neutrino cross sections from a theoretical perspective luis alvarez-ruso ific, valencia

Neutrino cross sections from a theoretical perspective

Luis Alvarez-Ruso

IFIC, Valencia

Euro

L. Alvarez-Ruso, IFIC, Valencia EuroNu

Introduction Neutrino-nucleus interactions are important for:

Oscillation experiments

º detection, Eº reconstruction, º flux calibration

Electron-like backgrounds:

NC ¼0 production (incoherent, coherent)

Photon emission in NC

Hadronic physics

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

Strangeness content of the nucleon spin

Nuclear physics

Information about: nuclear correlations, MEC, spectral

functions

nuclear effects: essential for the interpretation of the data


Introduction Most relevant processes in the few-GeV region:

Quasielastic scattering

Single pion production (incoherent and coherent)


QE scattering º detection:

Eº reconstruction:

Assumes that

Important for oscillations:

QE ¾ affect the expected sensitivities to oscillation parameters

Example: Fernandez, Meloni, arXiv:1010.2329

¯ beam hypothetical exp.: < Eº > 0.3 GeV, 16O target

Sensitivities to µ13 and ±CP vary ~ 10-30 % depending on the

nuclear CCQE model

º¹ n ! ¹ ¡ p

E º =2mnE ¹ ¡ m2

¹ ¡ m2n + m2

p

2(mn ¡ E ¹ + p¹ cosµ¹ )

P (º¹ ! º¿ ) = sin2 2µ23 sin2 ¢ m223L

2E º


º QE scattering The (CC) elementary process:

where

Vector form factors: extracted from e-p, e-d

data

Axial form factors:

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

FA (Q2) = gA

µ1+

Q2

M 2A

¶ ¡ 2

; FP (Q2) =2M 2

Q2 + m2¼

FA (Q2)dipole ansatz PCAC


º QE scattering The (CC) elementary process:

gA = 1.267 Ã ¯ decay

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 )

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

Hadronic correction (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)

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

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

inclusive processes: with only Re[Vopt]

Complex optical potential

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


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)Marteau, Delorme, Ericson, NIMA 76 (2000)Nieves et al., PRC 70 (2004)


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

º QE scattering

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



Proposed solutions:

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

However, MA>1 GeV is incompatible with:

data

¼ electroproduction on p (at low Q2)

NOMAD: MA = 1.05 § 0.02(stat) § 0.06(sys) GeV Lyubushkin et al.,

EPJ C63

º QE scattering

ºd; ¹ºp



Proposed solutions:

MA=1.37 GeV (RDWIA) Butkevich, arXiv:1006.1595

Fit to d¾/dQ2 (shape only)

Better than RFG at low Q2

º QE scattering



Proposed solutions:

MA=1.37 GeV (RDWIA) Butkevich, arXiv:1006.1595

Fit to d¾/dQ2 (shape only)

Good description of double differential cross section

º QE scattering



Proposed solutions:

MA=1.6 GeV (Spectral Function) Benhar, Coletti, Meloni, PRL 105

(2010)

Fit to d¾/dQ2

º QE scattering



Proposed solutions:

MA=1.343 § 0.060 GeV (Spectral Function) Juszczak, Sobczyk,

Zmuda, arXiv:1007.2195

Fit to double differential c. s. including flux uncertainty

Momentum transfer cut qcut = 500 MeV to exclude IA breakdown

region: insufficient to reconcile MiniBooNE with exp. on deuterium

º QE scattering


º QE scattering Comparison to MiniBooNE ¾

Many body RPA Martini et al., PRC 80 (2009), 81 (2010)

RPA: small reduction Large 2p-2h contribution to º 12C mainly from (2),(3),(3’)




RPA: small reduction Large 2p-2h contribution to º 12C mainly from (2),(3),(3’) MEC absent (but important for (e,e’) in the dip region)

12C(e,e’)X

Gil, Nieves, Oset, NPA627




RPA: small reduction Large 2p-2h contribution to º 12C mainly from (2),(3),(3’) Prediction: smaller 2p-2h contribution to anti-º 12C Detailed tests against e-scattering data are necessary


1¼ production Reactions

Incoherent:

Coherent:

CC

NC

Relevant for oscillations

NC ¼0: e-like background to º¹ ! ºe searches (µ13 & ± $ CP

violation)

Source of CCQE-like events (in nuclei), needs to be

subtracted for a good Eº reconstruction

ºl A ! l ¼X

ºl A ! l¡ ¼+ A

º A ! º ¼0 A



Incoherent:

Coherent:

CC

NC



violation)



ºl A ! l ¼X

ºl A ! l¡ ¼+ A

º A ! º ¼0 A

Leitner, Mosel, PRC 81


1¼ production Elementary process:

Dominated by resonance production

At Eº ~ 1 GeV: ¢(1232)

N-¢ transition current:

Form factors , Helicity amplitudes (A1/2, A3/2, S1/2)

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:

Dominated by resonance production

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 N-¢ transition current

Helicity amplitudes can be extracted from data on ¼ photo- and electro-production

Unitary isobar model MAID Drechsel, Kamalov, Tiator, EPJA 34 (2007) 69

Uses world data for all 4 star resonances with W<2 GeV

Unitary isobar model+Regge-pole BG at high energies I. Aznauryan, PRC67

Dispersion relations CLAS (JLab) data 1st and 2nd resonance regions: ¢(1232), N*(1440), N*(1520),

N*(1535)

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-¢ transition current

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 CA

5(0) and MA ¢

From ANL and BNL data on with 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 GeV, 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 J. Sobczyk et al.

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)

GiBUU

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

¼, N but also ¢ are propagated

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


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

1¼ production

NuWro

Athar et al.

GiBUU


Coherent pion production

CC

NC

Takes place at low q2

Very small cross section

At q2 » 0, axial current not suppressed

1¼ production

ºl A ! l¡ ¼+ A

º A ! º ¼0 A

NEUTHiraide@NuInt09


1¼ production Coherent pion production models

PCAC

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

coherent pion production to ¼A elastic scattering

Extrapolated to q2 0

R&S: describe ¼A in terms of ¼N scattering

B&S, P&S: use ¼A data

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

q2=0 limit neglects important angular dependence at low

energies

R&S: The ¼A elastic description is not realistic

B&S,P&S: spurious initial ¼ distortion present in ¼A but

not in coh¼

Rein & Sehgal NPB 223 (83) 29 Berger & Sehgal, PRD 76 (2007),79 (2009)Paschos & Schalla, PRD 80 (2009),


1¼ production Coherent pion production models

PCAC

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

coherent pion production to ¼A elastic scattering

Extrapolated to q2 0

R&S: describe ¼A in terms of ¼N scattering

B&S, P&S: use ¼A data

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: ¾ ¼ 78 £ 10-40 cm2

Rein & Sehgal NPB 223 (83) 29 Berger & Sehgal, PRD 76 (2007),79 (2009)Paschos & Schalla, PRD 80 (2009),


1¼ production Coherent pion production

Microscopic 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)



Boyd et al., AIP Conf. Proc. 1189



SciBooNE: PRD 81 (2010)

NC ¼0 ¾ compatible with R&SCC¼+/NC¼0=0.14+0.30

-0.28 Theoretical models predict CC¼+/NC¼0 » 1-2 !

Boyd et al., AIP Conf. Proc. 1189


Conclusions

New data with high statistics available

Comparison shows discrepancies that await explanation (not

fits)

QE: 2p2h and MEC more important that in (e,e’) at fixed energy

Incoherent 1¼ production data underestimated

Comparison to inclusive data is needed

SciBooNE CC¼+/NC¼0=0.14+0.30-0.28 for 1¼ coherent is

incompatible with theoretical results



Model dependence in data: Background (CCQE-like) depends on the ¼ propagation

(absorption and charge exchange) model (NUANCE)

Eº reconstruction (unfolding)

º QE scattering

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



Incoherent:

Coherent:

CC

NC



violation)



ºl A ! l ¼X

ºl A ! l¡ ¼+ A

º A ! º ¼0 A

Leitner, Mosel, PRC 81

neutrino cross sections from a theoretical perspective luis alvarez-ruso ific, valencia

Documents