Why Cross Sections Are Important

1411

Neutrino oscillation experiments measure the charged-current and neutral-current event

1412

rates in their detectors, which can generically be expressed as

1413

R(�x) =

process�

i

target�

j

Φ(E_ν)×σ_i(E_ν,�x)×�(�x)×T_j×P(ν_A→ν_B) (4.1)

where R(�x) is the total event rate for all processes as a function of the reconstructed

1414

kinematic variables�x,Φ_ν(E_ν) is the neutrinoflux as a function of the neutrino energy

1415

E_ν,σ_iis the neutrino cross section for a particular interaction process,�is the detection

1416

efficiency and T_j is the number of target nuclei in the detector fiducial volume for

1417

target type j. It is obvious from this equation that in order to measure the neutrino

1418

oscillation probability P(ν_A → ν_B), the unoscillated flux must be well measured, the

1419

neutrino cross section must be known, and the detector efficiency must be understood.

1420

Any assumptions in the neutrino oscillation model must also be well tested. If any

1421

of these components is not well modelled, the final oscillation measurement may be

1422

biased. Large uncertainties on any of these components will limit the sensitivity of an

1423

experiment.

1424

In reality, not all interaction processes are signal for each experiment, the other

pro-1425

cesses become backgrounds, which must be taken into account if they can mimic the

1426

signal in the detector. For T2K, the dominant interaction process is Charged-Current

1427

Quasi-Elastic scattering (CCQE), as shown in Fig. 4.1. Although this implies that

1428

CCQE is the most important process for the T2K oscillation analysis, there are

signif-1429

icant contributions from resonant pion production (RES) and deep inelastic scattering

1430

(DIS), which have to be well modelled as these will produce significant contributions.

1431

Note that Fig. 4.1 shows the cross sections divided by the neutrino energy, so the cross

1432

section for the tail of the T2K flux is significantly larger than at the peak.

(GeV)

CCQE-like CC RES CC INC CCQE CC DIS T2K flux

(a) νµ–¹²C (/Eν)

4 ^CCQE-like_CCQE ^{CC RES}_{CC DIS} ^{CC INC}_{T2K flux}

(b) ν¯µ–¹²C (/Eν)

Figure 4.1: NEUT v5.3.3 νµ and νµ cross-section predictions after NIWG 2014 tuning (Section 6.4.1), divided by neutrino energy for both neutrino mode and anti-neutrino mode running.

1433

4.1.1 What Can Be Measured

1434

In Eq. (4.1), σ_i(E_ν,�x) is the contribution from the ith interaction process. Examples

1435

of interaction processes on nucleons are:

1436

• Charged-Current Quasi-Elastic (CCQE):

1437

(ν–⁾

l +n(p)→l⁻⁽⁺⁾+p(n) (4.2)

• Neutral-Current Singleπ⁰ (NC1π⁰):

1438

(ν–⁾

l +n, p→⁽ν–⁾

l +n, p+π⁰ (4.3)

Unfortunately, we do not observe interaction processes on nucleons. Instead, we can

1439

only see final state topologies on nuclear targets. After a neutrino interacts inside

1440

a nucleus, the particles produced at the vertex have to propagate through the dense

1441

nuclear medium, where many (if not the majority) outgoing hadrons will re-interact

1442

(“final state interactions” or “FSI”). So instead of CCQE events, all we can observe

1443

are events with a topology of a single charged lepton, and no pions and any number

1444

of nucleons (CC0π). However, in the case of a charged-current inclusive analysis, i.e.

1445

considering all the charged-current interaction processes rather than an exclusive one,

1446

detecting the presence of a muon is an unquestionable signature (production of

lepton-1447

pairs in thefinal state is very unlikely at the T2K flux).

1448

The cross-section terms which enter into Eq. (4.1), σi(Eν,�x), for oscillation

ex-1449

periments are a function of true kinematic variables, and the neutrino energy.

Un-1450

fortunately, we cannot reconstruct the neutrino energy or other quantities like four

1451

momentum transfer,Q², on an event by event basis. The available observables are only

1452

thefinal state particle kinematics, smeared by the detector resolution; the relationship

1453

to true quantities is an assumption of our underlying simulation.

