of Physics Neutrino Interactions
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
In these two lectures I will cover a range of topics on the interactions of neutrinos with matter, focusing on interactions in the energy range of interest to accelerator experiments (few hundred MeV - 100 GeV). Lecture 1: reviewing the fundamentals Neutrino interactions in the Standard Model Scattering from electrons, quarks, nucleons and nuclei Hadronic systems in neutrino scattering Lecture 2: contemporary topics Nuclear effects in neutrino scattering Interaction physics and oscillation experiments Frontiers in neutrino interaction physics
Introduction
The goals of this talk are the following:
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
1. To broadly describe the important physical processes necessary to understand neutrino-nucleus interactions in the few-GeV region. 2. To highlight ways in which these interaction physics topics impact oscillation measurements. 3. Identify areas of current interest in neutrino interaction physics that will be explored in upcoming experiments.
Neutrinos in the Standard Model
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Dear Radioactive Ladies and Gentlemen: I beg you to receive graciously the bearer of this letter who will report to you in detail how I have hit on a desperate was to escape from the problems of the ... continuous beta spectrum ... and the law of conservation of energy. I admit that my way out may look rather improbable at first since if the neutron (neutrino) existed it would have been seen long ago. But nothing ventured, nothing gained. ... Well, dear radioactive friends, weigh it and pass sentence! Unfortunately, I cannot appear personally in Tubingen, for I cannot get away from Zurich on account of a ball which is held here on the night of December 6-7. With best regards to you and to Mr. Baek, Your most obedient servant, W. Pauli
Before decay
After decay
n
e p
Neutrino Milestones
Do neutrinos exist? You betcha!!
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Observation confirmed (2000) DONUT Experiment
From LEP we know that N = 3
Reines and Cowan First detection 1956? (1995 Nobel Prize)
Brookhaven 2 Experiment (Lederman, Schwartz, Steinberger 1988 Nobel Prize)
For 40 years, "non-oscillation" neutrino physics was neutrino physics!
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Reines-Cowan discovery SuperK, SNO, Soudan2, and the BNL 2 experiment K2K, miniBoone, MINOS... fundamental properties fundamental properties masses and MNS matrix
1950 1960 1970 1980 1990 2000
hadronic weak currents observation of neutral currents cross sections Bubble Chambers: BNL, ANL, FNAL, CERN, Serpukhov counter experiments: CDHS, CHARM CCFR, NuTEV
structure functions (F2, F3) parton universality electroweak studies sin2(w) strange sea studies QCD measurements cross sections
Neutrinos as probes to understand matter and interactions
Neutrino Oscillations
Since the mid-90's the focus in neutrino research has shifted to the study of oscillation phenomena.
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Measuring the neutrino mixing matrix using neutrinos from the sun, atmosphere, reactors, and accelerators. Next generation experiments will be returning to some old questions!
Oscillation Experiments
Super-Kamiokande
Expt. K2K MINOS T2K NOA Dates 1998-2005 2005+ 2008+ ? E (GeV) 1 ~ 3-10 0.7 2.2
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Current/Future long baseline experiments;
Mass (kt) 50 5.4 50 20
NOA
MINOS
Fermi Theory
p J(p) J(N)
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Developed by Fermi in 1932 to describe nuclear -decay inspired by the success of "current-current" description of electromagnetic interactions:
p p n
e J(e) e
e
J(e)
M em
$ #1' = eu p " u p & 2 ) #eu e " ue %q (
(
)
(
)
MCC = G u n " u p u# " ue
(
)(
)
Extended to include other Lorentz terms (vector, axial-vector, scalar, and pseudo-scalar terms). Parity ! conserved! not Weak interactions are maximally parity violating: J " u# $ (1% $ 5 )ue
Only left-handed fermions, and right-handed anti-fermions, participate in the CC weak interaction!
(
)
!
Electroweak Theory
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
SU(2) L " U(1)Y
g sinW
introduces two coupling constants (g, e)
Electroweak unification describes electromagnetic ( exchange), charged current weak interactions (W+/W- exchange), and neutral current weak interactions (Z0 exchange).
