18/02/2016Nuclear and Particle Physics,1 Weak interactions, P, C and CP Introduction Need of neutral currents Electroweak and Higgs Parity in weak interactions Helicity of the neutrino, C and CP Pion decay The K 0 K 0 system K S regeneration Strangeness oscillation CP violation neutrino oscillations mixing, GIM mechanism and CKM matrix

18/02/2016Nuclear and Particle Physics,2 Introduction Weak interaction governs radioactive decays, decays which don’t conserve strangeness, charm, bottom or top, and reactions where neutrinos are present. Weak interactions are described by the exchange of vector bosons who are the carriers of the weak force. They were discovered in 1983: the W +, W - and Z 0. Contrary to the massless photon and gluon, these vector mesons are very massive:

18/02/2016Nuclear and Particle Physics,3 The need for neutral currents Weak interactions were thought to be only of the charged-current type. These reactions were mediated by W ±. This caused a problem: This process has a divergent cross section – unless a neutral vector boson Z 0 also exists. g – weak coupling

18/02/2016Nuclear and Particle Physics,4 Electroweak and Higgs Another divergent process is: unless Z 0 exists, and the weak coupling g is approximately equal to the electromagnetic coupling e Exact cancellation is true only for massless electron. For finite electron mass, need to introduce a new scalar particle – the Higgs particle.

18/02/2016Nuclear and Particle Physics,5 Mass estimate of the Higgs

This is where we are today 18/02/2016Nuclear and Particle Physics,6

18/02/2016Nuclear and Particle Physics,7 Neutrino interactions W exchange gives Charged-Current (CC) events and Z 0 exchange gives Neutral-Current (NC) events. In CC events, the outgoing lepton determines if neutrino or antineutrino in initial state.

18/02/2016Nuclear and Particle Physics,8 Weinberg-Salam model Electroweak interactions are mediated by four massless bosons, arranged in a triplet and a singlet, in multiplets of ‘weak isospin’ and ‘weak hypercharge’. The triplet belongs to the group SU(2) and the singlet to the group U(1)  model of Weinberg – Salam referred to as SU(2) x U(1). By a mechanism introduced by Englert-Brout-Higgs, a scalar boson (Higgs) generates through ‘spontaneous symmetry breaking’ (see ferromagnet) three very massive vector bosons, W ± and Z 0, while the fourth particle, the photon, remains massless. The whole Lagrangian can be expressed as follows: weak CCweak NCem NC This gives that e = g sin  W, where  W is the Weinberg mixing angle.

18/02/2016Nuclear and Particle Physics,9 The weak isospin triplet is composed of three massless gauge bosons W +, W - and W 0. In addition there is a weak iso-singlet B 0. In the theory of Weinberg-Salam, the particles observed in nature are mixtures of B 0 and W 0 :

18/02/2016Nuclear and Particle Physics,10 Spontaneous Breakdown of Rotational Symmetry before dinner once dinner starts

18/02/2016Nuclear and Particle Physics,11 Number of generations First signs for existence of Z 0 Measurement of Z 0 and evidence for 3 generations

18/02/2016Nuclear and Particle Physics,12 Parity in weak interaction Parity operator was introduced by Wigner in 1927 in context with atomic physics, and was believed to be a universal law. The  -  puzzle was the first indication that P conservation is not universal. The following decays were known of particles around 500 MeV: Experimental data indicated J(  ) = J(  ) = 0. The  -  puzzle:

18/02/2016Nuclear and Particle Physics,13 Parity non-conservation Lee and Young pointed out that all the evidence for P conservation came from strong and electromagnetic interactions. They hypothesized that P is not conserved in weak interactions. The decay times of  and  were consistent with the decay being a weak one   and  are the same particle, K meson, but do not conserve parity in the decay. They are eigenstates of Parity in strong and em interactions, but not in weak ones. predicted that P will not be conserved in radioactive decays. Was confirmed by Wu in 1957 and Lee (31) and Young (35) were awarded the Nobel prize in Physics in 1957.

