Alysia Marino, University of Colorado Boulder NA61/SHINE Beyond 2020 Workshop University of Geneva July 27, 2017 OUTLINE

OVERVIEW OF HADRON PRODUCTION MEASUREMENTS FOR NEUTRINO EXPERIMENTS

➤ Why hadron production measurements? ➤ In Situ Flux Measurement Strategies ➤ Overview of external data in various momentum ranges ➤ Data below 18 GeV/c ➤ Around 31 GeV/c ➤ Around 60-160 GeV/c ➤ What more is needed?

2 WHY DO WE NEED HADRON PRODUCTION MEASUREMENTS?

➤ Important to understand neutrino source when making measurements using neutrinos for measurements of ﬂavor oscillation and neutrino interaction physics ➤ For atmospheric neutrinos and accelerator-based neutrino sources the processes leading to neutrino production are complex and often not very well-modeled by MC T2K NEUTRINO FLUX PREDICTION PHYSICAL REVIEW D 87, 012001 (2013)

Data: 17 mrad bin 400 1.6 2.8 Fit: 17 mrad bin + An example of hadron Data: 57 mrad bin NA61 π (a)Weights/MC NA61 π+ Weights 1.4 2.6 Fit: 57 mrad bin 300 production predictions for T2KData: 107 mrad bin 2.4 Fit: 107 mrad bin 1.2 at left. Data disagrees with MC 2.2 (mrad) 200 π by 30% or more in some θ Weight 1 Al/Be regions.R 2 100 0.8 1.8

0 0.6 1.6 0510 15 20 3 p (GeV/c) Phys1.4 Rev D 87 012001 (2013) π 468 10 12 14 16 18 p (GeV/c) 400 1.6 FIG. 17. Examples of the material scaling exponent ﬁt for a - (b) NA61 π Weights 1.4 few angular bins in the [27] Kþ data. 300 1.2 The differential production weight that is applied to a

(mrad) 200 given simulated interaction that produces hadrons is the π Weight θ 1 ratio of the production in data and simulation: 100 0.8 dn ;p ;A ½dp ð in Þdata W pin;A dn : (4) ð Þ¼ ;pin;A MC 0 0.6 dp 0 5 10 15 20 ½ ð Þ p (GeV/c) For interactions of 31 GeV=c protons on carbon that pro- π duce or K in the phase space covered by the NA61/ 300 Æ þ 1.6 SHINE data, the construction of the ratio in Eq. (4) is + (c) NA61 K Weights straightforward since the differential production data pro- 1.4 vided is already in the form in Eq. (3), at the correct beam 200 momentum, and on the correct target material. The weights 1.2 applied to differential production in FLUKA simulated

(mrad) interactions are shown in Fig. 16. K Weight

θ 1 100 The reweighting of tertiary pion production from nucleon interactions requires extrapolations from the NA61/ 0.8 SHINE data to lower incident nucleon momentum and other target materials, since tertiary production can happen 0 0.6 0 2 4 6 8 in interactions within the horns (aluminum). Tertiary pions p (GeV/c) can also be produced in the interactions of secondary K neutrons, in which case data for the isospin symmetric FIG. 16 (color online). The differential production weights reaction (p C X for n C X) are þ ! Æ þ þ ! Ç þ from NA61/SHINE data for þ (top), À (middle) and used to calculate weights. The same invariance is assumed Kþ (bottom). for interactions on the Al nuclei, although the isospin invariance of the nucleus is slightly broken. 2. Hadron differential production reweighting The scaling of differential production rates to different incident nucleon momenta is carried out assuming Feynman The differential production reweighting is evaluated scaling [41]. The Feynman variable, xF, is defined as using the differential multiplicity in the momentum, p, of pL the produced particle and its angle, , relative to the xF ; (5) ¼ pL max incident particle: ð Þ TABLE XIII. Parameters for material scaling. dn 1 d ;p ;A ;p ;A : (3) dp ð in Þ¼ p ;A dp ð in Þ abc d e prodð in Þ Bonesini et al. [42] 0.74 0:55 0.26 0.98 0.21 Fit to data 0.75 À0:52 0.23 1.0 (fixed) 0.21 The cross section p ;A depends on the incident À prodð in Þ Fit to K data 0.77 0:32 0.0 1.0 (fixed) 0.25 particle momentum, pin, and target nucleus, A. À

