Theoretical Neutrino Physics Hitoshi Murayama (Berkeley) EPS Aachen July 22, 2003

EPS2003 Hitoshi Murayama2 Milind Diwan “Neutrino physics is so simple. There are no hadronic corrections. We don’t need theorists.”

Why You Need Theorists in Neutrino Physics Hitoshi Murayama (Berkeley) EPS Aachen July 22, 2003

EPS2003 Hitoshi Murayama4 Outline A Little Historical Perspective Interpretation of Data & Seven Questions –Solar Neutrino –Interpretation without LSND –Interpretation with LSND –Nature of neutrino mass Models of Flavor Conclusions

A Little Historical Perspective

EPS2003 Hitoshi Murayama6 Rare Effects from High-Energies Effects of physics beyond the SM as effective operators Can be classified systematically (Weinberg)

EPS2003 Hitoshi Murayama7 Unique Role of Neutrino Mass Lowest order effect of physics at short distances Tiny effect (m /E ) 2 ~(eV/GeV) 2 =10 –18 ! Interferometry (i.e., Michaelson-Morley)! –Need coherent source –Need interference (i.e., large mixing angles) –Need long baseline Nature was kind to provide all of them! “neutrino interferometry” (a.k.a. neutrino oscillation) a unique tool to study physics at very high scales

EPS2003 Hitoshi Murayama8 Grand Unification electromagnetic, weak, and strong forces have very different strengths But their strengths become the same at GeV if supersymmetry A natural candidate energy scale  ~10 16 GeV  m ~0.003eV m ~(  m 2 atm ) 1/2 ~0.03eV m ~(  m 2 LMA ) 1/2 ~0.007eV Neutrino mass may be probing unification!

Interpretation of Data Seven Questions

EPS2003 Hitoshi Murayama10 What we learned since Budapest Atmospheric  s are lost. P= –26 (SK, Hayato) converted most likely to  (>99%CL) Solar e is converted to either  or  (>5  ) (SNO, Poon) Reactor anti- e are lost (99.95%CL) (KamLAND, Lesko) Only the LMA solution left for solar neutrinos Tiny neutrino mass: the first evidence for incompleteness of Minimal Standard Model

Solar Neutrino Problem Finally Solved After 35 Years!

EPS2003 Hitoshi Murayama12 SNO Result Only e produced in the Sun Wrong Neutrinos   are coming from the Sun! Somehow some of e were converted to  on their way from the Sun’s core to the detector  neutrino flavor conversion!

EPS2003 Hitoshi Murayama13 KamLAND result First terrestrial expt relevant to solar neutrino problem Dec 2002 Expected #events:86.8±5.6 Background #events: 0.95±0.99 Observed #events:54 No oscillation hypothesis Excluded at 99.95%

EPS2003 Hitoshi Murayama14 No other solution than oscillation Neutrino decay –Wrong energy dependence Spin-resonant flip –Relies on a large solar magnetic field New flavor-changing neutral current –Relies on a high solar matter density Violation of the equivalence principle –Relies on the strong solar gravitational potential

EPS2003 Hitoshi Murayama15 March 2002 April 2002 with SNO Dec 2002 with KamLAND Progress in 2002 on the Solar Neutrino Problem

EPS2003 Hitoshi Murayama16 Solar Neutrino Spectrum pp 7 Be 8B8B

EPS2003 Hitoshi Murayama17 We don’t get enough We need survival probabilities of 8 B: ~1/3 7 Be: <1/3 pp: ~2/3 Can we get three numbers correctly with two parameters?

EPS2003 Hitoshi Murayama18 Matter Effect CC interaction in the presence of non- relativistic electron Neutrino Hamiltonian Electron neutrino higher energy in the Sun

EPS2003 Hitoshi Murayama19 Adiabatic Use “instantaneous” eigenstates + and – For the LMA region, the dynamics is adiabatic: there is no hopping between states

20 Solar Neutrino Astrophysics Davis and Bahcall started solar neutrino work because they wanted to probe physics of the sun Finally one can fit all solar neutrino data together with KamLAND to measure all major components: pp, 7 Be, 8 B (Bahcall, Peña-Garay) Solar luminosity confirmed Possible concern: density perturbation (Reggiani)

