photon emission in neutral current interactions with ...advisors: drs. juan m. nieves and luis...

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Introduction Theoretical Model Comparison with MiniBooNE Estimates Summary

Photon Emission in Neutral Current Interactionswith Nucleons and Nuclei

En Wang

IFIC, Universidad de Valencia, Spain

Jan 14, 2015

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Overview

1 IntroductionA brief resumeIntroduction of NCγ theoretical study

2 Theoretical ModelNCγ on the nucleonIncoherent NCγ on nucleiCoherent NCγ on nuclei

3 Comparison with MiniBooNE Estimates

4 Summary

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IntroductionA brief resume

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Who am I?

Name: En Wang

Date of birth: Dec. 1985

Marital status: Married

The place of birth: Henan,China

Figure : Shao-Lin temple, Henan

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Education

Ph.D — 03.2011 – 12.2014

IFIC, University of Valencia & CSIC, Valencia, SpainTitle: Electroweak processes in nucleons and nuclei at intermediateenergiesAdvisors: Drs. Juan M. Nieves and Luis Alvarez-Ruso

Master — 09.2007 – 07.2010

Department of Physics, Zhengzhou University, Henan, ChinaTitle: Study of meson properties in quark modelsAdvisor: Prof. De-Min Li

Bachelor — 09.2003 – 07.2007

Department of Physics, Zhengzhou University, Henan, ChinaTitle: Study of mass spectra of the charmoniumAdvisor: Prof. De-Min Li

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Research

♣ Neutrino-nucleon and neutrino-nucleus interaction;Photon emission in neutral current interactions atintermediate energies

♣ Effective hadron interactions with chiral symmetry:Resonances and unitary re-summations

♣ Photo-production of the Λ(1520) resonance

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Introduction of NCγ theoretical study

8/44


e-like events in the MiniBooNE experimentE

vents

/MeV

0.5

1.0

1.5

2.0

2.5

Data (stat err.)+/

µ from eν+/

from Keν0

from Keν

misid0

πγ N→ ∆

dirtotherConstr. Syst. Error

Neutrino

(GeV)QEνE

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Events

/MeV

0.0

0.2

0.4

0.6

0.8

1.0

1.2 Antineutrino

3.01.5

neutrino-mode excess:162.0± 47.8 events

antineutrino-mode excess:78.4± 28.5 events

A. Aguilar-Arevalo et al., PRL110(2013),161801.

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vents

/MeV

0.5

1.0

1.5

2.0

2.5

Data (stat err.)+/

µ from eν+/

from Keν0

from Keν

misid0

πγ N→ ∆


Neutrino

(GeV)QEνE

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Events

/MeV

0.0

0.2

0.4

0.6

0.8

1.0

1.2 Antineutrino

3.01.5

This anomaly of e-like events

Oscillation: not explained by 1, 2,3 families of sterile neutrino.J. Conrad, et al., AHEP2013(2013), 163897; C. Giunti, etal., PRD 88(2013), 073008.

Lorentz violation. T. Katori PRD74(2006), 105009.

Radiative decay of heavy neutrinos.S. Gninenko, PRL 103(2009),241802.

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vents

/MeV

0.5

1.0

1.5

2.0

2.5

Data (stat err.)+/

µ from eν+/

from Keν0

from Keν

misid0

πγ N→ ∆


Neutrino

(GeV)QEνE

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Events

/MeV

0.0

0.2

0.4

0.6

0.8

1.0

1.2 Antineutrino

3.01.5

It could have its origin in poorly under-stood background and unknown system-atics.

MiniBooNE detector cannotdistinguish the signature producedby electrons or photons.

