or hadrons. In the latter case the state was observed in production in a Drell-Yan-like channel pn J X X X

Transcription

1 Physics 557 Lecture 12 Even More particles heavy flavors: The exciteent of the 1970 s continued with the observation in 1974 (continuing through 1976) of a new quark flavor (recall that the sae period also saw the observation of the third lepton generation, the τ). The recognition of a new flavor was triggered by the observation of a new state in the sae channel as the photon at both an e + e - achine SPEAR (at SLAC), where the state was called the Ψ, and a proton accelerator (at rookhaven), where it was called the J. In the forer case the process is direct foration + * * + e e γ Ψ / J γ e e or or * + γ µ µ hadrons. (12.1) In the latter case the state was observed in production in a Drell-Yan-like channel pn J X X X * Ψ / + γ + µ + µ +. (12.2) The actual production process involves the direct Drell-Yan electroagnetic channel seen at SLAC and various hadronic odes that we will discuss in ore detail below. These discoveries led to Nobel Prizes for urt Richter at SLAC and Sa Ting at rookhaven. The observed state was quickly recognized to have quantu nubers I G = 0 -, J PC = 1 - -, i.e., a φ-like state but with the previously predicted (see below) char quark replacing the strange quark, This particle has ass and width φ = ss Ψ / J = cc. (12.3) Ψ / J Ψ / J = ± MeV, Γ = 92.9 ± 2.8 kev. (12.4) The distinctive feature is the very narrow width. Recall that the decay width of the φ is greater than 4 MeV, corresponding doinantly to decays to KK, i.e., to strange quark conserving channels. It was quickly learned that the 0 - chared esons, which correspond to the isospin doublet K s and which are labeled the D s, have asses and lifeties Lecture 12 1 Physics 557 Winter 2016

2 + 0 D cd D uc ;, 0 = = D cu D dc D = ± = ± MeV, τ s, D ± ± 0 0 = ± 0.05 MeV, τ 0 0 = ± s. D, D D, D (12.5) Thus the chared quark conserving decay channel into DD is not kineatically available to the Ψ/J, i.e., the ass of the Ψ/J is less than 2 D. The only allowed strong decays occur through the OZI violating channels where thecc quarks annihilate into 3 (or ore) gluons. These channels are quite suppressed (recall that the strong coupling α s is a running coupling that becoes saller at larger ass scales) and electroagnetic decay odes are copetitive. This point is illustrated by the following approxiate branching ratios, R R R R Ψ/ J hadrons * Ψ/ J γ hadrons * Ψ/ J γ e e Ψ/ J γ µ µ * ± 0.5% (via strong interactions), ± 0.30% (via electroagnetic interactions), 5.971± 0.032%, 5.961± 0.033%. (12.6) Note the approxiate factor of two between the lepton pair electroagnetic (1 photon) channels and the electroagnetic hadronic channel. The naïve theoretical expectation for this factor includes the sae color factor of three that we observed in the weak decays of the τ ties the electric charges squared of the quarks involved ( Qu Qd Qs 3 ) + + = resulting in a final factor of 2. We will discuss this factor again in the context of e + e - physics. The purely hadronic decays of the Ψ/J involve a vast nuber of channels, ost of which contain an odd nuber of pions (recall that the Ψ/J has G = -1). At the 8.8 % level there are also decays where a photon replaces one of the (3) gluons (so 3 2 αs ααs with a loss in rate of about a factor of 10) and one observes final states with a photon and an even nuber of pions. The other expected ground states for the esons containing a char quark are also observed. These include the 1 - states, Lecture 12 2 Physics 557 Winter 2016