012001-15 CURRENT AND FUTURE ACCELERATOR-GENERATED NEUTRINO BEAMS

➤ Initiated by protons with energies from 8 GeV to 120 GeV ➤ Previously CNGS beamline ran with 400 GeV protons

Icarus SBND MicroBooNE BNB 8 GeV p NuMI J-PARC ν 120 GeV p 30 GeV p LBNF beam NOvA T2K to SURF Minerva HyperK (proposed) 60-120 GeV p 4 DUNE Beamline Experiment T2K NEUTRINO FLUX PREDICTION PHYSICAL REVIEW D 87, 012001 (2013) direction of SK or a randomly chosen point in the near The hadrons are labeled as secondary hadrons if they are detector planes. The neutrino energy in the center of mass produced in interactions of the original protons, and frame is assigned based on the decay kinematics. The neu- tertiary hadrons if they are produced by interactions of trino is then boosted into the laboratory frame under the hadrons other than the original proton. The breakdown of assumption that it points towards the desired detector, and the predicted flux for a given flavor by the final hadron in the probability of production in the selected direction is the interaction chain is shown in Table X. The e and e stored as an event weight. In addition to this probability, originating from secondary or tertiary pions are from sub- the neutrino flavor, energy and ancestors’ truth information sequent muon decays. A significant fraction of the fluxes are stored. The neutrino flux spectrum is obtained by weight- come from tertiary pions and kaons, so it is important to ing each event with the stored probability. For neutrinos investigate hadron interaction data at both the T2K beam produced with energy less than 4 GeV, the storage of events momentum and for lower momentum hadrons. is prescaled (and event weights are adjusted accordingly) to allow for sufficient statistics in the high energy tail of the flux 1. Data used for hadronic interaction reweighting prediction without producing prohibitively large file sets. The pion and kaon differential production measurements used for obtaining the T2K flux predictions are summa- C. The simulation of hadronic interactions rized in Table XI. As discussed in Sec. IVA, the hadronic interactions in To predict the neutrino flux, T2K relies primarily on the the target are modeled with FLUKA2008. Outside of the measurements of pion [11] and kaon [12] yields by the target, where GEANT3 controls the simulation, interac- NA61/SHINE experiment at the CERN SPS. These data tions are modeled with GCALOR. The chain of hadronic were taken with a thin (2 cm) graphite target and the same interactions for each simulated event producing a neutrino proton beam energy as that of T2K. The results are based on is saved, and reweighted based on hadron interaction mea- the data collected in 2007 during a first, limited statistics, surements is applied to the simulated events. run with about 6:7 105 registered events. An additional The hadron interaction data used are thin target data, data set, taken with theÂ target removed, was used to account described in Sec. IV C 1, that include measurements of for the contamination by particles produced in interactions inelastic cross sections and differential hadron production. of the proton beam occurring outside the target. Unlike the case of the thin target measurements, particles Charged particles are identified by using the measure- traversing the T2K target encounter a significant amount of ment of the specific energy loss (dE=dx) and of the time material and can undergo multiple interactions. In addition of flight (ToF). The combined information of ToF and particles can also interact with the material outside the dE=dx is needed in the 1–4 GeV=c momentum range target. A step-by-step reweighting procedure is therefore where different particle species have similar values for applied to the hadronic interaction chain in each event. their specific energy loss. A calibration of the mean The weights are applied to the following: dE=dx as a function of the momentum with an accuracy 0 (1) differential production of Æ, KÆ and KL in the of 0.1% was required to limit the systematics on the interactions of protons on the target materials particle identification at the level of 1%. (Sec. IV C 2). Charged pion differential production cross sections were (2) interaction rates for p, Æ and KÆ that affect the measured as a function of the pion laboratory momentum in rate of interactions that produce hadrons, as well as 10 intervals of the pion laboratory polar angle relative to the the attenuation of hadrons that may decay to pro- proton beam direction, covering the range from 0 to 420 mrad. NEUTRINO PRODUCTION duce a neutrino (Sec. IV C 3). The considered momenta range from 0:2GeV=c up to 19:6GeV=c depending on the polar angle is illustrated in TABLE X. The fraction of the neutrino flux by the final hadron Fig. 15.Formomentaaboveabout7:5GeV=c alowerlimiton in the interactionNeutrino chain after Parents hadron interaction in T2K reweighting is the polar angle is set by the limited detector acceptance in applied. the forward region. The experimental errors, dominated by the Flux percentage of each (all) flavor(s) systematic uncertainties, are discussed in Sec. VA1. Parent e e TABLE XI. Differential hadron production data relevant for Secondary + the T2K neutrino flux predictions. p π Æ 60.0(55.6)% 41.8(2.5)% 31.9(0.4)% 2.8(0.0)% p KÆ 4.0(3.7)% 4.3(0.3)% 26.9(0.3)% 11.3(0.0)% Beam momentum 0 Experiment (GeV=c) Target Particles KL 0.1(0.1)% 0.9(0.1)% 7.6(0.1)% 49.0(0.1)% Tertiary p NA61/SHINE [11,12] 31 C Æ, Kþ + + 34.4(31.9)% 50.0(3.0)% 20.4(0.2)% 6.6(0.0)% target π π Æ Eichten et al. [27] 24 Be, Al, ... p, Æ, KÆ KÆ 1.4(1.3)% 2.6(0.2)% 10.0(0.1)% 8.8(0.0)% Allaby et al. [28] 19.2 Be, Al, ... p, Æ, KÆ K0 horn L 0.0(0.0)% 0.4(0.1)% 3.2(0.0)% 21.3(0.0)% BNL-E910 [29] 6.4–17.5 Be Æ Phys Rev D 87 012001 (2013)