1454

So we cannot measure the cross section, σ_i(E_ν,�x), for the ith interaction process

1455

as is required for oscillation analyses. Instead, we measure some topology-based cross

1456

section�σ_k, which is integrated over the T2Kflux, as a function of some outgoing particle

1457

whereσi is the contribution of true interaction processi to thefinal state topologyk.

1459

Theorists and other users of the data (for example the T2K’s Neutrino Interactions

1460

Working Group [143]) want to compare and constrain their σ_i(E_ν,�x) with data from

1461

�

σ_k(�x). Because of the complexity of that comparison, they need a lot of data, ideally

1462

from multiple experiments. What the cross-section community most desperately lacks

1463

at the moment is high quality data free of model-dependence. Without new data, it

1464

will not be possible to develop new interaction models (σ_i(E_ν,�x)) or parametrise

cross-1465

section uncertainties well enough to make high precision measurements of oscillation

1466

parameters (Eq. (4.1)).

1467

4.1.2 Reconstructed Energy from Lepton Kinematics

1468

In Section 4.1.1 we stated that the true neutrino energy cannot be reconstructed on

1469

a event by event basis. In general, the energy can be reconstructed in two ways:

1470

calorimetrically or kinematically. For a calorimetric reconstruction, all the involved

1471

particles should be fully contained in the detector, which is not the case for ND280.

1472

For a kinematic reconstruction, angles and momenta of all the particles produced in the

1473

neutrino-nucleon interaction should be known, but even in a 100 % efficient detector,

1474

we can only measure those observables after they get possibly modified by the final

1475

state interactions, as explained in Section 4.1.1.

1476

Nevertheless, in the case of a CCQE process (Eq. (4.2)), the only outgoing particle

1477

is a lepton, which being a minimum ionising particle, it is assumed not to interact

1478

before exiting the nucleus, i.e. it is unaffected by FSI. Therefore, for a CCQE process

1479

from aν_µ, the true neutrino energy can be easily found knowing the muon momentum

1480

p_µ and the angle θ_µ between the directions of the incoming neutrino and the outgoing

1481

the neutron, the proton and the muon respectively;V is the binding energy (in MeV);

1484

E_µ is the energy of the muon, i.e. �

p²_µ+m²_µ.

1485

However, we can only select a sample of CC0π events rather than of CCQE events,

1486

again because of the final state interactions, as explained in Section 4.1.1. Since the

1487

CCQE processes are dominant in a CC0πselection, and even in a CC-inclusive selection

1488

below 1 GeV (Fig. 4.1), in these cases the distribution of a quantity defined in the

1489

Even if E_QE(p_µ, cosθ_µ) does not correspond to the true neutrino energy (except

1492

for CCQE processes), it can always be interpreted simply as a function of the muon

1493

kinematics, thus model-independent, also on a event-by-event basis. With respect to

1494

pµ, EQE(pµ, cosθµ) is more sensitive to the detector smearing, thus also to model

dis-1495

crepancies, as a reconstruction shift is more likely to be washed out in p_µ than in

1496

E_QE(p_µ, cosθ_µ). IndeedE_QE(p_µ, cosθ_µ) is related to theflux shape, which is very

sen-1497

sitive to the beam geometry. Furthermore,E_QE(p_µ, cosθ_µ) has the advantage of having

1498

less migrations among bins in the smearing matrix, which helps the unfolding to resolve

1499

the detector smearing (Section 7.1). Given its excellent resolution, E_QE(p_µ, cosθ_µ) is

1500

the quantity more sensitive to any shifts in the Monte Carlo simulation. Eventually,

1501

the T2K oscillation analyses at the far detector Super-Kamiokandeare performed as a

1502

function of this same quantityE_QE.

1503

For these reasons, the cross-section results presented in this thesis are performed as

1504

a function ofEQE(pµ, cosθµ).

1505

Dans le document Measurement of the water to scintillator charged-current cross-section ratio for muon neutrinos at the T2K near detector (Page 113-117)