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Neutrino Interactions: Challenges in the current theoretical

picture

Luis Alvarez-Ruso

Universidade de Coimbra

Universidade de Coimbra L. Alvarez-Ruso

Outline

Motivation

º-induced quasielastic scattering

Single pion production (incoherent and coherent)


Motivation

Oscillation experiments

Goal: Precision measurements of ¢m232, µ23 in º¹

disappearance

Understanding Eº reconstruction is critical

Kinematical determination of Eº in a CCQE event

Rejecting CCQE-like events relies on accurate knowledge of

nuclear dynamics and FSI (¼, N propagation, ¼ absorption)

º¹ n ! ¹ ¡ p

E º =2mnE ¹ ¡ m2

¹ ¡ m2n + m2

p

2(mn ¡ E ¹ + p¹ cosµ¹ ) exact only for free nucleons wrong for CCQE-like events

P (º¹ ! º¿ ) = sin2 2µ23 sin2 ¢ m223L

2E º


Motivation


Goal: Precision measurements of ¢m232, µ23 in º¹

disappearance

Understanding Eº reconstruction is critical

Kinematical determination of Eº in a CCQE event

Rejecting CCQE-like events relies on accurate knowledge of

nuclear dynamics and FSI (¼, N propagation, ¼ absorption)

Implications for oscillation measurements: T. Leitner, Poster 56 C20

º¹ n ! ¹ ¡ p

E º =2mnE ¹ ¡ m2

¹ ¡ m2n + m2

p

2(mn ¡ E ¹ + p¹ cosµ¹ ) exact only for free nucleons wrong for CCQE-like events

P (º¹ ! º¿ ) = sin2 2µ23 sin2 ¢ m223L

2E º

GENIEEº = 1 GeV


Motivation


Goal: º¹ ! ºe searches (µ13 & ± $ CP violation)

Electron-like backgrounds:

NC ¼0 production (incoherent, coherent)

Photon emission in NC (candidate for low Eº

excess@MiniBoonne)

Aguilar-Arevalo et al., PRL98 (2007) 231801


Motivation

Hadronic physics

Nucleon and Nucleon-Resonance (N-¢, N-N*) axial form factors

MINERvA: first precision measurement of axial nucleon ff at Q2>1 GeV.

Strangeness content of the nucleon spin (isoscalar coupling

GsA):

probed in NCQE :NCQE(p)/NCQE(n) or NC(p)/CCQE

Experiments are performed with nuclear targets )

Nuclear physicsnuclear effects are essential for the interpretation of the data.Information about:

Nuclear correlations

Meson exchange currents

Nucleon and resonance spectral functions

º¹ (p;n) ! º¹ (p;n)


º QE scattering

The (CC) elementary process:

where

Vector form factors:

Extracted from e-p, e-d data

º¹ (k) n(p) ! ¹ ¡ (k0) p(p0)

M =GF cosµCp

2l®J ®

l® = ¹u(k0)°®(1¡ °5)u(k)

J ® = ¹u(p0)·°®F V

1 +i

2M¾®̄ q¯ F V

2 + °¹ °5FA +q¹

M°5FP

¸u(p)

F V12 = F p

12 ¡ F n12

GE = F1 +q2

2mNF2

GM = F1 + F2

Ã electric ff

Ã magnetic ff


º QE scattering

At low Q2:

MV = 0.71 GeV, GE/GM ¼ 1/¹p

At high Q2:

½(r) = ½0e¡ r =r0 ) GE (Q2) = GE (0)µ

1+Q2

M 2V

¶ ¡ 2

Bodek et al., EPJC 53 (2008)


º QE scattering


where

Axial form factors:

gA = 1.267 Ã ¯ decay

MA = 1.016 § 0.026 GeV ( ) Bodek et al., EPJC 53 (2008)

º¹ (k) n(p) ! ¹ ¡ (k0) p(p0)

M =GF cosµCp

2l®J ®

l® = ¹u(k0)°®(1¡ °5)u(k)

J ® = ¹u(p0)·°®F V

1 +i

2M¾®̄ q¯ F V

2 + °¹ °5FA +q¹

M°5FP

¸u(p)