18/02/2016Nuclear and Particle Physics,14 The Wu experiment Wu performed the parity-conservation test, immediately after it was suggested by Lee and Young. She studied  -decay of polarized 60 Co. Parity operation on the  decay changes momentum direction of electrons but does not change spin direction. If P conserved, no forward-backward asymmetry expected.

18/02/2016Nuclear and Particle Physics,15 Wu experiment (2) Cooled the sample of 60 Co nuclei to 0.01 K in presence of external magnetic field  obtained polarized nuclei with spins aligned in magnetic field direction. A and B measure the two photons, and the anthracene scintillation counter measure the intensity of the  emission. The magnetic field direction is changed from up (full dots) to down (open circles). A clear asymmetry is observed, which disappears as the system warms up and the polarization stops.

18/02/2016Nuclear and Particle Physics,16 Helicity and P, C Helicity of a particle is defined as its spin projection along its direction of motion. J p A particle is called right handed if its helicity is positive, > 0, and left handed if it is negative, < 0. An electron can exist in two states: e R and e L. The parity operation P turns a right handed particle into a left handed one because the parity operation reverses the momentum vector but not the spin one. The operation of charge conjugation C does not change the handiness of the particle but changes it to its antiparticle. p +1 Right-handed p Left-handed

18/02/2016Nuclear and Particle Physics,17 Helicity of the neutrino M. Goldhaber (PR 109(1958)1015) measured the helicity of the neutrino in a K-capture of Europium-152: The excited state of Samarium with total angular momentum J=1 decays to its ground state with the emission of a photon: Select photons which were emitted in the direction of the decaying 152 Sm*. The helicity of the neutrino is the same as that of the photon  measuring the helicity of the photon measures the helicity of the neutrino. J=0 J=1 J=0 K-capture ,960 MeV

18/02/2016Nuclear and Particle Physics,18 Helicity of neutrino (2) Electron capture K shell, l=0 photon emission Eu at rest Select photons in Sm* dir n Neutrino, Sm in opposite dirns e-e- Momenta, p spin OR  S=+ ½ S=- ½ Left-handed S=+ 1 S=- 1 right-handed Left-handed right-handed Helicities of forward photon and neutrino same Measure photon helicity, find neutrino helicity

18/02/2016Nuclear and Particle Physics,19 Helicity of neutrino, P, C, CP Experiment showed that all photons come out with negative helicity  the neutrino is left-handed. A similar experiment with e + on 203 Hg showed that the antineutrino exists only as right-handed. Neutrinos are close to massless. This means that relativistic fermions which can be treated as massless would exist also only as left-handed, with the anti-fermion being right-handed. (suppression of ‘forbidden’ states – m 2 /2E 2 ) The implication of having only left- handed neutrino is breaking of P and C conservation: However, CP can be conserved: C P CPCP

18/02/2016Nuclear and Particle Physics,20 C P CP Parity Inversion Spatial mirror Charge Inversion Particle-antiparticle mirror

18/02/2016Nuclear and Particle Physics,21 Pion decay The pion decays with a puzzling branching ratio: Since the pion spin (and helicity) is 0, the decay in its rest frame has the following configuration: The neutrino is left-handed  the lepton also has to be left-handed, to conserve helicity. In positron decay mode, the positron is relativistic  must behave like the antineutrino  exists only as e + R, which suppresses this decay mode. In muon decay mode, muon not relativistic  can exist both as right- handed and as left-handed. In the decay it is always left-handed. Thus muons from pion decay are polarized as left-handed, to cancel the left-handed neutrino.

