Particules Élémentaires, Gravitation et Cosmologie Année Le Modèle Standard et ses extensions. The Flavour Sector

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1 Particules Élémentaires, Gravitation et Cosmologie Année Le Modèle Standard et ses extensions Cours VIII: 29 février f 2008 The Flavour Sector

2 Particle Physics in one page L SM = 1 4 Fa µνf aµν + i ψ Dψ +ψ i λ i j ψ j h + h.c. + D µ h 2 V (h) +N i M i j N j The gauge sector (1) The flavour sector (2) The EWSB sector (3) The!-mass sector (4) (if Majorana) The quadrant of nature whose laws can be summarized in one page with absolute precision and empirical adequacy One century to develop it, from Maxwell on Can it be the end of the story?

3 The 3 Theorems of the flavour sector (in spite of the many parameters in ) L +! i " i j! j h + h.c. (the 2nd line of page 1) * Theorem 1: Neglecting!-masses, L e,l µ and L! are separately conserved (and CP is exact in the lepton sector) Theorem 2: In the quarks, all flavor violations reside in the weak charged-current amplitude proportional to a unitary matrix u i = (u,c,t) W d j = (d,s,b) = V i j A with VV + = 1 * Theorem 3: Neglecting!-masses, CP is violated in as much as V is intrinsically complex, i.e. a single phase " is nonzero (*with some qualifications - see below)

4 Theorem 1: Neglecting neutrino masses, L e,l µ and L! are separately conserved* (and CP is exact in the lepton sector) Proof: L (lept) = i L i DL i + i e c i Dec i + e i! e i je c j(v + h) + (N terms) Since! e = VL T! e dv R with d for diagonal can redefine ( ) V R e c e c VL! ph V L L = so that V L e (!ph e ph ) L ph L (lept) = i L ph DL ph + i e c ph Dec ph + e T ph! e de c ph(v + h) + (N terms) Essential that! and e are rotated simultaneously, since Z µ ē! µ e, Z µ "! µ " but also W µ ē! µ "! (m e ee c + m µ µµ c + m!!! c )(1 + h/v) (*up to very small quantum effects, (perhaps relevant in the early universe)

5 Theorem 2: In the quarks, all flavor violations reside in the weak charged-current amplitude proportional to a unitary matrix Proof: u i = (u,c,t) W d j = (d,s,b) = V i j A with VV + = 1 L (quarks) = i Q DQ + i u c Du c + i d c Dd c +u T U T L! u du R u c (v + h) + d T D T L! d dd R d c (v + h) hence, this time, by going to the physical basis, all diagonal currents, and, remain unchanged, but not Jµ em Jµ Z W µ ū! µ d W µ ū ph U L D + L! µd ph = W µ ū ph V! µ d ph with V = U L D + L (Note the asymmetry between quarks and leptons!)

6 Testing the Theorems Qualitative, but highly significant: L e,l µ and L! -Violations BR(µ e +!) < BR(µ eēe) < L µ e+γ A( µσ νµe)f νµ CR(µ e in Ti) < A < e α m µ m ν π mw 2 m W BR SM and weaker but still significant in the " case Quantitative: (highly interrelated) (with!-masses included) VV + = 1 Calculable Flavour Changing Neutral Current processes (FCNC) CP-asymmetries (see next lecture) (A major change in the 2000 s)

7 Ready: at PSI!! My own favorite Uniform test offieldflavour Physics Gradient field µ e+γ Bc = 1.26T current = 359A Five coils with three different diameters Compensation coils to suppress the stray field around the LXe detector High-strength aluminum stabilized superconductor MEG magnet (1.46 BR(µ!thin 0.2 e +!) < 1.2X 0)10 11 Current limit cm Aluminum, (not only the LHC) 5 An experiment, MEG, just starting at PSI PSI:sensitivity SUGRA indications aiming at aµ!e" factorsearch of 100at better LFV induced by slepton mixing Two good reasons to believe in it: 1. Unification Experimental limit 2. Neutrino oscillations Our goal Not in the SM! SUSY SU(5) predictions

8 VV + = 1! i V ai 2 = 1 a = 1,2,3 3 rel.s (Type I) Type I:! i V ai V ib = 0 a b 6 rel.s (Type II) V ud 2 + V us 2 + V ub 2 = (11) N N + e +! V ud f ud (0) d u + e + ν V ud = (27) K! + e + " V us f us (0) V us = (21) s u + e + ν B X u + l + ν V ub b u + l + ν (about 1 ppm precision!) (0.3 ppm) (1%) V ub = 4.31(30) 10 3 (10%) isospin, SU(3) ~ conserved in QCD (about 1% precision for the second row, when u " c)

9 FCNC processes (genuine and calculable) 1. Interesting because absent at tree level (hence sensitive to new physical phenomena!?) (Theor. 2: only the W-int.s produce flavor change, not the Z!) 2. Genuine? E.g.: b s c c? No 3. Calculable? E.g.: sd d s? Yes this diagram, but how about its gluon dressing? It depends on the typical momentum of the int. lines: If small (# 1 GeV) not calculable, if large yes.!m K K (the real part ) no! K (the imag. part ) yes (see next lecture) s d W b s W u i u j c c d s = V CKM (asymptotic freedom of QCD)

10 The actual computation of a FCNC process 1. The short-distance EW loop 2. The gluon dressing Ô : an effective operator with a $ known coefficient C (a low energy experiment is insensitive to the internal structure of the loop) a gluon not a W g :generally divergent C(! S log M m,! S) M = M W,m t m = m c,m b Need to re-sum all orders (RG) in α S log M m 3. The matrix element for the actual physical process A i f = C < f Ô i > Need some non perturbative technique or some exp. data

11 The Flavour Precision Tests 1 ( = CP-conserving measurements) Observable elementary process exp. error theor. error ɛ K sd ds 1% 10 15% K + π + νν s d νν 70% 3% K 0 π 0 νν s d νν 1% m Bd bd db 1% 25% A CP (B d ΨK S ) bd db 5% < 1% B d X s + γ b s + γ 10% 5 10% B d X s + ll b s + ll 25% 10 15% B d X d + γ b d + γ 10 15% B d ll b d ll 10% B d X d + ll b d + ll 10 15% m Bs bs sb < 1% 25% A CP (B s Ψφ) bs sb 1% B s ll b s ll 10% (When blank, data still lacking)

12 '#! '$ % VV + = 1 complex represented plane in as: the complex plane as:! "#! "$ %!!" " #!" # $!" $! &#! &$ % the angle! has # no physical meaning, only (the angle shape # has it) no physical meaning, only the shape has it) a non degenerate triangle = CP violation (see below) The Flavour tests 1 in particular: in particular: V ud V ub +V cd V cb +V td V tb = 0 % &m d # &m s & &m d ! V ub /V cb + B ) ( ' (only (only using using CP-conserving measurements) $ CKM f i t t e r FPCP 2007

13 For an overall picture of flavour physics, need to discuss CP as well See this afternoon lecture