FA (Q2) = gA

µ1+

Q2

M 2A

¶ ¡ 2

; FP (Q2) =2M 2

Q2 + m2¼

FA (Q2)dipole ansatz PCAC

ºd; ¹ºp


º QE scattering


MA= 1.016 § 0.026 GeV ( ) Bodek et al., EPJC 53 (2008)

MA from ¼ electroproduction on p:

Connected to FA at threshold and in the chiral limit (m¼ =0)

Using models to connect with data )MA

ep= 1.069 § 0.016 GeV Liesenfeld et al., PLB 468 (1999) 20

A more careful evaluation in ChPT Bernard et al., PRL 69 (1992) 1877

MA = MAep - ¢MA , ¢MA =0.055 GeV ) MA = 1.014 GeV

º¹ (k) n(p) ! ¹ ¡ (k0) p(p0)

FA (Q2) = gA

µ1+

Q2

M 2A

¶ ¡ 2

ºd; ¹ºp

hr2A ie = hr2

A i º +3

64f ¼

µ1¡

12¼2

¶;hr2

A i =12

MA2


º QE scattering

Relativistic Global Fermi Gas Smith, Moniz, NPB 43 (1972) 605

Impulse Approximation

Fermi motion

Pauli blocking

Average binding energy

Explains the main features of the (e,e’) inclusive ¾ in the QE

region

Fails in the details (nuclear dynamics needed): talk by O. Benhar

f (~r;~p) = £(pF ¡ j~pj)

PPauli = 1¡ £(pF ¡ j~pj)

E =q

~p2 + m2N ¡ ²B


º QE scattering

Spectral functions of nucleons in nuclei

The nucleon propagator can be cast as

Sh(p) Ã hole (particle) spectral functions: 4-momentum (p)

distributions of the struck (outgoing) nucleons

§ Ã nucleon selfenergy

Better description of (e,e’) inclusive ¾ (O. Benhar’s talk)

G(p) =Z

d!Sh(! ;~p)

p0 ¡ ! ¡ i²+

Zd!

Sp(! ;~p)p0 ¡ ! + i²

Sp;h(p) = ¡1¼

Im§ (p)[p2 ¡ M 2 ¡ Re§ (p)]2 + [Im§ (p)]2

Benhar et al., PRD 72 (2005)Ankowski, Sobczyk, PRC 67 (2008)Nieves et al., PRC 70 (2004) Leitner et al., PRC 79 (2009)


º QE scattering

Relativistic mean field

Impulse Approximation

Initial nucleon in a bound state (shell)

ªi : Dirac eq. in a mean field potential (!-¾ model)

Final nucleon

PWIA

RDWIA: ªf : Dirac eq. for scattering state

Glauber

Problem: nucleon absorption that reduces the c.s.

Can be used to study:

1N knockout (with only Re[Vopt])

Complex optical potential

Martinez et al., PRC 73 (2006)Budkevich, Kulagin, PRC 76 (2007)


Local Fermi Gas

Space-momentum correlations absent in the GFGReasonable for medium/heavy nucleiMicroscopic many-body effects are tractable

(calculations in infinite nuclear matter)

º QE scattering

pF (r) = [32¼2½(r)]1=3

Convolution model:Ciofi degli Atti, Simula, PRC 53 (1996)


º QE scattering

RPA long range correlations

Incorporates N-hole and ¢-hole states

V: ¼, ½ exchange, Landau-Migdal parameter g’

Describes correctly ¹ capture on 12C and LSND CCQE

Collective effect: important at low Q2 for º QE

Singh, Oset, NPA 542 (1992)Nieves et al., PRC 70 (2004)


º QE scattering

Comparison to MiniBooNE ¾

At Eº =0.8 GeV: ¾th ~ 4.5-5 < ¾MB ~ 7 £ 10-38 cm2

CCQE models with MA~1 GeV cannot reproduce MiniBooNE ¾

Source: Boyd et al., AIP Conf. Proc. 1189 Data: MiniBooNE, PRD 81, 092005 (2009)

more on CCQE data in M. Wascko’ talk


º QE scattering


Model dependence in data: Background (CCQE-like) depends on the ¼ propagation (absorption and charge exchange) model (NUANCE)Eº reconstruction (unfolding)

