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50 years of the Glashow–Iliopoulos–M aiani mechanism Shanghai plays host to GIM celebration J Liu J In 1969 many weak amplitudes could ical model of wea k interact ions.” be accurately calculated with a model To s id e s t e p t h i s pr o bl e m, G l a s h o w, I l i- of just three quarks, and Fermi’s con- o p o u l o s a n d M a i a n i br o u g ht i n t h e fo u r t h stant and the Cabibbo angle to couple “charm” quark, already introduced by t h e m. O n e e x c e p t i o n w a s t h e r e m a r k a bl e Bjorken, Glashow and others, with its suppression of strangeness-changing typical coupling to the quark combi- n e ut r a l c u r r e nt s. Jo h n I l io p o u lo s, Sh e l- nation left alone in the Cabibbo theory: don Lee Glashow and Luciano Maiani c ↔ sC = – s i n θC d + c o s θC s. A m pl it u d e s for boldly solved the mystery using loop s → d w it h u or c o n t h e s a m e fe r m i o n l i n e d i a g r a m s fe a t u r i n g t h e r e c e nt l y h y p o t h- would cancel exactly for mc = m u, sug- esised charm quark, making its exist- gesting a more natural means to suppress e n c e a s ol i d pr e d i c t i o n i n t h e pr o c e s s. To strangeness-changing neutral-cur- celebrate the 50th anniversary of their Happy anniversary Hong-Jian He, John Ellis, John Iliopoulos, rent processes to measured levels. For insight, the trio were guests of honour Sheldon Lee Glashow, Verónica Riquer and Luciano Maiani at a mc >> m u, a residual neutral-current effect at an international symposium at the celebration of 50 years of the GIM mechanism in Shanghai. w o u l d r e m a i n, w h i c h, b y i n s p e c t i o n, a n d T. D. L e e I n s t it ut e a t S h a n g h a i Ji a o To n g for dimensional reasons, is of order G 2 Universit y on 29 October 2019. sinθC cos θC (Gm c ). This was a real sur- The Glashow–Iliopoulos–Maiani cos θ, – sin θ prise: the “small” UV cutoff needed in (GIM) mechanism was conceived in d s the simple three-quark theory became an 1969, submitted to Physical Review D on W e s t i m a t e o f t h e m a s s o f t h e fo u r t h q u a r k, 5 M a r c h 1970, a n d p u bl i s h e d o n 1 O c t o b e r u, c u, c which was indeed sufficiently large to of that year, after several developments W have escaped detection in the unsuccess- had defined a conceptual framework ful searches for charmed mesons that had – for electroweak unification. These –s d been conducted in the 1960s. i n c lu d e d Ya n g–M i l l s t h e or y, t h e u n i v e r- sal V–A weak interaction, Schwinger’s sin θ, cos θ Embarrassment averted suggestion of electroweak unification, With the two quark doublets included, G l a s h o w’s d e fi n it io n o f t h e e l e c t r o w eak a detailed study of strangeness chang- group SU(2)L × U ( 1 ) Y, Cabibbo’s theory of ing neutral current processes gave mc semileptonic hadron decays and the ≈ 1.5 GeV, a value consistent with more u, c formulation of the leptonic electroweak recent data on the masses of charmed gauge theory by Weinberg and Salam, d s mesons and baryons. Another aspect with spontaneous symmetry breaking of the GIM cancellation is that the weak induced by the vacuum expectation value WW charged currents make an SU(2) algebra of new scalar fields. together with a neutral component that The GIM mechanism then called for a has no strangeness-changing terms. – fourth quark, charm, in addition to the –s d Thus, there is no difficulty in including t h r e e i nt r o d u c e d b y G e l l-M a n n, s u c h t h a t u, c t h e t w o q u a r k d o u bl e t s i n t h e u n i fie d e l ec- the first two blocks of the electroweak troweak group SU(2)L × U ( 1 ) Y of Glashow, 0 –0 theory are made each by one lepton and In the loop One-loop quark diagrams for K – K mixing in the We i n b e r g a n d S a l a m. T h e 1970 GI M p a p e r one quark doublet, [(νe, e), (u, d)] and light of the GIM mechanism. The charm–quark amplitudes have the noted that “In contradistinction to the

[(νµ, µ), (c, s)]. Quarks u and c are cou- same magnitude but opposite sign as for up-quark lines, leading to conventional (three-quark) model, the pled by the weak interaction to two a perfect cancellation, cos θ sin θ + (–sin θ) cos θ = 0, in the case couplings of the neutral intermediary – super­positions of the quarks d and s: where mc = mu, suggesting an explanation for the suppression of now hy p erc h a rge c on s er v i ng – c aus e no u ↔ d C, w it h d C t he Cabibbo combi nat ion processes with strangeness-changing neutral currents. embarrassment.” dC = cos θC d + sin θC s, a n d c ↔ sC, w it h s C the The GIM mechanism has become a 2 orthogonal combination. In subsequent amplitudes of order G sinθC cosθC (GΛ ), cornerstone of the Standard Model, y e a r s, a t h i r d g e n e r a t i o n, [(ντ, τ), (t, b)] w a s where G is the Fermi constant, Λ is an and gives a precise description of the predicted to describe CP violation. No fur- ultraviolet cutoff and GΛ2 (dimension- observed flavour-changing neutral-cur- ther generations have been observed yet. less) is the first term in a perturbative r e nt pr o c e s s e s for s a n d b q u a r k s. For t h i s expansion that could be continued to take reason, flavour-changing neutral cur- Charming prediction higher order diagrams into account. To rents are still an important benchmark The GIM mechanism was the solu- c o m pl y w it h t h e s t r ic t l i m it s e x i s t i n g a t and give strong constraints on theories tion to a problem arising in the sim- t h e t i m e, o n e h a d t o r e q u i r e a s u r pr i s i n g l y that go beyond the Standard Model in plest weak interaction theory with one small value of the cutoff,Λ , of 2–3 GeV, to t he TeV reg ion. charged vector boson coupled to the b e c o m p a r e d w it h t h e n a t u r a l l y e x p e c t e d C a bi b b o c u r r e nt s. A s p oi nt e d o ut i n 1968, value: Λ = G –1/2 ≈ 300 GeV. This problem Hong-Jian He T. D. Lee Institute, strangeness-changing neutral-current w a s t a k e n s e r i o u s l y b y t h e GI M a ut h or s, Shanghai Jiao Tong University and + – 0 –0 processes, such as K L → µ µ and K – K who wrote that “It appears necessary to Luciano Maiani T. D. Lee Institute and mixing, are generated at one loop with d e p a r t f r o m t h e or i g i n a l p h e n o m e n ol o g- Università di Roma.

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