Quasielastic Scattering at MiniBooNE Energies

transcript

L. Alvarez-Ruso1, O. Buss2, T. Leitner2, U. Mosel2

1. U. Murcia 2. U. Giessen

L. Alvarez-Ruso, Universidad de Murcia NUINT09

IntroductionMiniBooNE has collected the largest sample of low energy º¹ CCQE events to date. Aguilar-Arevalo et. al., PRL 100 (2008) 032301

Mineral Oil: CH2

º flux

CCQE is relevant for oscillation experimentsCCQE is interesting by itself:

Axial form factor of the nucleon (MA)

Nuclear correlations

< Eº > ~ 750 MeV

IntroductionThe shape of hd¾/dcosµ¹dE¹i is accurately described by a Global Fermi Gas Model Smith, Moniz, NPB 43 (1972) 605 with: EB = 34 MeV, pF = 220 MeV

MA = 1.23 § 0.20 GeV

consistent with MA = 1.2 § 0.12 GeV (K2K)

higher than MA = 1.01 § 0.01 GeV ( BBBA07)

MA = 1.05 § 0.08 GeV (mainly 12C, 3-100 GeV, NOMAD)

E minp = ·

µqM 2 + p2

F ¡ ! + EB

¶; · = 1:019§ 0:011

ºd; ¹ºp;(e;e0¼) ;

The modelOur aim: realistic description of CCQE in nuclei

compare to MiniBooNE data (modified Smith-Moniz ansatz)Relevant hadronic degrees of freedom: ¼, N, ¢(1232)

Ingredients: Elementary process Fermi motion Pauli blocking Nuclear bindingNucleon spectral functionsMedium polarization (RPA)

and also Non CCQE background (cannot be separated from CCQE in a model independent way)

º¹ n ! ¹ ¡ p

The modelElementary amplitude for

where and

BBBA07

º¹ (k) n(p) ! ¹ ¡ (k0) p(p0)

M =GF cosµCp

2l®J ®

l® = ¹u(k0)°®(1¡ °5)u(k)

J ® = ¹u(p0)h³

°®¡ q=q®

1 + i2M ¾®̄ q̄ F V

2 + °¹ °5FA + q¹

M °5FP

F V1;2(Q

FA (Q2) = gA

³1+ Q2

´ ¡ 2; FP (Q2) = 2M 2

Q2+m2¼FA (Q2)

Q2 = ¡ (k ¡ k0)2

gA = 1:26 neutron ¯ decay MA = 1 GeV

Using PCAC and ¼-pole dominance:gA2f ¼

= f N N ¼m¼

Goldberger-Treiman

The modelLocal Fermi Gas

pF (r) = [32¼2½(r)]1=3

Fermi Motion of initial nucleons: f (~r;~p) = £(pF (r) ¡ j~pj)

Pauli blocking of final nucleons:

PPauli = 1¡ £(pF (r) ¡ j~pj)

Mean field potential Density and momentum dependentParameters fixed in p-Nucleus scattering Teis et. al., Z. Phys. A 346 (1997) 421

Nucleons acquire effective masses Me® = M + U(~r;~p)

The modelSpectral functions

The momentum distribution of a nucleon with 4-momentum p is

For final nucleons (above the Fermi sea)

is obtained from with a dispersion relation assuming that at the pole position:

For initial nucleons (holes) we take

S(p) = ¡1¼

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

§ nucleon selfenergy

Im§ = ¡p

(p2)¡ coll(p;r) ; ¡ coll = h¾N N vrel icollisionalbroadening GiBUU

p(pole)0 =

q~p2 + M 2

Re§ Im§

Im§ ¼0

S(p) ! ±(p2 ¡ M 2e®)

The modelRPA nuclear 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®

11+ g0Â0

Â0 dipole susceptibility

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

(gA )e®

gA» 0:9Wilkinson, NPA 209 (1973) 470

The modelRPA nuclear correlations

Following 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

( µ¤2

¼¡ m2¼

¤2¼¡ q2

¶2 ~q2

q2 ¡ m2¼

g0= 0:6 (§ 0:1)

The modelRPA nuclear 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

Incorporates explicitly ¼ and ½ exchange and ¢-hole states

Can be inserted in a unified framework to study QE, 1¼, N-knockout, etc

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 at MiniBooNE energies

The modelNon CCQE background (GiBUU transport model)

Most relevant processes:

Details in the talk by Tina Leitner

º¹ N ! ¹ ¡ ¢

¢ N ! N N

¢ ! N ¼ ¼N N ! N N

followed by (¼ less decay mode)

or by and then (¼ absorption)

ResultsComparison to inclusive electron scattering data

Missing strength in the deep region: more complete many-body dynamics required Gil et. al., NPA 627 (1997)

543 RPA less relevant than in the weak case

ResultsDifferential cross sections averaged over the MiniBooNE flux

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

and forward angles

ResultsCCQE + non-CCQE background (measured quantity)

non¡ CCQEtotal CCQE ¡ like

ResultsComparison to the modified Smith-Moniz ansatz (shape)

The effect of RPA brings the shape of the Q2 distribution closer to experiment keeping MA = 1 GeV

All curves are normalized

to the same area

ResultsChanging g’ = 0.5-0.7

Leaves the shape unaltered

Small changes in the integrated cross section h¾i =3.1-3.4 £ 10-38 cm2

ResultsChanging MA

The experimental shape is better described with MA=1 GeV

There are large differences in the integrated cross section

MA [GeV] 0.8

h¾i [£ 10-

38cm2]2.5

ConclusionsWe have developed a model for CCQE starting form a Local Fermi Gas but incorporating important many body corrections: nucleon spectral functions, medium polarization (RPA).RPA: strong reduction at low q2 (quenching) Good description of the shape of the MiniBooNE q2 distribution with MA=1 GeV

A larger integrated CCQE cross section would require MA>1 GeV

ConclusionsThere is (nuclear) physics beyond the naive Fermi Gas Model.

Quasielastic Scattering at MiniBooNE Energies

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