Source: Boyd et al., AIP Conf. Proc. 1189 Data: MiniBooNE, PRD 81, 092005 (2009)


º QE scattering

Comparison to MiniBooNE ¾Proposed solutions:

MA=1.35 § 0.17 GeV (RFG) MiniBooNE, PRD 81, 092005 (2010)

MA=1.37 § 0.05 GeV (RMF) Butkevich, arXiv:1006:1595

However, MA>1 GeV is incompatible with:

data¼ electroproduction on p (at low Q2)NOMAD, Lyubushkin et al., EPJ C 63 (2009) 355

ºd; ¹ºp


º QE scattering

Comparison to MiniBooNE ¾Many body, RPA, calculation Martini et al., PRC 80 (2009)

Lesson: Many-body dynamics beyond 1p1h is important


º QE scattering


Models should be compared to <d2¾/dT¹ dcosµ¹>…

… preferably to CCQE + CCQE-like

Inclusive data are desirable

MiniBooNE, PRD 81 (2010)


1¼ production

Reactions

Incoherent:

Coherent:

CC

NC

ºl A ! l ¼X

ºl A ! l¡ ¼+ A

º A ! º ¼0 A


1¼ production

Elementary process:

Dominated by resonance production

At Eº ~ 1 GeV: ¢(1232)

N-¢ transition current:

Form factors , Helicity amplitudes

ºl N ! l ¼N 0

M =GF cosµCp

2l®J ®

J ¹ = ¹Ã¹

"ÃCV

3M

(g¯ ¹ =q¡ q̄ ° ¹ ) +CV

4M 2(g¯ ¹ q¢p0¡ q̄ p0¹ ) +

CV5

M 2(g¯ ¹ q¢p¡ q̄ p¹ )

!

°5

+CA

3M

(g¯ ¹ =q¡ q̄ ° ¹ ) +CA

4M 2(g¯ ¹ q¢p0¡ q̄ p0¹ ) + CA

5 g¯ ¹ +CA

6M 2q̄ q¹

#

u


1¼ production

Elementary process:


Rein-Sehgal model: Rein-Sehgal, Ann. Phys. 133 (1981) 79.

Used by almost all MC generators

Relativistic quark model of Feynman-Kislinger-Ravndal with

SU(6) spin-flavor symmetry

Helicity amplitudes for 18 baryon resonances

Lepton mass = 0

Corrections:

Poor description of ¼ electroproduction data on p

ºl N ! l ¼N 0

Kuzmin et al., Mod. Phys. Lett. A19 (2004) Berger, Sehgal, PRD 76 (2007)Graczyk, Sobczyk, PRD 77 (2008)


1¼ production

Elementary process:


Rein-Sehgal model:

Used by almost all MC generators

Relativistic quark model of Feynmann-Kislinger-Ravndal with

SU(6) spin-flavor symmetry

Helicity amplitudes for 18 baryon resonances

Lepton mass = 0

Corrections:

Poor description of ¼ electroproduction data on p

ºl N ! l ¼N 0

Kuzmin et al., Mod. Phys. Lett. A19 (2004) Graczyk, Sobczyk, PRD 77 (2008) Berger, Sehgal, PRD 76 (2007)

Leitner et al., POS NUFACT08


1¼ production

N-¢ transition current

Unitary isobar model MAID has been used to extract N-R

helicity amplitudes (A1/2, A3/2, S1/2) from world data on ¼

photo- and electro-production for all 4 star resonances with W<2 GeV

Drechsel, Kamalov, Tiator, EPJA 34 (2007) 69

J ¹ = ¹Ã¹

"ÃCV

3M

(g¯ ¹ =q¡ q̄ ° ¹ ) +CV

4M 2(g¯ ¹ q¢p0¡ q̄ p0¹ ) +

CV5

M 2(g¯ ¹ q¢p¡ q̄ p¹ )

!