NC π0 where the γγ decay is notidentified

∆→ Nγ decay - one of the largestbackground

(A. Aguilar-Arevalo et al., PRL110(2013), 161801)

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Theoretical Model

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NCγ on the nucleons and nuclei

NCγ reaction on nucleons

ν(k) + N(p)→ ν(k ′) + N(p′) + γ(qγ)

NCγ on nuclei consists of incoherent and coherent reactions,

ν(k) + A(p)→ ν(k ′) + X (p′) + γ(qγ)

ν(k) + AZ |gs(pA)→ ν(k ′) + AZ |gs(p′A) + γ(qγ)

At the relevant energies for MiniBooNE, the reaction is dominatedby the excitation of the ∆(1232) resonance but there are alsonon-resonant contributions that, close to threshold, are fullydetermined by the effect ive chiral Lagrangian of stronginteractions.

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Amplitude for NCγ on the nucleon

The reaction is,

ν(k) + N(p)→ ν(k ′) + N(p′) + γ(qγ)

The amplitude is given by,

Mr =GF e√

2lαJ αr

=GF e√

2uν(k ′)γα(1∓γ5)uν(k)×

(iε∗(r)µ u(p′)Γµαu(p)

),

the ∓ is for neutrino and antineutrino, respectively.

ε∗(r)µ is the photon polarization vector.

Γµα is the hadronic matrix element.

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Model for the hadronic matrix elements

Z

N

γ

NN N

NN

Z γ

γ

Z γ

N N

π0

Z

N

γ

∆ N N ∆ N

Z γ

γ

Z

N

γ

N∗N N N

Z γ

N∗

First row: direct and crossednucleon pole terms

Second row: direct andcrossed ∆(1232) pole terms

Third row: direct andcrossed heavier resonance[N(1440), N(1520) andN(1535)] pole terms

Forth row: t-channel πexchange term

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Nucleon pole terms

ΓµαN = JµEM(qγ)(/p + /q + M)JαNC (q)DN(p + q)

+JαNC (−q)(/p′ − /q + M)JµEM(−qγ)DN(p′ − q)

where J = γ0J†γ0, and DN is the nucleon propagator, given by,

DN(p) =1

/p −M.

The weak NC and electromagnetic (EM) currents are given by,

JαNC (q) = γαF 1(q2) +i

2MσαβqβF 2(q2)− γαγ5FA(q2),

JµEM(qγ) = γµF 1(0) +i

2MσµνqγνF 2(0),

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Nucleon pole terms

The weak NC and EM currents:



JµEM(qγ) = γµF 1(0) +i

2MσµνqγνF 2(0),

The NC vector form factors:

F(p)1,2 = (1− 4 sin2 θW )F

(p)1,2 − F

(n)1,2 − F

(s)1,2

F(n)1,2 = (1− 4 sin2 θW )F

(n)1,2 − F

(p)1,2 − F

(s)1,2

F(p)1,2 — (p, n) EM form factors

F(s)1,2 — strange EM form factors, to be neglected!!!

F(N)1 =

GNE + τGN

M

1 + τ, F

(N)2 =

GNM − GN

E

1 + τ, N = p, n

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Nucleon pole terms

The weak neutral current:



The NC axial form factors (dipole parametrization):

F(p,n)A = ±FA − F

(s)A , (+→ p, − → n)

FA(q2) = gA

(1− q2

M2A

)−2

gA = 1.267, mA = 1.016 GeV.

F(s)A — strange axial form factors, to be neglected!!!

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∆(1232) pole terms

Γµα = JδµEM(p′, qγ)Λδσ(p + q)JσαNC (p, q)D∆(p + q),

+JδαNC (p′,−q)Λδσ(p′ − q)JσµEM(p,−qγ)D∆(p′ − q),

where the propagator D∆ is,

D∆(p) =1

p2 −M2∆ + iM∆Γ∆(p2)

,

Λµν is the spin 3/2 projection operator, which is given by in themomentum space,

Λµν(p∆) = −(/p∆+M∆)

[gµν − 1

3γµγν − 2

3

pµ∆pν∆M2

∆

+1

3

pµ∆γν − pν∆γ

µ

M∆

].

Γ∆ is the resonance width.