EPS2003 Hitoshi Murayama21 Loose Ends Energy dependence in the solar neutrino survival probability not fully demonstrated –pp, 7 Be solar neutrino experiments Nobody has seen “oscillation,” i.e., the survival probability dips and comes back up –Atmospheric: MINOS –Solar/reactor: continued KamLAND Evidence for  “appearance” in atmos still not strong enough (99%CL) –OPERA, ICARUS

EPS2003 Hitoshi Murayama22 Low-Energy Solar Neutrinos Solar neutrino data suggest energy- dependent survival probability  tests MSW effect  12  Helps interpretation of CP violation, double beta decay data 7% 1% 20%

EPS2003 Hitoshi Murayama23 Verify Oscillation Even atmospheric neutrino data do not show “oscillation” yet  MINOS, J-PARC   m 2 23,  23, mass hierarchy and  13 KamLAND data is consistent with overall suppression  continued running   m 2 12

Interpretation Without LSND

EPS2003 Hitoshi Murayama25 Three-generation Framework Standard parameterization of MNS matrix for 3 generations atmospheric ??? solar

EPS2003 Hitoshi Murayama26 Three-generation Solar, reactor, atmospheric and K2K data easily accommodated within three generations sin 2 2  23 near maximal  m 2 atm ~ 3  10 –3 eV 2 sin 2 2  12 large  m 2 solar ~ 7  10 –5 eV 2 sin 2 2  13 =|U e3 | 2 < 0.05 from CHOOZ, Palo Verde Because of small sin 2 2  13, solar (reactor) & atmospheric oscillations almost decouple Gonzalez-Garcia, Peña-Garay  2 /dof=136/173

EPS2003 Hitoshi Murayama27 Seven Questions Dirac or Majorana? Absolute mass scale? How small is  13 ? CP Violation? Mass hierarchy? Verify Oscillation? LSND? Sterile neutrino(s)? CPT violation?

EPS2003 Hitoshi Murayama28 Seven Questions Dirac or Majorana? Absolute mass scale? How small is  13 ? CP Violation? Mass hierarchy? Verify Oscillation? LSND? Sterile neutrino(s)? CPT violation?

EPS2003 Hitoshi Murayama29 Now that LMA is confirmed... Dream case for neutrino oscillation physics!  m 2 solar within reach of long-baseline expts Even CP violation may be probable –neutrino superbeam –muon-storage ring neutrino factory Possible only if: –  m 12 2, s 12 large enough (LMA) –  13 large enough

EPS2003 Hitoshi Murayama30  13 decides the future The value of  13 crucial for the future of neutrino oscillation physics Determines the required facility/parameters/baseline/energy Two paths to determine  13 –Long-baseline accelerator neutrino oscillation –Reactor neutrino experiment with two detectors

EPS2003 Hitoshi Murayama31 Shootout (Lindner)

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EPS2003 Hitoshi Murayama34 Seven Questions Dirac or Majorana? Absolute mass scale? How small is  13 ? CP Violation? Mass hierarchy? Verify Oscillation? LSND? Sterile neutrino(s)? CPT violation?

EPS2003 Hitoshi Murayama35 Intepretation With LSND

EPS2003 Hitoshi Murayama36

EPS2003 Hitoshi Murayama  Signal Excess positron events over calculated BG

EPS2003 Hitoshi Murayama38 Sterile Neutrino LSND, atmospheric and solar neutrino oscillation signals  m 2 LSND ~ eV 2  m 2 atm ~ 3  10 –3 eV 2  m 2 solar < 10 –3 eV 2   Can’t be accommodated with 3 neutrinos   Need a sterile neutrino New type of neutrino with no weak interaction 3+1 or 2+2 spectrum?

EPS2003 Hitoshi Murayama39 Sterile Neutrino disfavored 2+2 spectrum: past fits preferred –Atmospheric mostly    –Solar mostly e  a (or vice versa) –Now solar sterile getting tight due to SNO  Disfavored –6 (Maltoni et al) 3+1 spectrum: sin 2 2  LSND =4|U 4e | 2 |U 4  | 2 –|U 4  | 2 can’t be big because of CDHS, SK U/D –|U 4e | 2 can’t be big because of Bugey  Disfavored –3 (Maltoni et al)

EPS2003 Hitoshi Murayama40 P LSND <0.10%P LSND < 0.20% More Sterile Neutrinos? Who said there is only one sterile neutrino? There could well be one for each generation Do more sterile neutrinos help? Maybe 3+2 better (Sorel, Conrad, Shaevitz)