012001-13 ➤ Secondary and tertiary interactions are also often signiﬁcant, so ideally want not just primary proton data, but also thick target data and lower energy hadron data to constrain reinteractions

5 HADRON PRODUCTION MEASUREMENT STRATEGIES

➤ In Situ measurements ➤ Several strategies have been employed in accelerator- generated neutrino beams ➤ Can involve very challenging detector environment! ➤ External hadron production measurements ➤ Useful for both accelerator-generated neutrino beams and atmospheric neutrinos ➤ Data on thin target and replica targets

6 16

TABLE III: Contributions to the uncertainty in the far-to-near flux ratio prediction. The uncertainties are quoted in %. The six columns refer to different bins in neutrino energy, as shown in the table in units of GeV. Source 0.0−0.5 0.5−1.0 1.0−1.5 1.5−2.0 2.0−2.5 2.5− Hadron interactions Primary interaction rate 0.3 0.9 0.9 2.1 0.2 0.3 π+ mult.andkinematics 0.7 2.0 1.8 2.1 2.9 4.7 Kaon multiplicity 0.1 <0.1 0.1 <0.1 0.1 4.9 Secondary interactions 0.3 1.2 2.0 2.1 0.4 0.7 Horn magnetic field Field strength 1.1 0.8 1.4 4.2 2.8 3.9 Field homogeneity 0.3 0.2 0.5 0.3 0.6 0.3 Primary beam optics Beam centering 0.1 <0.1 <0.1 <0.1 0.1 0.1 Beam aiming 0.1 <0.1 <0.1 0.1 0.4 0.2 Beam spread 0.1 0.7 1.7 3.4 1.0 3.2 IN SITU MEASUREMENTS - HADRON DETECTOR INTotal BEAMLINE 1.4 2.7 3.6 6.5 4.28.5

2750 To decay ◦ volume angle with respect to beam direction is 30 .

Pion monitor Top view Spherical 150 An array of 20 PMTs (modiﬁed R5600-01Q made by ➤ Gas volume mirror Hamamatsu Corporation) is set 3 m away from the beam Can be a very high rate, very high ~ Design on May 11,’98 ~ 14

900 center to avoid excess exposure to radiation. The size of Al foil experiment at CERN as input to the pion production 2448 the PMT outer socket is 15.5 mm in diameter and the radiation environment 470 230 200 Focal length 3464mm simulation. The HARP experiment precisely measured 0.5 190 sensitive area of the photocathode is 8 mm in diame- Beam window the positively-charged pion production in the interactions 910 ter. They are arranged vertically at 35 mm intervals. of 12.9 GeV/c protons in a thin aluminum target [16]. 2100 From The array can be moved by a half pitch of the inter- ➤ 0.4 2nd Horn Example: PIMONThe HARP experimentin K2K took data in 2001 and 2002 in val along the array, and hence 40 data points (one point the CERN PS T9 beamline, in order to study in a sys- 275 for every 1.75 cm) are taken for a Cherenkov light dis- tematic and accurate way hadron production for a vari- 0.3 Beam view 332 ety of produced hadrons (pions and kaons in particular) tribution. The relative gain among 20 PMTs was cal- ➤ 200 with large phase space coverage. Data were taken as a (arbitrary units) Photo detector ibrated using Xe lamp before the measurements. The Cherenkov detector after horns 0.2 20 PMTs function of incident beam particle type (protons, pions), ND gain ratio between neighboring PMTs was also checked Φ beam momentum (from 1.5 to 15 GeV/c), nuclear tar- 910 using Cherenkov photons during the run. The error on