°5

+CA

3M

(g¯ ¹ =q¡ q̄ ° ¹ ) +CA

4M 2(g¯ ¹ q¢p0¡ q̄ p0¹ ) + CA

5 g¯ ¹ +CA

6M 2q̄ q¹

#

u


1¼ production


N-¢(1232) helicity amplitudes from MAID

N-¢(1232) is not a pure M1 transition , A3/2 A1/2 , S1/2 0

J ¹ = ¹Ã¹

"ÃCV

3M

(g¯ ¹ =q¡ q̄ ° ¹ ) +CV

4M 2(g¯ ¹ q¢p0¡ q̄ p0¹ ) +

CV5

M 2(g¯ ¹ q¢p¡ q̄ p¹ )

!

°5

+CA

3M

(g¯ ¹ =q¡ q̄ ° ¹ ) +CA

4M 2(g¯ ¹ q¢p0¡ q̄ p0¹ ) + CA

5 g¯ ¹ +CA

6M 2q̄ q¹

#

u


1¼ production


Axial form factors

J ¹ = ¹Ã¹

"ÃCV

3M

(g¯ ¹ =q¡ q̄ ° ¹ ) +CV

4M 2(g¯ ¹ q¢p0¡ q̄ p0¹ ) +

CV5

M 2(g¯ ¹ q¢p¡ q̄ p¹ )

!

°5

+CA

3M

(g¯ ¹ =q¡ q̄ ° ¹ ) +CA

4M 2(g¯ ¹ q¢p0¡ q̄ p0¹ ) + CA

5 g¯ ¹ +CA

6M 2q̄ q¹

#

u

CA4 = ¡

14CA

5

CA6 = CA

5M 2

m2¼+ Q2 Ã PCAC

CA3 = 0Ã Adler model

CA5 = CA

5 (0)µ

1+Q2

M 2A ¢

¶ ¡ 1


1¼ production

N-¢ axial form factors: determination of CA5(0) and MA ¢

From ANL and BNL data onwith large normalization (flux) uncertainties

Graczyk et al., PRD 80 (2009) Deuteron effects

Non-resonant background absent

CA5(0) =1.19 § 0.08, MA ¢ = 0.94 § 0.03 GeV

Hernandez et al., PRD 81 (2010)

Deuteron effects

Non-resonant background fixed by chiral symmetry

CA5(0) =1.00 § 0.11, MA ¢ = 0.93 § 0.07 GeV

20 % reduction of the GT relation

CA5 (0) =

g¢ N ¼f ¼p6M

¼1:2 Ã off diagonal GT relation

º¹ d ! ¹ ¡ ¼+ pn


1¼ production

Incoherent 1¼ production in nuclei

Large number of excited states ) semiclassical treatment

¼ propagation (scattering, charge exchange), absorption

(FSI)

Most models cannot calculate this reaction channel.

Exceptions:

MC generators: NUANCE, NEUT, GENIE, NuWro

Cascade: Ahmad et al., PRD 74 (2006)

Transport: GiBUU


1¼ production

Incoherent 1¼ production in nuclei (FSI)

NuWro Poster 75 (B04), J. Sobczyk

Intranuclear cascade

¼ propagation: empirical ¼-N vacuum ¾

¼ absorption: ¼-A absorption data

Ahmad et al., PRD 74 (2006)

Cascade (~NuWro)

In-medium modification of ¢ spectral f. (only in the production

mech.)

GiBUU

Transport: ne approach for eA, ºA, pA, ¼A reactions

¼, N but also ¢ are propagated

Main absorption mech.: ¢ N ! N N, ¼ N N ! N N


1¼ production

GiBUU Leitner et al., PRC 73 (2006)

Effects of FSI on pion kinetic energy spectra strong absorption in Δ regionside-feeding from dominant ¼+ into ¼0 channelsecondary pions through FSI of initial QE protons

º¹ + 56F e! ¹ ¡ ¼X E º = 1 GeV


Comparison to the ¾(CC¼+)/¾(CCQE-like) ratio at MiniBooNE

1¼ production

NuWro

Athar et al.