EPS2003 Hitoshi Murayama41 WMAP+2dF+Lyman  Maltoni, Schwetz, Tortola, Valle hep-ph/ Pierce, HM Hannestad Spergel et al ∑m <0.7eV (95%)

EPS2003 Hitoshi Murayama42 CPT Violation? “A desperate remedy…” LSND evidence: anti-neutrinos Solar evidence: neutrinos If neutrinos and anti-neutrinos have different mass spectra, atmospheric, solar, LSND accommodated without a sterile neutrino (HM, Yanagida) Best fit to data before KamLAND (Strumia)

EPS2003 Hitoshi Murayama43 KamLAND impact However, now there is an evidence for “solar” oscillation in anti-neutrinos from KamLAND Barenboim, Borissov, Lykken: evidence for atmospheric neutrino oscillation is dominantly for neutrinos. Anti- neutrinos suppressed by a factor of 3. New CPT violation:

EPS2003 Hitoshi Murayama44 KamLAND impact However, now there is an evidence for “solar” oscillation in anti-neutrinos from KamLAND Barenboim, Borissov, Lykken: evidence for atmospheric neutrino oscillation is dominantly for neutrinos. Anti- neutrinos suppressed by a factor of 3. However fit not good (Gonzalez-Garcia, Maltoni, Schwetz) MINOS atmospheric data will settle this New CPT violation:

EPS2003 Hitoshi Murayama45 LSND not as oscillation Maybe LSND detected anomalous decay of muon (Babu, Pakvasa) Lepton-number violation KARMEN disfavors it –BR<0.009 (90%) while LSND wants BR=0.019–0.040 No signal at Mini-BooNE Predicts Michel parameter  =  0.75 Current accuracy:  =0.7518± TWIST experiment at TRIUMF measures Michel parameter down to a few times 10 –4

EPS2003 Hitoshi Murayama46 Seven Questions Dirac or Majorana? Absolute mass scale? How small is  13 ? CP Violation? Mass hierarchy? Verify Oscillation? LSND? Sterile neutrino(s)? CPT violation?

EPS2003 Hitoshi Murayama47 Extended Standard Model Massive Neutrinos  Minimal SM incomplete How exactly do we extend it? Abandon either –Minimality: introduce new unobserved light degrees of freedom (right-handed neutrinos) –Lepton number: abandon distinction between neutrinos and anti-neutrinos and hence matter and anti-matter Dirac or Majorana neutrino Without knowing which, we don’t know how to extend the Standard Model

EPS2003 Hitoshi Murayama48 Seesaw Mechanism Why is neutrino mass so small? Need right-handed neutrinos to generate neutrino mass To obtain m 3 ~(  m 2 atm ) 1/2, m D ~m t, M 3 ~10 15 GeV (GUT!) Neutrinos are Majorana, but R SM neutral

EPS2003 Hitoshi Murayama49 Neutrinoless Double-beta Decay The only known practical approach to discriminate Majorana vs Dirac neutrinos 0  : nn  ppe – e – with no neutrinos Matrix element  =  i m i U ei 2 Current limit | | ≤ about 1eV m 3 U e3 2 <<m 3 and we can typically ignore m 3 =m 1 cos 2  12 +e i  m 2 sin 2  12 –possible cancellation due to unknown Majorana phase Fortunately, they cannot cancel exactly because the maximal angle  12 excluded by SNO: cos 2  12 –sin 2  12 =cos 2 2  12 >0.07 (1  )

EPS2003 Hitoshi Murayama50 Three Types of Mass Spectrum Degenerate –All three around >0.1eV with small splittings –Possible even after WMAP+2dF: m<0.23eV –May be confirmed by KATRIN, cosmology –| |=|  i m i U ei 2 |>m cos 2 2  12 >0.07m Inverted –m 3 ~0, m 1 ~m 2 ~(  m 2 23 ) 1/2 ≈0.05eV –May be confirmed by long-baseline experiment with matter effect –| |=|  i m i U ei 2 |>(  m 2 23 ) 1/2 cos 2 2  12 >0.0035eV Normal –m 1 ~m 2 ~0, m 3 ~(  m 2 23 ) 1/2 ≈0.05eV –| |=|  i m i U ei 2 | may be zero even if Majorana