MCC
# g &# 1 &# g ) & "% J (% 2 (% J ( $ 2 '$ MW '$ 2 '
G g2 = 2 2 8MW
The "weak" force is weak because of large MW.
!
!
Electroweak Unification
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
W/Z propagator: 1/(q2-M2) propagator: 1/q2 At large Q2, one measures the weak and electromagnetic interactions on an equal footing. Neutrino experiments are often focused on the "total (CC,NC) cross section" - despite the connection to electromagnetic interactions not a useful concept for electron scattering experiments!
Helicity, Handedness, and Chirality
Helicity: the spin component in the direction of motion
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
1#p "= 2 p
is reversed in a Lorentz boost which overtakes the particle. A good quantum number but frame-dependent. Chirality ("handedness"):
+1/2 positive helicity -1/2 negative helicity
!
1 1 " 5 ) u = uR ,L ( 2
in the massless limit the chirality operator is equal to the helicity operator. For a massive particle creation of a left-handed chiral state produces an admixture of helicity states. Typically the right-helicity contribution is of order ml/E.
!
Weak interaction (V-A) maximally violates parity, produces only left-handed neutrinos (and right handed anti-neutrinos).
Helicity and Handedness
Why do pions decay to muons and not electrons?
" + (J = 0)
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
+ (J = 1/2) !
!
!
" (J = 1/2)
2 2 2 "(# $ e) me (m# % me ) 2 = 2 & 1'10%4 2 2 "(# $ ) m (m# % m ) 2
Why is neutrino-less double-beta decay a probe of neutrino ! mass?
right-handed left-handed
B. Kayser, hep-ph/0506165
Neutrino-Electron Scattering
Consider the following processes (CC only): e e e e e e e e
e(k)
W
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
e(k')
e
W
e
e(p)
e(p')
e
e
Define some kinematic variables: q = momentum transfer = k-k' s = (CMS energy)2 = (p+k)2 = me2 + 2 me E y = inelasticity = (p q)/(p k) Q2 = 4-momentum transfer = -q2 in lab: y = (E-Ee)/E = /E = energy transfer
Neutrino-electron scattering
e e
e(k)
W
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
e e
e(k') e
e e
e e
e
W
e(p)
e(p')
( p)
e
e
In CM:
y = (1-cos)/2
e(k')
!
In CM:
e
*
(k)
*
e(p)
(p')
J=0 : M = constant
= G2s/ E(GeV)x10-41 cm2
J=1: M ~ d1-11(*)=(1-cos*)/2 = (G2s/) / 3
NC Neutrino-Electron Scattering
For NC reactions:
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
j " u# (v f $ a f # 5 )u
v f = (T3 f " 2e f sin 2 #W ) a f = T3 f
!
(k)
e
e
! (k')
Z
In this case both right and left-handed electrons can participate: LH: -1/2 + sin2W RH: sin2W
e(p)
e(p')
LL-->LL: d/dy = 2G2s/ (1/4 -sin2w + sin4w) LR-->LR: d/dy = 2G2s/ (sin4w) (1-y)2
Neutrino - Electron Scattering
1. Cross section is proportional to energy 2. LL,RR interactions are flat in y, LR,RL go as (1-y)2 3. Ratio of total cross section for LR/LL is 1/3
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
For neutrino-electron scattering: d/dy = (constant) means that d/dQ2 =(constant) also. No matter what the length scale probed by the W/Z, the electron looks the same - like a point particle!
2 Qmax
"=
s /2 Including the lepton mass in the calculation introduces a minimum Q2 ! cutoff and correction terms of the order ml2/s.
2 Qmin
# dQ2
d" 2 2 $ (Qmax % Qmin ) dQ2
s /2
ignoring masses Q2max = (pi-pf)2=s
!
!