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∆(1232) pole terms

The weak NC and EM currents are given by,

JβµNC (p, q) =

[CV

3

M(gβµ/q − qβγµ) +

CV4

M2(gβµq · p∆ − qβpµ∆)

+CV

5

M2(gβµq · p − qβpµ)

]γ5 +

CA3

M(gβµ/q − qβγµ)

+CA

4

M2(gβµq · p∆ − qβpµ∆) +

CA5

M2gβµ +

CA6

M2qβqµ,

JβµEM(p,−qγ) = −[CV

3

M(gβµ /qγ − q′βγ γ

µ) +CV

4

M2(gβµqγ · p∆c − qβγ p

µ∆c)

+CV

5

M2(gβµqγ · p − qβγ p

µ)

]γ5,

p∆ = p + q = p′ + qγ and p∆c = p′ − q = p − qγ .

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N −∆(1232) form factors

NC vector form factors and EM transition form factors:

CVi — NC vector form factors

CVi — EM transition form factors

The NC vector form factors are related to the EM ones

CVi (q2) = (1− 2 sin2 θW )CV

i (q2) (1)

The EM form factors can be related to the helicity amplitudesA1/2, A3/2 and S1/2.

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The relation between EM form factors and helicityamplitudes

N −∆ EM form factor CVi can be obtained from the helicity

amplitudes, A1/2, A3/2 and S1/2, which extracted from pionphoto- and electro-production.

A1/2 =

√2πα

kR

⟨S∗z =

1

2

∣∣∣ε(+)µ JµEM

∣∣∣ Sz = −1

2

⟩1√

2M√

2MR

,

A3/2 =

√2πα

kR

⟨S∗z =

3

2

∣∣∣ε(+)µ JµEM

∣∣∣ Sz =1

2

⟩1√

2M√

2MR

,

S1/2 = −√

2πα

kR

⟨S∗z =

1

2

∣∣∣∣∣ |~k |√Q2ε(0)µ JµEM

∣∣∣∣∣ Sz =1

2

⟩1√

2M√

2MR

,

We adopt the parametrization of the helicity amplitude obtained inthe MAID analysis.(D. Drechsel, et al., EPJA 34(2007),69 andhttp://www.kph.uni-mainz.de/MAID)

http://www.kph.uni-mainz.de/MAID

20/44


N −∆(1232) form factors

we assume a standard dipole form for the axial NC form factors

CA5 (Q2) = −CA

5 (0)

(1 +

Q2

M2A

)−2

,

CA6 (Q2) =

M2

m2π + Q2

CA5 (Q2),

CA4 (Q2) = − CA

5 (Q2)

4,

CA3 (Q2) = 0,

the cross section of NCγ strongly depends on CA5 (q2).

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Off diagonal Goldberger-Treiman relations

The off diagonal GT relation amounts to

CA5 (0) = −

√2

3

f ∗

mπfπ (2)

The axial coupling CA5 (0) is now expressed in terms of f ∗/mπ

extracted from the ∆→ πN decay width.

CA5 (0) = 1.0± 0.11 and mA = 0.93 GeV, fitted to theν-induced π production (νµp → µ−pπ+) ANL and BNLbubble chamber data.E. Hernandez, et al., PRD 81(2010), 085046.

the uncertainties of our model mainly comes from theCA

5 (0) = 1.0± 0.11.

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t-channel π exchange term

The hadronic matrix element π pole term is given by,

Γµα = −iCp,ngA

4π2f 2π

(1

2− 2sin2θW

)εσδµαqγσqδ(/p′−/p)γ5Dπ(p′ − p),

where,

Cp,n = ±1

Dπ(p) =1

p2 −m2π

← π propagator

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N∗ pole term [N(1440), N(1520) N(1535)]

Z

N

γ

N∗N N N

Z γ

N∗

(a) (b)

The hadronic matrix elements of N(1440), N(1535) aresimilar to that of nucleon pole.the hadronic matrix elements of N(1520) is similar to that of∆(1232) pole terms.N − N∗ vector form factors can be obtained from helicityamplitudes.We have assumed a standard dipole form for the axial formfactors.The axial couplings are obtained by the off diagonalGoldberger-Treiman relations.

