arXiv:hep-ph/9910404v1 19 Oct 1999 ieraymd ihenergies high ready-made vide ssm ag assae ev flavours Heavy scale. mass large some is as aynwpyiseet r upesdby suppressed factors are effects physics new many cause di- us straitjacket. Model extract Standard finally our from may rectly flavours heavy that epoie yteltieadnwprubtv ehius h fu The for techniques. ratio perturbative branching new small and determinatio relatively lattice the physic accurate the onto for by window necessary provided a provide be are may calculations it QCD hopes who Precise one of perspective the stemaueeto sin of measurement the as just clues, pa- indirect welcome Model provide closed, may rameters Standard is window of this measurements Standard if precision even the However, beyond physics Model. wel- on a provide window may come flavours heavy on based that or- is hope who perspective the personal muon: My the that? an- dered about to want question or Rabi’s Model, are swer Standard you the maybe with topic, love thesis in your was it problems, challenging perhaps many has subject ques- the this tion: to answers honourable many are There ? Flavours Heavy Study Why 1. cont the an in Super-Kamiokande masses from data lepton oscillation and recent quark the of by motivated unification grand the including n hudntexclude not But should unification. grand one supersymmetric of hint a Abstract: ELLIS John farltvl ag au for value large relatively a of UUEO EV-LVU PHYSICS HEAVY-FLAVOUR OF FUTURE measuring possible FLAVOURS HEAVY H-11 eea23 Geneva 1211 - CH CERN Division, Physics Theoretical ev aor r odpae olo,be- look, to places good are flavours Heavy ∝ PROCEEDINGS K ( E/M dcywnoso hsc eodteSadr oe,i h aeo wake the in Model, Standard the beyond physics on windows -decay α h rset o h oigGle g fhayflvu physics heavy-flavour of Age Golden coming the for prospects The and 8 ) n γ where , h potnte o esrmnso rare of measurements for opportunities The . priori a E 2 θ ENT/938hep-ph/9910404 CERN-TH/99-318 steeeg and energy the is W ǫ ′ /ǫ E tLPprovided LEP at ial,rltost te set fflvu hsc r discusse are physics flavour of aspects other to relations Finally, . h possibility the ∼ m Q B oany so , d Q → pro- M π + π − r icse,icuigatraiesrtge for strategies alternative including discussed, are eri h omo rltvl)bgcontribu- perhaps big e.g., mode, (relatively) decay a rare a of to form tion be- the ap- physics either in might of This the pear Model. signature in Standard some better, the yond CKMology finding do of to hope order in QCD eγ l stppyis[] nsm oeso flavour of models some in [1]: m physics top exam- is prime ple The physics. compar- light-flavour by with enhanced ison be may effects physics new µ coupling xml,w hl e ae hti ls fsu- of class a in models that GUT another later persymmetric As see shall physics. we flavour example, of door the unlocks rwa hsc sdaigt ls:teSLC the close: a to elec- drawing precision is of physics era troweak The dawning. now surely is quadrilateral? a be to out turn triangle unitary a will the to perhaps contribution e.g., small decay, (relatively) common a of or tion), + t ). /M µ rmti esetv,w edt understand to need we perspective, this From naycs,tegle g fhayflavours heavy of age golden the case, any In − ) () n etil h o ur Yukawa quark top the certainly and 0(1), = > λ 2 t × B () ohr a etekythat key the be may here so 0(1), = 10 so K aaees n may and parameters, CKM of ns easaervee rey sare as briefly, reviewed are decays ueo Kooyi h aeof wake the in CKMology of ture elsewhere. d − 10 eodteSadr Model. Standard the beyond s x fnurn-asmodels neutrino-mass of ext teSadr oe predic- Model Standard (the B h establishment the f ( r icse from discussed are τ ev lvus8 Flavours Heavy → µγ ) ≫ B ( B B ( d µ → d, → Heavy Flavours 8 John ELLIS has been terminated and LEP will cease opera- gluons that do not flip spin, it predicts large po- tion in 2000. At the same time, new opportuni- larization [2]. However, this has not been seen [7, ties for precision flavour physics are opening up: 4], either in charmonium or bottomonium pro- BaBar, BELLE, CLEO III, CDF/Dφ at RUN II, duction. etc. Naked heavy-flavour production is notoriously difficult to calculate [6]. Near threshold, there are large [α ln2(1 4m2 /sˆ)]n corrections to be 2. QCD Challenges s − Q resummed, and at high energies there are large 2 n [αs ln(ˆs/4mQ/)] effects. These provide poten- Even though 1 αs(mQ) in heavy-quark physics, ≫ tially large enhancements, with O(Λ/mQ) am- the crucial challenge here is: how to calculate ac- biguities at threshold. The cross section for ¯bb curately in a theory whose perturbative expan- production measured at the Tevatron collider [4] sion parameter α (m ) α ? The traditional s Q ≫ em is about 2.5 times higher than the best theoreti- approximation scheme for any observable is to cal prediction available. At HERA, the status of write it in the form the theoretical predictions is particularly confus- c c b b Λ ing [8]: σexp/σtheory 1, whilst σexp/σtheory Cn(αs(µ), ) < On(µ) > (2.1) ∼ ∼ µ 4! Of particular interest to HERA-B is the cross- n X section they should expect. Unfortunately, it is where the Cn are coefficient functions, µ a factor- currently not possible for theory to provide pre- ization scale, and the < On > operator matrix cise guidance [6]: estimates lie in the range elements or condensates to be calculated non- perturbatively, e.g., using lattice techniques. Un- σb 7.6 to 45 mb (2.2) HERA−B ∼ fortunately, because of weakness and/or stupid- with significant uncertainties associated with the ity, we can only calculate to some finite order choice of mb,µ and proton structure functions. in αs. However, we know that the perturba- tion series is at best asymptotic, and there are Heavy quarkonia offer interesting opportuni- in general renormalons. The scheme dependence ties to determine αs, if the systematic errors in they introduce can be absorbed into higher-twist the required lattice calculations can be controlled terms, but we can only calculate a few of these, to the level needed. The NRQCD value from the e.g., in heavy-quark effective theory (HQET) [2]. χc J/ψ system is [2] Not only are perturbative expansions asymptotic, − MS but there may be effects that are invisible in any αs (MZ )=0.1174(15) (19) (...) (2.3a) approximation scheme. As discussed here [3], ′ there may be singularities away from the light- whilst that obtained from the ψ and J/ψ is 2 2 cone, at x = 0, even x . There are ex- MS | | 6 | | → ∞ α (MZ )=0.1173(21) (18) (...) (2.3b) amples such as instantons and the ’t Hooft model s of such breakdowns of duality, but the practical where in each case the last parenthesis (...) is to importance of such effects is not clear. accommodate the lattice errors associated with the extrapolations needed in mu,d,s and sending Some of the primary QCD puzzles in heavy- the lattice size a 0. The values (2.3) are to be flavour physics are provided by production cross → compared with sections in hadron-hadron collisions. The Teva- tron cross sections for J/ψ and ψ′ production [4] αMS (M )=0.119 0.002 (LEP@Z [9]) , s Z ± are much larger than expected in a na¨ıve colour- 0.120 0.003 (τ decay [10])(2.4) singlet model, leading to the proposal of colour- ± octet dominance [5, 2]. This reproduces well The extension of NRQCD to the tt¯ system can the large-pT dependence, but the overall normal- benefit from the extremely large mass of the t ization is not well determined theoretically [6]. quark and its relatively short lifetime, as in the Since the colour-octet mechanism invokes soft E1 potential NRQCD (PNRQCD) approach [11].
2 Heavy Flavours 8 John ELLIS
The numbers (2.3), (2.4) are of interest for Also of direct experimental interest are the esti- testing supersymmetric GUT predictions. It is mates [18] also possible to extract from τ decays [10, 12] ∆Γ τB− +61 =0.16 (3) (4) , =1.03 0.2 0.3 m (1 GeV) = 234 MeV (2.5) Γ τ 0 ± ± s −76 BS B (2.11) which is to be confronted with the lattice value [13] 0 The ratio τΛb /τB could probably benefit from further analysis. ms (1GeV)=130to180MeV (2.6)
In addition to its great importance for QCD and The lattice calculations of heavy-hadron semi- leptonic-decay form factors are now also very com- CKMology, the value of ms is also of interest for testing models of flavour. Bottomonium spec- petitive [18, 19]. They can be calculated directly 2 MS MS in the physical region of q , obviating the need troscopy can be used to estimate mb (mb ). Here, a significant advance has recently been made for any extrapolation to extract CKM matrix el- with the calculation of the two-loop lattice match- ements. ing factor, which removes an ambiguity of several The interpretation of non-leptonic B decays hundred MeV, resulting in the value [13] has been beset by greater theoretical uncertain- MS MS ties, but there have recently been promising de- mb (mb )=4.3 0.1 GeV (2.7) ± velopments in the formulation of the problem [20]. A precise value for mb is also of interest for test- A typical non-leptonic decay amplitude may be ing the predictions of GUTs [14] and models of written schematically as flavour, as discussed later. G A = F V CKM C (µ) < F Q (µ) B > √ n n | n | Other aspects of heavy-hadron spectroscopy 2 n discussed here, such as hybrids [15] and excited X (2.12) D∗∗ and B∗∗ states [16], have intrinsic QCD in- where our (my) primary objective is the extrac- CKM terest, but are not so important in a larger con- tion of the different CKM matrix elements Vn , text. and the essence of the problem is that the hadronic matrix elements < F Q (µ) B > are often not | n | Turning now to heavy-flavour decay matrix suitable for lattice evaluations. It is an old idea elements, it seems that lattice calculations are that these might factorize, e.g., in two-body de- now taking over as the most precise for many cays: applications. Compare, for example, the QCD sum-rule numbers for decay constants [17]:
3 Heavy Flavours 8 John ELLIS
M M1 1
B TI B M2 M (a) 3
M M2 1
B (a)
M2
M1 (b)
M1 TII B B
M2
(c) M2 Figure 2: Examples of the renormalization-group- (b) invariant classification of diagrams for B decays [23],
including (a) a ‘dolphin’ diagram for B → M1 +M2 + Figure 1: Contributions to the decay of a B meson M3 decay, and (b) B → M1 + M2 decay, which may into two light mesons M , , that may be factorized 1 2 (c) be deconstructed to exhibit rescattering. The (a) with a 2 → 2 hard-scattering kernel TI , and (b) wavy lines denote generic-four-quark operators. with a 2 → 4 hard-scattering kernel Tll [20].
