Challenges in Neutrino-Nucleus Scattering* Andreas S. Kronfeld - - PowerPoint PPT Presentation

Challenges in Neutrino-Nucleus Scattering*

Andreas S. Kronfeld Fermilab & IAS TU München Lattice 2018 | Michigan State University July 27, 2018

*esp. those connected to lattice QCD

Neutrino Oscillations

• Suppose you have a neutrino beam and two enormous vats of neutrons,
• ne nearby and the other far away:

Alex Himmel, Wine & Cheese Seminar, June 15 @ Fermilab

1 2 3 4 5

Reconstructed Neutrino Energy (GeV)

2 4 6 8 10 12

Events / 0.1 GeV

FD Data Prediction

• syst. range

σ 1- CC

µ

ν Wrong Sign: Total bkg. Cosmic bkg.

Neutrino beam NOvA Preliminary All Quartiles

νμ

POT / 0.1 GeV

1 2 3 4 5 50 100 150 200

POT / 0.1 GeV 10 Events / 8.03 10

Data Simulation

• syst. range

σ 1- CC

µ

ν Wrong Sign: Total Background Neutrino beam Area Normalised

NOvA Preliminary

νμ

Shape-only systs. Area-normalized MC scaled +1.3%

1 2 3 4 5

Reconstructed Neutrino Energy (GeV) 103 Events/0.1 GeV

νμ

2

• The “disappearance” can be explained as an interference effect, if the

muon couples to more than one (i.e., three) mass eigenstates.

• Simplest extension of Standard Model has neutrino Yukawa couplings:

where the Na fields (right-handed neutrinos) are gauge singlets.

• The last term (“Majorana mass term”) violates (global) lepton number but

but imposing global symmetries is unappealing.

• Other fields: Ei = lepton singlet; Φ = Higgs doublet; Li = lepton doublet.

L = ···+

3

∑

j,i=1

y(e)

ji ¯

Ej ˜ Φ†Li +

nN

∑

a=1 3

∑

i=1

y(ν)

ai ¯

NaֆLi +

nN

∑

a=1

ma ¯ NaCNa +···

Neutrino Oscillations

3

• The PMNS matrix is to neutrino & lepton-flavor physics as the Cabibbo-

Kobayashi-Maskawa (CKM) matrix is to quark-flavor physics: where l ininj {e,n,t} labels flavor and j ∈ {1, 2, 3} labels mass eigenstate.

• Like CKM, PMNS has three mixing angles, θlj, & a CP-violating phase, δ.
• With Majorana mass terms, two fewer field phases absorbed into fields, so

two more CP-violating phases, αi, i ∈ {1, 2}, are physical ← 0νββ.

` ∈ {e,µ,τ}

Pontecorvo–Maki–Nakagawa–Sakata Matrix

4

U =   Ue1 Ue2 Ue3 Uµ1 Uµ2 Uµ3 Uτ1 Uτ2 Uτ3   = [U]` j

Systematic Uncertainties

62

20 − 20

)

• 3

10 × (

23

θ

2

Uncertainty in sin

Statistical Uncertainty Systematic Uncertainty Beam Flux Near-Far Differences Detector Response Normalization Muon Energy Scale Neutrino Cross Sections Detector Calibration Neutron Uncertainty

NOvA Preliminary

0.05 − 0.05

)

2

eV

• 3

10 × (

32 2

m ∆ Uncertainty in

Statistical Uncertainty Systematic Uncertainty Beam Flux Near-Far Differences Normalization Detector Response Neutron Uncertainty Muon Energy Scale Neutrino Cross Sections Detector Calibration

NOvA Preliminary

0.5 − 0.5

π /

CP

δ Uncertainty in

Statistical Uncertainty Systematic Uncertainty Neutron Uncertainty Beam Flux Muon Energy Scale Normalization Detector Response Neutrino Cross Sections Detector Calibration Near-Far Differences

NOvA Preliminary

Most important systematics:

• Detector Calibration

– Will be improved by the 2019 test beam program

• Neutrino cross sections

– Particularly nuclear effects (RPA, MEC)

• Muon energy scale
• Neutron uncertainty – new with ν̅’s

Alex Himmel, Wine & Cheese Seminar, June 15 @ Fermilab

Systematic Uncertainties

62

20 − 20

)