24/44


NCγ cross section on the nucleon for neutrino

0

4

8

12

16

σ(1

0-4

2 c

m2)

Eν (GeV)

p-νAllNR∆

NucleonN(1520)

n-ν

0

0.01

0.02

0.03

0.4 0.8 1.2 1.6 2.0

p-νN(1440)N(1535)π

0.4 0.8 1.2 1.6 2.0

n-ν

25/44


The cross section of NCγ on nucleon for antineutrino

0

2

4

6

8

σ(1

0-4

2 c

m2)

Eν (GeV)

p-–νAll

NR∆

NucleonN(1520)

n-–ν

0

0.01

0.02

0.4 0.8 1.2 1.6 2.0

p-–νN(1440)

N(1535)π

0.4 0.8 1.2 1.6 2.0

n-–ν

26/44


Incoherent NCγ on nuclei

27/44


NCγ on nuclei

It consists of the incoherent and coherent reactions.

ν(k) + A(p)→ ν(k ′) + X (p′) + γ(qγ)

For the incoherent reaction, the final nucleus is either broken orleft in some excited state.

ν(k) + AZ |gs(pA)→ ν(k ′) + AZ |gs(p′A) + γ(qγ)

For the coherent reaction, the final nucleus is left in its groundstate.

28/44


Nuclear effects

Fermi motion

We adopt the relativistic local Fermi gas approximation. Thetarget nucleon moves in a local Fermi sea of momentum kFdefined as a function of the local density of protons and neutrons,independently.

Pauli blocking

Final nucleons are not allowed to take occupied states.

In-medium modification of ∆ properties

The ∆ resonance acquires a selfenergy because of several effectssuch as Pauli blocking of the final nucleon and absorptionprocesses: ∆N → NN, ∆N → NNπ or ∆NN → NNN.

29/44


Incoherent reaction

The differential cross section for the incoherent reaction is,

dσA = 2

∫d3~r

∫d3~p

(2π)3nN(~p, ~r)

[1− nN(~p′, ~r)

]dσN ,

Relativistic Local Fermi Gas: kF (~r) =[3π2ρ(~r)

]1/3

Fermi motion: n(~r , ~p) = Θ(kF (~r)− |~p|)Pauli blocking: 1− n(~r , ~p)

where kF (~r) is the Fermi momentum, given by,

kF (~r) =[3π2ρ(~r)

]1/3,

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In-medium modification of the ∆(1232) resonance

For propagator D∆ is,

D∆(p) =1

p2 −M∆2 + iM∆Γ∆(p2)

,

Replace

Γ∆/2→ ΓPauli∆ /2− ImΣ∆(ρ)

ΓPauli∆ — free width of ∆→ Nπ modified by Pauli blocking

ImΣ∆(ρ), including many body process:∆N → NN, ∆N → NN and ∆NN → NNN

E. Oset and L. Salcedo, NPA 468(1987), 631.

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Incoherent reaction

0

30

60

90

120

150

180

σ (

10

-42cm

2)

Eν (GeV)

ν-12

C

(a)

0.89-1.11All-FreeAll-Fullno N*-Freeno N*-Full

0

20

40

60

80

0.0 0.4 0.8 1.2 1.6 2.0

–ν-

12C

(b)

0.89-1.11All-FreeAll-Fullno N*-Freeno N*-Full

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Coherent NCγ on nuclei

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Coherent reaction

The amplitude is given by,

Mr =GF√

2lαJ

αcoh(r),

the hadronic current Jαcoh(r) is given by,

Jαcoh(r) = ieε∗(r)µ

∫d3~r e i(~q−~qγ)·~r (ρpΓµαp + ρnΓµαn )

nuclear correction: Γ∆/2→ ΓPauli∆ /2− ImΣ∆(ρ)

coherent sum of all nucleons:

ΓµαN =1

2

∑i

Tr[uΓµαi ,Nu

](3)

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Coherent reaction

0

3

6

9

12

15

σ (

10

-42cm

2)

Eν (GeV)

ν-12

C

(a)

0.89-1.11Allno N*∆

N+∆(Zhang)

0

3

6

9

12

0.0 0.4 0.8 1.2 1.6 2.0

–ν-

12C

(b)

