Neutrino-induced quasielastic scattering

Neutrino-induced quasielastic scattering

Luis Alvarez-Ruso

Neutrino-induced quasielastic scattering from a theoretical

perspectiveLuis Alvarez-Ruso

L. Alvarez-Ruso Instytut Fizyki Teoretycznej, Uniwersytetu Wroclawskiego, Nov. 09

Outline

Motivation

º scattering on the nucleon

Quasielastic scattering models

Experimental status and comparison to data

Conclusions


Motivation

º – Nucleus interactions (in the QE region) are important for:

Oscillation experimentsº oscillations are well established ))

Goal: Precise determination of oscillation parameters: ¢m2ij,

µij, ±

º are massive flavors are mixed

0

@ºe

º¹

º¿

1

A = V

0

@º1

º2

º3

1

A

V =

0

@1 0 00 cosµ23 sinµ23

0 ¡ sinµ23 cosµ23

1

A

0

@cosµ13 0 sinµ13 e¡ i±

0 1 0¡ sinµ13 ei± 0 cosµ13

1

A

0

@cosµ12 sinµ12 0

¡ sinµ12 cosµ12 00 0 1

1

A


Motivation


Oscillation experiments Precision measurements of ¢m23

2, 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


Oscillation experiments Precision measurements of ¢m23

2, 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

GENIEEº = 1 GeV


Motivation


Hadronic physics

Nucleon axial form factors

MINERvA: first precision measurement of GA at Q2>1 GeV.

Deviations from the dipole form?

Strangeness content of the nucleon spin (isoscalar coupling

GsA):

probed in NCQE reactions

Best experimental sensitivity in ratios: NCQE(p)/NCQE(n) or

NC(p)/CCQE

Experiments are performed with nuclear targets ) nuclear effects are essential for the interpretation of the

data.

º¹ (p;n) ! º¹ (p;n)


Motivation


Nuclear physics

Excellent testing ground for nuclear many-body mechanisms,

nuclear structure and reaction models

Relativistic effects

Nuclear correlations

Meson exchange currents (MEC)

Nucleon and resonance spectral functions

º-nucleus cross sections incorporate a richer information on nuclear structure and interactions than e-nucleus ones



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



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)



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


QE scattering models

Inclusive electron-nucleus scattering (crucial test for any º-nucleus model)Relativistic Global Fermi Gas Smith, Moniz, NPB 43 (1972) 605

Impulse ApproximationFermi motionPauli blocking Average binding energy Explains the main features of the inclusive cross sections in the QE region

f (~r;~p) = £(pF ¡ j~pj)

PPauli = 1¡ £(pF ¡ j~pj)

E =q

~p2 + m2N ¡ ²B

Ankowski@NuInt09



Inclusive electron-nucleus scatteringRelativistic Global Fermi Gas Smith, Moniz, NPB 43 (1972) 605

However

GFG overestimates the longitudinal response RL

“FG is certainly too simple to be right. Nuclear dynamics must be included in the picture” Benhar@NuInt09



Inclusive electron-nucleus scatteringSpectral 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

Can be extended to the excitation of resonances in nuclei

G(p) =Z

d!Sh(! ;~p)

p0 ¡ ! ¡ i´+

Zd!

Sp(! ;~p)p0 ¡ ! ¡ i´

Sp;h(p) = ¡1¼

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




Hole spectral function: 80-90 % of nucleons occupy shell model statesThe rest take part in the NN interactions (correlations); located at high momentum

n(~p) =R

d! Sh(! ;~p)

Meloni@NuInt09

Benhar et al., PRD 72 (2005) Ankwowski & Sobczyk, PRC 77 (2008)




Hole spectral function:80-90 % of nucleons occupy shell model statesThe rest take part in the NN interactions (correlations); located at high momentum

Particle spectral functionsOptical potential: U = V – i W V ~ 25 MeV Ã fitted to p-A dataW:

Benhar et al., PRD 72 (2005) Ankwowski & Sobczyk, PRC 77 (2008)

W=¾ ½ v /2 Correlated Glauber approximation

(straight trajectories, frozen spectators) Benhar et al., PRC 44 (1991) 2328



Inclusive electron-nucleus scattering

Spectral functions of nucleons in nuclei: Results Ankowski@NuInt09

40Ca



Inclusive electron-nucleus scattering

Spectral functions of nucleons in nuclei: Results Ankowski@NuInt09

40Ca


Inclusive electron-nucleus scatteringSpectral functions in a Local Fermi Gas Leitner et al., PRC 79 (2009)

Space-momentum correlations absent in the GFGOK for medium/heavy nucleiMicroscopic many-body effects are tractableCan be extended to exclusive reactions: (e,e’ N), (e,e’ ¼), etc


pF (r) = [32¼2½(r)]1=3



Space-momentum correlations absent in the GFGOK for medium/heavy nucleiMicroscopic many-body effects are tractableCan be extended to exclusive reactions: (e,e’ N), (e,e’ ¼), etc


pF (r) = [32¼2½(r)]1=3



Mean field potential

Density and momentum dependent

Parameters fixed in p-Nucleus scattering

Nucleons acquire effective masses


Me® = M + U(~r;~p)