0.1 600 get material (from hydrogen to lead), and nuclear target the relative gain calibration is estimated to be 10% for ➤ thickness (from 2% to more than 100% hadronic inter- Mom limited >2 GeV/c, since 110 the June 1999 run and 5% for the November 1999 run. action length fraction). Secondary tracks are efficiently 0 14 reconstructed in the HARP forward spectrometer via a 0123 Saturation of the PMTs was observed in the June 1999 below thisset ofuninteracted drift chambers located upstream primary and downstream E (GeV) run, which was corrected by a second order polynomial experiment at CERN as input to the pion production FIG. 12:Phys. A schematic Rev. view D 74, of the 072003 pion monitorν (2006) (PIMON). with respect to a dipole magnet. Particle identification The PIMON0.5 consists of a gas vessel, a spherical mirror, and an function. The uncertainty due to this correction was es- simulation.for The forward HARP tracks experiment is obtained precisely with a time-of-flight measured sys- 0.5 array of 20 photomultiplierHARP Measurement tubes. The gas vessel is filled with timated to be 4% [10]. protonsthe positively-charged aretem, aabove Cherenkov pion threshold production Cherenkov detector, in the and interaction an electromag- s freon gas R-318Pion (C Monitor4F8). A wedge-shaped spherical mirror is netic calorimeter. 0.4 The gas vessel is filled with freon gas R-318 (C4F8). of 12.9 GeV/c protons in a thin aluminum target [16]. set inside the gasCho-CERN vessel Compilation and Cherenkov light produced by the 0.4 Its refractive index n is varied by changing the gas The HARPIn experiment particular, the took recent data HARP in 2001 pion and production 2002 in mea- pions in the beam, represented by the concentric circles in the thresholdsurement [16] is directly relevant for the K2K F/N flux the CERN PS T9 beamline, in order to study in a sys- figure,0.3 is reflected by the mirror and directed to the array of pressure using the external gas system. The data are ratio because it is obtained for the same proton beam taken at several refractive indices ranging between n = tematic andmomentum accurate way(12.9 hadron GeV/c)andnucleartargetmaterial production for a vari- photo-multiplier0.3 tubes which is set in the focal plane. (arbitrary units) 1.00024 1.00242 to make PIMON sensitive to different ➤ ety of produced(aluminum) hadrons as (pions those used and to kaons produce in particular) the K2K neu- 0.2 For Eν from 1-2.5 GeV, SK pion momenta.− The refractive index was not adjusted Φ with large phasetrino beam. space Moreover, coverage. beam Data MC were simulations taken show as a that (arbitrary units) 0.2 beyond n =1.00242 since the primary protons also emit function ofthe incident forward beam pion productionparticle type region (protons, measured pions), in HARP, ND 0.1 constrainedbeam momentum30 < θnearπ (from< 210 mrad,1.5 flux to 0. 1575

trino beam.minum, Moreover, while secondary beam MC hadronic simulations interactions show are that deﬁned Φ uncertainty of about 30% is assumed for the uncertainty the forwardto pion be hadronic production interactions region that measured are not primary in HARP, ones. In the following, the assumptions on systematic uncertain- in the0.1 proton-aluminum hadronic interaction length. The 30 < θπ < ties210 a mrad,ﬀecting 0 neutrino.75

➤ In Situ measurements are the best option to reduce systematics associated with interactions outside the target, and to reduce uncertainties due to focusing and alignment ➤ But very high rates! ➤ Ideally you’d like a few protons per spill, or perhaps up to one proton per RF bucket ➤ Still at least 9 orders of magnitude below normal beam intensity ➤ Also very high radiation means that data must be taken at start of run and detectors will not likely survive for repeat measurements with replacement or upgraded targets and horns

