, he offers ], and three papers, by François Englert and Robert Brout, 3 15 ] on the mechanism of BCS theory: as “BCS Energy Gap” and N 12 , m 6 : “The BCS theory assumed athe condensate medium of was charged not pairs gauge oftive invariant. electrons excitations or There of holes, were pairs hence found (Nambu-Goldstone intrinsicallyand modes) massless they that collec- turned restored into the broken plasmons symmetries, by mixing with the Coulomb field.” The broken symmetry in superconductivity is not just continuous, but it is the gauged sym- We note in passing that Englert,The Brout underlining and is Higgs mine. received the EPS Prize in 1997, and the Wolf Prize in 2004. In reference to the , Nambu himself uses [ Nambu later reflects [ 2 3 his opinion on mass generation in the Standard Model [ metry of electromagnetism itself. Thus,modes as ... we turned quoted into from the Nambu plasmons above,effect by in the a mixing “Nambu-Goldstone gauge with invariant the way Coulomb (asThe field.” insisted claim This by to Nambu), explains which the the is Higgs Meissner nothing mechanismBCS but is theory the itself of Higgs by course Mechanism. Philip a Anderson contentious [ one. There is the argument based on ous in a subsequent paper bylet Goldstone, me Salam continue and with Weinberg. Though Weinberg’s words: gettingtilting ahead the “Broken of hat; approximate ourselves, this symmetry produces is a illustrated small by restoring force, slightly analogous to the small mass of the pion.” by , and by Gerald Guralnik, Carl Hagen and Tom Kibble [ superconductivity. He further comments [ more detail the general mechanism of mass generation for the gauge field. But IGinzburg-Landau thought theory the plasma which wasexamples a of forerunner BCS of type the of SSB, present such Higgs as description. other interpretations as to the nature of the HiggsThe field Penetrating Analogy and the Meissner effect had already established it Higgs “effective” field, citing the Ginzburg–Landau theory [ He found that zero modesessence of necessarily the Goldstone emerged theorem. because Let theican us not hat” broken repeat illustrates symmetry the the mathematics. is point, It continuous, sothe is let well the LHC,” known me that delivered quote a at directly “Mex- from the Steven BCS@50 Weinberg’s talk celebration “From BCS [ to Nobel 2008 — telltale signs ofner gauge effect invariance calculation — strictly that, gaugeantiparticle despite invariant. interacting the with broken He each symmetry, further otherwas rendered observes crucial to the for that form Meiss- understanding “a a the pair mechanism bound“Nambu-Goldstone of by boson” state of which a with zero gauge particle zero mass. invariance was and Let energy restored. us and digress. This momentum” Nambu-Goldstone is Boson the and Higgs Mechanism “Though the hat is invariant underthe rotations axis about of a symmetry, vertical somewhere axis, onforce a around the small ball the brim will brim.” of come the This to hat, is rest but precisely off it the can content move of freely the with Goldstone no Theorem restoring [ PoS(FPCP2009)047 . The ], and N 22 m 2 quarks  QCD d , π realization u m George Wei-Shu Hou mass; and collective ], on the grounds of statistics. 21 N ↔ ) invariance m ], and the fact that it took another 5 γ . ¯ chirality 20 unknown d , u 4 is (meson boundstate) Strong Interactions chiral ( + π hypothetical ]). π 19 ] “Axial Vector Current Conservation in Weak invariance of the bare baryon field is not rigorous, 5 PT). For clarity, perhaps we need to backtrack to 18 5 χ γ , + SB), and light had been shed on why χ invariance; energy gap 5 SB vs. BCS theory, and we would need a few formulas. γ χ ↔ electrons and spin energy gap p electric charge gauge invariance phonon exchange Superconductivity ) constituents, whereas collective excitations udd ( uud theory of weak interactions and CVC in 1958, many were interested in a possibly A mesons. He went on to conclude that “It is interesting that pseudoscalar mesons − illustrates the full power of