• 3

10 × (

23

θ

2

Uncertainty in sin

Statistical Uncertainty Systematic Uncertainty Beam Flux Near-Far Differences Detector Response Normalization Muon Energy Scale Neutrino Cross Sections Detector Calibration Neutron Uncertainty

NOvA Preliminary

0.05 − 0.05

)

2

eV

• 3

10 × (

32 2

m ∆ Uncertainty in

Statistical Uncertainty Systematic Uncertainty Beam Flux Near-Far Differences Normalization Detector Response Neutron Uncertainty Muon Energy Scale Neutrino Cross Sections Detector Calibration

NOvA Preliminary

0.5 − 0.5

π /

CP

δ Uncertainty in

Statistical Uncertainty Systematic Uncertainty Neutron Uncertainty Beam Flux Muon Energy Scale Normalization Detector Response Neutrino Cross Sections Detector Calibration Near-Far Differences

NOvA Preliminary

Most important systematics:

• Detector Calibration

– Will be improved by the 2019 test beam program

• Neutrino cross sections

– Particularly nuclear effects (RPA, MEC)

• Muon energy scale
• Neutron uncertainty – new with ν̅’s

Alex Himmel, Wine & Cheese Seminar, June 15 @ Fermilab

Looking Forward

• Statistical errors will be reduced via much larger exposure.
• Dominant systematic uncertainty will soon be that from νA cross section:
• other large ones connected to statistics, test beam, and/or cross section

itself.

• Taxpayers are eager to find out about CP and to test the three-family paradigm!
• $109 for LBNF/DUNE

6

Oscillation Probabilities

• Probability of a charged lepton of flavor α to be emitted from the source

with a neutrino of mass mj and energy E, which converts at the detector to a charged lepton of flavor β: with upper (lower) sign for ν (ν); ultrarelativistic neutrino p ≈ E − m2/2E.

• The key to the measurement is the neutrino energy, which cannot be

measured.

• It must be reconstructed from energy-momentum four-vectors of final-state

particles.

• What incident energy E could turn a nucleus into the final state?

ν

¯ ν

P

αβ = ∑ j,k

Uα jU∗

β jU∗ αkUβk e±i∆m2

jkL/2E

7

• Oscillation experiments make a(n) (anti)neutrino beam and aim it at nuclei

such as 12C, 16O, 40Ar.

• A nucleus can be thought of as a collection of nucleons.
• “A riddle, wrapped in a mystery, inside an enigma”—
• a flavor change, wrapped in a nucleon, inside a nucleus.

8

Nuclear Structure

• A huge challenge:
• nuclear theorists use a unified formalism describes many things and

can be systematically improved—

• many-body theory, with interactions that are tuned to data or—
• can be cast as a chiral effective theory (nucleons in a pion cloud);
• not QCD, although sometimes called “ab initio”.
• Full error budgets are yet to come and may be impossible.
• Measure “data over here” to constrain nuclear model; then trust validated

models “over there” where oscillation parameters are determined.

9

Hadronic Physics—nN Scattering

• Hard, but easy compared to nuclear theory.
• Avoid trap: nuclear model with nucleonic ingredients inconsistent with

QCD:

• even if tuned up “here” such a thing would be scary “over there”.
• Therefore, aim to get scattering amplitudes from first principles.
• Two approaches:
• nN or nN scattering experiments in the Tokai, NuMI, or LBNF beam;
• lattice QCD with error budgets as comprehensive as those for CKM.

10

¯ ν p

νd

νN

Outline

• Introduction
• My view of the problem
• A little nuclear theory (of initial state)
• Thoughts on target calculations
• Outlook
• (not a review talk ☚ Green, Friday, 9:30)

11

nA Scattering

νA

The Collision

p pX p1 k = Eν(1, Ω) φb(Eν) kʹ l q = k – kʹ = ∑pi + pX – p = (ω, q)

i

Useful discussion of kinematics by Donnelly

13

The Collision

p pX p1 k = Eν(1, Ω) φb(Eν) kʹ l q = k – kʹ = ∑pi + pX – p = (ω, q)

i

p2

knock out 2nd nucleon: sign of “2p2h” Useful discussion of kinematics by Donnelly

13

30 cm Run 3493 Event 27435, October 23rd, 2015

14

dσ[P

b]

dEµd cosθ =

Z

dσ(Eν) dEµd cosθ P

b(Eν)dEν

Statement of the Problem I

• Neutrino-nucleus (A) scattering: nA —> mXn,, where Xp can be A, an

excitation of A, Aʹp, Aʹpπ, …, smithereens. Similarly for nA —> mXn,.