3 * + *0 D D * ± = ± 0.05 MeV, Γ = ± MeV D, :. *0 * D D *0 *0 = ± 0.08 MeV, Γ < 2.1 MeV D, D (12.7) For all charge states the priary decay odes are πd as we would expect, although there is little phase space for this decay and hence sall widths. We also expect two isosinglet chared and strange esons, corresponding to the quark states cs and sc, and they are observed, + s ( = 1, = 1) ( = 1, = 1) cs D C S P, I ( J ) = 0( 0 ), sc D C S D ± s s = ± = ± MeV, τ s. (12.8) The corresponding 1 states also see to have been observed at ±0.4 MeV, Γ < 1.9 MeV, but the data is less coplete. Although these data on asses iply that the char quark has a ass of order 1.5 GeV (and therefore far fro degenerate with the less assive quarks), we can still consider the full range of states iplied by the assuption of a flavor SU(4) syetry. The corresponding SU(4) representations can be found at the PDG web site (see the quark odel section, Fig. 14.1) and in the appendix to these lectures. Note that the representations are now 3-diensional (they were 2-D for SU(3) and 1- D for SU(2)). Candidates for all of the predicted states have been observed but the quantu nubers (J P ) have not been confired in all cases. Consult the PDG tables for ore details. As noted above, in another triuph for syetries and theoretical physics, the existence of the char quark had, in fact, been predicted in The context of this prediction is now called the GIM echanis after the authors, S. Glashow, J. Iliopoulos and L. Maiani (the latter was the Director General of CERN, who ade the decision in 2000 to shut down LEP II even though there was soe evidence of the Higgs boson). In 1970 it was already thought that the weak interactions involved not only the coon charged current interactions, e.g., µ ν + e ν (12.9) µ e, involving the then known weak interaction doublets Lecture 12 3 Physics 557 Winter 2016

4 ν e ν, µ u,, e µ d cosθc + ssinθc (12.10) but also neutral current interactions which are diagonal in the individual states of each doublet. This expectation was confired in 1973 using neutrino beas at CERN to observe events of the for ν N ν + X, (12.11) although it was not until 1983 that the existence of both the W ± and Z 0 particles were directly confired. Still, back in 1970, it was a theoretical conundru to believe in a neutral weak current but to observe no flavor changing neutral currents (FCNC s). In particular, one would expect, based on the weak isodoublet structure above, to observe neutral current coupling of the for (just the squares of the eleents of the doublet) 2 2 S = 0 : uu + dd cos θc + ss sin θc (12.12) S = 1: sd + ds sinθ cos θ. However, the flavor changing decays of strange particles via the neutral current are observed to be strongly suppressed copared to the charged current, e.g., C C K π ν ν = 0.51± K π µ ν µ (12.13) This unacceptable situation was rescued by GIM, who (in keeping with our usual technique) postulated a new particle. They noticed that good things happened if a new Q = 2/3 quark, the c quark, fored a second weak doublet with the Cabibborotated strange quark. Thus we would have the two doublets u c,. d cosθc + ssinθc s cosθc d sinθc (12.14) With this second weak isodoublet, the neutral couplings look like Lecture 12 4 Physics 557 Winter 2016

5 θc S = 0 : uu + cc + dd + ss cos + dd + ss sin = uu + cc + dd + ss 2 2 S = 1: sd + ds sd ds sinθ cosθ = 0. C C θ C (12.15) Thus, as long as the quarks occur in coplete ultiplets, i.e., coplete generations, the neutral current is diagonal and the FCNC s are highly suppressed, in agreeent with data. The insight of syetries had again led the way! The ixing of the s and d quarks now assues the canonical for d θc cosθc sinθc d =, s θc sinθc cosθ C s (12.16) where the states on the left are in the basis of the weak interactions (the lower ebers of the weak isodoublets) and those on the right are in the ass eigenstate basis (the lower ebers of the strong isodoublets). This 2 x 2 ixing structure will soon assue a 3 x 3 for when we introduce the third generation of quarks. Note that the choice to characterize the ixing in ters of the down-type quarks is purely by convention (and history). It could as well be perfored in ters of the up-type quarks. Note also, as entioned previously, that to be able to define ixing we need two distinct basis sets. In this case the two are provided by the ass (flavor) eigenstates and the charged weak current interaction states. The second weak isodoublet explains the observed structure of the weak decays of the D esons. The Cabibbo favored char changing decays are c s and c s. Thus it is no surprise that approxiately 90 % of all final states in D decay have a K present. The study of these decays has provided a warehouse of inforation about the weak interactions that we will address in a later lecture. The end of the golden decade of the 1970 s saw the detection of the 5 th quark, the botto (soeties beauty) or b quark in Again it was the vector state that was seen in the Drell-Yan process at Ferilab, and subsequently in e + e - physics, that pointed to the new quark. The vector state is the ϒ (the upsilon), I G (J PC ) = 0 - (1 - - ), ϒ = ± 0.26 MeV, Γ = ± 1.25 kev. (12.17) Lecture 12 5 Physics 557 Winter 2016