Nambu’s analogy. Considering that the “hypothetical ↔ V 1 SB. Nambu’s analogy between the BCS theory of superconductivity, and spontaneously broken chiral interaction χ broken symmetry elementary particle The quasi-particles near the Fermi surface of a superconductor is a coherent mixture of electron Table Although the true dynamics was not yet known, Nambu went further to construct dynamical Nambu followed a keen interest in understanding gauge invariance in the presence of SSB. and hole states with momentum what Nambu saw in the nucleon with chiral symmetry breaking, eventually resulting in the Nambu–Jona-Lasinio (NJL) model [ fermions” were put forth 4decade years (after before the the emergence modellatter of [ to QCD be that accepted, tookof Nambu’s the what insight place by and of analogy mesons isWe the really should truly are, “unknown” remember even that penetrating. interaction) before color for the SU(3) HeHere was rather the saw also he difficult proposed through dynamics followed by was the Gell-Mann’s him understood. quark veil [ possibility model of paper, fractionally but charged unfortunatelyproton quarks. did (neutron) not has With follow the the latter, simplest we have the familiar picture that the the foundations of chiral perturbation theory ( Interactions,” Nambu constructed theTreiman axial relation vector in current, a and satisfactoryof way, having BCS he derived theory: made the the gaugeexcitations Goldberger– penetrating invariance analogy from his understanding possibly because of a smallwas bare mass not of entirely the order correct,Sakata of the model the pion was insight becoming mass.” was clearer! Althoughspontaneous clearly the Yukawa’s pion Chiral last profound: has Symmetry statement become Breaking what the ( Nambu–Goldstone was boson behind of the Fermi–Yang– automatically emerge in this theoryand as baryon mass bound splitting states would imply of that the baryon pairs. The nonzero meson masses He was certainly more aproposal of particle and field theorist, than a condensed matter . With the Nobel 2008 dominant part of ourthrough body mass, or that of the Earth orTable the 1: Sun or thesymmetry of visible the strong Universe, interactions arose (adapted from Ref. [ conserved axial vector current. In the paper [ PoS(FPCP2009)047 (2.1) (2.2) ] “As 22 (3) chiral ]. Nambu U(1), and R × 22 , SU 6 × Going further, “It (3) 4 SB, and the SSB of George Wei-Shu Hou L χ U(1) × , SB established as the non-Abelian , − , χ p + , is the gap parameter [ , , † p − 2 1 PT works at long distance when QCD φ ψ ψ SU(2) χ φ ψ φ ψ , m m × ]. These were of course later proven by , 2 . The Dirac mass corresponds to the gap + + 2 5 + + m 23 γ φ − 1 2 , SB to interface with data. p + + ψ ψ , + χ † 2 p − p p 2 p p 6 · · ψ ψ ε p p p σ σ q ε ε ± − ± − ======2 1 E − + E , , ψ ψ p p E E † − ψ ψ E E PT is applicable. This is the precursor to effective field theories. χ in a superconductor is created by the interaction, let us assume that the mass of a φ , which touches base with our former discussion. But from here, NJL states [ are eigenstates of the chirality operator φ 2 .” (italics are mine) This is the starting point not only in constructing the NJL model, is the kinetic energy from the Fermi surface, and , 1 p ψ ε PT, and effective field theories in general. Note that We are familiar with Weinberg’s usage of the Higgs mechanism to break SU(2) The relativistic cutoff would take the place of the (nonrelativistic) Fermi surface. SSB is clearly an integral part of the Standard Model, both inWith dynamical the “unknown” interaction of spontaneous/dynamical We see the power of one person’s insight through analogy. (3). But, just as in the NJL model, even when QCD is not applicable in the strong coupling the nucleon mass is a manifestation of some unknown primary interaction between originally χ 4 V symmetry is dynamically broken down bySU QCD, as well as explicitregime quark (low energy), masses, to approximate his conjecture that non-Abelian gauge theoryafter is renormalizable, SSB and that