# Presentation: 892272

**L’Aquila Univ. & INFN**
**Yale - July. 11th, 2006**

- References:
-  _[http://fphy.hep.okayama-u.ac.jp/NuInt05/](http://fphy.hep.okayama-u.ac.jp/NuInt05/)__*** ***_(in printing on Nucl. Phys. B)
-  _[http://NuInt04.lngs.infn.it](http://NuInt04.lngs.infn.it/)_ (Nucl. Phys.B - Proc.Supll. 139, 2005)
-  _[http://www.ps.uci.edu/~NuInt02](http://www.ps.uci.edu/~NuInt02)_
- _[http://neutrino/kek.jp/NuInt01](http://neutrino/kek.jp/NuInt01)_*** ***(Nucl. Phys.B - Proc.Supll. 112, 2002)

**   **
**	*****Neutrino cross-sections:***
**	****	****current studies**
**	****	****and experimental programs**

**The discovery of the neutrino **_**non-standard**_** properties (mass and mixing) **
**refocused on various aspects, both theoretical and experimental,**
** ****of neutrino **_**standard**_** properties (e.g. cross-sections):**
**The ***********-Nucleus Cross-Section***** and related ****Nuclear Effects**** represents **
**(one of) the most important sources of uncertainty in the**
**“****Intermediate**** ********-Energy**** ****Range****”: ****0.5 - 5 GeV**
**of interest for the next generation oscillation studies.**
**QUESTIONS **about the neutrino cross section:
- [A] How well do we know (have we measured) it  ?
- [B] How  well do we understand it theoretically ?
- [C] How well do we need to know  it
- 	for Oscillation Studies ?
- [D] What new Experimental Programs can be most
- 	 effective to improve our Knowledge?

_**	**_

**Notes:**
Controllare SNO

## 45 systematic error terms in SK Atm- analysis 

- (T. Kajita - **NuInt05**,Sept.05)

- (0, Free parameter)  Flux, Nu-int, Fit; absolute normalization
- (1) Flux; (nu_mu + anti-nu_mu) / (nu_e + anti-nu_e) ratio ( E_nu < 5GeV )
- (2) Flux; (nu_mu + anti-nu_mu) / (nu_e + anti-nu_e) ratio ( E_nu > 5GeV )
- (3) Flux; anti-nu_e / nu_e ratio ( E_nu < 10GeV )
- (4) Flux; anti-nu_e / nu_e ratio ( E_nu > 10GeV )
- (5) Flux; anti-nu_mu / nu_mu ratio ( E_nu < 10GeV )
- (6) Flux; anti-nu_mu / nu_mu ratio ( E_nu > 10GeV )
- (7) Flux; up/down ratio
- (8) Flux; horizontal/vertical ratio
- (9) Flux; K/pi ratio
- (10) Flux; flight length of neutrinos
- (11) Flux; spectral index of primary cosmic ray above 100GeV
- (12) Flux; sample-by-sample relative normalization ( FC Multi-GeV )
- (13) Flux; sample-by-sample relative normalization ( PC + Up-stop mu )

- (25) Reduction for FC
- (26) Reduction for PC
- (27) Reduction for upward-going muon
- (28) FC/PC separation
- (29) Hadron simulation (contamination of NC in 1-ring -like)
- (30) Non- BG ( flasher for e-like )
- (31) Non- BG ( cosmic ray muon for mu-like )
- (32) Upward stopping/through-going mu separation
- (33) Ring separation
- (34) Particle identification for 1-ring samples
- (35) Particle identification for multi-ring samples
- (36) Energy calibration
- (37) Energy cut for upward stopping muon
- (38) Up/down symmetry of energy calibration
- (39) BG subtraction of up through 
- (40) BG subtraction of up stop 
- (41) Non-e contamination for multi-GeV 1-ring electron
- (42) Non-e contamination for multi-GeV multi-ring electron
- (43) Normalization of multi-GeV multi-ring electron
- (44) PC stop/through separation

- Flux (13)

-  interaction (11)

- Detector, reduction
- and reconstruction (20)