• Measure 4-momentum of muon, probably of proton, maybe of a few more

charged particles; just consider muon:

• Cross section proportional to lepton & hadron tensors:

muon energy & direction

νbA → µ−Xp dσ(Eν) ∝ LµνWµν Wµν ∝ ∑

Xp

⌦ A| ˆ J†

ν|Xp

↵⌦ Xp| ˆ Jµ|A ↵ ¯ νbA → µ+Xn

DUNE flux as a probability density.

15

• The hadronic tensor depends on the four-vectors qμ and pν = MTυν

(lab frame is (essentially) nucleus rest frame; use υ to make invariant):

• HEP calls the Wi “structure functions” (especially when A = N); while

NP calls them “nuclear responses” (especially when A ≠ N).

• HEP (Bjorken) writes ν = q⋅υ; NP denotes this “energy transfer” ω.
• Everyone writes Q2 = –q2 > 0.
• NP sometimes writes q2 for 3-momentum aka |q|2.

W µν(q, p) = W1(q2,q·υ)eµν +W2(q2,q·υ)dµν +W3(q2,q·υ)cµν eµν = gµν −qµqν/q2, cµν = iεµνρσυρqσ, dµν = (υµqν +υνqµ)/q·υ −υµυνq2/(q·υ)2 −gµν

16

Energy Scales

• Thermal, molecular motion:
• Energy transfer ω = Eν – El:
• Beam energy Eν:
• Binding energy (per nucleon):
• Pion mass:
• Fermi motion of nucleons:
• Nuclear mass:

kBT = 7.5 meV, 16/A meV; 200 MeV < ω < Eν – ml; 1 GeV < Eν < 5 GeV (DUNE); 8.6 MeV (40Ar); 140 MeV; 250 MeV; 0.94A GeV, A ∈ {1, 2, 12, 16, 40}.

17

• So we have to know the Wi reliably—for me this means a curve plus an

(empirical) error band.

• The energies cover a range in which both

nuclear and nucleonic effects are important:

• quasielastic—scatter off “whole nucleon”;
• resonance—enough energy for Δ, N*, Nπ;
• shallow inelastic scattering—many pions,

but not enough for OPE;

• deep inelastic scattering—but Q2 not huge

in oscillation experiments.

Statement of the Problem II

Formaggio & Zeller, arXiv:1305.7513

18

• So we have to know the Wi reliably—for me this means a curve plus an

(empirical) error band.

• The energies cover a range in which both

nuclear and nucleonic effects are important:

• quasielastic—scatter off “whole nucleon”;
• resonance—enough energy for Δ, N*, Nπ;
• shallow inelastic scattering—many pions,

but not enough for OPE;

• deep inelastic scattering—but Q2 not huge

in oscillation experiments.

Statement of the Problem II

Formaggio & Zeller, arXiv:1305.7513

18

Nuclear Theory

• The A nucleons in a nucleus are described by the Hamiltonian:
• Fit to scattering data.
• Reproduced by πN EFT [Mereghetti].
• Could also be extracted from lattice QCD.

Nuclear Hamiltonian

nucleon kinetic energy; nucleon mass MN two-body potentials; e.g., Argonne v18 three-body potentials; e.g., Illinois 7

20

H = − 1 2MN

A

∑

i=1

r2

i +∑ i<j

vi j + ∑

i<j<k

Vi jk

• Compute level splittings in nuclei up to 12C:

light nuclei

• 100
• 90
• 80
• 70
• 60
• 50
• 40
• 30
• 20

Energy (MeV)

AV18 AV18 +IL7 Expt.

0+

4He

0+ 2+

6He

1+ 3+ 2+ 1+

6Li

3/2− 1/2− 7/2− 5/2− 5/2− 7/2−

7Li

0+ 2+

8He

2+ 2+ 2+ 1+ 0+ 3+ 1+ 4+

8Li

1+ 0+ 2+ 4+ 2+ 1+ 3+ 4+ 0+

8Be

3/2− 1/2− 5/2−

9Li

3/2− 1/2+ 5/2− 1/2− 5/2+ 3/2+ 7/2− 3/2− 7/2− 5/2+ 7/2+

9Be

1+ 0+ 2+ 2+ 0+ 3,2+

10Be

3+ 1+ 2+ 4+ 1+ 3+ 2+ 3+

10B

3+ 1+ 2+ 4+ 1+ 3+ 2+ 0+ 0+

12C

Argonne v18 with Illinois-7 GFMC Calculations

24 November 2012

Big Success

21

Nuclear EFT(s)

from D. R. Entem and R. Machleidt, ‘17 see also:

• P. Reinert, H. Krebs, E. Epelbaum, ‘18
• M. Piarulli et al, ‘16
• M. Piarulli et al, ‘14
• A. Nogga, R. Timmermans, B. van Kolck, ‘05
• D. Kaplan, M. Savage, M. Wise, ‘96
• LECs are fit to data in 2- and 3-nucleon systems
• and predict light-nuclear observables

Mereghetti, Monday, 10:00

22

time-ordered PT, Weinberg (1997)

• The A nucleons interact with the neutrino via an electroweak current:
• Extract one-body currents from nN or nN scattering, or—
• computed with lattice QCD.
• Two-body currents can be described by meson-exchange in πN EFT.

Neutrino-Nucleus Interaction

“one-body” currents; aka form factors “two-body” current; i.e., ff of <NN|Jn|NN>

23

Jµ = ∑

i

jµ

i +∑ i<j

jµ

i j

hNN|Jµ|NNi

¯ ν p

νd

Mereghetti, Monday, 10:00

External currents in chiral EFT

Axial current: ¯ qτ +γµγ5q

from A. Baroni et al, ‘16

gA two-nucleon currents

• similar expansions for external currents

e.g. vector, axial, scalar, pseudoscalar, tensor

• for SM operators, LECs can be fit to data
• for BSM operators, need LQCD!

24

time-ordered PT

Return of the Hadron Tensor

• Recall
• Approximate (quasielastic region):
• Perhaps at higher energies

.

25

dσ(Eν) ∝ LµνWµν Wµν ∝ ∑

Xp

⌦ A| ˆ J†

ν|Xp

↵⌦ Xp| ˆ Jµ|A ↵ hX p(p0

1)| ˆ

Jµ|Ai ⇡

AZ

∑

n=1

hX p| ˆ ap0

1 jµ(q) ˆ

apn|Ai, hp(q +p)| ˆ aq+pn jµ(q) ˆ ap|n(p)i = hp(q +p)| ¯ uγµ(γ5)d|n(p)i

hA| ˆ Jµ ˆ Jν|Ai $ hn| ¯ dγµ(γ5)u ¯ uγν(γ5)d|ni

Liang, Monday, 4:50

Priority vs Difficulty

importance to neutrino oscillations (my evolving vague impression) difficulty in lattice QCD (let’s discuss) f K→π

+

FNC

A

FNC

P

FCC

P

νN ! N0,∆,Nπ,... NN forces πN forces s¯ s in N FCC

A

f B→π

+

hNN|J|NNi

hd|Jµ|di

Baroni, Thurs., 10:30

26

Lattice-QCD Calculations

Form Factors

• Hadronic matrix elements of the weak currents are decomposed into

Lorentz covariant forms, multiplied by form factors:

• The q2 dependence is constrained by unitarity and analyticity:
• essential to retain this feature when combining discrete box-momenta

to obtain a curve. hp(p p p)|V µ

¯ ud|n(k

k k)i = ¯ up(p p p)γµun(k k k)F1(q2)+ qν 2MN ¯ up(p p p)iσµνun(k k k)F2(q2), hp(p p p)|Aµ

¯ ud|n(k

k k)i = ¯ up(p p p)γµ

?γ5un(k

k k)FA(q2)+ 2MNqµ q2 ¯ up(p p p)γ5un(k k k)FP(q2), qµ = kµ pµ

28

• When data are poor (large uncertainties, limited q2 range), any functional

form will do, as long as the shape is not aggressively stupid.

• Nucleon form factors of employ “dipole Ansatz”:
• Instead use properties of field theory: analyticity, unitarity, .…
• For example, the “z expansion”, Padé approximants (dispersion relation is

Stieltjes), .…

A Word on Parametrizations

29

f (t) = gA

• 1−t/M2

A

2

• When data are poor (large uncertainties, limited q2 range), any functional

form will do, as long as the shape is not aggressively stupid.