would reordering not of perturbation change the renormalizability [ gauged dynamics of color SU(3), weit, recall and the the correct breakthrough selection of of the asymptoticeven gauge freedom though group that by Han preceded Gross and and Nambu Wilczek (and had Fritzsch proposed and it Gell-Mann), much earlier. So, the global SU ’t Hooft and Veltman. What we wish to stress is that, while a single complex Higgs doublet field electroweak gauge interactions. massless fermions, the sameinto interaction pions also being responsible forbut the binding of nucleon pairs the energy gap Dirac particle is also due tois some perhaps interaction not between a massless coincidence bare thatwe fermions.” there would exists like such to an regard entity our in theorythat the as form dealing of with the nucleons pion. and mesons. For this The reason, implication would be doesn’t, and even lattice QCD calculations call on 3. Spontaneous Symmetry Breaking and SU(3) where Nobel 2008 saw an analogy with the (relativistic) Dirac equation, which reads, in the Weyl representation, where parameter PoS(FPCP2009)047 ]. 24 (4.1) decay + K of Eq. (4.1) factor for the quarks, Gell- vs. U(1) breaking, s θ particle.” 1) decays [ + × π Λ = 06, which is and . , sin George Wei-Shu Hou S d θ = ∆ , , 2 u ε ··· quark mixture 0 and 1 currents had been + = 1 2 O beta decay was in the right decay of the 26 could account for available − , on the path to Kobayashi and . S 14 β ) 0 ∆ 97, then 2 . ππ ε ] in their work “The Axial Vector 0 ' ” they suggested to + θ = 25 → , 1 1 2 0 C L 1 together to be something like: 0) and changing ( )( theory to compare e.g. θ factor to − K ) Λ = = A 2 θ ε sin S ε S − s ], something that is not in common use. ∆ ], where, dispensing with the need of a “basic + ∆ + 4 V + n 1 19 ( ( ], “the Cabibbo Theory, with the Cabibbo angle,” C 7 α θ quark in weak interactions is a mixture, γ 19 0 and ¯ p d ] of CPV in µ cos = Note added in proof, G S d 26 ∆ = = 0 ) 1 d = S ∆ ( 97. In a “ α . 0 GV ∼ + µ are the would-be Nambu–Goldstone ! α G / Z GV G and W mass eigenstates. ]; SSB is already an experimental fact, and regardless of the true origin of the SSB, 6 s , “quickly became a standard framework for the weak interactions. It turned out to be . He proposed a “unit length” of strength, i.e. a cos and ◦ µ d O data implied “... consider the vector current for and likewise for the axial vector current. If of the right order of magnitude for explaining the low rate of 0, 1 currents, and found that a near universal value of 13 ν Unfortunate perhaps for Cabibbo, the unitary transform of In 1964 Gell-Mann put forth the quark model [ The proliferation of strange hadrons caused Sakata to proposeIn his his seminal substructure paper “Unitary model, Symmetry and their Leptonic Decays” of 1963, Nikola Cabibbo made Besides the experimental discovery [ 14 + = ∼ = µ S C of the consider 3 years earlier by Gell-Mann and Maurice Lévy [ Current in Beta Decay,” asthat Cabibbo acknowledges in his footnote 4. Gell-Mann and Lévy noted Maskawa, there is one more important step, which is the mechanism proposed by Sheldon Glashow, neutral baryon singlet,” he discusses the“quarks” simpler (here, (and Gell-Mann calling is it moving more beyond the elegant) Sakata non-integer model). charged With the Writing before quarks, he used SU(3) currents and θ universal and an ever-increasing multitude ofof data weak could interactions.” be In fitted quark into language, it. the It has been a cornerstone the longitudinal 4. Gell-Mann–Lévy–Cabibbo and GIM: from 3 to 4 Quarks weak decay also pointed to some universal behavior. a comprehensive study of strangeness conserving ( Nobel 2008 developing a vacuum expectation value (v.e.v.) is thethe simplest realization Higgs of field SU(2) does notHiggs have field to [ be elementary. One needs only an effective Ginzburg–Landau– to for the first time.stating In “We so thus obtain doing, all Gell-Mann the refers features both of Cabibbo’s to picture.” his previous work with Lévy, as well as ∆ data. He noted