quasielastic scattering at miniboone energies
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Quasielastic Scattering at MiniBooNE Energies. L. Alvarez-Ruso 1 , O. Buss 2 , T. Leitner 2 , U. Mosel 2. 1. U. Murcia 2. U. Giessen. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A A A. Introduction. - PowerPoint PPT PresentationTRANSCRIPT
Quasielastic Scattering at MiniBooNE Energies
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
L. Alvarez-Ruso, Universidad de Murcia NUINT09
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
But
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) ;
L. Alvarez-Ruso, Universidad de Murcia NUINT09
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
L. Alvarez-Ruso, Universidad de Murcia NUINT09
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®
q2
´F V
1 + i2M ¾®̄ q̄ F V
2 + °¹ °5FA + q¹
M °5FP
iu(p)
F V1;2(Q
2)
FA (Q2) = gA
³1+ Q2
M 2A
´ ¡ 2; FP (Q2) = 2M 2
Q2+m2¼FA (Q2)
Q2 = ¡ (k ¡ k0)2
PCAC
gA = 1:26 neutron ¯ decay MA = 1 GeV
Using PCAC and ¼-pole dominance:gA2f ¼
= f N N ¼m¼
Goldberger-Treiman
L. Alvarez-Ruso, Universidad de Murcia NUINT09
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)
L. Alvarez-Ruso, Universidad de Murcia NUINT09
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
e®
Re§ Im§
Im§ ¼0
S(p) ! ±(p2 ¡ M 2e®)
L. Alvarez-Ruso, Universidad de Murcia NUINT09
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®
gA=
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
L. Alvarez-Ruso, Universidad de Murcia NUINT09
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
m2¼
( µ¤2
¼¡ m2¼
¤2¼¡ q2
¶2 ~q2
q2 ¡ m2¼
+ g0
)
g0= 0:6 (§ 0:1)
J A®
L. Alvarez-Ruso, Universidad de Murcia NUINT09
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
But
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
L. Alvarez-Ruso, Universidad de Murcia NUINT09
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)
L. Alvarez-Ruso, Universidad de Murcia NUINT09
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
L. Alvarez-Ruso, Universidad de Murcia NUINT09
ResultsDifferential cross sections averaged over the MiniBooNE flux
L. Alvarez-Ruso, Universidad de Murcia NUINT09
ResultsDifferential cross sections averaged over the MiniBooNE flux
RPA correlations cause a considerable reduction of the c.s. at low Q2
and forward angles
L. Alvarez-Ruso, Universidad de Murcia NUINT09
ResultsCCQE + non-CCQE background (measured quantity)
non¡ CCQEtotal CCQE ¡ like
= 0:1
L. Alvarez-Ruso, Universidad de Murcia NUINT09
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
L. Alvarez-Ruso, Universidad de Murcia NUINT09
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
L. Alvarez-Ruso, Universidad de Murcia NUINT09
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
1.0
1.2
h¾i [£ 10-
38cm2]2.5
3.2
3.7
L. Alvarez-Ruso, Universidad de Murcia NUINT09
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
L. Alvarez-Ruso, Universidad de Murcia NUINT09
ConclusionsThere is (nuclear) physics beyond the naive Fermi Gas Model.
L. Alvarez-Ruso, Universidad de Murcia NUINT09
ConclusionsThere is (nuclear) physics beyond the naive Fermi Gas Model.