18/02/2016Nuclear and Particle Physics,22 The system The two neutral Kaons are two distinct particles in strong and em interactions, with definite strangeness numbers. Their decay is however through weak interactions, which does not conserve strangeness. Thus the two states can mix. One can have transitions between the two states: This situation is unique for the K system – for light quarks. For heavy ones, one has the same situation for the neutral charm meson D and the neutral bottom meson B. A  + can not turn into a  - (electric charge), a neutron will not turn into an antineutron (baryon number). Weak interactions can not distinguish between. The observed physical particles which decay are a linear combination of them. 0 K

18/02/2016Nuclear and Particle Physics,23 CP of the neutral K system The mixing happens in such a way as to produce eigenstates of operators which are conserved in weak interactions. Since CP seems to be conserved in weak interactions, we need to create combinations which are eigenstates of CP. Chose the arbitrary phases  =  ’ = 1. Clearly the K 0 s are not eigenstates of CP, but one can form linear combination which are

18/02/2016Nuclear and Particle Physics,24 K 1, K 2, K S, K L There are two components in the decay of the neutral K: a short lived state, which decays into 2  and is called K S, and a longer living K which decays into 3 , denoted K L. Their life times are: Since  0 has C=+, the CP of the  0  0 system is determined by their P, and the same is true for the  0  0  0 system. Thus: One therefore associates the experimentally observed states K S and K L with K 1 and K 2.

18/02/2016Nuclear and Particle Physics,25 K S regeneration Can verify experimentally the superposition scheme of the neutral K. Start with a pure K 0 beam, obtained from the reaction  - p  K 0 . The K 0 beam moves in vacuum for length corresponding to ~100  (K S ). Only 50% beam intensity left, consisting of K L. This beam interacts strongly with a target (see figure). Strong interaction will pick up its two eigenstates of SI: K 0 and K 0. Started with pure K 0, yet have K 0 after long distance. Was confirmed experimentally by finding reaction K 0 p  +

18/02/2016Nuclear and Particle Physics,26 Regeneration (2) The two components of K L which pass through target are both reduced in intensity after interacting with target. The reduction is not the same for both components because: The reason for this: there are no S=+1 baryons. What do we find after K L passes the target? Denote:

18/02/2016Nuclear and Particle Physics,27 Regeneration (3) The strangeness content of the beam which emerges from the block is therefore In terms of Since  the short lived K 1 (K S ) has been regenerated. This was confirmed experimentally by detecting  decays.

18/02/2016Nuclear and Particle Physics,28 Strangeness oscillation K 0 has a definite strangeness (S=+1) when produced in a strong interaction: However, some time after the production, the traveling K 0 becomes a superposition of two components with S=+1 and S=-1. The intensities of these two components are a function of time and oscillate. This oscillation enable the measurement of the small mass difference  m between K 0 S and K 0 L. At t=0: At time t, the two components evolve differently with time:

18/02/2016Nuclear and Particle Physics,29 Strangeness oscillation (2) For unstable particles with mass m and lifetime  = 1/ , the time dependent wavefunction, in the particle rest system, is expressed: Therefore we can write We see a non-zero amplitude for which started as a pure K 0

18/02/2016Nuclear and Particle Physics,30 Strangeness oscillation (3) The intensities of the two components, after time t, is: Only they can produce S=-1 baryons (  hyperons). Measuring number of hyperons as function of the distance gives How can one measure experimentally the number of ? Although K 1 and K 2 are mixtures of K 0 and, which have identical masses, they have a small mass difference.

18/02/2016Nuclear and Particle Physics,31 CP violation Are K 1 and K 2 the particles appropriate for the weak force? This is true if CP is conserved, as they are eigenstates of CP. A test of CP conservation in weak interactions would be to look for a 2  decay of K 2. If CP is conserved, this decay is forbidden. Used the AGS accelerator at Brookhaven. 30 GeV proton beam. Be target. K  were produced in p+Be collisions. Collimator at 4.5 m from the target, magnet at 6.5 m, 2nd collimator at 18 m. K 1 decayed before reaching the 2nd collimator.