6 Note the interesting feature that, although the ass is 3 ties that of the Ψ/J, the width of thisbb state is actually saller than the cc state. The pseudoscalar states with the botto quantu nuber include the doublets + 0 ub bd,, 0 = = db bu 0 0 = ± = ± MeV, τ s, ± ± = ± = ± MeV, τ s. (12.18) As with the Ψ/J, these states are too assive to participate in a botto conserving strong interaction decay of the ϒ. Hence the strong decays of the ϒ ust violate the OZI rule and involve the eission of at least 3 gluons. Thus we expect the rate of strong decays to scale as α s 3, the running coupling of the strong interaction, evaluated here at the scale set by ϒ, ties any further shrinkage of the wave function itself (see the HW). Thus the appropriate coupling for these strong decays of the ϒ is saller than for the Ψ/J. The ϒ is observed to have an electro-weak branching ratio of about 2.5± 0.1 % into each of the channels e + e -, µ + µ - and τ + τ -. There is a branching ratio of approxiately 2.2 % into radiative decays, where a photon replaces one of the gluons entioned above, and approxiately % into Ψ/J + X. The weak decays for the s are deterined by the expanded ixing described by the CKM (Cabibbo, Kobayashi and Maskawa) ixing atrix d Vud Vus Vub d s = Vcd Vcs V cb s, b Vtd Vts V tb b (12.19) where, as above, the basis on the left is weak isospin and on the right is strong isospin, the ass eigenstates. The indices label the relevant flavor changing decays. For the case of b, i.e., decay, the doinant ter is V bc and there are sizeable branching ratios to Dπ states. Aside: An iportant feature of the ixing atrix in Eq. (12.19) is that it contains not only 3 (real) ixing angles, but it also allows 1 physically relevant phase (which cannot be rotated away by a QM allowed redefinition of the states). This phase is the siplest explanation of the observed CP violation in the hadronic sector, as we Lecture 12 6 Physics 557 Winter 2016

7 will eventually discuss. For now let us quickly review the counting that shows this phase can be present and why having (at least) 3 generations of quarks is required. Consider first the ore general case where we have N generations of left-handed up and down type quarks, described by the N-diensional vectors U L and D L. The flavor content of the charged current (flavor changing) interaction then looks like CC U VD (12.20) ~, Flavor L L where the atrix V is playing the sae role as in Eq. (12.19). Since we want the weak interaction to conserve quark nuber, V ust be a NxN unitary atrix. This eans it is described by N 2 real paraeters (2N 2 real paraeters for a general NxN coplex atrix, but with N 2 constraints fro V V = 1). Fro our experience with real rotations, O(N), we know that N(N-1)/2 of these paraeters can be thought of as actual ixing angles (just the nuber of independent 2-D planes in an N- diensional world). The reaining N(N+1)/2 paraeters can be thought of as phases. However, we know that we are free to perfor a global (space-tie iα k independent) change of the phases of the 2N quarks, qk e qk, without changing any of the other physics. Further, an overall (flavor independent, α k = α ) change of phase does not change V in Eq. (12.20) (i.e., only the relative phase changes of the iα iα quarks will change V, e V e = V ). Hence the nuber of relevant phases we can reove by an appropriate choice of phases for the quarks is 2N 1. So finally the nuber of reaining free (and relevant) phases in V are N(N+1)/2 (2N 1) = (N-1)(N-2)/2. Hence there no relevant phases for N = 1 or N = 2, and exactly 1 for N = 3, along with the 3 Cabibbo-type ixing angles for N = 3. Returning to the previous discussion, the cast of botto pseudoscalar states is copleted by the isoscalar char and strange states 0 0 ( s s ) = ( sb bs ),,, 0 0 s s + ( c c ) = ( cb bc ) MeV, τ s,,,, = ± = ± = ± = ± GeV, τ s. ± ± c c (12.21) There is also evidence for the corresponding vector states, the * s, with a ass of ± 0.2 MeV but confiration of the I, J and P quantu nubers of these states Lecture 12 7 Physics 557 Winter 2016