8 EXTERNAL MEASUREMENTS

➤ Will summarize external data to predict ﬂuxes in accelerator- generated neutrino beams and atmospheric neutrinos ➤ Existing data mostly has primary momenta in the range of 9 GeV/c to 450 GeV/c ➤ Will focus on the available external data here. Subsequent talks will provide examples of how this data is used and their needs ➤ NuMI Flux Prediction needs for NOvA and Minerva - See L. Aliaga’s talks ➤ T2K and HyperK Fluxes - See talks from M. Wascko, F. Di Lodovico, M. Hartz, K. Sakashita, M. Friend, M. Pavin ➤ DUNE - See L. Fields’ talk

9 SCALING OF HADRON PRODUCTION ABOVE ~30 GEV

d3 ➤ E Feynman argued that invariant cross section ( d 3 p ) should be more or less constant with pT and xF, where xF =2pL⇤ /ps 20➤ Others have M. Bonesini scaled et al.: by On particlex R production= E⇤/E for highmax⇤ energy neutrino beams

3 2

) 10 ) 10 2 2

/GeV + /GeV + 3 π 3 K From Eur. Phys. J. C 20, 10 2 10 (mb c (mb c 3 3 13 (2001) /dp /dp σ σ 3 3

E d 10 E d 1

-1 1 10 Dashed = fit to 400 and 450 GeV p + Be data

-1 -2 10 10 scaled in pT and xR

Fig. 5. Comparison between the pro- -2 17 mrad -3 Points = data for 24 10 10 57 mrad posed parameterization of NA56/SPY 87 mrad GeV[6] and NA20p + [4] Be data interactions (dotted line) and the one-pion (left) and one-kaon (right) 127 mrad -3 -4 inclusive invariant cross sections in pBe 10 10 0 5 10 15 20 0 5 10 15 20 interactions at 24 GeV as measured by p (GeV/c) p (GeV/c) Lab Lab [29] 10

100 GeV/c protons on carbon target [7], where the ex- y = 1 log((E + p )/(E p )) is the rapidity of the pro- 2 L − L trapolation from Be to C has been made using formulae duced particle and ymax is the maximum rapidity kine- (9) and (10). As discussed above xR = E∗/Emax∗ has been matically available to that particle, has also been tried. used as scaling variable. The agreement between pion data At variance with the previuos longitudinal variables, ∆y shown in the figure and our empirical parameterization is is Lorentz invariant and scales the phase space at differ- excellent up to about x 0.8. A good agreement is also ent centre-of-mass energies independently of the reference found when kaon data are∼ considered, although the preci- frame. Although we find a somewhat improved agreement sion of kaon data from [7] is poorer. to data in this case, scaling to data collected with 24 Figure 5 shows a comparison of our parameterization GeV/c protons is only approximate even with this vari- with one-particle inclusive production data measured with able. 24 GeV/c protons hitting a Beryllium target [29]. In that Still, in the centre-of-mass energy range of interest for work, Lorentz invariant particle densities ω(pLab, θ) were present high-energy neutrino beams, the agreement be- measured as a function of the particle momentum pLab tween our parameterization scaled according to xR and and production angle θ. These data have been converted the data is satisfactory. into invariant cross sections using the relation

d3σ 1 4.3 Yields from finite length targets E = σ ω(p , θ) (11) × dp3 2 abs Lab With reference to (1), the differential particle production where σabs is the absorption cross section for pBe [31]. along the target can be parameterized as: A reasonable agreement is observed in the shape of the distributions for π+ and K+, although the estimated pro- dY (E,p ,z) N ρλ p3 d3σ T = 0 p E f(z) (12) duction of π+ is about 35 15% lower than that mea- dz A E ! × dp3 " sured. This is also true for± negative pions, not displayed in the figure, while the agreement is somewhat worse for where f(z)dz is the probability that the outgoing particle the other particles. be produced at a depth z to z + dz inside the target and Given its general interest, we have tested the scaling the other quantities have been introduced in Sect. 2.1. hypothesis on the same data also using xF and xLab = In general f(z) will also depend on the production an- p/pinc, the latter defined as the ratio of the momentum gle of the secondary particle [16]. In the naive reabsorption of the detected particle in the laboratory reference frame model introduced in Sect. 2.1, one has: to the momentum of the incoming proton, as longitudi- 1 z/λ z′(z,θ)/λ nal variables. A better agreement with π± data is ob- f(z,θ)= e− p e− s (13) tained, if xLab is used, which however shows a worse agree- λp ment to kaon data3. The variable ∆y = y y, where max − which can be obtained by differentiating the target effi- 3 All the variables are off roughly by the same amount in the ciency F (L) of (2), with z′(z,θ) representing the target description of the K/π production ratio length that the produced hadron has to cross to escape M. Bonesini et al.: On particle production for high energy neutrino beams 19