Overview
Elastic / Quasi-elastic: p --> p n --> p Single pion production e.g. n --> p 0 Multi-pion production / DIS N --> + X Neutrino - nucleus coherent scattering A --> + A A --> 0 A
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
In the energy range of interest to upcoming Neutrino - electron scattering oscillation experiments, many processes contribute! e --> e
Neutrino-Nucleon Scattering
Start with the most general Lorentz-invariant form for the hadronic current. Eliminate "second class" currents -S,T.
n
W
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
p
enters (ml/M)2
parity-violating
e
Comparing to electron scattering:
e'
p
p point-like Dirac particle with mass M
Neutrino-Nucleon Scattering
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Form factors F(Q2) encapsulate information about the structure of the object we are scattering from. E.g. for electron scattering when we take into account the fact that the proton is not a point object but an extended object with some charge r r r r iq x 3 distribution (x), we find form factors
F( q )=
# "( x )e
d x
!
G. Giacomelli, CERN-JINR, QCD161:C15:1985.
Neutrino - Nucleon Scattering
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Since the form factors are functions of Q2 alone, comparing scattering at different beam energies but fixed Q2 gives one a way of extracting independently GE and GM (Rosenbluth separation). Conserved Vector Current (CVC): allows us to relate the vector part of the weak current to the electromagnetic current. Partially Conserved Axial Current:
2 0 " A # = f # m#
Adler's Theorem: The low Q2 behavior of the hadronic current is proportional to the current. ! Since dJ =0 for a conserved current the low Q2 behavior is dominated by the axial current.
" %2 $ ' 1 2 F(Q ) = $ ' Q2 $1+ ' MV 2 & #
MV=0.84 GeV/c2
Neutrino-Nucleon Scattering
From CVC:
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
So far, so good, but what about the axial current?
FA(Q2=0) ~ -1.26 determined from beta decay Q2 dependence can only be measured in neutrino scattering, The focus of many of the early bubble chamber experiments!
Neutrino-Nucleon Scattering
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
"dipole form"
With the dipole form there is a single parameter mA (~1 GeV/c2) that needs to be measured.
Measuring the axial vector mass
Measuring the total quasi-elastic cross section: difficult because of the large uncertainty on the normalization of the neutrino flux Measuring the shape of the Q2 distribution for quasi-elastic events.
Ideally from a light target where nuclear effects are small. More sensitive to energy scale uncertainties. Sensitive to non-QE backgrounds whose Q2 dependence is even more poorly known.
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Challenge is typically determining the efficiency and purity of a quasielastic sample, particularly in a nuclear target.
Dipole FA
(Q2)?
Bodek et al. hep-ex/0602017
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
In addition the assumption that FA(Q2) has a dipole dependence can be examined. Separation of GE, GM using new techniques (polarization transfer) disagree with the previous Rosenbluth-separated results and show large deviations from the dipole form at large Q2. Measuring the high-Q2 behavior of the axial current will be a task for future experiments.
Deep Inelastic Scattering
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
In describing Deep Inelastic Scattering we are usually interested in the inclusive cross section (summing over all final states). e.g. electron scattering with spectrometer at fixed angle measuring E'.
k' k P q W
Q2 = "q 2 # 4 EE'sin 2
$ 2
W 2 = (P + q) 2 = M 2 + 2M" # Q2
#
!
Formally:
!
A " L# W
hadronic tensor
W " =
1 $ (2# )4%(q + p & pX ) p j ' (0) X X j " (0) p 4# X
Wi (x,Q2) = Structure Functions
W " = #W1g " +
!
W2 W3 W # i$ "%& + q q" 22 ! M2 2M 2 M W W +( p q" + q p" ) 52 + i( p q" # q p" ) 6 2 M 2M
Deep Inelastic Scattering
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Measurements made at SLAC and elsewhere in the 1960's turned up several surprises:
Substantial cross section at large invariant masses Q2 dependence unlike form factors - flat ! scaling of the structure functions, I.e. W(Q2,) --> F(x)
x = Q2/(2M)
Fig. from "Deep Inelastic Scattering", Devenish and Cooper-Sarker, OUP (2004).
Exciting hadronic resonances like the (1232)
Parton model
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
These experimental results were well explained by the parton model - in particular that the partons are the spin 1/2 quarks.