- (14) MA in QE and single-
- (15) QE models (Fermi-gas vs. Oset's)
- (16) QE cross-section
- (17) Single-meson cross-section
- (18) DIS models (GRV vs. Bodek's model)
- (19) DIS cross-section
- (20) Coherent- cross-section
- (21) NC/CC ratio
- (22) nuclear effect in 16O
- (23) pion spectrum
- (24) CC cross-section

## Neutrino  Energy of O(1 GeV): 

- -Interactions on p-n/ q-q
- in C, O, Fe, Ar, Pb,.. **Nuclei**

- Well known problem:
**Experimental Data rather poor and**
**affected by large errors**

**Neutrino  Energy of ****O****(1 GeV): **
**a natural choice for LBL **
**(precision measurements) experiments**

- X-Section Natural Decompositions:
******tot**** = ********Q-El  ******** ********Res**** ******** ********DIS**
**      ****	****        ****= ********0 ******** ******** ********1 ******** ******** ********2 ******** ******** ...**

##   [Q-El] Quasi-Elastic Scattering on free N

**Dynamics described by Current-Current ****L****agrangian**
**J ****had**** = ****V - A****  defined through ****Nucleon Weak Form Factors****:**
**V****ector F.F. [F****V****1****(Q****2****), F****V****2****(Q****2****)], related to **_**El.M.**_** F.F. ****(**_**Hp. CVC**_**),**
**A****xial F.F. [F****A****(Q****2****)] and PseudoScalar F.F. [F****PS****(Q****2****)] **
_**Note:**_** Vector F.F. can be (are) determined from **_**e**__**-scattering exp**_**.**
**            ****Axial F.F.  ****	****	****	****     (assumed dipolar form) with**** *****M******A *****free parameter**
**                 ****PseudoScalar F.F. term in Xsect is proportional to ****(****m****l****/M****p****)****2**
**	****i.e.**** ****relevant only for ********l ****= **********

- J lept

- J had

**G**

_**Q-el scattering on **__**N**__** **__***bound***__** **__**in A**_**:  the rise of ****Nuclear Effects**** **
**      ****(i.e. non-perturbative effects of strong interactions inside the target)**
**	******** ****Absence of a well defined model**

**  ****[********Q****-****E****l****] **_**Quasi-Elastic Scattering on **__***free***__** N**_
**  ****(low Q****2****, x=1, W=M****p****):****  **
**	****	**l  + n  l- + p

## 	 [Res] Resonance Excitation

- mass of hadronic final  state

**E******

******3/2**

**N ****1/2**

**M****p**

**	**** ****[********Res****] Resonance Excitation**
**  ****(low Q****2****, large x, W):  **l  + N  l- + l- + n + N’

**From theoretical point of view:**** the Most complicated channel.**
**	****E.g.: (FKR) ****N = 3q**** system bound by harmonic potential in ground state**
**********, ****N********* corresponds to excited states, decaying with ******** production**
**	****Each decay channel results from superposition and interference between**
**	****	****allowed resonance amplitude [Rein & Seghal, .... ].**
_**If **__***N***__** **__***bound***__** **__**in A**_**  Nuclear Effects, final state (re)interactions are even more severe. **
**From experimental point of view: ****the least precisely measured channel**

## [DIS](Deep) Inelastic Interactions

**Dynamics described by SM (massive W****±****)**
**J ****had**** defined through Nucleon Structure Functions:                        **
**Precise high-Q****2**** DIS data available**
**(from *****e-N*****  and v*****-N*****  experiments)**
**Limited Impact of Nuclear Effects but..**
**How to connect RES and low-Q****2**** DIS**
**  ****regimes still unclear (“twilight zone”)**
**Note: ****F****4**** and F****5** **in Xsect proportional to ****(****m****l****2****/M****N****)**** ****i.e.**** ****relevant only for ********l ****= **********

**[********DIS****]****(Deep) Inelastic Interactions**
**	****[x ******** (0,1), large Q****2****]**   	       l  + N  l- + X

