Physics

Nov 29, 2018

Material included from Yury Kolomensky’s 2013 Physics 226 class And from the SLAC Summer Institute 2015 in the Standard Model

• Left-handed neutrinos form weak isodoublet with charged lepton partners • Right-handed charged leptons are isosinglets       νe νµ τµ eL µL τL

eR µR τR

• Within the SM, ν are massless and no RH ν (LH ν) exist • Can extend SM by introducing ν mass and giving RH ν no weak charge (no gauge interactions)

I These are called “sterile neutrinos” But Neutrinos Might Be Special

• Masses much smaller than those of other elementary particles

I Mass may not be from the Higgs Mechanism I May be telling us something about Grand Unification • Three generations with mass-mixing matrix

I Unlike quark CKM matrix, neutrino mixing matric not nearly diagonal I May help explain matter-antimatter asymmetry of universe (leptogenesis) • Much has been learned about ν’s in the past 15 years, but much still needs to be learned Where do they come from: Sources of Neutrinos

• Solar neutrinos + I Fusion processes: νe for example from pp → de νe • Atmospheric neutrinos

I Decays of pions created in upper atmosphere − − − π → µ νµ; µ → e − νeνµ + Charge Conjugate Summing over both charges of π, 2:1 ratio of νµ to νe − • Reactors: νe from neutron decay n → pe νe

• Accelerators: νµ and νµ from π and K decay (small contribution from νe) Note: Most of these ν have quite low momentum Neutrino Cross Section

• Neutrino interation cross section is small

− − − + σ(ν`e → ` νe) ≈ σ(ν`n → ` p) ≈ σ(ν`p → ` n) G s G = F = F 2mE π π ν E ∼ 10−41 ν cm2 GeV

• Eg for solar neutrinos (Eν ≈ 10 MeV) cross section is 9 × 10−44cm2 (9 × 10−20 barns) Neutrino Interactions Used for Detection

• Low energy solar and reactor neutrinos − I Charge current for νe: νen → e p I Elastic νe scattering for all flavors: νxe → νxe for x = e, µ τ + I Inverse β-decay for νe: νep → e n Active detection via Cherenkov or scinitillator, or chemical separation

• High energy atmospheric and accelerator neutrinos

I Charge current transitions on nuclei Standard HEP charge particle detection techniques (scintillators, bubble chamber, drift chambers, etc) The First Experiment: Homestake

• Between 1970 and 1994 Homestake experiment (Ray Davis) measured νe flux from 37 37 Cl + νe → Ar + e; chemical extraction • Observed flux much lower than predicted by (SSM) Possible Explanations of the Homestake Result

• The calculation is wrong

I Experiment only sensitive to small part of ν flux: B neutrino rate (more on next slide) I This part is extremely dependent on temperature of core of sun • Experiment is wrong

I Need to collect 100 Ar atoms from 615 tons of chlorine • Neutrinos are oscillating and changing flavor 37 I Detection using interaction with Cl only works for νe We know now that the last explanation is correct Davis received Nobel Prize in 2002 The Physics of Solar Neutrinos Neutrino Spectrum from the Sun Pioneer Solar Neutrino Experiments Gallium Experiments: SAGE and GALLEX

• Homestake sensitive only to B neutrinos: small fraction of flux and sensitive to temperature of sun’s core • To measure flux that is connected to sun’s luminosity must detect ν from pp reaction

I Requires threshold of < 400 keV • Two experiments started in ∼ 1990 to use reaction 71 − 71 νe + Ga → e + Ge (threshold 233 keV) • The origin of the flix for these experiments is 54% pp, 27% Be, 10% B and 9% other ν • Radiochemical extraction: only count neutrinos, can’t measure energy spectrum or angular distribution (do the ν really come from the sun?) • Integration over long time period before collection To make more progress, need real-time detection of neutrinos and ability to measure spectrum and angular distribution Water Cherenkov Detectors (KamiokaNDE, KamioKande II and Super-K)

• Detect B neutrinos through elastic scattering off elections: − − νe e → νe e • Electrons follow direction of incident ν

I Can demonstrate that ν point to sun What Did These Experiments Find? Possible Explanation: ν Oscillations

• Propagation of flavor eigenstate να in terms of mass eigenstates νi:

N X ∗ −iEit |να(t)i = Uαie |vii i=1 • probability:

N 2 X 2 −iEit ∗ P (να → νβ, t) = |hνb| |να(t)i| = Uβie Uαi i=1 Two Flavor Case

• Make math easy by limiting things to 2 flavor case      cos θ sin θ ν1 νe νµ = − sin θ cos θ ν2

• Neutrino mass small comparted to momentum

p m2 m2 E + i = p2 + m2 ' p + i ' p + i 2p 2E

• Oscillation probability

∆(m2)  P (ν → ν , t) = sin2 (2θ) sin2 t e µ 4E Replacing time t with length L traveled

• Oscillation probability

 L  P (ν → ν , t) = sin2 (2θ) sin2 1.27∆(m2) e µ E

with L in m and E in MeV

Now, let’s look at some experiments and ask if consistent with oscillation hypothesis Super Kamiokande: Detection Technique

• Study 8B (and hep) neutrinos via

− − νx + e → νx + e

• Underground to reduce background • 50 ktons of pure water • For νe both NC and CC interactions • Look for Cherenkov radiation ring possible from electron traveling through • For νµ and ντ only NC interactions possible water − − I Phototubes located on outer σ(νµ,τ + e ) ∼ 0.15 × σ(νe + e ) radius of detector • High statistics ∼ 15 events/day • Real time measurement

I Can study time variations • Measurements of energy spectrum

Why Heavy Water?

• Aim is to measure ν flux independent of flavor • Utilize 3 interactions to do this: − − I Elastic scattering off electrons (ES): νe e → νe e

• Detection efficiency νe : νµ : ντ is 6:1:1 due to NC contribution for νe • Same measurement as SuperK − I Charged current (CC): νe d → p p e

• Only νe • Electron carries most of momentum, so B energy spectrum can be measured

I Neutral Current (NC): νx d → n p νx • All ν species • Signal is n capture in 3 different stages of experiment Art McDonald SNO Results

• Incontroversial evidence for νµ,τ from the sun

• νe produced in sun oscillate before reaching earth • Overall flux summed over all species agrees with Standard Solar Model KamLAND

• Only experiment to detect neutrinos in solar mass range that are not from sun • From reactors in Japan (and Korea): ve • Low energy, moderate distances

Combining the KamLAND and Solar Neutrino Data

• Reminder: In simplified 2 species model   2 2 2 L P (ν1 → ν2, t) = sin (2θ12) sin 1.27∆(m ) 21 E 2 • Neutrinos from sun fully mixed: good measurment of sin (2θ12) • Measurement of oscillation frequency from KamLAND: good 2 measurement of ∆(m21)

I tan θ12 ∼ 0.4 ⇒ sin θ12 ∼ 0.5 ν1 is about half νe

2 −5 I ∆m21 ∼ 7 × 10 (by definition m1 < m2) Very small mass difference between ν2 and ν1

I These data don’t tell us how

much νµ or ντ there is in ν1 Atmospheric Neutrinos (I)

• Initial measurements a biproduct of searches for • Large water Cherenkov detectors • Decays of pions created in upper atmosphere − − − − (π → µ νµ; µ → e νeνµ) + Charge Conjugate

I Ratio νµ : νe ≈ 2 : 1 I Much smaller L/E than for solar case: little time for 1 ←→ 2 oscillations. Can study 2 ←→ 3 and/or 1 ←→ 3 I Cannot separate these two options without additional experiments

• Reactor νe experiments (, , T2K, Daya Bay), discussed later, indicate that θ13 is small • ⇒ atmospheric experiments largely sensitive to θ23 (2 ←→ 3) Atmospheric Neutrinos (II)

• Neutrinos detected through CC interactions

• Kamiokande in 1988 noticed it sees only (59 ± 7)% of νµ it expects • Same effect observed by IMB in 1992 • High statistics analysis from SuperK studying zenith-angle dependence of νµ and νe yield in two bins of energy (see next two pages) Distinguishing νe and νµ CC interactions

• Study fully contained events with one Cherenkov ring

I Muons leave clean rings

I Electrons radiate leaving busier rings with evidence of radiation • Direction of ring correlates to ∼ 15◦ with incident direction of ν • Amount of light correlated with energy of incident ν SuperK results on Atmospheric Neutrinos