Hole spectral function:The correlated part of Sh is neglected

Particle spectral function:

Re§ is obtained from Im§ with a dispersion relation fixing the pole position at

I


Im§ ¼0 Sh(p) ! ±(p2 ¡ M 2e®)

Gil, Nieves, Oset, NPA627Ciofi degli Atti et al.,PRC41

Im§ = ¡p

(p2)¡ coll(p;r) ; ¡ coll = h¾N N vrel i Ã Collisional broadening

p(pole)0 =

q~p2 + M 2

e®



Inclusive electron-nucleus scatteringSpectral functions in a Local Fermi Gas:

Results Leitner et al., PRC 79 (2009)



Good description of the dip region requires the inclusions of 2p2h contributions from MEC Gil, Nieves, Oset, NPA627

Important for º: source of CCQE-like events



RPA long range correlations

“In nuclei, the strength of electroweak couplings may change from their free nucleon values due to the presence of strongly interacting nucleons” Singh, Oset, NPA 542 (1992) 587

For the axial coupling gA :

The quenching of gA in Gamow-Teller ¯ decay is well

established

(gA )e®

gA=

11+ g0Â0

Â0 dipole susceptibility

g’ Lorentz-Lorenz factor ~1/3 Ericson, Weise, Pions in Nuclei

(gA )e®

gA» 0:9 Wilkinson, NPA 209 (1973) 470



RPA long range correlations Nieves et. al. PRC 70 (2004) 055503

In particular

¼ spectral function changes in the nuclear medium ) so does

VN N = ~¿1~¿2¾i1¾

j2[q̂i q̂j VL (q) + (±i j ¡ q̂i q̂j )VT (q)]+ g~¾1~¾2 + f 0~¿1~¿2 + f I 1I 2

VL =f 2

N N ¼

m2¼

( µ¤2

¼¡ m2¼

¤2¼¡ q2

¶2 ~q2

q2 ¡ m2¼

+ g0

)

J A®



RPA long range correlations

RPA approach built up with single-particle states in a Fermi seaSimplified vs. some theoretical models (e.g. continuum RPA) Applies to inclusive processes; not suitable for transitions to discrete states

But

Incorporates explicitly ¼ and ½ exchange and ¢-hole states

Has been successfully applied to ¼, ° and electro-nuclear reactions

Describes correctly ¹ capture on 12C and LSND CCQE Nieves et. al. PRC 70 (2004) 055503

Important at low Q2 for CCQE at MiniBooNE energies



RPA long range correlationsComparison to inclusive electron-nucleus data LAR@NuInt09



RPA long range correlationsCCQE on 12C averaged over the MiniBooNE flux LAR et al., arXiv:0909.5123



RPA long range correlationsCCQE on 12C averaged over the MiniBooNE flux LAR et al., arXiv:0909.5123

RPA correlations cause a reduction of ¾ at low Q2 and forward angles



Relativistic mean fieldImpulse ApproximationInitial nucleon in a bound state (shell)

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

Final nucleonPWIARDWIA: ªf : Dirac eq. for scattering state

Glauber Has been used to study 1N knockout Problem: nucleon absorption that reduces the c.s.

Complex optical potential



Relativistic mean field

RPWIARPWIA

RDWIARDWIA

RPWIARPWIA

RDWIARDWIA

Giusti et al., arXiv:0910.1045



Relativistic mean fieldImpulse ApproximationInitial nucleon in a bound state (shell); no correlations

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

Final nucleonPWIADWIA: ªf : Dirac eq. for scattering states

Glauber Has been used to study 1N knockout Problem: nucleon absorption that reduces the c.s.

Complex optical potential



Green function approach Meucci et al., PRC 67 (2003) 054601

QE

The imaginary part of the optical potential is responsible for

the redistribution of the flux among the different channels

Suitable for inclusive and exclusive scattering



Green function approach Meucci et al., PRC 67 (2003) 054601

16O(e,e’)X



(Super)scaling Barbaro et al., arXiv:0909.2602

First kind scaling:

F (! ; j~qj) =d¾

d d!

Z¾ep + N ¾en

F = F (Ã0(! ; j~qj))

)

12C



(Super)scaling

First kind scaling:

Second kind scaling: independent of A

First + Second scaling = Superscaling

F (! ; j~qj) =d¾

d d!

Z¾ep + N ¾en

F = F (Ã0(! ; j~qj))f (Ã0) = pF F (Ã0)

Ã’ < 0 scaling regionÃ’ > 0 scaling violation



(Super)scalingScaling violations reside mainly in the transverse channel



(Super)scalingThe experimental superscaling function (fit using RL data)

Constraint for nuclear modelsRelativistic Fermi Gas

Exact superscalingWrong shape of f(Ã’)



(Super)scalingThe experimental superscaling function (fit using RL data)

Constrain for nuclear modelsRelativistic mean field describes the asymmetric shape of f(Ã’)



(Super)scalingSuperscaling in the ¢ regionExperimental superscaling function

At Ã’¢ > 0 other resonances, etc contribute



(Super)scalingSuperscaling Analysis SUSA

Calculate with Relativistic Fermi GasReplace fRFG ! fexp



(Super)scalingSuperscaling Analysis SUSA




(Super)scalingSuperscaling Analysis SUSA for º-A Amaro et al., PRL 98 (2007) 242501


SUSA: ~ 15 % reduction of ¾ with respect to RFGScaling approach fails at !.40 MeV, |q|.400 MeV: collective effects


Experimental status

Data!

