Challenges in Neutrino-Nucleus Scattering* · Antineutrino beam NOvA Preliminary ... y(e) ji E ¯ j F˜ †Li + nN Â a=1 3 ... • The PMNS matrix is to neutrino & lepton-ﬂavor

Challenges in Neutrino-Nucleus Scattering*

Andreas S. KronfeldFermilab & IAS TU München

Lattice 2018 | Michigan State UniversityJuly 27, 2018

*esp. those connected to lattice QCD

http://www.tum-ias.de/

http://www.fnal.gov/

Neutrino Oscillations

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

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

νμandνμDataattheFarDetector

66

Total Observed 65Best fit prediction 50

Cosmic Bkgd. 0.5Beam Bkgd. 0.6

Unoscillated 266

0 1 2 3 4 5Reconstructed Neutrino Energy (GeV)

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FD DataPrediction

syst. rangeσ1-CCµνWrong Sign:

Total bkg.Cosmic bkg.

Neutrino beam NOvA Preliminary

All Quartiles


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Antineutrino beam NOvA Preliminary

All Quartiles

νμνμ



Unoscillated 730

48

0 1 2 3 4 5 (GeV)recoE

0

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1

1.5 PO

T20

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Eve

nts

/ 8.0

33

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NOvA PreliminaryNeutrino Mode

CCµν CCµν

CCeν CCeν

NC

Total MC ND data

νe

0 1 2 3 4 5 (GeV) RHCrecoE

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CCµν CCµν

CCeν CCeν

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νe


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PO

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.1 G

eV20

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nts

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syst. rangeσ1- CCµνWrong Sign:

Total Background

Antineutrino beamArea Normalised

NOvA Preliminary

νμShape-onlysysts.Area-normalizedMCscaled-0.5%


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syst. rangeσ1- CCµνWrong Sign:

Total Background

Neutrino beamArea Normalised

NOvA Preliminary

νμShape-onlysysts.Area-normalizedMCscaled+1.3%

νμ Spectra νe-likeSpectraνμandνμDataattheFarDetector

66



Unoscillated 266


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vent

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νμνμ



Unoscillated 730 �2

http://theory.fnal.gov/events/event/results-from-nova-3/

• 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

Âj,i=1

y(e)ji E jF†Li +nN

Âa=1

3

Âi=1

y(n)ai NaF†Li +nN

Âa=1

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Neutrino Oscillations

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• 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.

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Pontecorvo–Maki–Nakagawa–Sakata Matrix

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U =

0

@Ue1 Ue2 Ue3Uµ1 Uµ2 Uµ3Ut1 Ut2 Ut3

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SystematicUncertainties

62

20− 0 20)-310× (23θ2Uncertainty 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 0.05)2 eV-310× (32

2m∆Uncertainty in



Beam Flux


Normalization

Detector Response

Neutron Uncertainty

Muon Energy Scale



NOvA Preliminary

0.5− 0 0.5π/CPδUncertainty in



Neutron Uncertainty

Beam Flux

Muon Energy Scale

Normalization

Detector Response




NOvA Preliminary

Mostimportantsystematics:• 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 ν’s



SystematicUncertainties

62

20− 0 20)-310× (23θ2Uncertainty in sin



Beam Flux


Detector Response

Normalization

Muon Energy Scale



Neutron Uncertainty

NOvA Preliminary

0.05− 0 0.05)2 eV-310× (32

2m∆Uncertainty in



Beam Flux


Normalization

Detector Response

Neutron Uncertainty

Muon Energy Scale



NOvA Preliminary

0.5− 0 0.5π/CPδUncertainty in



Neutron Uncertainty

Beam Flux

Muon Energy Scale

Normalization

Detector Response




NOvA Preliminary

Mostimportantsystematics:• 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 ν’s



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?