If our parton carries a fraction x of the nucleons energy and momentum, then requiring on-shell (massless) quarks gives: p'2 = (xP+q)2 = 0 x = Q2/(2M)
The fact that the structure functions were functions of x alone indicates that the probability of there being a quark with momentum fraction x is independent of the scattering process (Q2). In particular for electron scattering:
F2 ( x) = " ei2 xf i ( x)
i
F2 = 2 x F1
DIS Formalism
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
QCD Factorization means that we can treat the scattering and later processes separately, they occur on very different timescales:
hard scatter: fast fragmentation: slow Justification for summing probabilities rather than amplitudes for -q scattering.
Justification for QCD factorization and other aspects of the parton model come from formal approaches, namely the operator product expansion of the hadronic tensor.
DIS and Partons
The structure functions can also be written in terms of the cross sections for absorption of different polarization states of the exchanged boson.
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Callen-Gross relation: F2 = 2xF1 (R=0)
ignoring lepton mass terms which bring in 3 additional structure functions.
Structure Function Extraction
2 d! "A GF = 2 2#x dxdQ
J. Morfin, DIS05
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
% 1 "A ( (1$ y ) 2 " A 2 "A 2 " F 2 (x,Q ) + xF 3 (x, Q ) + F 2 (x, Q 2 ) $ xF 3A (x, Q 2 ) * '2 2 & )
(
)
(
)
2 ( d! " A GF % 1 "A ( 1$ y )2 " A 2 "A 2 " = F 2 (x,Q ) $ xF 3 (x, Q ) + F 2 (x, Q 2 ) + xF 3A (x, Q 2 ) * 2 dxdQ2 2#x ' 2 & )
+ y2 FL
(
)
(
)
! x,Q ,(1" y)
(
2
2
G2 2 x #
)
Neutrino Statistical + 5% systematic Anti-Neutrino Statistical only R = Rwhitlow
X = 0.1 - 0.125 Q2 = 2 - 4 GeV2 Meant to give an impression only! Kinematic cuts in (1-y) not shown.
(1-y)2
-quark scattering
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
From our discussion of neutrino-electron scattering we found that the helicity combinations (LL,RR = q, q) are J=0 combinations with flat-y dependence, and LR,RL combinations (q, q) are J=1 combinations with (1-y)2 dependence. From weak-isospin we see that neutrinos scatter from T3=-1/2, anti-nu from T3=+1/2
d" #p G 2 s = xd(x) + xs(x)+ xu(x)(1% y) 2 dxdy $
(
) )
q contribution
d" # p G 2 s = xd(x)+ xs(x) + xu(x)(1% y) 2 dxdy $
(
(ignoring c, b,t quarks., c quark mass)
Structure Functions and PDFs
F2" ," = 2# x(Qi (x)+ Qi (x))
i
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
xF3" ," = 2# x(Qi (x)$ Qi (x))
i
Parton distributions are usually written for the proton, neutron PDFs are given by isospin symmetry: un(x)=dp(x) etc. Since we are usually scattering from targets with roughly equal numbers of neutrons and protons it is often convenient to talk about scatering from an "isoscalar" target. =(p+n)/2 For targets like iron with a neutron excess a small correction is applied to achieve this.
!
WA25 - CERN
Structure Functions
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Recall Neutrinos have the ability to directly resolve flavor of the nucleon's constituents: interacts with d, s, u, and c while interacts with u, c, d and s. Using Leading order expressions:
! F 2 " (x,Q 2) = x u + u + d + d +2s + 2c ! F 2 " (x,Q 2) = x u + u + d + d +2s+ 2c
] ] ! xF 3 " (x,Q 2 ) = x[ u + d - u - d - 2s + 2c] ! xF 3 " (x,Q 2 ) = x[ u + d - u - d +2s - 2c]
! ! F 2 - xF 3 = 2(u + d + 2c) = 2U + 4c ! ! 2 F - xF 3 = 2(u + d + 2s ) = 2U + 4s ! ! xF 3 - xF 3 = 2[(s + s ) " (c + c)] = 4s - 4c
[ [
Taking combinations of the Structure functions
Momentum distributions
It is straightforward to relate the structure functions from charged lepton and neutrino scattering. The fact that they are in good agreement justifies our earlier claims of parton universality!
