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)
Universidade de Coimbra L. Alvarez-Ruso
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
Universidade de Coimbra L. Alvarez-Ruso
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)
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
Universidade de Coimbra L. Alvarez-Ruso
Motivation
Oscillation experiments
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
Universidade de Coimbra L. Alvarez-Ruso
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)
Universidade de Coimbra L. Alvarez-Ruso
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
à electric ff
à magnetic ff
Universidade de Coimbra L. Alvarez-Ruso
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)
Universidade de Coimbra L. Alvarez-Ruso
º QE scattering
The (CC) elementary process:
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
Universidade de Coimbra L. Alvarez-Ruso
º QE scattering
The (CC) elementary process:
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
Universidade de Coimbra L. Alvarez-Ruso
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
Universidade de Coimbra L. Alvarez-Ruso
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)
Universidade de Coimbra L. Alvarez-Ruso
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)
Universidade de Coimbra L. Alvarez-Ruso
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)
Universidade de Coimbra L. Alvarez-Ruso
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)
Universidade de Coimbra L. Alvarez-Ruso
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
Universidade de Coimbra L. Alvarez-Ruso
º QE scattering
Comparison to MiniBooNE ¾
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)
Universidade de Coimbra L. Alvarez-Ruso
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
Universidade de Coimbra L. Alvarez-Ruso
º QE scattering
Comparison to MiniBooNE ¾Many body, RPA, calculation Martini et al., PRC 80 (2009)
Lesson: Many-body dynamics beyond 1p1h is important
Universidade de Coimbra L. Alvarez-Ruso
º QE scattering
Comparison to MiniBooNE ¾
Models should be compared to <d2¾/dT¹ dcosµ¹>…
… preferably to CCQE + CCQE-like
Inclusive data are desirable
MiniBooNE, PRD 81 (2010)
Universidade de Coimbra L. Alvarez-Ruso
1¼ production
Reactions
Incoherent:
Coherent:
CC
NC
ºl A ! l ¼X
ºl A ! l¡ ¼+ A
º A ! º ¼0 A
Universidade de Coimbra L. Alvarez-Ruso
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
Universidade de Coimbra L. Alvarez-Ruso
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)
Universidade de Coimbra L. Alvarez-Ruso
1¼ production
Elementary process:
Dominated by resonance production
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
Universidade de Coimbra L. Alvarez-Ruso
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
Universidade de Coimbra L. Alvarez-Ruso
1¼ production
N-¢ transition current
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
Universidade de Coimbra L. Alvarez-Ruso
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
Universidade de Coimbra L. Alvarez-Ruso
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
Universidade de Coimbra L. Alvarez-Ruso
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
Universidade de Coimbra L. Alvarez-Ruso
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
Universidade de Coimbra L. Alvarez-Ruso
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
Universidade de Coimbra L. Alvarez-Ruso
Comparison to the ¾(CC¼+)/¾(CCQE-like) ratio at MiniBooNE
1¼ production
NuWro
Athar et al.
GiBUU
Universidade de Coimbra L. Alvarez-Ruso
1¼ production
NC ¼0 production at MiniBooNE
Good description of shapeIntegrated ¾ : factor 2 smaller
GiBUU vs MiniBooNET. Leitner, PhD Thesis
Universidade de Coimbra L. Alvarez-Ruso
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
Universidade de Coimbra L. Alvarez-Ruso
1¼ production
Coherent pion 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
Universidade de Coimbra L. Alvarez-Ruso
1¼ production
Coherent pion 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
Universidade de Coimbra L. Alvarez-Ruso
1¼ production
Coherent pion 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
Universidade de Coimbra L. Alvarez-Ruso
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)
Universidade de Coimbra L. Alvarez-Ruso
1¼ production
Coherent pion productionMicroscopic models
Medium effects reduce considerably de cross sectionPion distortion shifts down the peak
Amaro et al., PRD 79 (2009)
Universidade de Coimbra L. Alvarez-Ruso
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)
Universidade de Coimbra L. Alvarez-Ruso
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
Universidade de Coimbra L. Alvarez-Ruso
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
Universidade de Coimbra L. Alvarez-Ruso
Conclusions
Road map:
1. Understand the measurements
2. Explain (not fit) data
3. Implement better models in MC
Thank you
Universidade de Coimbra L. Alvarez-Ruso
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
Universidade de Coimbra L. Alvarez-Ruso
Electron scattering
Inclusive electron-nucleus scattering at intermediate energiesSpectral functions of nucleons in nuclei: Results Ankowski@NuInt09
40Ca
Universidade de Coimbra L. Alvarez-Ruso
º QE scattering
But
RPA correlations cause a considerable reduction of the c.s. at low Q2
Universidade de Coimbra L. Alvarez-Ruso
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