that, thoughdirection. overshooting Paraphrasing a the bit, Nobel the Committee [ cos to maintain universality. Althoughpursued by they Cabibbo did (who not hadthe press more wording further, “Gell-Mann–Lévy–Cabibbo” data theory available), this [ and is may the be same why the program Nobel as Committee that uses Mann puts the electromagnetic current in the modern form, and uses the PoS(FPCP2009)047 , 3 µ λ ν × , ] on n (com- , 29 p 0 K quark, then ]. u 31 . importance. amplitude cancels pair, and George Wei-Shu Hou − 0 µ d 0 3 quark. This “charm” ¯ As for “a 6-plet model, + d / µ 7 2 universal matrix, is something called the + → ) ]. CKM ¯ sd ] that CPV is needed to explain 30 ( motivated by CPV n V 0 28 × K n -component vector fields. n 2 form. Targeting CPV, they conclude that × , then the but they also use Sakata’s notation of C and they give their parametrization of the 3 6 θ boson would couple to a 8 8 0 for the SU(3) triplet of quarks. cos ] in 1970, in the paper titled “Weak Interactions with Z s λ 27 that connects two , + U C . So it came natural to the two Nagoya graduates. N e θ , real and orthogonal ...,” and in this way they arrived at the ν degrees of freedom in the of Eq. (4.1) enters the with the ], that our usual exercise (in our Particle Physics course) of phase freedom P ] of CP violation in neutral kaon system in 1964 came as a 2 ] “... suitable redefinitions of the relative phases of the quarks sin U 0 ) 19 , which was not observed. GIM pointed out that, if one adds the 1 d d 26 27 − as ...” the familiar 2 − as used by GIM), renders the “Cabibbo rotation” complete. − µ 0 -violation,” they note that “in this case we cannot absorb all phases n U + 3 quark (the charge was actually kept free in the work). At Nagoya, = / 0 P µ CP pair implies the existence of a new charge s 2 ) = ( 0 1 -violation exist in the quartet scheme without introducing any other new s + of 0 s − 5 CP n ] of the unitary matrix 2 ]. Nor do they refer to GIM, ( 32 − 23 2 n coupling to ¯ ) should decay to 0 Z sd in modern notation ( for the 4th, charge c ζ The experimental discovery [ The I bless the young postdoc(s) reading this to make similar impact at a tender age. Knowledge of GIM was acknowledged in the Nobel Lecture of Maskawa [ KM quickly dispensed with the “quartet” model, that “With an appropriate phase convention GIM uses the Sakata model notation of The case of extra right-handed quarkI doublets learned were from already the considered Nobel by Committee Rabindra [ Mohapatra [ The pursuit of CP violation was taken up by Makoto Kobayashi and Toshihide Maskawa (KM). The GIM paper did mention [ 2 rotation matrix. But they were not concerned with CP violation. 6 5 7 8 × 5. Insight of Kobayashi–Maskawa: 6 Quarks for CPV away. This works also atflavor the changing loop neutral currents level (FCNC) (violated are only suppressed,usage by which of difference is unitarity consistent in of with masses), quark experiment! guaranteeing mixing This that matrix is the foundation of flavorquark, loop calculations. another interesting model of of matrix elements into theunitary phase matrix. convention...,” The 3 “generation” Standard Model was born — Iwasawa decomposition [ fields.” So they consider adding new fields, such as extra scalar doublets. “no realistic models of of the quartet field we can take September 1st, 1972 tojust Progress 28 of years old, Theoretical andWeinberg’s Physics, paper Maskawa [ the 32. Japanese Although journal. the title states Kobayashi “renormalizable,” was they refer only to was demonstrated to be different from of quark fields, the may be performed in order2 to make Both received their Ph.D. from Nagoya Universitywent (hence immersed to in Kyoto the University Sakata school), after andsubmitted graduation. both the Barely 5 paper months “CP after Violation Kobayashi in had arrived, the the Renormalizable two Theory of Weak Interaction” [ the school of Sakata, people were independently thinking of the existence of a 4th quark after surprise. Before long, however, Andrei Sakharov pointed out [ plus Lepton–Hadron Symmetry.” If the Nobel 2008 Jean Iliopoulos and Luciano Maiani (GIM) [ in the Glashow–Weinberg–Salam theory, the posed of ¯ orthogonal combination the absence of antimatter in our Universe, so understanding CPV gained PoS(FPCP2009)047 (6.2) . 