Neutrinos. Thanks to Ian Blockland and Randy Sobie for these slides. spin particle with no electric charge; weak isospin partners of charged leptons

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1 Neutrinos Thanks to Ian Blockland and Randy Sobie for these slides spin particle with no electric charge; weak isospin partners of charged leptons observed in 193, in 1962 and in the 199s neutrino physics is very topical solar neutrino problem, neutrino mixing, neutrino masses Physics 424 Lecture 1 Page 1

2 discovery Physics 424 Lecture 1 Page 2

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4 discovery Physics 424 Lecture 1 Page 4

5 # # ) Do Neutrinos Have Mass? Although we have always known that neutrinos are light, it is an experimental matter to determine just how light. As far as direct measurements go: Flavor Mass Limit Process " ( ' $&% There is no fundamental reason (e.g., a symmetry) why. The Standard Model assumes that neutrinos are precisely massless; accomodating non-zero masses is in many respects straightforward. Physics 424 Lecture 1 Page

6 mass measurement Physics 424 Lecture 1 Page 6

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8 + # ' # $. -, * mass measurement LEP experiments measured the limit on the decays. E π [GeV] 4 4 MeV mass using m ν = MeV m ν = 1 MeV π +/- Monte Carlo m π [GeV] Physics 424 Lecture 1 Page 8

9 Neutrino Mixing Supposing that neutrinos have mass, we must now allow a mixing between the weak eigenstates and the mass eigenstates, just as we have done for the quarks. The neutrino analogue of the CKM matrix is the Maki-Nakagawa-Sakata (MNS) matrix. Like the CKM matrix, the MNS matrix can be parametrized in terms of 3 mixing angles and 1 CP-violating complex phase. We label the neutrino mass eigenstates (in order of ascending mass) as,, and. Physics 424 Lecture 1 Page 9

10 Neutrino Deficits In 1967, Ray Davis put 1, gallons of dry-cleaning fluid in a tank a mile underground to try to measure the solar neutrino flux. The measured flux (inferred from 1 Cl to Ar conversion every 2 days) was about a factor of 3 below the theoretical expectations from the Standard Solar Model. Similar neutrino deficits were later observed for the atmospheric neutrinos generated by cosmic rays. Surprisingly, both experiment and theory turned out to be right and these effects are now understood as neutrino oscillation effects. Physics 424 Lecture 1 Page 1

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13 ) / ) ) Neutrino Oscillations: 2 Flavor Model We will now illustrate how neutrino oscillations work in the context of a 2-neutrino model. Neutrinos are always produced as weak eigenstates. Suppose that at we produce an electron neutrino: Neutrinos propagate as mass eigenstates. In a 2-neutrino model, the weak eigenstates and the mass eigenstates are related by Physics 424 Lecture 1 Page 13

14 ) 1. - ;< : > ) >? > ' Neutrino Oscillations: Propagation In terms of the mass eigenstates, our original is When a particle propagates in free space, it accumulates a phase of. Assuming that the spatial momentum of the original is passed on to and, the energy of each neutrino is given by : = : : Physics 424 Lecture 1 Page 14

15 @ : < : < : : N ) R < : < : 9 Q 4 ) ED ACB Neutrino Oscillations: The two mass eigenstates pick up different phases as they propagate, so that 687 ;GH < 4 ;GF 1.-/ ) Going back to flavor eigenstates, this is ; F 1.-/ ) ;GH < 4 is then to The probability of an oscillation from 1.-/.-/ IKJLM OPO ; H ; F OPO Physics 424 Lecture 1 Page 1

16 UTS R < : < : 9 Q 4 ) [: 9 Y ' ' 4 ) `. / _ ' ) a ) / /? U f e = g?cu c a Q h ' ) a j ' % Neutrino Oscillations: OVO ;WH ; F OVO.-/ IKJLM ^] \< ; F ;GH [: \< ; F ;GH Z 687 X = 9 = and 'dc b = a With f =? ir = ' f b 6 7.-/ I JLM. "lk - f ' ). -m = Physics 424 Lecture 1 Page 16