3. CKMology functions and a 2 4 hard-scattering kernel T . → II This approach formalizes perturbative QCD fac- Pride of place in this discussion goes to the uni- torization and FSI, but does not include power tarity triangle discussed here in more detail in [26], corrections. Some of these could be important, of which I now discuss various aspects in turn [27]. particularly if they contain large chiral factors: sin 2β : The theory of the CP-violating asym- 0 2 metry in B J/ψ KS decay is gold-plated, ΛQCD mπ 1 → (2.14) since the penguin contributions are expected to mb × ΛQCD(mu + md) ≃ 2 be very small, and FSI are unimportant [28]. This decay is also experimentally gold-plated, and is not very small! the asymmetry has already been ‘measured’ by A useful phenomenological complement to CDF [29]: this analysis is provided by diagramatic approaches sin 2β =0.79(39)(16) (3.1) based on Wick rotations [22, 23], as illustrated in Fig. 2, which can be improved using the renor- We will soon have B-factory measurements with malization group to become scale and scheme a precision expected to attain 0.12 to 0.05 [30, ± independent. In the honour of our Southamp- 31], and eventually measurements at hadron ma- ton hosts, I propose that Fig. 2a be baptized a chines may attain a precision 0.01. It should ± ‘dolphin’ diagram 1. Note that Fig. 2b includes also be borne in mind that the available statis- rescattering, as deconstructed in Fig. 2c. tics could be doubled by including additional de- cay modes such as B0 J/ψK , ψ′K , etc. → L S 1See [24] for an unexpurgated account of the baptism Measuring sin 2β does not determine β uniquely, of ‘penguin’ diagrams [25]. but the ambiguity could be removed by comple-
4 Heavy Flavours 8 John ELLIS mentary measurements, e.g., comparing B where the dots denote small corrections, one finds d → J/ψK∗ and B J/ψφ can fix cos2β, and the the lower limit γ > 710. It is possible, in princi- s → cascade decay B J/ψ(K0 πℓν) can be ple, to extract γ from the following combination d → → used to measure cos2β sin(∆mK tK ) [28]. of CP-violating asymmetries:
0 ± That was the good news ... and now for the ACP (π K ) ± 0 A˜ ACP (π K ) bad news ... ≡ R∗ − = 2¯ǫ3/2 sin γ sin φ + ... (3.6) sin 2α : The prime candidate for measuring this quantity was B0 π+π−, which was unseen by → where φ is a strong-interaction phase: by mea- CLEO until just recently. The good news is that suring both A˜ and R∗, both γ and φ can be de- this mode has now been observed [32]: termined [37].
0 + − +.18 −5 B(B π π )=(0.47−.15 .13) 10 (3.2) Other channels offering prospects for mea- → ± × (−) (−) ± 0 ± 0 0 ∗0 but the bad news is that this is a factor 4 below suring γ include [28] B D K , B D K , ∼ (−) (→−) → ± ∓ ∗± ∓ BS D K [38] and B0 D π [39], all of B(B0 K+π−)=(1.88+.28 .06) 10−5 (3.3) → s → → −.26 ± × which may fairly be described as ‘challenging’. The small ratio (3.2), (3.3) means that there must LHCb has studied, in particular, the second of be considerable penguin pollution, which intro- these channels, and concludes that it could reach a precision of 100 in γ. Hadron machines, such duces ambiguity in the determination of sin 2α [33], ± since penguins and trees have different phases. as the LHC, are clearly the ‘Promised Land’ for The improvement in theoretical calculations pos- Bs physics, which will surely flow with plenty of sible using isospin [34] or U-spin relations [35], or CP-violating ‘milk and honey’ [40]. the new approach to amplitude factorization [20] may enable some of the penguin pollution to be B cleaned up, but only a target error δα = 100 4. Rare Decays ± may be realistic. Under these circumstances, al- ternative ways to measure sin 2α become more These offer good opportunities to measure Stan- interesting. One suggestion [36] is the B ρπ → dard Model parameters [41], and may also be Dalitz plot, but here there are questions concern- able to open windows on physics beyond the Stan- ing the attainable statistics and the sensitivity in dard Model [42]. the presence of background, and another is to use ∗± ∓ B D π decays, which looks tough [28]. As an example, b sγ is related to Vst, and → → is also sensitive to MH± and (mt˜,mχ± ) in super- γ : In view of the above imbroglio, in partic- symmetric extensions of the Standard Model. To ular, there is increased interest in constraining make a precise calculation, one must resum the and/or measuring γ. One line of attack [37] is to n+m 2 2 m large QCD logarithms: (αs/π) [ln(mb /M )] . use B± π±K0, π0K± and π±π0 decays which → In the Standard Model, the three-loop anomalous receive contributions from penguins, electroweak dimension and the two-loop matching conditions penguins and tree diagrams (whose phase is γ). are known [43], so a relatively precise prediction Using can be made:
± ± 0 B(B π K ) −4 R∗ → =0.47 0.24 (3.4) B(b sγ)=(3.32 0.14 0.26) 10 ≡ 2B(B± π0K±) ± → ± ± × → (4.1) andǫ ¯ =0.24 0.06,δ =0.64 0.15, in the This is to be compared with the experimental 3/2 ± EW ± inequality value:
−4 1 √R∗ B(b sγ)=(3.15 0.35 0.32 0.26) 10 R − δEW cos γ + ... (3.5) → ± ± ± × ≡ ǫ¯3/2 ≤ | − | (4.2)
5 Heavy Flavours 8 John ELLIS
400 The decays b s,dℓ+ℓ− provide additional Excluded 95% CL → 350 Not Excluded, LO used opportunities for testing such theories, in par-
Higgsino DM ticular via the measurement of a CP-violating 300 forward-backward asymmetry. Personally, I also 250 have a soft spot for b s, dνν¯ decay, though this → 200 will be very difficult to observe. (GeV) 2 M 150 The decay B µ+µ− is expected to appear s → with a branching ratio of (3.5 0.1) 10−9 in the 100 ± × Standard Model. For comparison, the present 50 experimental upper limit is 2.6 10−6. On the × 0 other hand, it should be measurable at the LHC: -300 -200 -100 0 100 200 300 µ (GeV) a CMS study indicates that as many as 26 events + − could be observed. Even the decay Bd µ µ Figure 3: Regions of the µ, M plane of the MSSM → 2 with an expected Standard Model branching ra- which are allowed for Higgsino dark matter (rectan- tio of (1.5 0.9) 10−10 may not lie beyond the gular box) but disallowed by the b → sγ analysis at ± × NLO (light shaded region): the dark shading indi- reach of the LHC. CDF already has established an upper limit of 8.6 10−7, and CMS may be cates a region allowed by a LO analysis. The fol- × lowing values of the other MSSM parameters have able to observe up to four events. These decays been chosen for this illustration: m0 = 1000 GeV, are vulnerable to physics beyond the Standard mA = 500 GeV and tanβ = 2.5 [46]. Model such as R violation in supersymmetric models, and so could provide an interesting win- dow on new physics. There is some concern about the theoretical pre- diction of the Eγ spectrum, and it might in prin- ciple be preferable to compare theory and experi- 5. Beyond the Standard Model ? ment in a restricted and more reliable range [44], but there is certainly no hint yet of any need for physics beyond the Standard Model. The best prospects for new physics at the TeV scale, and hence the most amenable to accelera- A NLO QCD calculation is available also in tor experiments, may be offered by the problem the MSSM [45], in the limit of mass, and hence associated with the Higgs sec- tor and/or supersymmetry. In the MSSM, all the µ (m ,m ,m˜ ) µ g˜ ≡ O g˜ q˜ t1 ≫ w˜ renormalizable couplings are related to those in (m ,m ± ,m ± ,m˜ ) (4.3) ≡ O W H χ t2 the Standard Model, including the gauge cou- pling g , the Yukawa couplings λ and their as- The comparison between (4.1), (4.2) is an impor- a ijk sociated CKM phases. In addition, there are the tant constraint on the MSSM parameter space, standard soft supersymmetry-breaking parame- as seen in Fig. 3 [46], where the NLO QCD cal- ters of the generic forms culation is used to exclude a region of parameter space that would otherwise be permitted for Hig- 1 (m2)j φiφ∗ , M V˜ V˜ , A λ φiφj φl gsino cold dark matter. However, the available 0 i j 2 a a a ijk ijk LO calculations are of limited accuracy when the (5.1) simplified limit (4.3) is applicable, so it would be i.e., scalar and gaugino masses and soft trilinear ¯ good to generalize the NLO QCD calculation be- couplings, respectively, and a term BµHH asso- yond the region (4.3) of MSSM parameter space. ciated with Higgs mixing. There is no good theo- 2 j retical reason known why the (m0)i should diag- The related decay b dγ is equally calcula- onalize in the same basis as the fermion masses, → ble, and provides a way of measuring Vtd. It may and they do not do so in generic string models, also provide an opportunity for physics beyond for example. However, there are important con- 2 j the Standard Model, such as supersymmetry. straints on the (m0)i from flavour physics and
6 Heavy Flavours 8 John ELLIS
CP physics [47], to which the most obvious so- yielded [59, 63] lution is that they are universal [48]. There are ǫ′ in particular two CP-violating phases which are Re = (7.7+6.0) 10−4 , (4.7+6.7) 10−4 ǫ −3.5 × −5.9 × constrained by the experimental upper limits on (5.4) the electric dipole moments of the electron and which might suggest a discrepancy with the ex- neutron, d and d . The interpretation of d is e n e perimental world average: cleaner, since there are several different operators contributing to d (e.g., involving s quarks [49] ǫ′ n Re = (21.2 4.6) 10−4 (5.5) as well as the valence u and quarks), which could ǫ ± × introduce cancellations, and hence make its inter- However, in view of the theoretical uncertainties, pretation more uncertain [50]. it seems safer to quote the following envelope of In addition to the above supersymmetric pos- predictions [59]: sibilities for new physics, one should also bear in ǫ′ mind the possibilities of non-standard soft super- 1 10−4 < Re < 28 10−4 (5.6) × ǫ × symmetry-breaking terms [51]: which is not in significant disagreement with ex- i ∗ ∗ i j φ φj φk, φ φ (5.2) periment (5.5). Nevertheless, it is clear that the measured value of