2 quark mixing , 10 A × − ], ) 2 d George Wei-Shu Hou 34 m − 2 s m come from the big wigs of )( 2 s m − quarks. Though the values are not did not 2 b is twice the area of the triangle of 0 (6.1) t m A = )( 2 d ∗ and tb , normalized to the weak scale, seems to m V b J ], he comments on the state of affairs of CP td − V 33 2 b , or when any pair of like-charge quarks are , where m A + i † d ∗ )( cb 9 2 u m V d m cd m 3 case demands nondegeneracy of the bi-vector space; V − , ) lepton and × 2 c † u + τ m ν m ∗ ub u )( V 2 c m h ud vanishes with m (and V J − τ 2 t m )( 2 u m − 2 t m triangle, and a nontrivial CPV phase in particular. However, at the more refined = ( J nontrivial What the B factories have checked in detail is that People often think Nambu as a cut above the other two recipients, and I concur. Nambu is a cut There is unfinished business, however. Towards the end of Kobayashi’s Nobel Lecture [ forms a level, the Iwasawa decomposition for the 3 violation studies. Though “B-factory results showviolation,” they that “allow quark room mixing for additional is source theWhat from dominant is new source physics.” even of This more calls CP enticing for is furtherof that studies. CP “Matter violation.” dominance Let of us the elucidate Universe this seems a requiring new little. source in physical terms this means allis like-charge quark effectively pairs back ought to to the becaptured 2 nondegenerate. the generation Otherwise, essence case, one of and this the through CPV her phase proposed invariant can measure be of removed. CPV [ Cecilia Jarlskog above most of us, maybe evenof a a good model fraction is of the itsStandard Nobel predictive Model recipients. impact! — But And is the here, indeed measure the very of KM success successful. model If — Cabibbo the captured flavor half (and of CPV) the part 2 of the Nobel 2008 6. Richness of KM: from tau to top; FPCP matrix, and he could account forone practically parameter, all then (tree KM level) predicted strangenessCPV the decay phase existence and of to production two with account additionalexistence for mixing of that angles, the enigmatic plus third the phenomena. generation crucial There is the underlying prediction of the fall short of what is needed for the Sakharov conditions by at least a factor of 10 predicted, masses and mixings account forStandard the major Model, number which of — calls dynamical outViolation — — for parameters is in just an the shaping explanation. the foundationof This for the the conference third next generation — step, fermions, i.e. Flavor measuring understandingof Physics their it CPV, properties, and is all. confirming the CP The that enterprise discovery it that isB honors indeed the factories, the insight as source of epitomized two young inKM’s men. Prize. the It This “CKM is is unitarity mostly our fit” the paybackof outcome (salutations to the of these to academic the two Cabibbo world gentlemen. again), just Thethe adds that fact West to they lead (or did the Russia?). to it allure. This from brings The a me, “remote” observation an part East Asian, satisfaction. which can be deducedEq. from (6.1). Im det Indeed,degenerate. one Kobayashi’s words sees that that “Matter dominance of theof Universe seems CP requiring violation” new source refers to the despairing situation that PoS(FPCP2009)047 s π K was A → ] “... , and s ∆ b unpre- B σ 37 m ∆ falls short ] on J 10%, as due 38 the Bardeen– penguin loop ∼ ∼ penguin and the − bsZ π in the 3 generation , and Nature would from 123 to 234 in decays [7, 8].” This + George Wei-Shu Hou paper [ s bsZ K (defined analogously . The prediction was 10 s → π by 0 B ψ φ K B / d Φ A J A ∆ Nature − → 0 s > But, shocked by the emergence B − 9 . 