## Overall goals: 

***Overall goals*****:**** **
**	****describe all three processes (****Q-E****l** **, RES, DIS****) for ****both ****e**** ****and**** ********at all energies **
****** **
**	****progress in modeling Nuclear Effects beyond RF-gas model**

**	****A new challenge - in the Intermediate-energy region -**

- Current **sparkling activity in **
**the theoretical field**
- of
- the ****-A interaction:

-  Nuclear Models and Nuclear Effects:
-  Random Phase Approximation
- Nuclear Many Body Theory
- Relativistic Shell-Model
- Nucleon Form Factors:
-  new parameterizations [BBA2003 => BBBA2005]
-  Strange F.F.
** **Q-El : new Xsect calculations
-  mass terms correction (mn-mp, **m****l** , rad.corr., ..)
-  tau polarization
- RES:
-  Nucleon and Pion re-scattering in Nuclear Matter
-  tau production
- DIS: PDF - from high-Q2 DIS data to low-Q2 to describe low-energy ****-data:
-  RES-to-DIS transition (quark-hadron duality)
- X-sect at NLO perturb. QCD
- PDF modification

- ... and the list is NOT complete ...

## Probability of removing a nucleon 

- Probability of removing a nucleon
- of momentum ***k*** leaving the residual system
- with excitation energy **E **
**NMBT**** calculation**:
- N-N and 3 N correlations are included
- in both Initial and Final State

**NMBT**** :****	****Nuclear Spectral Function SF(*****k*****,E)**
** ****	****e-A scattering =  ******** ********(e-N)******** ****SF****    [****Benhar *****et  al*****.]**
**	****	****where ********(e-N)**** is the ****e-free *****N*****   Xsect (*****IA***** -*****Impulse Approx*****.) and**
**	****	****  ****SF=P (*****k***** ,E)**** is the nuclear ****Spectral Fcn****. from ****N****uclear ****M****any ****B****ody ****T****h.**

**SF’s from NMBT (for light Nuclei) successfully **
**used in the analysis of A(*****e,e’*****) data**
**and extended to ****16****O(********,****l****); ********=********e****, ************[****Q-E****l** **]**

- “Spectral function for Argon” now available !! (A. Ankowski)

## SF

- IA+SF

- RFG

- IA+SF+FSI

- E**** = 1 GeV

***w.r.t. RFG*** (standard ****-MC):
-  Xsect suppression at low-Q2 in agreement with recent ****-data !! (see next slides)
-  Quenching in final lepton Energy distribution, fundamental for future ****-experiments
- 	aiming at 1% or better precision !!
-  Fin. State Interaction is 10% effect: need of quantitative validation from new exp. ****-data

- Benhar & Coll.

**SF**

**SF+FSI**

**RFG**

- H. Nakamura,Sakuda, Seki

- + 16O  +X

##  New -Data

- Active beams (intermediate ****-Energy): **KEK** (Japan), **FNAL-MiniBooNE** (US)

-  Beam - Mean ****-Energy: 700 MeV; 0.5% ******e** contamination
-  Detector - 800 t Mineral Oil, Cherenkov + dlyd Scint. Light
-  60,000 CC Q-El evts collected

-  **MiniBooNE:**

**CC Q-El:**   **Q****2**** distr**.                                     **E********distr**.

**Notes:**
Add miniboone

## Future Measurements: a new dedicated challenge in the Intermediate energy region: 

_**Future Measurements**_**:**** ****a new dedicated challenge in the Intermediate energy region: **

## Slide 13

## Detector Requirements:

**Detector Requirements:**

## Slide 15

## Slide 16

## ... nothing else to do???

- The fundamental properties of -interactions
- have been probed  by ***bubble-chamber experiments***

- BEBC -
- Bubble Chamber - 30 t - CERN 1976

- ICARUS - T600
- Electronic Bubble Chamber - PAVIA 2001

**LAr technology is the modern version of **
**(electronic)  bubble-chamber concept ...**

## T600

- 158 MeV

- 752 MeV

-  = 141o

- Minv = 650 MeV

- Run 975, Event 151

- Minv =140 MeV

- Collection view

-  = 25o

- 140 MeV

-  Reconstruction of -showers and
- 0 identification

- (error evaluation in progress)