CCQE, NCQE, º, anti-º

MiniBooNE (12C), SciBooNE (16O), MINOS (Fe), NOMAD (12C)

and puzzles…


Experimental status

MiniBooNE Largest sample of low energy (< Eº > ~ 750 MeV) º¹ CCQE events to date. Aguilar-Arevalo et. al., PRL 100 (2008) 032301 The shape of hd¾/dcosµ¹dE¹i is accurately described by the Relativistic Global Fermi Gas Model with: EB = 34 MeV, pF = 220 MeV

But

ϰ=1.007 § 0.007

MA=1.35 § 0.17 GeV

Large ¾ compared to GFG

with MA=1 GeV

E minp = ·

µqM 2 + p2

F ¡ ! + EB

¶

Katori, arXiv:0909.1996


Experimental status

However:

The physical meaning of ϰ is obscure

ϰ, MA values depend on the background from CC1¼

Background subtraction depends on the ¼ propagation

(absorption and charge exchange) model

NUANCE: constant suppression of ¼ production

Model dependent Eº reconstruction (unfolding)


Experimental status

However:

The physical meaning of ϰ is obscure

ϰ, MA values depend on the background from CC1¼

Background subtraction depends on the ¼ propagation

(absorption and charge exchange) model

NUANCE: constant suppression of ¼ production

Model dependent Eº reconstruction (unfolding)

Better compare to:



Experimental status

NOMAD Lyubushkin et al., EPJ C 63 (2009) 355

CCQE on 12C at high 3-100 GeV energies (DIS is dominant)No precise knowledge of the integrated º flux ) Normalization of CCQE ¾ from processes with better know ¾ (DIS, IMD) CCQE ¾ measured from combined 2-track (¹,p) and 1-track (¹) samplesFrom measured CCQE ¾ : MA = 1.05 § 0.02(stat) § 0.06(sys) GeV

Consistent with MA extracted from Q2 shape fit of 2-track sampleMiniBooNE vs NOMADKatori, arXiv:0909.1996


Interpretation

MA > 1 GeV?

MA from ¼ electroproduction on p: Bernard et al., J Phys. G

Using Current Algebra and PCAC

Valid only 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

E (¡ )0+ (q2) =

r

1¡k2

4M 2

e8¼f ¼

½FA (q2) +

gA q2

4M 2 ¡ 2q2GVM (q2)

¾

hr2A ie = hr2

A i º +3

64f ¼

µ1¡

12¼2

¶;hr2

A i =12

MA2


Interpretation

Can nuclear effects explain the shape of the MiniBooNE Q2 distribution?Spectral functions:

Benhar & Meloni, arXiv:0903.2329


Interpretation

Can nuclear effects explain the shape of the MiniBooNE Q2 distribution?Spectral functions:

LAR, Leitner, Buss, Mosel, arXiv:0909.5123


Interpretation

Can nuclear effects explain the shape of the MiniBooNE Q2 distribution?RPA:

RPA brings the shape closer to experiment keeping MA = 1 GeV

LAR, Leitner, Buss, Mosel, arXiv:0909.5123


Can CCQE nuclear models explain the size of MiniBooNE ¾?

Ex. at Eº =0.8 GeV: ¾th ~ 5 < ¾MB ~ 7 £ 10-38 cm2

CCQE models with MA~1 GeV cannot reproduce MiniBooNE ¾

Interpretation

Sobczyk@NuInt09



Interpretation

Can CCQE nuclear models explain the size of MiniBooNE ¾?Many body RPA calculation Martini et al., arXiv:0910.2622


Interpretation

Can CCQE nuclear models explain the size of MiniBooNE ¾?Many body RPA calculation Martini et al., arXiv:0910.2622

Lesson: Many-body dynamics beyond 1p1h is important

Open questions:

Is the Q2 distribution also well described by CCQE+2p2h?

Role of MEC

Is the comparison proper ?

Comparison to inclusive data is needed

NOMAD results?


Conclusions

º-A scattering in the CCQE region is relevant for oscillation, hadron and nuclear physics

New data (K2K, MiniBooNE, SciBooNE, MINOS, NOMAD)

MINERvA in the future

A good understanding of (semi)inclusive ºA (together with eA) cross section in the QE and resonance regions is required for the (model dependent) separation of mechanisms: only then more

precise determinations of Eº background will be possible

The physical meaning of ϰ, MA needs to be clarified

The role nuclear effects should be established

Theoretical progress has to be incorporated in the MC

Documents

Neutrino-induced quasielastic scattering