8 is still incoplete. The doinant decay is to γ, as there is no phase space for a decay channel with a pion. Recall that the * - ass splitting (like the D* - D, K* - K and π - ρ) is thought to be a (strong) hyperfine effect, which depends on the quark ass like 1/ Q. Thus, with each successively larger ass quark, we should observe saller splitting. Fro the standpoint of the strong interactions, one of the ost interesting features of both the cc and bb systes is how closely the spectra of states atch those observed in the QED syste of positroniu. This point is illustrated in the following figures, which illustrate the levels of the three systes in typical nuclear physics (as opposed to atoic physics) spectroscopic notation n 2S+1 l J, with n the principal quantu nuber. First, the spectru of the QED systes looks as follows. Note the broken energy scale representing the fact that principal quantu nuber splitting is uch larger than the other splittings. The scale for the other splittings is of order 10-5 ev. Lecture 12 8 Physics 557 Winter 2016

9 Next we turn to the char quark syste. Note in this case the broad states (strong interaction decays) for the states above the DD threshold, which is not present in the QED case. Note also the presence of the 0 - state. Like the corresponding positroniu state, this state can decay into a 2-vector boson state (gluons in this case), unlike the 1 - state that can decay only into a iniu of 3 gluons. Thus it is no surprise that the η c (2980) (Γ ηc ~ 29 MeV) is uch broader than the Ψ(3097) (Γ Ψ ~ 93 kev). Lecture 12 9 Physics 557 Winter 2016

10 Finally the spectru for the botto quark case looks as follows. So the question arises, why do these spectra look so siilar? First we understand that all 3 systes describe nonrelativistic ferion anti-ferion pairs. Further, in the QED case, we know that the basic binding coes fro the 1/r potential of electroagnetis, which yields energies for the states that depend on the principal quantu nuber (like 1/n 2 ). The states are further separated by the spin-orbit interaction (the fine splitting, separating states of different l) and the spin-spin interaction (the hyperfine splitting, separating states of different total S). For the QCD case with heavy quarks we ust consider copact wave functions with characteristic radius of order 1/ Q << 1 f. In this short distance liit the strong coupling is rather sall (although still uch larger than α EM ) and we expect the QCD potential to also have a coulob, 1/r for. A useful phenoenological for for the full QCD potential is 4 αs ( r) VQCD ~ + κr. (12.22) 3 r Lecture Physics 557 Winter 2016

11 The first ter is the short distance liit of the color interaction with the appropriate prefactor forqq in a color singlet (as we have noted earlier). The second, linear ter represents the confineent facet of QCD in a fashion that is suggested by the linear Regge trajectories of the previous lecture. The naive picture of the self-interacting flux (the gluons) that connects the quark and antiquark is provided in the following figure. The idea is that, atqq separations short copared to 1 f, we see coulob like flux structure, i.e., a flux density that falls off like 1/r 2. At separations coparable to 1 f (and larger), the self-interactions of the flux (the glue) confines it to a flux tube with approxiately fixed (transverse) size of order 1 f, i.e., a fixed flux density. The forer situation yields a potential energy that behaves as 1/r at sall r while the flux tube leads a potential that increases linearly with r at large r. The siilar 1/r potential for all three cases leads to the siilar spectra of states. The larger agnitude of α s (> α EM ) and the effect of the linear ter lead to soewhat different relative roles for the principal quantu nuber, fine splitting and hyperfine splitting. The relative role of the first is reduced while the role of the last two varies with the heavy quark ass. The linear ter in the potential also leads to an increasing nuber of states below the threshold for unsuppressed strong decays. A reasonable description of the eson spectra is supplied with the above potential using α s ~ 0.2 and κ ~ 1 GeV/f, as suggested by the Regge behavior discussion in the previous lecture. y 1980 we were again back in the soup with 3 observed down-like quarks and only 2 up-like. As noted in our discussion of FCNC s (and also in the context of the cancellations of certain triangle anoalies that we will discuss soon) it seeed necessary that there be a sixth quark, the top quark (also once called truth to go with the beauty quark). For reasons yet to be explained, but alost surely very iportant, the top quark turns out to be very heavy, = ± 0.51± 0.71 GeV, (12.23) t Lecture Physics 557 Winter 2016