_**high resolution calorimetry**_** and **
**	****(virtually) unlimited active mass **

******0**** candidate**

**... ****with additional**

## K+

**A**

**B**

**C**

**D**

***K+***

**μ+**

***e+***

- μ+

***T*****P **** ****> 40 MeV (range > 2 cm)**

- T600

- Run 939 Event 46

- 50 lt-prototype

****

**p**

****

****

****

_**Muon and hadron Identification**_

_** **__**interaction**__ _
-    (with p-recoil reconstruction
-           down to ***T*****P **** ****> 40 MeV**)

## 50 lt-prototype

-  Quasi-elastic EVENT

-  DIS EVENT

**Precise measurement of Event kinematics**
**full 3D Reconstruction**

## Precise -Ar Cross Sections (and associated A=40 nuclear effects) is a necessary

- preliminary step toward future application of LAr-technology in
- precise -oscillation experiments

- So far******-Ar** interactions have (only) been studied with the **ICARUS 50-lt prototype**
- exposed to the WANF (high energy) -beam.
***A dedicated paper (from recent re-analysis of data collected in ‘97) is ready for ***
***publication (based on ******86 selected quasi-elastic “golden events******”). ***
- Dedicated ***high statistics*** measurements in the intermediate energy range would be
- highly envisaged. An intense off-axis -beam, such as **at a near location on **
**the NuMI beamline, would be ideal for this task.**
**The ICARUS LAr-TPC technology fulfills all possible experimental requirements**
** ****for precise Cross Section Measurements**

**Possibility of using a ****O****(100 t)-LAr detector at a near location on the NuMI beamline**
**will be discussed later at this Workshop**

## Back-up slides

## 	Nuclear Models:

-      nuclear response (e.g. NN correlations);***Nuclear Shell Model***  is effective in this energy range (up to  A ≈60).

- _when ____ Energy increases_ (reactions sensitive to Giant-Res. Strength), Random Phase Approximation methods
-    (***RPA and CRPA***) have been developed  to describe the collective excitations of the Nucleus
-    (1p-1h excitations of the correlated   ground-state)

-  _**At  intermediate **__****__** Energy**__ _ individual (quasi-free) Nucleons are off scattered and
- the remaining (A-1) nucleons can be treated as “spectators”.
***Form Factors***  have to be suitably determined and parameterized(from e-N and -N experiments).
***Fermi Gas model *** is effective (depending on parameters - Fermi Momentum and
- Binding Energy - to be determined from e-scattering exp.s)
-  ... but other more sophisticated models (***NMB Th***.) can be adopted.

**	****Nuclear Models:**

## RES Cross Section:

**RES Cross Section:**

## 			The twilight zone

- The  challenge:
***Understanding of RES scattering in terms of quark-parton Model***,
-      i.e. understanding high **x** **PDF’s** at very **low-Q****2**
- Different methods under study, e.g.:
- 1) Effective LO approach[Bodek, Yang]:
- Use “effective L.O. PDFs”  with a new scaling variable
-  	(**x****Bj**  w) to  absorb target mass,
- 	higher twist, missing higher orders
-  Good results for DIS *p,d(e,e’)*  F2 SF.
-  Axial Low-Q2 PDF’s also available, but need to compare
- 	to Low-energy ****-data to get exact parameter

## Conclusion/Perspectives in-physics: 

**NOW**
- recognized as a well established, necessary step toward a
**second generation oscillation experiments.**
**********beams in the FeW-GeV energy range are (and other soon will be) available in Japan and US.****  **
** ****First important results from running experiments start to come out**** **
** ****Proposals for ****dedicated**** ****experiments are submitted/approved.**** **

_**Conclusion/Perspectives in**__****__**-physics:**_
-  unprecedented  richness with a wide spectrum of   ******-** beams
- available or approved for the next decade of experiments.

**The ****NuInt**** ****community, ****with the important contribution from (e,e’) people,**
**has favored  all this and  will certainly continue to play a significant role in the field.**