18/02/2016Nuclear and Particle Physics,32 Observation of K 2  Two spectrometers: –Spark chamber –Magnet –Scintillator –Water Cherenkov counter Spark chambers were triggered on a coincidence between water Cherenkov (v>0.75 c - pions) and scintillation counters. This removed most slow particles produced in collisions of neutrons

18/02/2016Nuclear and Particle Physics,33 Results Observed about 50 events out of 23,000 decays where K 2   +  -  CP is violated  the particles ‘seen’ by the weak interactions are K S and K L, which are superpositions of the CP eigenstates K 1 and K 2 : Why is CP violated? One possible explanation: CP is conserved in weak interactions, and the violation is due to some ‘superweak’ force. CP violation should also be seen in case of D 0 and B 0. There is a special B- factory at SLAC, where the BaBar collaboration is seeing some encouraging signals for this effect. Another experiment in KEK, BELLE, is also seeing the same results. Both results are still preliminary.

18/02/2016Nuclear and Particle Physics,34 Implications of CP violation Can convey to intelligent alien the absolute distinction between left and right: CP violation is also demonstrated in the leptonic decay of K L : Can communicate that we define the neutrino as the one associated with the more abundant leptonic decay mode of the long-lived K L -particle. This establishes a common matter- antimatter convention which allows the alien to identify uniquely our handedness convention.

18/02/2016Nuclear and Particle Physics,35 Matter-antimatter asymmetry Combining GUT with CP violation can explain the net baryon number in the universe (Andrei Sakharov, 1967, ‘baryogenesis’): at times less then s after the Big Bang, temp still higher than K, superheavy gauge bosons X and anti-X (M X ~10 15 GeV) equally produced and remained in thermal equilibrium: universe expended and cooled. X and anti-X can no longer be produced. Expansion of universe destroyed equilibrium; expansion faster than the bosons could interact  large numbers of bosons began to decay. because of CP violation, decay rate of X to quark is slightly more rapid than that of anti-X to anti-quark  the average value of the baryon number states bigger than antibaryons, creating a net baryon number in the present universe.

18/02/2016Nuclear and Particle Physics,36 Highlights of neutrino history 1930 Pauli postulates neutrino existence 1953 Clyde Cowan and Fred Reines discover electron neutrino (Nobel 1995) 1957 Neutrino oscillations predicted by Pontecorvo 1962 discover the muon neutrino (Nobel 1988) 1973 Neutral current neutrino interactions observed 1974 discover tau particle (Nobel 1995) and assumed existence of tau neutrino (experimental evidence – 2000) 1989 Only 3 light neutrino families 1998 the Super-Kamiokande collaboration announce evidence of non-zero neutrino mass (Nobel 2002)

18/02/2016Nuclear and Particle Physics,37 Quark mixing In the SM, there is symmetry between leptons and quarks. There is lepton universality (unless there is a reason to break it – see  decay), so expect also existence of quark universality. Does it work? For simplicity, assume 3 leptons and 3 quarks. The weak decays can be classified into two categories: those which do not change strangeness,  S=0, and those where strangeness is changed by one unit,  S=1. The  decay of the neutron, and that of the  are the respective examples: On the quark level, in the decay a d (s)  u with the emission of W - :

18/02/2016Nuclear and Particle Physics,38 Cabibbo model Quark universality would require that n and   -decays should occur with about equal strength (apart from phase space factors). Experimentally the  S=0 decay is about 20 times stronger than the  S=1 decay. Cabibbo suggested the following solution (1963): the eigenstates of the quarks in weak interactions are different from those in strong interactions. previous example Cabibbo’s conjecture was that the quarks that participate in the weak interaction are a mixture of the quarks that participate in the strong interaction.