12 and its existence was not confired until 1995 at the Tevatron Collider at Ferilab. The top quark was detected not via the vector bound state, as with char and botto (see below and note that we have no e + e - achines of 350 GeV anyway), but directly fro its weak decays. In the proton-antiproton collisions at Ferilab top-anti-top quark pairs are produced either via the annihilation of a valence quark-antiquark pair into a virtual gluon, which couples to the top pair, or fro the coupling of a gluon fro each bea hadron directly to the top pair (called the Einhorn-Ellis echanis in soe quarters). [We will study such processes in ore detail when we get to the strong interactions.] The top quarks then decay weakly into real W s and (priarily) b quarks. The W s then decay into either lepton pairs or quark pairs, with the latter producing jets in the final states. The b quarks for esons, whose decays close to the interaction region (i.e., after short ties) are detected in vertex detectors, typically strips of silicon. Thus what we see in the detector is pp tt + X + W b W b + X or or + µ ν µ ν + X µ µ qq qq + X 4 jets + + X + qq µ ν + X or µ ν qq + X µ µ 2 jets + µν + + X. (12.24) Reconstructing such events is clearly a challenge, but is now essentially standard procedure at the LHC where vast nubers of top quarks are being produced. One of the iportant features of the systeatics of top quark studies arises directly fro its huge ass. Since it is assive enough to decay into a real W, its decay width is proportional to just a single factor of the Feri constant, and not G F 2 as we had for all lighter particles. Keeping effects of the W ass in the phase space integration but ignoring both the ass of the botto quark and higher order ters in the weak and strong couplings we have (we will do the details shortly) F t W W 2 2 t t G Γt Wb ~ 1.5 GeV. (12.25) 8π 2 Lecture Physics 557 Winter 2016

13 0.19 The corresponding experiental (PDG) nuber is GeV. While this is unabiguously a weak interaction decay, the width is that of a super strong decay (recall the ρ has a width of only 150 MeV). The corresponding tie scale is of order 0.5 x s, an order of agnitude saller than the tie for a photon, or a gluon, to travel a distance of 1 f. Thus the top and anti-top quarks produced at Ferilab and the LHC decay long before they have an opportunity to interact strongly and for bound states (i.e., they decay before they hadronize ). The top quark syste in the laboratory is not characterized by the spectra of bound states that we saw in charoniu and bottooniu (even though, as we saw above, the linear, confining potential would predict that ~ 10 such states would exist if we turned off the weak interactions). In suary, we now have all the ferions that we need (odulo the RH neutrinos). Particle Spin Q EM SU(2) L Weak SU(3) Strong Mass Electron ½ -1 LH-2, RH MeV ν e ½ LH < 2 ev Muon ½ -1 LH-2, RH MeV ν µ ½ LH < 0.19 MeV Tau ½ -1 LH-2, RH ± 0.12 MeV ν τ ½ LH < 18.2 MeV u quark ½ 2/3 LH-2, RH to 3.0 MeV d quark ½ -1/3 LH-2, RH to 5.3 MeV c quark ½ 2/3 LH-2, RH ±0.025 GeV s quark ½ -1/3 LH-2, RH ± 5 MeV t quark ½ 2/3 LH-2, RH ± 0.5 ± 0.7 GeV b quark ½ -1/3 LH-2, RH ±0.03 GeV The asses indicated in the table are the current quark asses. These particles constitute 3 coplete generations, differing only in their asses. The question reains, why 3 generations and not 1 or 2? (Do we really need CP violation?) Next we will discuss the syetries of the interactions and the required vector (gauge) particles. Lecture Physics 557 Winter 2016