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Nuclear Effects in DIS
When DIS experiments were first carried out on nuclear targets, another surprise. Despite the fact that the energy scales invoved are considerably larger than the O(10 MeV) scale associated with nuclear structure, large differences were seen in the structure functions in certain kinematic regions.
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Nuclear Effects in DIS
1.2 1.1 1 0.9 0.8
shadowing
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
EMC NMC E139 E665
Fermi motion
0.7 0.001
EMC effect
sea quark
0.01
x
0.1
valence quark
1
F2 / nucleon changes as a function of A. Measured in m/e - A not in n - A
Good reason to consider nuclear effects are DIFFERENT in n - A.
Presence of axial-vector current. SPECULATION: Much stronger shadowing for n -A but somewhat weaker "EMC" effect. Different nuclear effects for valance and sea --> different shadowing for xF3 compared to F2 . Different nuclear effects for d and u quarks.
QCD and scaling violations
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
At higher order in QCD the nucleon looks somewhat different:
Calculations of the structure functions in terms of parton distributions now are somewhat more complicated and involve the "splitting functions"
Pqq(x/y) = probability of finding a quark with momentum x within a quark with momentum y Pgq(x/y) = probability of finding a quark with momentum x within a gluon with momentum y.
QCD and scattering
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
QCD therefore predicts the Q2 evolution of the structure functions in terms of the coupling s.
Heavy quark production
Production of heavy quarks like charm requires a re-examination of the parton kinematics:
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
(q + "p) = m
2
2 c
"P
2 q 2 + 2"p q + " 2 M 2 = mc
!
!
Q +m Q +m "# = 2M$ Q2 / x 2 % mc ( Charm identified through decays " # x'1+ 2 * to +, di-muon events allow measurement of: & Q ) CKM matrix elements
mc - from threshold behavior s and sbar quark distributions
2
2 c
2
2 c
"slow rescaling" - The effects of the ~ 1 GeV charm mass are not negligible even at 100 GeV neutrino energy.
!
Coherent Scattering
Z 0 P N N
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
PCAC prediction starting from Adler's relation (q2 =0). Assumptions about the q2 dependence, and the treatment of the pion-nucleus scattering. Characterized by a small energy transfer to the nucleus, forward going .
Rein-Sehgal model: 1. 2. 3. 4. Purely axial (CC) = 2 (NC) (A) ~ A1/3 Relatively less important for increasing A
Recent K2K SciBar Result
M. Hasegawa et al. - hep-ex/0506008
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Expect 470 CC coherent events according to Rein-Sehgal Find 7.6 50.4 The measurement of the CC channel is currently a topic of some interest. NC measurements agree well with Rein-Sehgal.
Hadronization
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Hadronization
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Since charged tracks were easy to identify and could be measured with good precision in bubble chamber experiments, there have been many publications on the characteristics of hadronic systems in neutrino interactions. In a nutshell (important observables to follow): At low invariant masses, characteristics of hadronic system are dominated by phase space, charge conservation, and isospin considerations. At large (W>2 GeV/c2) invariant masses hadronic systems produced in neutrino systems are quite similar to those produced in charged lepton and hadron scattering.
Hadronization
Charged particle multiplicity: <nch> = a + b ln(W2)
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Hadronization
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Multiplicity distributions are well described by KNO scaling: Mutiplicity distributions can be described by a unversal function independent of W. Levy function: c in the range 7-9.
Hadronization
Substantial differences are seen in the fragmentation of the target and current regions of the hadronic system. CERN WA-21: Nucl.Phys.B223:269,198 3
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Fragmentation Functions
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
" Da (z)=
1 dN N dz
!
Basic Options - Rein-Seghal
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
incoherent sum of resonances in Rein-Seghal implementation. Q2 dependence not modified according to Paschos, Sakuda et al hep-ph/0408185
Nuclear Physics
Fermi motion Nuclear binding Pauli blocking
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Impulse Approximation
Identical assumption to that in the parton picture of DIS:
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
fundamental cross section for nucleon scattering
Calculable in nuclear many-body theory with some experimental input.