Re(ǫ′/ǫ) tends to favour rela- i tively large values of Imλ , Λ(4) and particularly where the φ are generic complex chiral scalar t MS fields, and R-violating interactions [52]. B6 [60, 63], as well as relatively small values of B8,ms and mt. The least one can say, within The recent confirmation by KTeV [53] and the context of the Standard Model, is that the ′ NA48 [54] of the surprisingly large value of ǫ /ǫ experimental value (5.5) requires big penguins: found previously by NA31 [55, 56] has rekindled exotic [65] emperors, maybe? interest in possible supersymmetric effects on CP- violating observables [57]. In the Standard Model, This being said, even incorporating the con- ′ + − the first crude calculation was made in [58], and straints from ǫ /ǫ and KL µ µ , there is a → has subsequently been greatly refined - the fact window of opportunity for a significant contri- that the data agree with the estimate ǫ′/ǫ bution from CP violation beyond the Standard ∼ 1/450 given in [58] is pure coincidence! One cal- Model. One possibility is an enhanced Zsd¯ ver- culates nowadays [59, 60, 61, 62, 63] tex, which could enhance substantially the ex- pected branching ratio for the rare CP-violating 0 0 + − ′ 2 Λ(4) decay mode KL π νν¯ , as well as KL π e e ǫ 130 MeV MS + + → → Re 13Imλt and K π νν¯ , so it would be interesting to ǫ ≃ ms(mc) 340 MeV → push the experimental sensitivities for all these 2.5 modes down to the Standard Model predictions, mt(mt) B6(1 Ωηη′ ) 0.4B8 which are B(K π0νν¯ )=0.4 10−10, B(K × " − − 165 GeV # L → × L → π0e+e−)=0.7 10−11 and B(K+ π+νν¯ ) = (5.3) × → 1.1 10−10, respectively. They could be as large × as B(K π0νν¯ ) = 1.2 10−10, B(K −4 L → × L → where Im λt = (1.33 0.14) 10 is the CP- π0e+e−)=2.0 10−11 and B(K+ π+νν¯ ) = ± × × → violating CKM factor, B6 is a penguin operator 1.7 10−10, respectively [57]. matrix element factor estimated to be 1.0 0.3, × ± Ωηη′ is an electroweak penguin correction and B8 There are many related opportunities for sig- is another matrix element factor estimated to be natures of physics beyond the Standard Model 0.8 0.2. Because of all the uncertainties [64] in b decays, notably [42]: squark mixing effects ± and the possibilities of cancellations, it is difficult in b dγ? unexpected CP violation in b → → to make a precise estimate of Re(ǫ′/ǫ). Formal sγ? rate enhancements and CP-violating asym- analyses by two theoretical groups have recently metries in b s,dℓ+ℓ−? enhanced rates for →
7 Heavy Flavours 8 John ELLIS
B µ+µ−? Other signatures to bear in mind linked in common GUT multiplets. The proto- s,d → are the possibilities that B J/ψK , φK and type relation was [14] → S S D0π0 might yield different values of β, and that the unitarity triangle could be distorted by new mb = mτ (6.1) contributions to Bs B¯s mixing [66]. − before renormalization. The effective value of mb Although they lie beyond the limits of heavy- varies with the energy scale, as has been verified flavour physics, I should also like to advertize by DELPHI at LEP [68], and the renormaliza- the physics interests of some related experiments. tion group can be used to calculate the physical MS MS One is a proposal for a new-generation exper- value of mb (mb ) if one knows the spectrum iment on the neutron electric dipole moment. of particles between here and mGUT (the Stan- Another is the possibility that µ eγ decay dard Model? the MSSM?). Starting from (6.1), → might show up ‘close’ to the present experimen- such a calculation yields [69] tal upper limit, which is motivated by the ev- mMS(mMS ) 4.5 to 5 GeV (6.2) idence for lepton flavour violation via neutrino b b ≃ oscillations, particularly in the context of super- in the MSSM, with the details depending on the symmetric GUTs [67]. A related heavy-flavour sparticle thresholds, the appropriate value of α , opportunity is provided by τ µ/eγ decay: es- s → etc. timates in the same supersymmetric GUT frame- > work suggest the possibility that B(τ e/µγ) However, the analogous relations: ms mµ −9 → ∼ ↔ 10 [67], which might be accessible to CMS at and m m are unsuccessful, which is not sur- d ↔ e the LHC. prising in the context of GUT models of flavour. These introduce higher-order terms in the mass matrices [70]: 6. Relations to Other Physics ? ǫn ǫm ǫp ǫn˜ ǫm˜ ǫp˜ m′ q r p˜′ q˜ r˜ mb ǫ ǫ ǫ mτ ǫ ǫ ǫ ′ ′ ↔ ′ ′ We have already seen many potential interfaces ǫp ǫr 1 ǫp˜ ǫr˜ 1 of heavy-flavour physics with extensions of the (6.3) Standard Model related to its outstanding prob- where ǫ is a small parameter, and the extra terms lems of mass (via the Higgs sector and supersym- (which are indicated only in order of magnitude) metry) and of unification (via GUTs). However, may be related to non-renormalizable interac- the outstanding contributions of the next gen- tions and/or approximate symmetries: U(1)? a eration of heavy-flavour experiments will surely non-Abelian group? be towards unravelling the problem of flavour, New light on such models may be cast [71] which is the most baffling puzzle raised by the by models of neutrino masses in GUTs and the Standard Model. It is not that we lack clues: emerging indications of neutrino oscillations. Most the flavour sector contains at least 13 parame- theoretical models of neutrino masses are based ters (6 quark masses, 3 lepton masses and the on the generic seesaw mechanism [72]: 4 CKM angles), most of which have been mea- sured to some level. Also, theorists abound with 0 m ν (ν ,ν ) L (6.4) ideas, but their predictions are more often qual- L R mT M ν R itative than quantitative. Perhaps the next gen- where each entry is to be understood as a 3 3 eration of heavy-flavour experiments will provide × more clues: it will certainly provide more precise matrix in flavour space, the νR are right-handed singlet states, m = (m ,m ) and M = (m ) measurements that may bust some of the GUT O q ℓ O GUT m . After diagonalization, (6.4) yields light flavour models. ≫ W neutrino masses GUTs can predict quark masses in terms of 1 m = m mT (6.5) lepton masses, because quarks and leptons are ν M
8 Heavy Flavours 8 John ELLIS and one naturally obtains m 10−2 eV if, e.g., What does this (very) light-flavour physics ν ∼ m 10 GeV and M 1013 GeV. Thanks to have to do with heavy flavours? There are impor- ∼ ∼ the matrices m and M appearing in (6.5), one tant implications for the interpretation of quark- can expect non-trivial mixing between the light- lepton mass unification relations, and hence for neutrino flavour eig- enstates, parametrized by a theories of flavour [71]. One effect is a change in mixing matrix Vν , and there will in general also the mass renormalization at scales µ: mνR <µ< be mixing between the charged-lepton flavour eigen- mGUT , which we parametrize by ξN . A second states, parametrized by Vℓ. Thus we obtain a effect is that non-trivial diagonalization of the measurable neutrino mixing matrix [73] (between lepton mass matrix (6.3) may alter significantly the neutrino and charged-lepton mass eigenstates) the relevant mass eigenvalue. For example, if analogous to V : CKM C 0 x2 x m0 = A , m0 = (6.7) † D 0 1 E x 1 VMNS = VℓVν (6.6) one finds after diagonalization that The mixing observed experimentally might arise m 1 from Vℓ, or Vν , or both, and any mixing in Vν D = 2 (6.8) might arise from m or M, a priori. The neutrino mE 1+ x mixing angles need not be small: one can easily As a result of these two effects, the appropriate construct models in which the powers of ǫ in the extrapolated ratio to compare with GUT predic- mass matrices (6.3) are different, the same is true tions is modified to [71] a fortiori of m, and we have no hints about the structure of M [74]. m˜ τ (mGUT ) 2 2 = (1+ x ) 2 (6.9) mb(mGUT ) s1+ ξN The indications from atmospheric neutrino data [75] are for maximal ν ν mixing with As a consequence, GUT mass unification can be µ − τ a difference in mass squared ∆m2 3 10−3 maintained for any value of tan β, the ratio of ∼ × eV2. The solar neutrino data indicate mixing of MSSM Higs vev’s, whereas it was often thought νe with νµ and/or ντ , with three possible scenar- possible only for tan β either very large or very ios: ∆m2 > 10−5 eV2 and large mixing, ∆m2 small. ∼ 10−5 eV2 ∼and small mixing, or ∆m2 10−10 ∼ eV and large mixing. The last alternative may be disfavoured by the electron energy spectrum 7. May You Live in Interesting Times measured by Super-Kamiokande, and the sec- ond solar scenario is being constrained by con- This used to be considered a curse in ancient straints on a day-night difference in the Super- China, but may nowadays be considered a bless- Kamiokande data. The first solar scenario will ing. You are now entering what may turn out to be probed by the KamLAND experiment, that is be the Golden Age of heavy-flavour physics, with already observing reactor neutrinos. The atmo- Babar, BELLE, CLEO III and HERA-B starting spheric neutrino region will be probed by long- to take data, CDF and Dφ soon returning to the baseline accelerator neutrino experiments: K2K fray, and LHCb and possibly BTeV on the hori- in Japan and MINOS in the U.S. are intended to zon. In parallel with this experimental cornu- look for νµ disappearance, and the CERN-Gran copia, many theoretical tools are maturing, such Sasso project is intended primarily to search for as the lattice, HQET, (P)NRQCD, etc. Thus, ντ appearance. The investment in these projects you, the heavy-flavour community, will soon be is modest compared to that in B factories and having plenty of fun. You will be able to measure experiments, but this may change. One of the precisely the parameters of the Standard Model, interesting options for the future is a ν factory perhaps revealing hints for new physics beyond based on a muon storage ring [76], which may the Standard model. If you are lucky, you may be able to extend the measurements of neutrino even find direct evidence for new physics. Happy oscillations to CP-violating observables [77]. hunting!
