Neutrino-induced quasielastic scattering

Neutrino-induced quasielastic scattering

Luis Alvarez-Ruso

Neutrino-induced quasielastic scattering from a theoretical perspective

Luis Alvarez-Ruso

Outline

Motivation

º scattering on the nucleon Quasielastic scattering models

Experimental status and comparison to data Conclusions

Motivation

º

Oscillation experiments

º oscillations are well established ))

Goal: Precise determination of oscillation parameters: ¢m²ij, µij, ±

º are massive flavors are mixed 0

@ º_e º_¹ º_¿

1

A = V 0

@ º₁ º₂ º₃

1 A

V = 0

@ 1 0 0

0 cosµ₂₃ sinµ₂₃ 0 ¡ sinµ₂₃ cosµ₂₃

1 A

0

@ cosµ₁₃ 0 sinµ₁₃e^{¡ i ±}

0 1 0

¡ sinµ₁₃e^{i ±} 0 cosµ₁₃

1 A

0

@ cosµ₁₂ sinµ₁₂ 0

¡ sinµ₁₂ cosµ₁₂ 0

0 0 1

1 A

Motivation

º

Oscillation experiments

Precision measurements of ¢m232, µ23 in º_¹ 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)

º_¹ n ! ¹ ^¡ p

E

= 2m

E

¡ m

¡ m

+ m

2(m

¡ E

+ p

cosµ

)

exact only for free nucleons wrong for CCQE-like events

P (º

! º

) = sin

2µ

sin

¢ m

L

2 E

Motivation

º

Oscillation experiments

Precision measurements of ¢m232, µ23 in º_¹ disappearance

Understanding Eº reconstruction is critical

Kinematical determination of Eº in a CCQE event

Rejecting CCQE-like events relies on accurate knowledge of nuclear

º_¹ n ! ¹ ^¡ p

E

= 2m

E

¡ m

¡ m

+ m

2(m

¡ E

+ p

cosµ

)

exact only for free nucleons wrong for CCQE-like events

P (º

! º

) = sin

2µ

sin

¢ m

L 2 E

GENIE E_º = 1 GeV

Motivation

º

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 G_sA):

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.

º_¹ (p;n) ! º_¹ (p;n)

Motivation

º

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

º scattering on the nucleon

The (CC) elementary process:

where

Vector form factors:

Extracted from e-p, e-d data

º

(k) n (p) ! ¹

(k

) p (p

)

M = G_F cosµ_C

p 2 l^®J _®

l

= ¹u(k

)°

(1¡ °

)u(k)

J _®= ¹u(p⁰)

·

°_®F₁^V + i

2M ¾_®¯ q^¯ F₂^V + °_¹ °₅F_A + q_¹

M °₅F_P

¸

u(p)

F

= F

¡ F

G

= F

+ q

2m

F

G

= F

+ F

à electric ff

à magnetic ff

º scattering on the nucleon

At low Q²:

M_V = 0.71 GeV, G_E/G_M ¼ 1/¹p

At high Q²:

½(r) = ½₀e^{¡ r =r0} ) G_E (Q²) = G_E (0) µ

1+ Q² M_V²

¶_{¡ 2}

Bodek et al., EPJC 53 (2008)

º scattering on the nucleon

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)

º

(k) n (p) ! ¹

(k

) p (p

)

M = G_F cosµ_C

p 2 l^®J _®

l

= ¹u(k

)°

(1¡ °

)u(k)

J _®= ¹u(p⁰)

·

°_®F₁^V + i

2M ¾_®¯ q^¯ F₂^V + °_¹ °₅F_A + q_¹

M °₅F_P

¸

u(p)

F_A(Q²) = g_A µ

1+ Q² M_A²

¶_{¡ 2}

; F_P (Q²) = 2M ²

Q² + m²_¼F_A(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 Approximation Fermi motion

Pauli blocking

Average binding energy

Explains the main features of the inclusive cross sections in the QE region f (~r; ~p) = £ (p_F ¡ j~pj)

P_{P auli} = 1¡ £ (p_F ¡ j~pj) E =

q

~

p² + m²_N ¡ ²_B

Ankowski@NuInt09

QE scattering models

Inclusive electron-nucleus scattering

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

However

GFG overestimates the longitudinal response R_L

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

QE scattering models

Inclusive electron-nucleus scattering

Spectral functions of nucleons in nuclei The nucleon propagator can be cast as

S_h(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! S

(! ;~ p)

p

¡ ! ¡ i´ + Z

d! S

(! ;~ p) p

¡ ! ¡ i´

S

(p) = ¡ 1

¼

Im § (p)