• Ratio of µ to e: (N /N ) µ e meas = 0.63±0.03±0.05 (Nµ/Ne)pred

• Up-Down Asymmetry of µ events:

A = 0.296 ± 0.048 ± 0.01

Detailed study of rate vs zenith angle compared to prediction without oscillations (blue) and with νµ-ντ oscillations (red) • Can also look at upward going µ produced from νµ-rock interactions Accelerator-based Experiments Can Probe This Region

Moving to Three Generations

     iδ      νe 1 0 0 C13 0 e S13 C12 S13 0 ν1  νµ  =  0 C23 S23   0 1 0   −S12 C12 0   ν2  iδ ντ 0 −S23 C23 −e S13 0 C13 0 0 1 ν3

where C and S are Cos and Sin • Above assumes Dirac neutrinos

I If Majorana (more later), another matrix with two more imaginary phases • Each submatrix explored with different set of experiments that probe different ranges of mass and mixing

I θ12: Solar (SK, SNO) and Reactors (KamLAND) I θ23 Atmospheric (SK) and Accelerators (K2K, Minos, NOvA) I θ13: Reactors (Daya Bay) and Accelerators (JPARC, Minos, NOvA)

One wrinkle: Matter Effects

• If ν traverse matter, they can interact

• Modification of mixing angle and ocsillation wavelength: called the MSW effect • We won’t worry about that here, but needs to be included when fitting data Characterizing Accelerator-Based ν Experiments

• Disappearanace vs Appearance

• Short Baseline vs Long Baseline Examples of Long Baseline Experiments

• T2K:

I νµ produced in Tokai Japan I Use SuperK as the detector ∼ 250 Km • Minos and NoVa

I νµ produced at Fermilab I Detected in Minnesota ∼ 800 Km In all cases, near detector used to measure produced ν-flux

Off-Axis Beams

• Both T2K and NoVa designed to study νµ → νe • use a “trick” to produce beam with ν-energy spectrum optimized about oscillation maximum • Site detector off the center of the beam direction

Combining all the experiments

• Factorize matrix to product of 2-neutrino oscillation sub-matrices • Plot allowed region in ∆(m2) vs sin2 (2θ) plane • Example to the left from PDG (and Hitoshi) • Plot summarizes all mixing data (several ∆(m2) and severla θ • Solar and Atmospheric results sensitive to ∆(m2) that differ by many orders of magnitude Relationship between ν masses

2 2 • ∆mSolar ≈ ∆m21 = (7.6 ± 0.2) × 10−5 eV2 2 2 2 • ∆mAT M ≈ |∆m32| = (2.4 ± 0.1) × 10−3 eV2 2 2 2 • ∆m21 + ∆m32 + ∆m31 = 2 2 2 2 2 2 m2 −m1 +m3 −m2 +m3 −m1 = 0 Current Best Neutrino Numbers How do neutrinos get mass?

• Neutrino mass many orders of magnitude smalle than other fermions

I Would require very small Yukawa coupling • Is mechanism for generating mass something other than the Higgs? • No right handed neutrino observed

I If exists, it must be heavy • See-saw mechanism

I Introduce a charge-conjugate left-handed heavy neutrino I 6 × 6 mixing matrix

 c b  L = ν , νC  ν νC  L L b a L L

where b, c << a 2 I Eigenvalues are m1 ≈ a, m2 ≈ c − b /a

• if a very large, m1 is large, m2 is small Are Neutrinos Dirac or Majorana?

Dirac Majorana ν 6= ν ν = ν 4 states 2 states νR, νL, νR, νL νL, νR Two sterile neutrinos mass term mass term  1  C C C C  L = mD ψLψR + ψRψL L = 2 mL ψLψR + ψRψL + ψL ψR + ψRψL Neutrinoless

• If ν are their own antiparticles, diagrams of the type above are possible • No missing energy so dielectron invariant mass determined only by the n-p mass difference 0ν ββ Decay

• Many experiments ongoing • Challenges: 26 28 I Lifetime long: ∼ 10 -10 years I Need good mass resolution and low background I Need large target mass • Underground experiments to shield from cosmic rays • Berkeley/LBNL involvement in several experiments

I CUORE I SNO+ I MAJORANA Unanswered Questions

• Are there additional generations of ν (perhaps sterile)? • How about the CP violating phase? • Are neutrinos their own antiparticles?