0.89-1.11Allno N*∆

N+∆(Zhang)

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Comparison with MiniBooNE Estimates

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CCQE reconstructed (anti)neutrino energy

Assuming that the visible energy (Ee) is generated by an electronfrom νe + n→ p + e− in a bound proton/neutron at rest, thereconstructed (anti)neutrino energy is given by,

EQEν =

2(MN − EB)Ee −[E 2B − 2MNEB + m2

e + ∆M2]

2 [(MN − EB)− Ee(1− cosθe)],

For a photon which is mis-identified as an electron in theMiniBooNE detector, we have to replace Ee and θe by Eγ and θγ .The binding energy EB = 34 MeV.(A. Aguilar-Arevalo et al., PRD 84(2011), 072005)

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The events

NCγ events at the MiniBooNE detector is given by,

dN

dEγd cos θγ= ε(Eγ)

∑l=νµ,νµ

N(l)POT ×

∑t=p, 12C

Nt

∫dEνφl(Eν)

dσl t(Eν)

dEγd cos θγ.

dσl t(Eν)/(dEγd cos θγ): cross section for NCγ on proton,incoherent and coherent reaction on Carbon

N(l)POT : the total number of protons on target (POT)

NνPOT = 6.46× 1020 and N ν

POT = 11.27× 1020

Nt : the number of protons/carbon nuclei in the target (806tons CH2)

ε(Eγ): energy dependent detection efficiency

φl(Eν): neutrino/antineutrino fluxes

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Beam flux and detection efficiency at MiniBooNE

0

5

10

15

20

25

φ×1

0-1

2/c

m2/P

OT

/50

Me

V

Eν (GeV)

ν-modeνµ –νµ

νe –νe

0

4

8

12

16

0 0.5 1.0 1.5 2.0 2.5 3.0

–ν-mode

νµ –νµ

νe –νe

0

0.04

0.08

0.12

0.16

0 0.4 0.8 1.2 1.6 2

e

E (GeV)

39/44


Comparison to the MB estimate

0

5

10

15

20

25

30

0.2 0.4 0.6 0.8 1 1.2 1.4

Events

/∆Q

E

EQEν (GeV)

ν-mode

0.89-1.111.0no N*MB

0

2

4

6

8

10

12

14

0.2 0.4 0.6 0.8 1 1.2 1.4

Events

/∆Q

E

EQEν (GeV)

–ν-mode

0.89-1.111.0no N*MB

40/44


Eγ distribution of the photon events

0

10

20

30

40

50

0.2 0.4 0.6 0.8 1 1.2 1.4

Events

/(0.1

GeV

)

Eγ (GeV)

ν-mode

0.89-1.111.0no N*MBZhang

0

4

8

12

16

20

0.2 0.4 0.6 0.8 1 1.2 1.4

Events

/(0.1

GeV

)

Eγ (GeV)

–ν-mode

0.89-1.111.0no N*MBZhang

41/44


cosθγ distribution of the photon events

0

6

12

18

24

30

-1 -0.5 0 0.5 1

Events

/(0.2

)

cosθγ

ν-mode

0.89-1.111.0no N*MB

0

2

4

6

8

10

12

-1 -0.5 0 0.5 1

Events

/(0.2

)

cosθγ

–ν-mode

0.89-1.111.0no N*MB

42/44


Summary

43/44


Summary

We have studied NCγ on nucleons and nuclei in theintermediate energy region (Eν ∼ 1 Gev).

Our model consists of nucleon pole, ∆ pole, heavierresonances pole and t-channel pion-exchange.

Large reduction (∼ 30%) on the cross section due to nucleareffects — Fermi motion, Pauli blocking and in-mediummodification of ∆ resonance.

Theoretical error dominated by N −∆ axial transitionproperties.

Our prediction is consistent with MiniBooNE estimate.

NCγ: insufficient to explain the excess of e-like events atMiniBooNE.

44/44


Thank you!

photon emission in neutral current interactions with ...advisors: drs. juan m. nieves and luis...

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