9 Heavy Flavours 8 John ELLIS
References [26] S. Plaszczynski, talk at this meeting. [27] For a recent discussion by an expert, see: [1] E. Simmons, hep-ph/9908488, and talk at this M. Gronau, hep-ph/9908343. meeting. [28] I. Dunietz, talk at this meeting. [2] I. Rothstein, talk at this meeting. [29] T. Affolder et al., CDF Collaboration, hep- [3] I. Bigi, M. Shifman, N. Uraltsev and A. Vain- ex/9909003; D. Bortoletto, talk at this meeting. shtein, Phys. Rev. D59 (1999) 054011; M. Shif- man, talk at this meeting [30] R. Waldi, talk at this meeting. [4] K. Sumorok, talk at this meeting. [31] S. Suzuki, talk at this meeting. [5] E. Braaten and S. Fleming, Phys. Rev. Lett. 74 [32] Y. Kwon et al., CLEO Collaboration, hep- (1995) 3327. ex/9908039; Y. Kubota, talk at this meeting. [6] P. Nason, talk at this meeting. [33] See, for example, J. Charles, Phys. Rev. D59 (1999) 054007 [7] K. Seth, talk at this meeting. [34] M. Gronau and D. London, Phys. Rev. Lett. 65 [8] C. Adloff et al., H1 Collaboration, hep- (1990) 3381. ex/9909029; F. Sefkow, talk at this meeting. [35] R. Fleischer, Phys. Lett. B459 (1999) 306. [9] LEP Electroweak Working Group, http://www.cern.ch/LEPEWWG. [36] H. Lipkin, Y. Nir, H. Quinn and A. Snyder, Phys. Rev. D44 (1991) 1454. [10] R. Barate et al., ALEPH Collaboration, hep- ex/9903015 and M. Davier, talk at this meeting. [37] M. Gronau, J.L. Rosner and D. London, Phys. Rev. Lett. 73 (1994) 21; R. Fleischer, [11] M. Beneke, talk at this meeting. Phys. Lett. B365 (1996) 399; R. Fleischer [12] See also A. Pich and J. Prades, JHEP 10 (1999) and T. Mannel, Phys. Rev. D57 (1998) 2752; 004, who quote the value ms(1GeV) = 164 ± M. Gronau and J.L. Rosner, Phys. Rev. D59 33 MeV. (1999) 113002; A.J. Buras and R. Fleischer, hep- [13] G. Martinelli, talk at this meeting. ph/9810260; M. Neubert and J.L. Rosner, Phys. Lett. B441 (1998) 403 and Phys. Rev. Lett. 81 [14] M.S. Chanowitz, J. Ellis and M.K. Gaillard, (1998) 5076; M. Neubert, talk at this meeting. Nucl. Phys. B128 (1977) 506; A.J. Buras, J. El- lis, M.K. Gaillard and D.V. Nanopoulos, Nucl. [38] R. Aleksan, I. Dunietz and B. Kayser, Z. Phys. Phys. B135 (1978) 66. C54 (1992) 653. [15] C. Michael, talk at this meeting. [39] R. Fleischer, Int. J. Mod. Phys. A12 (1997) 2459; for further strategies using Bd(s) → [16] V. Ciulli, talk at this meeting. + − → Dd(s)Dd(s) and/or Bd(s) J/ψKS decays, see: [17] V. Braun, talk at this meeting. R. Fleischer, Eur. Phys. J. C10 (1999) 299. [18] S. Hashimoto, hep-latt/9909136 and talk at this [40] N. Harnew, Nucl. Instrum. Meth. A408 (1998) meeting. 137, and talk at this meeting. [19] L. Lellouch, talk at this meeting. [41] C. Greub, talk at this meeting. [20] M. Beneke, G. Buchalla, M. Neubert and [42] A. Masiero, talk at this meeting. 83 C. Sachrajda, Phys. Rev. Lett. (1999) 1914. [43] M. Ciuchini, G. Degrassi, P. Gambino and [21] S.J. Brodsky and P. Lepage, Phys. Rev. D22 G.F. Giudice, Nucl. Phys. B527 (1998) 21. (1980) 2157. [44] A.L. Kagan and M. Neubert, Eur. Phys. J. C7 [22] M. Ciuchini, E. Franco, G. Martinelli and L. (1999) 5. B501 Silvestrini, Nucl. Phys. (1997) 271. [45] M. Ciuchini, G. Degrassi, P. Gambino and [23] A.J. Buras and L. Silvestrini, hep-ph/9812392; G.F. Giudice, Nucl. Phys. B534 (1998) 3. L. Silvestrini, talk at this meeting. [46] J. Ellis, T. Falk, G. Ganis, K.A. Olive, [24] M. Shifman, hep-ph/9510397. M. Schmitt and M. Spiropulu, in preparation. [25] J. Ellis, M.K. Gaillard, D.V. Nanopoulos and [47] J. Ellis and D.V. Nanopoulos, Phys. Lett. 110B S. Rudaz, Nucl. Phys. B131 (1977) 285. (1982) 44.