[p

¡ M

¡ Re § (p)]

+ [Im § (p)]

QE scattering models

Inclusive electron-nucleus scattering

Spectral functions of nucleons in nuclei Hole spectral function:

80-90 % of nucleons occupy shell model states

The rest take part in the NN interactions (correlations); located at high momentum

n(~ p) = R

d! S

(! ;~ p)

Meloni@NuInt09

Benhar et al., PRD 72 (2005)

Ankwowski & Sobczyk, PRC 77 (2008)

QE scattering models

Inclusive electron-nucleus scattering

Spectral functions of nucleons in nuclei Hole spectral function:

80-90 % of nucleons occupy shell model states

The rest take part in the NN interactions (correlations); located at high momentum

Particle spectral functions

Optical potential: U = V – i W V ~ 25 MeV Ã fitted to p-A data W:

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

QE scattering models

Inclusive electron-nucleus scattering

Spectral functions of nucleons in nuclei: Results Ankowski@NuInt09

40Ca

QE scattering models

Inclusive electron-nucleus scattering

Spectral functions of nucleons in nuclei: Results Ankowski@NuInt09

40Ca

Inclusive electron-nucleus scattering

Spectral functions in a Local Fermi Gas Leitner et al., PRC 79 (2009)

Space-momentum correlations absent in the GFG OK for medium/heavy nuclei

Microscopic many-body effects are tractable

Can be extended to exclusive reactions: (e,e’ N), (e,e’ ¼), etc

QE scattering models

p

(r) = [

¼

½(r)]

Inclusive electron-nucleus scattering

Spectral functions in a Local Fermi Gas Leitner et al., PRC 79 (2009)

Space-momentum correlations absent in the GFG OK for medium/heavy nuclei

Microscopic many-body effects are tractable

QE scattering models

p

(r) = [

¼

½(r)]

Inclusive electron-nucleus scattering

Spectral functions in a Local Fermi Gas

Mean field potential

Density and momentum dependent

Parameters fixed in p-Nucleus scattering Nucleons acquire effective masses

QE scattering models

M

= M + U(~ r;~ p)

Inclusive electron-nucleus scattering

Spectral functions in a Local Fermi Gas

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

QE scattering models

Im § ¼0

Gil, Nieves, Oset, NPA627 Ciofi degli Atti et al.,PRC41

Im § = ¡ p

(p

)¡ (p;r) ; ¡ = h¾ v i

p^(pole)₀ = q

~

p² + M_e®²

QE scattering models

Inclusive electron-nucleus scattering

Spectral functions in a Local Fermi Gas:

Results Leitner et al., PRC 79 (2009)

QE scattering models

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

Important for

º

QE scattering models

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 g_A :

The quenching of g_A in Gamow-Teller ¯ decay is well established

(g

)

g

= 1 1+ g

Â

Â₀ dipole susceptibility

g’ Lorentz-Lorenz factor ~1/3

Ericson, Weise, Pions in Nuclei

(g

)

g

» 0:9

QE scattering models

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

In particular

V

= ~ ¿

~ ¿

¾

¾

[^ q

q ^

V

(q) + (±

¡ ^ q

q ^

)V

(q)]+ g~ ¾

~ ¾

+ f

~ ¿

~ ¿

+ f I

I

V_L = f_{N N ¼}² m²_¼

( µ ¤²_¼¡ m²_¼

¤²_¼¡ q²

¶₂

~ q²

q² ¡ m²_¼ + g⁰ )

QE scattering models

RPA long range correlations

RPA approach built up with single-particle states in a Fermi sea Simplified vs. some theoretical models (e.g. continuum RPA)

Applies to inclusive processes; not suitable for transitions to discrete states

But

Incorporates explicitly

¼

½

Has been successfully applied to

¼

°

¹

Nieves et. al. PRC 70 (2004) 055503

Important at low Q² for CCQE at MiniBooNE energies

QE scattering models

RPA long range correlations

Comparison to inclusive electron-nucleus data LAR@NuInt09

QE scattering models

RPA long range correlations

CCQE on ¹²C averaged over the MiniBooNE flux LAR et al., arXiv:0909.5123

QE scattering models

RPA long range correlations

CCQE on ¹²C averaged over the MiniBooNE flux LAR et al., arXiv:0909.5123

QE scattering models

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

Has been used to study 1N knockout

Problem: nucleon absorption that reduces the c.s.