18/02/2016Nuclear and Particle Physics,39 Cabibbo angle This mixing was originally postulated by Cabibbo (1963) to explain certain decay patterns in the weak interactions and originally had only to do with the d and s quarks. d’ = d cos  + s sin  Thus the form of the interaction (charged current) has an extra factor for d and s quarks The Cabibbo angle can be measured using data from the following reactions: From the above branching ratio’s we find:  c = 0.27 radians d u W-W- cos  c s u W-W- sin  c Purely leptonic decays (e.g. muon decay) do not contain the Cabibbo factor: u ++ W+W+ cos  c or sin  c d, s 

18/02/2016Nuclear and Particle Physics,40 Extension to 4 quarks (GIM) Adding a fourth quark actually solved a long standing puzzle in weak interactions, the “absence” (i.e. very small BR) of decays involving a “flavor” (e.g. strangeness) changing neutral current: However, Cabibbo’s model could NOT incorporate CP violation and by 1977 there was evidence for 5 quarks! In Glashow, Iliopoulos, and Maiani (GIM) proposed to extend the model of Cabibbo by postulating the existence of a fourth quark – charm.

18/02/2016Nuclear and Particle Physics,41 The Cabibbo-Kobayashi-Maskawa (CKM) model In 1972 (2 years before discovery of charm!) Kobayashi and Maskawa extended Cabibbo’s idea to six quarks: 6 quarks (3 generations or families) 3x3 matrix that mixes the weak quarks and the strong quarks (instead of 2x2) The matrix is unitary  3 angles (generalized Cabibbo angles), 1 phase (instead of 1 parameter) The phase allows for CP violation Just like  c had to be determined from experiment, the matrix elements of the CKM matrix must also be obtained from experiment.

42 CKM Matrix The CKM matrix can be written in many forms: 1) In terms of three angles and phase: The four real parameters are ,  12,  23, and  13. Here s=sin, c=cos, and the numbers refer to the quark generations, e.g. s 12 =sin  12. This matrix is not unique, many other 3X3 forms in the literature. This one is from PDG ) In terms of coupling to charge 2/3 quarks (best for illustrating physics!) 3) In terms of the sine of the Cabibbo angle (  12 ). This representation uses the fact that s 12 >>s 23 >>s 13. “Wolfenstein” representaton Here =sin  12, and A, ,  are all real and approximately one. This representation is very good for relating CP violation to specific decay rates. 18/02/2016Nuclear and Particle Physics,

43 CKM Matrix The magnitudes of the CKM elements, from experiment are (PDG2008): There are several interesting patterns here: 1)The CKM matrix is almost diagonal (off diagonal elements are small). 2)The further away from a family, the smaller the matrix element (e.g. V ub <<V ud ). 3)Using 1) and 2), we see that certain decay chains are preferred: c  s over c  d D 0  K -  + over D 0   -  + (exp. find 3.8% vs 0.15%) b  c over b  uB 0  D -  + over B 0   -  + (exp. find 3x10 -3 vs 1x10 -5 ) 4)Since the matrix is supposed to be unitary there are lots of constraints among the matrix elements: So far experimental results are consistent with expectations from a Unitary matrix. But as precision of experiments increases, we might see deviations from Unitarity. 18/02/2016Nuclear and Particle Physics,

44 Measuring the CKM Matrix No one knows how to calculate the values of the CKM matrix. Experimentally, the cleanest way to measure the CKM elements is by using interactions or decays involving leptons.  CKM factors are only present at one vertex in decays with leptons. V ud : neutron decay: n  pe d  ue V us : kaon decay: K 0  p + e - e s  ue V bu : B-meson decay: B -  (  or  + )e - e b  ue V bc : B-meson decay: B -  D 0 e - e b  ce V cs : charm decay: D 0  K - e + e c  se V cd : neutrino interactions:  d   - c d  c D 0  K - e + e c u s u e,  W K-K- D0D0 V cs Amplitude  V cs Decay rate  |V cs | 2 18/02/2016Nuclear and Particle Physics,

18/02/2016Nuclear and Particle Physics,45 Neutrino mass – we will skip this chapter from here to th3 end Are neutrinos massless? Difficult to measure mass of neutrino. Only upper limits were available. The best came for the electron-neutrino from study of Kurie plots from  decay: One studies the momentum spectra of the electron, the tail of which is sensitive to the anti-neutrino mass. In addition to the simple kinematics, one needs to apply nuclear corrections, which are not always very unambiguous.