6, with significance above 2 π . + C 0 effect in K dependence of the 0 − 0 → t 2 t 0 quark ... to explain the Belle result and B m quarks near or above the unitarity bound 0 0 t A t / 0 − b 0 Stop here if you wish. π + ]. The gain is mostly in large Yukawa couplings. ] this theme in the past few years ( K 10 39 -violating phase in → [ 40 100 GeV (worse if v.e.v. is used), then + . It occurred to me in late summer 2007, which I put B CP 15 ∼ 10 7 with a somewhat different argument, after A . 10 − T 0 ≡ ∼ − π ], together with Makiko Nagashima and Andrea Soddu, that K 35 A . Although the (combination of) errors are still under discussion, ) on the basis of a finite 5 to s ∆ . B 0 Φ ψφ / brings in a new CPV phase. Stressing that the J b ' − 0 t s V → B by a factor of 10 s 0 degeneracy limit, which is justified in our world. ∗ s t Φ 9 s B V - − d ” gains a factor of 10 the observation of a large can condense through (the origins of) large Yukawa coupling. Concurrent with 234 × J I’m a born-again 4th generationist! 5 ¯ . ] to sin2 QQ 0 , but for decays. The prevailing wind since a few years is to brush aside the staggering, 1 36 φ ∼ a priori B in 2004, I demonstrated [ box diagrams are closely linked, we made a prediction of sin2 / γ β π ¯ n direct CPV difference of b s / K Encouraging results followed at the Tevatron. I am grateful to CDF for the wording [ Another thing I enjoyed learning in the same time frame, prior to Nambu getting his prize, To me, this mouthful, as wellThis as is the valid oxymoronic in “enhanced the color-suppressed ...,” are clear symptoms. Nambu had a critical opinion on the nature of the Higgs field and fermion mass generation, At this conference, considerable effort is spent on the theoretical understanding of charmless A little more than a year ago, I made an unsettling observation. I learned about Jarlskog’s A B 9 10 ↔ ∆ n ¯ s to a large, hadronically enhancedof color-suppressed amplitude Eq. (6.2), then “ forth in arXiv:0803.1234, that if there is a 4th generation, and if one shifts Nambu’s “biased opinion,” the Higgstroweak boson gauge would symmetry then be become due composite. toof 500–600 condensation GeV? Could of Bob SSB Holdom of has explored elec- [ is that heavy measured by the CDF experiment in 2006. did I learn more clearlytroweak the phase simple transition dimensional temperature analysis of argumentof that, when scaled by the elec- likely use this. Who can argue with the “.1234” number returned by arXiv on March 8, 2008? Hill–Lindner work 20 years ago), which is in fact nothing but the NJL model!! Interestingly, there It seems that one would have enough CPV for matter dominance of the Universe some source of newtransition. physics ... contributing to George the Hou predicted electroweak the penguin presence which of governs a the it could be due to the 4th generation: the nondecoupled predicted while Kobayashi noted that hisfalls CPV short phase of what with is Maskawa, needed for theof matter Kobayashi–Maskawa–Nambu? one dominance In confirmed of the the by following, Universe. I the turn Icaution B to then that offer ask: factories, — a Can (personal) there perspective, be with a the redux Nobel 2008 7. Epilogue: KM–N Redux? A Perspective improved [ refers to our prediction of sin2 it is astounding that the worlddeviating central that value of much 2008 from is the about Standard Model (predicted from replacing hadronic invariant as a young postdoc, but only through the writing of the Belle dicted is tailor-made, while b to sin2 relation of Eq. (6.1)). This is astounding, as theorists only look at central values. PoS(FPCP2009)047 George Wei-Shu Hou ” It is tantalizing that ] the “holographic 4th 13 (1964) 508; 41 ibid. by 2010-2011; it could be eas- s B Φ 13 (1964) 585. ]). The article is published in CERN Courier in 9 130 (1963) 439. ibid. gain in CPV may be enough as the source of CPV 11 15 ibid. Maybe there is a 4th Generation! ]. If found, we would have brought heaven on earth, and with luck, the riddle of elec- 42 G.S. Guralnik, C.R. Hagen and T.W.B. Kibble, 2008, see http://cerncourier.com/cws/article/cern/32522. (1962) 965. Vol 13). Nambu’s 65 birthday, an event held in Chicago. 