GiBUU


1¼ production

NC ¼0 production at MiniBooNE

Good description of shapeIntegrated ¾ : factor 2 smaller

GiBUU vs MiniBooNET. Leitner, PhD Thesis


Coherent pion production

CC

NC

Takes place at low q2

Very small cross section but

relatively larger than in coherent

¼ production with photons or electrons

At q2 » 0 the axial current is not

suppressed while the vector is

Models: PCACMicroscopic

1¼ production

ºl A ! l¡ ¼+ Aº A ! º ¼0 A

NEUTHiraide@NuInt09


1¼ production


PCAC models: Rein-Sehgal model NPB 223 (83) 29

In the q2=0 limit, PCAC is used to relate º induced

coherent pion production to ¼A elastic scattering

Continuation to q2 0: (1-q2/1 GeV2)-2 factor

Describes ¼A in terms of ¼N scattering

Subtracts the spurious initial ¼ distortion present in ¼A

but not in coherent pion production

Problems: Hernandez et al., PRD 80 (2009) 013003

q2=0 limit neglects important angular dependence at low

energies

The ¼A elastic description is not realistic


1¼ production


PCAC: Paschos & Schalla, PRD 80 (2009), Berger & Sehgal, PRD 76

(2007),79 (2009)

In the q2=0 limit, PCAC is used to relate º induced

coherent pion production to ¼A elastic scattering

Extrapolate to q2 0

Directly use ¼A cross section ) spurious initial ¼

distortion present in ¼A but not in coherent ¼ production

is not subtracted

Smaller ¾ than RS

Problems of PCAC models: less relevant as the energy

increases

NOMAD: ¾=72.6 § 8.1(stat) § 6.9(syst) £ 10-40 cm2

Consistent with RS: Consistent with RS: ¾¾ ¼¼ 78 78 ££ 10-40 cm2

see L. Camilleri’s talk


1¼ production

Coherent pion productionMicroscopic models:

¢ excitation is dominant

¢ properties change in the nuclear medium

¼ distortion: DWIA with optical potential based on ¢-hole

model

Singh et al., PRL 96 (2006)LAR et al, PRC 76 (2007)Amaro et al., PRD 79 (2009)Nakamura et al., PRC 81 (2010)


1¼ production

Coherent pion productionMicroscopic models

Medium effects reduce considerably de cross sectionPion distortion shifts down the peak

Amaro et al., PRD 79 (2009)


1¼ production

Coherent pion productionMicroscopic models:

¢ excitation is dominant

¢ properties change in the nuclear medium

¼ distortion: DWIA with optical potential based on ¢-hole

model

Treatment is consistent with incoherent ¼ production

Valid only at low energies

¾»£CA

5 (0)¤2

Singh et al., PRL 96 (2006)LAR et al, PRC 76 (2007)Amaro et al., PRD 79 (2009)Nakamura et al., PRC 81 (2010)


1¼ production

Coherent pion productionComparison to MiniBooNE NC ¼0:

35 % reduction in RS model

Data seem to prefer a CA5(0)~1.2

(in agreement with the GT relation)

rather than a smaller one.

But a subtraction of a large

incoherent ¼0 background is

performed

Anderson@NuInt09


1¼ production

Coherent pion productionComparison to SciBooNE: arXiv:1005.0059

NC ¼0 ¾ compatible with RS

CC¼+/NC¼0=0.14+0.30-0.28

Theoretical models predict CC¼+/NC¼0 » 1-2 !

But a subtraction of a large incoherent ¼ background is performed


Conclusions

Road map:

1. Understand the measurements

2. Explain (not fit) data

3. Implement better models in MC

Thank you


º QE scattering

Relativistic Global Fermi Gas Smith, Moniz, NPB 43 (1972) 605

Explains the main features of the (e,e’) inclusive c. s. in the

QE region

Ankowski@NuInt09


Electron scattering

Inclusive electron-nucleus scattering at intermediate energiesSpectral functions of nucleons in nuclei: Results Ankowski@NuInt09

40Ca


º QE scattering

But

RPA correlations cause a considerable reduction of the c.s. at low Q2


1¼ production

Elementary processSato & Lee model Nacamura@NuInt09

Dynamical model for ¼ production with °, e, ºStarting with an effective H: ¼N, ¢N ) T-matrix obtained from coupled channel Lippman-Schwinger eq.Good agreement with data

Bare ¢N renormalized by meson clouds (30 %): reconciles the empirical value with quark model results

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nucleonresonance n

qe regionfails

maep ma