18/02/2016Nuclear and Particle Physics,46 THE BETA-DECAY SPECTRUM OF TRITIUM

18/02/2016Nuclear and Particle Physics,47 Kurie Plot coulomb correction p e E e  |(E 0 – E e )| if m  =0 E e

18/02/2016Nuclear and Particle Physics,48 RECENT MAINZ DATA 10 -YEARS OF NEUTRINO MASS FROM TRITIUM EXPERIMENTS

18/02/2016Nuclear and Particle Physics,49 Neutrino oscillations In a similar way to strangeness oscillations, one can also have neutrino oscillations if the weak eigenstate neutrinos are mixtures of neutrinos of definite mass. Assuming only two massive neutrinos (two-flavor oscillations): One can calculate the probability of detecting a neutrino of a certain flavor at a distance L from the original neutrino source:

18/02/2016Nuclear and Particle Physics,50 Neutrino sources for experimentation

18/02/2016Nuclear and Particle Physics,51 Super-Kamiokande and K2K Toyama SKSK KEK Super-Kamiokande Neutrino Observatory K2K (KEK to Kamiokande) long baseline experiment Neutrino beam generated at KEK (national HEP lab) 98% , mean E 1.3 GeV Beam goes through the earth to Super-K, 250 km away

18/02/2016Nuclear and Particle Physics,52 Super-Kamiokande US-Japan collaboration (100 physicists) 50,000 ton ring- imaging water Cherenkov detector Inner Detector: 11,146 50cm PMTs, non- reflective liner

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18/02/2016Nuclear and Particle Physics,54 Produced by cosmic rays in upper atmosphere (altitude Z=15~20 km)    µ  + µ (anti- µ ) µ   e  + e (anti- e ) + anti- µ ( µ ) Expect 2 µ :1 e (Note: Super-Kamiokande does not distinguish between  and anti- ) Atmospheric Neutrinos

18/02/2016Nuclear and Particle Physics,55 Type of Events Look for  µ + n -> µ + p  e + n -> e + p  µ + p -> µ + p +   e + p -> e + p +   tmospheric neutrinos ~ GeV Use information from Cerenkov Rings from µ and e to reconstruct events

18/02/2016Nuclear and Particle Physics,56 Event Summary R = We expected R=1!

18/02/2016Nuclear and Particle Physics,57 Zenith Angle Distribution Lost by oscillation of 

18/02/2016Nuclear and Particle Physics,58 Atmospheric neutrino results no-oscillations expectation best-fit (  m 2 ~ 3x10 -3 eV 2 ) DATA

18/02/2016Nuclear and Particle Physics,59 Solar neutrinos ExperimentReaction Observed/ expected rate SAGE 71 Ga+ e  71 Ge+e ±0.07 GALLEX 71 Ga+ e  71 Ge+e ±0.08 HOMESTAKE 37 Cl+ e  37 Ar+e ±0.04 KAMIOKA e +e -  e +e ±0.06

18/02/2016Nuclear and Particle Physics,60 K2K – accelerator neutrinos Observed 108 events in Super-K, while the expected number is for the no-oscillation hypothesis.

18/02/2016Nuclear and Particle Physics,61 Why build a detector at the South Pole? Earth Detector cosmic ray To look for the neutrino’s interaction product (e, ,  ) To use the earth as a filter To reject backgrounds

18/02/2016Nuclear and Particle Physics,62 Ice Cube Location of Ice Cube AMANDA South Pole

18/02/2016Nuclear and Particle Physics, m 2400 m AMANDA South Pole IceTopRunway Structure of Ice Cube 80 Strings 4800 Optical Modules 1 k ㎥ volume AMANDA within IceCube Energy Range 10E+7eV ～ 10E+20eV

18/02/2016Nuclear and Particle Physics,64 AMANDA

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