111002. University of Illinois at Urbana–Champaign (Ref. [ So, are we in for a KM–N redux? The 10 And that would be the ultimate tribute to the insights of Kobayashi, Maskawa, and Nambu. [1] E. Fermi and C.N. Yang, Phys. Rev.[2] 76 (1949) S. 1739. Sakata, Prog. Theor. Phys. 16[3] (1956) 686. See http://www.eken.phys.nagoya-u.ac.jp/sakata50/index.html. [4] M. Gell-Mann, Phys. Lett. 8 (1964)[5] 214. Broken Symmetry: Selected Papers of Y. Nambu (World Scientific Series in 20th[6] Century Physics, From Nambu’s Nobel Lecture slides, which can[7] be found See at http://www.scientificamerican.com/article.cfm?id=profile-yoichiro-nambu, by http://nobelprize.org. M. Mukerjee. [8] L.M. Brown, Prog. Theor. Phys. Suppl. 86 (1986) 1. This is the[9] festschrift volume See celebrating the BCS@50 event celebrated at Illinois, http://www.conferences.uiuc.edu/bcs50/schedule.html. [17] V.L. Ginzburg and L.D. Landau, Zh. Eksp. Teor. Fiz. 20 (1950) 1064. [16] F. Englert and R. Brout, Phys. Rev. Lett. 13 (1964) 321; P. W. Higgs, [14] J. Goldstone, Nuovo Cim. 19 (1961) 154; J. Goldstone, A. Salam and[15] S. Weinberg, P.W. Anderson, Phys. Phys. Rev. 127 Rev. 110 (1958) 827; generation.” I was therefore more than pleased with Nambu receiving the 2008 Nobel Prize. troweak symmetry breaking could be unveiled by the heaviness of the new chiral quarks. References [10] J. Bardeen, L.N. Cooper and J.R.[11] Schrieffer, Phys. Rev. Y. 108 Nambu, Phys. (1957) Rev. 1175. 117 (1960) 648. [12] Y. Nambu, “From Yukawa’s Pion to Spontaneous Symmetry Breaking,” J. Phys. Soc. [13] 76 (2007) S. Weinberg, “From BCS to the LHC,” talk given at BCS@50, held on 10-13 October 2007 at the for the matter dominance ofplings, the hence Universe (remember, the the dynamical fermion effectThis masses may alone are work to really even me Yukawa above cou- is the reason electroweak phase enough transition that scale). “ Nobel 2008 is an AdS/CFT correspondence to this strong coupling regime, called [ the Tevatron could bring indirect evidence forily this pursued through at sin2 LHCb,and once ATLAS data experiments could arrives. discover, or Moretime rule important, out, [ direct the existence search of at a the 4th generation LHC in by 3-5 the years CMS PoS(FPCP2009)047 George Wei-Shu Hou 12 (Belle Collaboration), Nature 452 (2008) 332. et al. http://nobelprize.org. G. Ünel, arXiv:0904.4698 [hep-ph]. Nobel 2008 [18] Y. Nambu, Phys. Rev. Lett. 4 (1960)[19] 380. From the Nobel Committee’s Scientific Background file, physadv08.pdf, which can be found[20] at G. Zweig, CERN Report 8419/TH.412, (1964),[21] unpublished. M.Y. Han and Y. Nambu, Phys. Rev.[22] 139 (1965) B1006. Y. Nambu and G. Jona-Lasinio, Phys. Rev.[23] 122 (1961) S. 345. Weinberg, Phys. Rev. Lett. 19 (1967)[24] 1264. N. Cabibbo, Phys. Rev. Lett. 10[25] (1963) 531. M. Gell-Mann and M. Lévy, Nuovo[26] Cim. 16 (1960) J.H. 705. Christenson, J.W. Cronin, V.L. Fitch and[27] R. Turlay, Phys. S.L. Rev. Glashow, Lett. J. 13 Iliopoulos (1964) and 138. L.[28] Maiani, Phys. Rev. A.D. D Sakharov, 2 Pisma (1970) Zh. 1285. Eksp. Teor. Fiz.[29] 5 (1967) M. 32. Kobayashi and K. Maskawa, Progr.[30] Theor. Phys. 49 See (1973) Maskawa’s 652. Nobel Lecture slides, which[31] can be found R.N. at Mohapatra, http://nobelprize.org. Phys. Rev. D 6[32] (1972) 2023. K. Iwasawa, Ann. Of Math, 50[33] (1949) 507. From Kobayashi’s Nobel Lecture slides, which[34] can be found C. at Jarlskog, http://nobelprize.org. Phys. Rev. Lett. 55[35] (1985) 1039; Z. W.S. Hou, Phys. M. C Nagashima 29 and (1985) A. 491. [36] Soddu, Phys. Rev. W.S. Lett. Hou, 95 M. (2005) Nagashima 141601. and A.[37] Soddu, Phys. Rev. CDF D public 76 note (2007) CDF/ANAL/BOTTOM/PUBLIC/9458, 016004. August 7,[38] 2008. S.W. Lin, Y. Unno, W.S. Hou, P. Chang [39] W.S. Hou, Chin. J. Phys. 47[40] (2009) 134 [arXiv:0803.1234 B. [hep-ph]]. Holdom, JHEP 0608 (2006) 076. [41] G. Burdman and L. Da Rold,[42] JHEP 0712 See (2007) the 086. recent brief summary by B. Holdom, W.S. Hou, T. Hurth, M.L. Mangano, S. Sultansoy and