• Nucleon form factors of employ “dipole Ansatz”:
• Instead use properties of field theory: analyticity, unitarity, .…
• For example, the “z expansion”, Padé approximants (dispersion relation is

Stieltjes), .…

A Word on Parametrizations

29

f (t) = gA

• 1−t/M2

A

2

not QCD

Axial Form Factor from Deuterium

• Meyer, Betancourt, Gran, Hill [arXiv:1603.03048]:

z

• 0.2

0.2 0.4

(z)

A

F

0.5 1

=4 z expansion

a

N = 1.014(14) dipole

A

m

dipole underestimates uncertainty!

z = √t+ −t −√t+ −t0 √t+ −t +√t+ −t0 f (t(z)) ∝ ∑

n

anzn

30

Axial Form Factor from Lattice QCD

• Gupta, Jang, Lin, Yoon, Bhattacharya (PNDME) [arXiv:1705.06834]:
• a ≠ 0 slope smaller than

deuterium & other data.

• Even continuum limit:

vs Meyer et al.:

• Caveat emptor expt “data”.

GA/gA Q2 [GeV2] 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5

rA = 0.46(6) fm

rA = 0.68(16) fm

31

Vector Form Factor from Lattice QCD

• Jang, Thursday, 9:50 AM.
• lattice QCD too high?
• Even continuum limit:

urE = 0.80(11) fm, vs CODATA: urE = 0.875(6) fm.

• i

GE = F1 – Q2 F2/M2.

GE/gV Q2 [GeV2] Kelly2004 CODATA2014: 0.875(6) fm dipole: 0.772(13) fm z-exp: 0.804(107) fm a15m310 a12m310 a12m220L a12m220 a12m220S a09m310 a09m220 a09m130 a09m130W a06m310 a06m310W a06m220 a06m220W a06m135 0.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1 1.2 1.4

z3+4

parametrization of experimental data

32

• Pragmatic inputs:
• vector form factors from ep

scattering (z parametrization) [Ye et al., arXiv:1707.09063];

• ss form factor from lattice QCD

[χQCD, arXiv:1705.05849];

• extract GA(Q2(z)) from

MiniBooNE;

• compare with BNL E734.
• Richards, Thursday, 12:20 PM.

Neutrino Phenomenology

33

s¯ s

• Pragmatic inputs:
• vector form factors from ep

scattering (z parametrization) [Ye et al., arXiv:1707.09063];

• ss form factor from lattice QCD

[χQCD, arXiv:1705.05849];

• extract GA(Q2(z)) from

MiniBooNE;

• compare with BNL E734.
• Richards, Thursday, 12:20 PM.

Neutrino Phenomenology

33

s¯ s

• Pragmatic inputs:
• vector form factors from ep

scattering (z parametrization) [Ye et al., arXiv:1707.09063];

• ss form factor from lattice QCD

[χQCD, arXiv:1705.05849];

• extract GA(Q2(z)) from

MiniBooNE;

• compare with BNL E734.
• Richards, Thursday, 12:20 PM.

Neutrino Phenomenology

33

s¯ s

MiniBooNE Excess

• What do lattice-QCD form factors say about this?
• Aguilar-Arevalo et al.

[arXiv:1805.12028].

34

• HALQCD Collab computes baryon-

baryon potentials in lattice QCD [nucl-th/0611096, arXiv:1711.01952].

• Implicitly assumes smoothness.
• ΞΞ (top); NN (bottom).
• Hard-core repulsion obvious.
• Attraction between 0.5 fm and 1.0 fm

(almost) visible.

• Doi, Friday, 5:50 PM.

Nucleon Forces

35

Outlook

Particle Physics Questions

• Mediator in direct dark matter detection (if detected)?
• Mediator of lepton flavor violation?

If detected, it won’t be neutrinos!

• How many sterile neutrinos are there (within reach)?
• Do leptons violate CP?
• What values do the neutrino masses take?
• What values do the PMNS matrix elements take?
• What, if any, is the relation of PMNS to CKM?

37

Lattice QCD Input

• Nucleon matrix elements: we know how to obtain them from QCD.
• Nucleus matrix elements (small ones, to test EFT).

Detmold, Tues, 2:40

• Controlled uncertainties:
• don’t introduce non-QCD assumptions;
• put together full error budgets.

38

• Decades of conversation and collaboration among experimenters and

QCD theorists led to

• We need to do this in the lepton sector! — André de Gouvêa

CKM vs PMNS

39

Thank you!

40