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Pab = Âj,k

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�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

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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

https://indico.fnal.gov/event/15949/session/2/contribution/275

nA ScatteringnA<latexit sha1_base64="R8cBAORFSoSsV/M846xiQdcn1cA=">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</latexit><latexit sha1_base64="R8cBAORFSoSsV/M846xiQdcn1cA=">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</latexit><latexit sha1_base64="R8cBAORFSoSsV/M846xiQdcn1cA=">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</latexit><latexit sha1_base64="R8cBAORFSoSsV/M846xiQdcn1cA=">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</latexit>

The Collision

p

pX

p1

k = Eν(1, Ω)φb(Eν)

kʹl

q = k – kʹ = ∑pi + pX – p = (ω, q)i

Useful discussion of kinematics by Donnelly

�13

http://www.int.washington.edu/talks/WorkShops/int_16_63W/People/Donnelly_B/Donnelly.pdf

The Collision

p

pX

p1

k = Eν(1, Ω)φb(Eν)

kʹl

q = k – kʹ = ∑pi + pX – p = (ω, q)i

p2

knock out 2nd nucleon: sign of “2p2h”

Useful discussion of kinematics by Donnelly

�13

http://www.int.washington.edu/talks/WorkShops/int_16_63W/People/Donnelly_B/Donnelly.pdf

30 cm Run 3493 Event 27435, October 23rd, 2015�14

https://microboone-exp.fnal.gov/public/approved_plots/Event_Displays.html

ds [Pb

]

dEµ d cosq=

Z ds(En)

dEµ d cosqP

b

(En)dEn<latexit sha1_base64="J8baF0UDCglO3h+e007wU+ipz+I=">AAAEWHichZNLb9QwEMe97Za2C/TFkYtFValIsCTbVsChqIiCOPAoUl/SerVynNmN1dgJ9gS6siLx7ThzhAtfBSdbBNstdKQk45n52Rn/7ShPpcUg+N6YmW3O3ZhfWGzdvHV7aXllde3YZoURcCSyNDOnEbeQSg1HKDGF09wAV1EKJ9HZiyp/8gmMlZk+xFEOPcWHWg6k4OhD/ZURGxguXMysHCrePegzhHN0UdkrXfyyz1RBYyYyyzAB5CXdpUxqbE1Qm75OF/evBv7MeFHGHsS1019ZD9rbO9tPgw6ddsJ2UNv63u77b18IIQf91ZmvLM5EoUCjSLm13TDIsee4QSlSKFussJBzccaH0PWu5gpsz9V7VNINH4npIDP+0Ujr6N+E48rakYp8peKY2Mu5KnhlLlJXhbsFDp70nNR5gaDFeP1BkVLMaKUDjaUBgenIO1wY6VugIuF+V9GrNbFANXeO6rxsbbSYBS+xHmLiGDeGj3wfvrJ0QTsEVVdo+CwypbiOHUt4OigdA20LA9U8ztVqWBylMNYwLF2n9DYJYiJNfD25NU1+LLweYK5nt2v20g/v29Qmk+w+ZWdg9MOgvbMD6lE98Ock9IPLa+8DTrKsemf5+GuUqwqmezX/h3x+ijm8hjm8YGr96at3z9/UV/Etz9spnvuj//t80387x5126Pv84O/AMzK2BXKX3CObJCSPyR55TQ7IERHkZ2OusdRYnv3RJM355uK4dKZxwdwhE9Zc+wWGZILJ</latexit><latexit sha1_base64="JhOZnLU/izVaiXI9geHa2sKQ0WE=">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</latexit><latexit sha1_base64="JhOZnLU/izVaiXI9geHa2sKQ0WE=">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</latexit><latexit sha1_base64="kH5AL+GVM/lmzLpZRWwd5iu7jSc=">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</latexit>

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

nbA ! µ�Xp

ds(En) µ LµnWµn

Wµn µ ÂXp

⌦A|J†

n |Xp↵⌦

Xp|Jµ |A↵

nbA ! µ+XnRelativity

DUNE flux as a probability density.

Poincare Group

Galilean Group

Why do we need it?

�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 µn(q, p) =W1(q2,q ·u)eµn +W2(q2,q ·u)dµn +W3(q2,q ·u)cµn

eµn = gµn �qµ qn/q2, cµn = ieµnrs ur qs ,

dµn = (uµ qn +un qµ)/q ·u �uµ un q2/(q ·u)2 �gµn<latexit sha1_base64="JbNVhHR2pjuBdjJdiOzgg5pt95c=">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</latexit><latexit sha1_base64="JbNVhHR2pjuBdjJdiOzgg5pt95c=">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</latexit><latexit sha1_base64="JbNVhHR2pjuBdjJdiOzgg5pt95c=">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</latexit><latexit sha1_base64="JbNVhHR2pjuBdjJdiOzgg5pt95c=">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</latexit>

�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

https://inspirehep.net/record/1236362

• 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 =� 12MN

A

Âi=1

r2i +Â

i< jvi j + Â

i< j<kVi jk

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• Compute level splittings in nuclei up to 12C:

Nuclear hamiltonian • Argonne v18 two-body potential reproduces the ~4300 np and pp scattering data below 350 MeV of the Nijmegen database with .�2 ' 1

• Illinois 7 three-body potential is needed to accurately describe the spectrum of light nuclei

-100

-90

-80

-70

-60

-50

-40

-30

-20

Ener

gy (M

eV)

AV18AV18+IL7 Expt.

0+

4He0+2+

6He 1+3+2+1+

6Li3/2−1/2−7/2−5/2−5/2−7/2−

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 v18with Illinois-7

GFMC Calculations24 November 2012

Big Success

�21

Nuclear EFT(s)

from D. R. Entem and R. Machleidt, ‘17

see also:P. Reinert, H. Krebs, E. Epelbaum, ‘18M. Piarulli et al, ‘16M. Piarulli et al, ‘14A. Nogga, R. Timmermans, B. van Kolck, ‘05D. Kaplan, M. Savage, M. Wise, ‘96

• LECs are fit to data in 2- and 3-nucleon systems• and predict light-nuclear observables

WARNING: unresolvedissues with power counting

• alternatives: pionless EFT, phenomenological potentials (AV18), . . .

Mereghetti, Monday, 10:00

�22

time-ordered PT, Weinberg (1997)


http://inspirehep.net/record/1517808



• 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 = Âi

jµi +Â

i< jjµi j

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Mereghetti, Monday, 10:00

External currents in chiral EFT

Axial current: q⌧+�µ�5q

from A. Baroni et al, ‘16

g

A

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

ds(En) µ LµnWµn

Wµn µ ÂXp

⌦A|J†

n |Xp↵⌦

Xp|Jµ |A↵

hX p(p01)|Jµ |Ai ⇡

A�Z

Ân=1

hX p|ap01

jµ(q)apn |Ai,

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hA|Jµ Jn |Ai $ hn|dgµ(g5)uugn(g5)d|ni<latexit sha1_base64="3HsoKj8/LWLVXvZmSGJ8JiefbxE=">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</latexit><latexit sha1_base64="U2TH67imWmjrrGs631q6KkoW0Ek=">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</latexit><latexit sha1_base64="U2TH67imWmjrrGs631q6KkoW0Ek=">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</latexit><latexit sha1_base64="cAGRH9p38ttJ+YAC909mkADn2LU=">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</latexit>

Liang, Monday, 4:50


Priority vs Difficultyim

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to n

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difficulty in lattice QCD

(let’s discuss)

f K!p+ FNC

A

FNCPFCC

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nN ! N0,D,Np, . . .

NN forces

pN forces

ss in N

FCCAf B!p

+

hNN|J|NNihd|Jµ |di

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Baroni,Thurs., 10:30

�26

http://inspirehep.net/record/753647?ln=en



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(ppp)|V µud |n(kkk)i= up(ppp)gµun(kkk)F1(q2)+

qn2MN

up(ppp)isµnun(kkk)F2(q2),

hp(ppp)|Aµud |n(kkk)i= up(ppp)gµ

?g5un(kkk)FA(q2)+2MNqµ

q2 up(ppp)g5un(kkk)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/M2A�2

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• 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/M2A�2

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not QCD

Axial Form Factor from Deuterium

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

z-0.2 0 0.2 0.4

(z)

AF

0

0.5

1=4 z expansionaN = 1.014(14) dipoleAm

dipole underestimates

uncertainty!