10 Heavy Flavours 8 John ELLIS
[48] R. Barbieri and R. Gatto, Phys. Lett. 110B [65] R. Fleischer and J. Matias, hep-ph/9906274. (1982) 211. [66] A. Ali and D. London, hep-ph/9907243. [49] J. Ellis and R. Flores, Phys. Lett. B377 (1996) [67] J. Ellis, M. Gomez, G. Leontaris, S. Lola 83. and D.V. Nanopoulos, CERN preprint CERN- [50] A. Bartl, T. Gajdosik, W. Porod, P. Stockinger TH/99-237. and H. Stremnitzer, Phys. Rev. D60 (1999) [68] P. Abreu et al., DELPHI Collaboration, Phys. 073003. Lett. B418 (1998) 430. [51] I. Jack and D.R.T. Jones, Phys. Lett. B457 [69] M. Carena, M. Olechowski, S. Pokorski and (1999) 101. C.E. Wagner, Nucl. Phys. B426 (1994) 269. [52] For a recent review, see: B.C. Allanach, [70] J. Ellis and M.K. Gaillard, Phys. Lett. 88B A. Dedes and H.K. Dreiner, Phys. Rev. D60 (1979) 315. (1999) 075014. [71] M. Carena, J. Ellis, S. Lola and C.E. Wagner, [53] A. Alavi-Harati et al., KTeV Collaboration, hep-ph/9906362. Phys. Rev. Lett. 83 (1999) 22; A. Barker, talk at this meeting. [72] M. Gell-Mann, P. Ramond and R. Slansky, Pro- ceedings of the Stony Brook Supergravity Work- [54] V. Fanti et al., NA48 Collaboration, hep- shop, New York, 1979, eds. P. Van Nieuwen- ex/9909022; P. Lubrano, talk at this meeting. huizen and D. Freedman (North-Holland, Ams- [55] G.D. Barr et al., NA31 Collaboration, Phys. terdam); T. Yanagida, Proceedings of the Work- Lett. B317 (1993) 233. shop on Unified Theories and Baryon Number [56] For a recent discussion how to combine these in the Universe, Tsukuba, Japan 1979, eds. A. results, see: G. D’Agostini, hep-ex/9910036. Sawada and A. Sugamoto, KEK Report No. 79- 18. [57] A. Masiero and H. Murayama, Phys. Rev. [73] Z. Maki, M. Nakagawa and S. Sakata, Prog. Lett. 83 (1999) 907; R. Barbieri, R. Contino 28 and A. Strumia, hep-ph/9908255; A.J. Buras, Theor. Phys. , 247 (1962). G. Colangelo, G. Isidori, A. Romanino and [74] J. Ellis, G.K. Leontaris, S. Lola and L. Silvestrini, hep-ph/9908371; G. Eyal, D.V. Nanopoulos, Eur. Phys. J. C9 (1999) 389. A. Masiero, Y. Nir and L. Silvestrini, hep- [75] J.M. Conrad, Review Talk at 29th International ph/9908382. Conference on High-Energy Physics (ICHEP [58] J. Ellis, M.K. Gaillard and D.V. Nanopoulos, 98), Vancouver, Canada, 23-29 Jul 1998, hep- Nucl. Phys. B109 (1976) 213. ex/9811009. [59] S. Bosch, A.J. Buras, M. Gorbahn, S. Jager, [76] Prospective study of muon storage rings at M. Jamin, M.E. Lautenbacher and L. Silvestrini, CERN, eds. B. Autin, A. Blondel and J. Ellis, hep-ph/9904408; A.J. Buras, hep-ph/9908395; CERN report 99-02. M. Jamin, talk at this meeting. [77] S.M. Bilenkii, C. Giunti and W. Grimus, [60] S. Bertolini, J.O. Eeg, M. Fabbrichesi and Phys. Rev. D58 (1998) 033001; A. De Ru- E.I. Lashin, Nucl. Phys. B514 (1998) 93; jula, M.B. Gavela and P. Hernandez, Nucl. S. Bertolini, M. Fabbrichesi and J.O. Eeg, hep- Phys. B547 (1999) 21; V. Barger, Y. Dai, ph/9802405; M. Fabbrichesi, hep-ph/9909224. K. Whisnant and B. Young, Phys. Rev. D59 (1999) 113010; K.R. Schubert, hep-ph/9902215; [61] T. Hambye, G.O. Kohler, E.A. Paschos and P.H. M. Tanimoto, hep-ph/9906516; A. Donini, Soldanet, hep-ph/9906434. M.B. Gavela, P. Hernandez and S. Rigolin, hep- [62] A.A. Bel’kov, G. Bohm, A.V. Lanyov and A.A. ph/9909254; A. Kalliomaki, J. Maalampi and Moshkin, hep-ph/9907335. M. Tanimoto, hep-ph/9909301; A. Romanino, [63] M. Ciuchini, E. Franco, L. Giusti, V. Lubicz hep-ph/9909425; M. Koike and J. Sato, hep- and G. Martinelli, hep-ph/9910236 and hep- ph/9909469. ph/9910237. [64] For a striking recent reminder of some of these uncertainties, see: T. Blum et al., hep- latt/9908025.
11