Complex optical potential

QE scattering models

Relativistic mean field

RPWIA RPWIA RDWIA RDWIA RPWIA RPWIA RDWIA RDWIA Giusti et al., arXiv:0910.1045

QE scattering models

Relativistic mean field

Impulse Approximation

Initial nucleon in a bound state (shell); no correlations ªi : Dirac eq. in a mean field potential (!-¾ model) Final nucleon

PWIA

DWIA: 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

QE scattering models

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

QE scattering models

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

16O(e,e’)X

QE scattering models

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

First kind scaling:

F (! ;j~ qj) =

d d!d¾

Z¾

+ N ¾

F = F (Ã

(! ;j~ qj))

)

12C

QE scattering models

(Super)scaling

First kind scaling:

Second kind scaling: independent of A First + Second scaling = Superscaling

F (! ;j~ qj) =

d d!d¾

Z¾

+ N ¾

F = F (Ã

(! ;j~ qj)) f (Ã

) = p

F (Ã

)

Ã’ < 0 scaling region Ã’ > 0 scaling violation

QE scattering models

(Super)scaling

Scaling violations reside mainly in the transverse channel

QE scattering models

(Super)scaling

The experimental superscaling function (fit using R_L data)

Constraint for nuclear models Relativistic Fermi Gas

Exact superscaling Wrong shape of f(Ã’)

QE scattering models

(Super)scaling

The experimental superscaling function (fit using R_L data)

Constrain for nuclear models

Relativistic mean field describes the asymmetric shape of f(Ã’)

QE scattering models

(Super)scaling

Superscaling in the ¢ region

Experimental superscaling function

At Ã’¢ > 0 other resonances, etc contribute

QE scattering models

(Super)scaling

Superscaling Analysis SUSA

Calculate with Relativistic Fermi Gas Replace f_RFG ! f_exp

QE scattering models

(Super)scaling

Superscaling Analysis SUSA

Calculate with Relativistic Fermi Gas Replace f_RFG ! f_exp

QE scattering models

(Super)scaling

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

Calculate with Relativistic Fermi Gas Replace f_RFG ! f_exp

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 (< E_º > ~ 750 MeV) º_¹ CCQE events to date.

Aguilar-Arevalo et. al., PRL 100 (2008) 032301

The shape of hd¾/dcosµ_¹dE_¹i is accurately described by the Relativistic Global Fermi Gas Model with: E_B = 34 MeV, p_F = 220 MeV

But

ϰ=1.007 § 0.007 M_A=1.35 § 0.17 GeV

Large ¾ compared to GFG with M_A=1 GeV

E_p^min = ·

µq

M ² + p²_F ¡ ! + E_B

¶

Experimental status

However:

The physical meaning of ϰ is obscure

ϰ, M_A 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 E_º reconstruction (unfolding)

Experimental status

However:

The physical meaning of ϰ is obscure

ϰ, M_A 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 E_º reconstruction (unfolding)

Better compare to:

Katori, arXiv:0909.1996

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) samples From measured CCQE ¾ : MA = 1.05 § 0.02(stat) § 0.06(sys) GeV

Consistent with M_A extracted from Q² shape fit of 2-track sample

MiniBooNE vs NOMAD

Katori, arXiv:0909.1996

Interpretation

M_A > 1 GeV?

M_A 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 (m_¼ =0) Using models to connect with data )

M_Aep= 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

M_A = M_Aep - ¢MA , ¢MA =0.055 GeV ) MA = 1.014 GeV E₀₊^{(¡ )}(q²) =

r

1¡ k² 4M ²

e 8¼f_¼

½

F_A(q²) + g_Aq²

4M ² ¡ 2q²G^V_M (q²)

¾

2 2 3 µ

12¶

2 12

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 M_A = 1 GeV

LAR, Leitner, Buss, Mosel, arXiv:0909.5123

Can CCQE nuclear models explain the size of MiniBooNE ¾?

Interpretation

Sobczyk@NuInt09

Katori, arXiv:0909.1996

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 E_º background will be possible

The physical meaning of ϰ, M_A needs to be clarified The role nuclear effects should be established

Theoretical progress has to be incorporated in the MC