z =p

t+� t �p

t+� t0pt+� t +

pt+� t0

f (t(z)) µ Ân

anzn

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�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 0.1 0.2 0.3 0.4 0.5

rA = 0.46(6) fm<latexit sha1_base64="VWVy2QzwDSKtag7AEgcobQLi6/E=">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</latexit><latexit sha1_base64="mgEHqmSSM2z3SFPUHP1EBXVCAzs=">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</latexit><latexit sha1_base64="mgEHqmSSM2z3SFPUHP1EBXVCAzs=">AAAD+HichZNfb9MwEMC9hj+j/OvgCSEhi2nSeKAkpR3wANpEhXgANKR2m9RUleNemqi2E2wHWqzA54AnXhDiBSS+BJ+Bb4OTDom2g56U5Hx3P1/Odw5SFivtur/WKs6p02fOrp+rnr9w8dLl2saVA5VkkkKXJiyRRwFRwGIBXR1rBkepBMIDBofB+HHhP3wNUsWJ6OhpCn1ORiIOY0q0NQ1q1+RgDz/Ebr25s71z652vYaJVaEKeD2qb1tpqPnAbeFnx6m4pm7s3PhTycX+wUfnpDxOacRCaMqJUz3NT3TdE6pgyyKt+piAldExG0LOqIBxU35Q15HjLWoY4TKR9hMal9W/CEK7UlAc2khMdqUVfYTzRF/CTzL1Mh/f7JhZppkHQWf4wY1gnuDgnPIwlUM2mViFUxrYETCMiCdX2NOcSFHunmk/y6lbVV2BbIEY6Mj6RkkxtHTYyN27dA15GCHhDE86JGBo/IizMjQ9CZRKKfYyZdUBPGfihzWa83DRyK/OgjmI5XE3eXSZfZbYfIFezzZJd+OG2YiqaZ9vYH4MUt916qwX8Trmwc+LZxWLuNuh51i/eSTr7Sm6KgOVa5f8h619iOiuYzjFT9h8/ebH3rLwqz0laZ3piR//PfON/KweNumfrfGnvwCM0k3V0Hd1E28hD99Aueor2URdR9B59Rt/Qd+et88n54nydhVbWjpmraE6cH78BUxRiPg==</latexit><latexit sha1_base64="UkBSuJemT7dikY0G6l4Nz3sJ7MY=">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</latexit>

rA = 0.68(16) fm<latexit sha1_base64="7+QmEho1WcuGZq3wxU5WN2E/0Ic=">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</latexit><latexit sha1_base64="dCcHLGzSkUWDXhfwRmkQQm2j9LM=">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</latexit><latexit sha1_base64="dCcHLGzSkUWDXhfwRmkQQm2j9LM=">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</latexit><latexit sha1_base64="2fCK+YPxBPPhY2/i4xH/rtt7NI8=">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</latexit>

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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.

• iGE = F1 – Q2 F2/M2.

Electric Form Factors GE (Q2) and Charge Radius hr2E i

GE/gV

Q2 [GeV2]

Kelly2004CODATA2014: 0.875(6) fm

dipole: 0.772(13) fmz-exp: 0.804(107) fm

a15m310a12m310a12m220La12m220a12m220S

a09m310a09m220a09m130

a09m130Wa06m310

a06m310Wa06m220

a06m220Wa06m135

0.0

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

⟨r 2E⟩ [fm2]

a15m310a12m310a12m220La12m220a12m220Sa09m310a09m220a09m130a09m130Wa06m310a06m310Wa06m220a06m220Wa06m135

14-pt11-pt10-pt (−a15)10∗-pt (−m220S)

dipolez2

z3

z4z2+4

z3+4z4+4

central value: 11-point extrapolation hr2E i(a,M⇡,M⇡L)

systematic error: di↵erence of rE from two physical ensembles

rE = 0.804(42)(98) fm from z-expansion fit @ z3+4

rE = 0.772(10)(8) fm from dipole fit

rE = 0.875(6) fm (CODATA-2014, electron) [Rev. Mod. Phys. 88, 035009 (2016)]

rE = 0.8409(4) fm (Lamb shift in muonic hydrogen) [EPJ Web Conf. 113,01006 (2016)]

Y.-C. Jang (BNL) Nucleon Form Factors from C-on-H (LATTICE 2018) July 26 10 / 23

z3+4

parametrization of experimental data

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http://www.apple.com

• 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

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MiniBooNE Excess

• What do lattice-QCD form factors say about this?

• Aguilar-Arevalo et al. [arXiv:1805.12028].

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• 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

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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?

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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.

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• 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

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Thank you!

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Challenges in Neutrino-Nucleus Scattering* · Antineutrino beam NOvA Preliminary ... y(e) ji E ¯ j F˜ †Li + nN Â a=1 3 ... • The PMNS matrix is to neutrino & lepton-ﬂavor

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