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18 ) % ' Curves (red, blue, black) for and frequency, respectively. A detector might sample the region qo % q o % j q o% npo % t Physics 424 Lecture 1 Page 18

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20 = f a f = Ways of Observing Neutrino Oscillations The oscillation probabilities depend on,,, and. We can either look for the appearance of a different neutrino flavor (usually limited by background) or we can measure the disappearance of the expected flavor (limited by calibration of source and target). Source Types Mode Advantage Solar Disappearance Great distance Atmospheric,,, Disappearance Variable distance Reactor Disappearance Low energy Accelerator, Either Control and Physics 424 Lecture 1 Page 2

21 t: q q % % % j ' q q 9 % % % j ' q u q 9 % % % Current Status The mixing matrix appears to feature very large mixing angles (LMA); the following gives a crude view of the sizes of the matrix elements: ' svs rvr svs rvr ) svs rvr Physics 424 Lecture 1 Page 21

22 (Mass) 2 m 2 atm > 2 mo. Green hatch: Red right: Blue left: Physics 424 Lecture 1 Page 22

23 CDHSW 1 KARMEN2 LSND NOMAD Bugey NOMAD CHORUS NOMAD BNL E776 CHORUS 1 3 Cl K2K CHOOZ Super-K+SNO +KamLAND SuperK PaloVerde m 2 [ev 2 ] 1 6 SNO KamLAND Super-K Ga 1 9 ν e ν X ν µ ν τ ν e ν τ ν e ν µ tan 2 θ Physics 424 Lecture 1 Page 23

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29 x ~ ~ m Neutrino Mass Terms If neutrinos do have a small mass, we could create Dirac mass terms (just like for and ). v w Since neutrinos do not carry non-zero quantum numbers, it is possible that a neutrino is its own antiparticle. Such a neutrino is known as a Majorana neutrino. Incorporating both Dirac and Majorana mass terms leads to the seesaw mechanism, whereby the presence of a right-handed neutrino at the GUT scale leads to zy, {} where is the Dirac mass of a typical Standard Model fermion and, as we ll soon see, is approximately. y, {} Physics 424 Lecture 1 Page 29

30 c Double Decay Certain unstable atoms, such as and, can decay to elements with two additional protons via double decay. ƒ m These decays cannot be regarded as two separate decays because the intermediate state is energetically off limits. As a result, double decay is one big process in which two separate neutrons simultaneously decay via. Because decay is a 3-body decay, the energy of the emitted electron is not fixed. Physics 424 Lecture 1 Page 3

31 ˆ ˆ Š b Supposing that neutrinos are Majorana particles, the two neutrinos involved in double decay can actually be merged into an internal line so as to produce neutrinoless double decay. The denotes the transition from suppression of. = to. This leads to a Now that each decay is essentially a 2-body decay, the energy of the electrons is fixed. Physics 424 Lecture 1 Page 31

32 vs. Physics 424 Lecture 1 Page 32

33 Summary Neutrino masses, although not present in the SM, can easily be incorporated, along with the MNS mixing matrix. to Œ ) leads to neutrino oscillations (observed) and may lead (searched for). Structure of the MNS matrix is becoming better known; next generation experiments will possibly measure CP violation in neutrinos Physics 424 Lecture 1 Page 33

Neutrino Basics. m 2 [ev 2 ] tan 2 θ. Reference: The Standard Model and Beyond, CRC Press. Paul Langacker (IAS) LSND 90/99% SuperK 90/99% MINOS K2K

Neutrino Basics. m 2 [ev 2 ] tan 2 θ. Reference: The Standard Model and Beyond, CRC Press. Paul Langacker (IAS) LSND 90/99% SuperK 90/99% MINOS K2K Neutrino Basics CDHSW m 2 [ev 2 ] 10 0 10 3 10 6 10 9 KARMEN2 Cl 95% NOMAD MiniBooNE Ga 95% Bugey CHOOZ ν X ν µ ν τ ν τ NOMAD all solar 95% SNO 95% CHORUS NOMAD CHORUS LSND 90/99% SuperK 90/99% MINOS K2K