P(p,E) is the spectral function, the probability of removing a nucleon of momentum p from the target, leaving the spectator system with excitation energy E.
O. Benhar, Jefferson Lab workshop on Intersections of Nuclear Physics with Neutrinos and Electrons (May, 2006).
Impulse Approximation
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
O. Benhar, Jefferson Lab workshop on Intersections of Nuclear Physics with Neutrinos and Electrons (May, 2006).
INTRANUKE Tuning
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Proton transparency JLAB Hall C
HERMES hep-ph/0502072
Oscillations + Cross Sections
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
The focus of experimental neutrino physics will continue to be on mixing phenomena and fundamental questions like Majorana vs. Dirac masses and the mass hierarchy. Future high-statistics experiments will be more sensitive to uncertainties in interaction physics At the same time the new beam facilities being developed to perform these oscillation experiments (J-PARC, NuMI, CNGS) will make possible new generations of experiments dedicated to neutrino interaction physics measurements.
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
From the APS Multi-Divisional Study on the Physics of Neutrinos
Among the APS study assumptions about the current and future program:
"determination of the neutrino reaction and production cross sections required for a precise understanding of neutrino-oscillation physics and the neutrino astronomy of astrophysical and cosmological sources. Our broad and exacting program of neutrino physics is built upon precise knowledge of how neutrinos interact with matter."
NuMI Kinematic Coverage
One of the biggest challenges comes in trying to build a simulation that can cover a wide range of neutrino energies. Wide band beams expose broad kinematics. Q2 = 1 GeV2 Piecing together models that cover different kinematic regions is challenging.
10.0
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Contours are 50%, 75%, 90%, 99%
Lines of constant W
4.0 2.0 1.2
Low E Beam Kinematics
Low energy beams Kinematic exposure from a 4-vector calculation using a cartoon miniBoone flux. (a guess, for illustrative purposes only) Quasi-elastic, , gap between them of primary importance, everything is low Q2! Contours are 50%, 75%, 90%, 99%
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Q2 = 1 GeV2
10.0
Lines of constant W
4.0 2.0 1.2
Free nucleon cross sections
Previous experiments focused on 3 regimes: Quasi-elastic scattering (red) Delta Production (green) "safe DIS": Q2>1 GeV2, W>2 GeV (blue) Large fraction of events in our peak region are in the "mystery" region in terms of detailed knowledge of the kinematics. Free nucleon models: DIS low Q2 modeling resonance modeling DIS / resonance transition region
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
where the oscillation signal is!
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
Intranuclear Rescattering
Visible Energy in Calorimeter is NOT energy!
absorption, rescattering final state rest mass nuclear binding energies
(D. Harris et al., hep-ex/0410005)
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
E = E + Ehad(vis) + Emiss
"Missing energy" determined from Monte Carlo. Very dependent on detector thresholds. How to estimate the uncertainty in this aspect of the simulation? Understanding the relevance of external data. In MINOS we have been very fortunate in that a nuclear experimentalist, Steve Dytman is leading the task of improving this piece.
Example: Low Q2 suppression
Q2 distribution for SciBar detector
H. Gallagher NuFact Summer School Aug 15-16, 2006 UCLA
K2K - SciBar
One such effect is the larger than expected suppression of events at low Q2 from K2K and miniBoone. All "known" nuclear effects taken into account: Pauli suppression, Fermi Motion, Final State Interactions. Variety of explanations examined: Pauli blocking of states? Smaller than expected CC coherent contribution? Missing lepton mass terms in resonance production cross sections. (Lalakulich-Paschos,Phys.Rev.D71:074003,2005 ) Nuclear shadowing (Kopeliovich, hep-ph/0409079 ) Importance of using correct form factors (non-dipole) for MA extraction affects Q2 distribution shape (Budd, Bodek, Arrington, hep-ex/0410055). After considerable study, K2K parametrized the deficit, folded back into their MC for...