EPS2003 Hitoshi Murayama51 WMAP again WMAP constraint: –m <0.23eV each (95%CL) Puts upper limit on the effective neutrino mass in the neutrinoless double beta decay (Pierce, HM) –| |=|  i m i U ei 2 |<  i m i |U ei 2 |<0.23eV –Heidelberg-Moscow: | |=0.11–0.56 eV –Reanalysis by Vogel: | |=0.4–1.3 eV

Models of Flavor

EPS2003 Hitoshi Murayama53 Typical Theorists’ View ca Solar neutrino solution must be small angle MSW solution because it’s cute Natural scale for  m 2 23 ~ 10–100 eV 2 because it is cosmologically interesting Angle  23 must be of the order of V cb Atmospheric neutrino anomaly must go away because it needs a large angle Wrong!

EPS2003 Hitoshi Murayama54 Surprises Prejudice from quarks, charged leptons: –Mixing angles are small –Masses are hierarchical In LMA, all mixing except U e3 large –Two mass splittings not very different –Atmospheric mixing maximal –Any new symmetry or structure behind it?

EPS2003 Hitoshi Murayama55 Question of Flavor What distinguishes different generations? –Same gauge quantum numbers, yet different Hierarchy with small mixings:  Need some ordered structure Probably a hidden flavor quantum number  Need flavor symmetry –Flavor symmetry must allow top Yukawa –Other Yukawas forbidden –Small symmetry breaking generates small Yukawas Try to find underlying symmetries from data (bottom-up) –Repeat Heisenberg, Gell-Mann–Okubo

EPS2003 Hitoshi Murayama56 Different Flavor Symmetries Altarelli-Feruglio-Masina hep-ph/ Hall, HM, Weiner Sato, Yanagida Vissani Barbieri et al

EPS2003 Hitoshi Murayama57 Lack of symmetry explains data Suppose there is no symmetry behind the neutrino masses and mixings (“anarchy”) Random 3 by 3 matrix MNS matrix distributed to the group invariant measure (Haba, HM) 3-D Kolmogorov–Smirnov test (de Gouvêa, HM) P=68%

EPS2003 Hitoshi Murayama58 Lower Bound on  13 Anarchy predicts flat distribution in cos 4  13 1D P KS = 2(1–cos 4  13 )~sin 2 2  13 for small  13 Lower bounds: –sin 2 2  13 >0.05 (95%CL) –sin 2 2  13 >0.01 (99%CL)

EPS2003 Hitoshi Murayama59 Critical Measurements sin 2 2  23 =1.00  0.01? –Determines a need for a new symmetry to enforce the maximal mixing sin 2 2  13 <0.01? –Determines if the flavor quantum number of electron is different from ,  Normal or inverted hierarchy? –Most symmetries predict the normal hierarchy CP Violation? –Plausibility test of leptogenesis

EPS2003 Hitoshi Murayama60 Dynamics behind flavor symmetry? Once flavor symmetry structure identified (e.g., Gell-Man– Okubo), what is dynamics? (e.g., QCD) Supersymmetry: –Anomalous U(1) gauge symmetry with Green-Schwarz mechanism Large Extra Dimensions: –Fat brane with physically separated left- and right-handed particles Technicolor: –New broken gauge symmetries at 100TeV scale

EPS2003 Hitoshi Murayama61 Large  23 and quarks Large mixing between  and  Make it SU(5) GUT Then a large mixing between s R and b R Mixing among right- handed fields drop out from CKM matrix But mixing among superpartners physical O(1) effects on b  s transition possible evading  e  b  s  constraints (Chang, Masiero, HM) Expect CP violation in neutrino sector especially if leptogenesis (Rodejohann)

EPS2003 Hitoshi Murayama62 Consequences in B physics Addt’l contrib to  m s CP violation in B s mixing (B s  J/   ) Addt’l CP violation in penguin b  s (B d  K s ) Very reasonable place for new physics to show up!

EPS2003 Hitoshi Murayama63 Harnik, Larson, HM, Pierce also Uli Nierste in Heavy Flavour session RR-dom case

EPS2003 Hitoshi Murayama64 Conclusions Enormous progress in neutrino data –Solar neutrino problem solved! Still some loose ends –Many forthcoming experiments Three-generation oscillation very reasonable LSND still unclear Cosmological constraints beginning to be interesting Next key:  13 –Long-baseline or reactor Neutrinos not stand alone –Need info from high-energy frontier, quark sector to address the origin of masses and mixing

Do We Need Theorists?