) 10 ) 2 x = 0.30 2 x = 0.30 Lab + Lab - xLab = 0.40 π xLab = 0.40 π

/GeV x = 0.50 /GeV x = 0.50

3 Lab 3 Lab xLab = 0.60 xLab = 0.60 xLab = 0.70 xLab = 0.70 x = 0.80 x = 0.80 (mb c Lab (mb c 10 Lab 3 3 xLab = 0.88 xLab = 0.88 17 /dp /dp σ σ 3 3 10 A. Pion productionE d data parametrization E d TABLE III: Sanford-Wang parameters and errors obtained by fitting the π+ (π−)datasets.Theerrors refer1 to the 68.27% confidence level for eleven pa- At low energies, it is common to use the empir- rameters (∆χ2 =12.6) for π+ and nine parameters ical data parametrization for pion production in 2 − (∆χ =10.4) for π . 17 proton-nucleus interactions1 originally developed by Sanford and Wang [29]. This parametrization has A. Pion production data parametrization -1 the functional form: 10 TABLE III: Sanford-Wang+ parameters and− errors ob- Parameter +π − π tained by fitting the π (π )datasets.TheerrorsFig. 4. Comparison between the pro- ± ± refer toc the1 68.27%(381 confidence.3 40.5) level (307 for.posed6 eleven19 parameterization.4) pa- of NA56/SPY 2 At low± energies, it is common to use the empir- rameters (∆χ2 =12.6) for π+ and nine parameters d σ(pA → π X) -1 p c (0.88 ± 0.07) (0.57[6]± and0.06) NA20 [4] data (line) and the ical data parametrizationc2 for pion production in 2 2 − 10= c1 exp[B]p (1 − ) , (∆χ =10.4) for π . one-pion inclusive invariant cross sec- dpdproton-nucleusΩ interactions originallypbeam developed by c3 (9.16 ± 0.95) (27.36 ± 1.06) -2 tions in pC interactions at 100 GeV as Sanford and Wang [29]. This parametrization(2) has 10 ± ± 0 0.2 0.4 0.6 0c4 0.2(1. 0.438 0.09) 0.6 (1.86measured0.04) by [7]. Positive (negative) pi- the functional form: p (GeV/c) + p (GeV/c) − where: T Parameterc5 (1.66π± 0.T12) (2.23πons± are0.04) shown in the left (right) panel M. Bonesini et al.: On particle production for high energy neutrino beams 19 c1 (381.3 ± 40.5) (307.6 ± 19.4) c6 (3.62 ± 0.14) (3.04 ± 0.08) 2 ± d σc4(pA → π X) p c (0.88 ± 0.07) (0.57 ± 0.06) p c2 2 ± 0 2 and neutral kaon= c1 exp[ productionB]p c(18 − is always) , estimated fromc7 (8) α(0has.05 been0.04) clearly observed - in K and Λ production by ) 10 ) − − − ± ± S 2 2 B = c3 dpdΩc6θ(p c7p cos θ)(3)p c3 (9.16 0.95) (27.36 1.06) x = 0.30 x = 0.30 c5 beam beam Lab + Lab in the- following. Skubic et± al. [26]. A suitable representation of the whole x = 0.40 x = 0.40 p c8 (128.6 61.8) - Lab π Lab beam π (2) c4 (1.38 ± 0.09) (1.86 ± 0.04)

/GeV x = 0.50 /GeV x = 0.50

3 Lab 3 Lab set of data can be obtained with the parameterization: x = 0.60 x = 0.60 where: α0 (0.69 ± 0.04) (0.72 ± 0.04) Lab Lab c5 (1.66 ± 0.12) (2.23 ± 0.04) xLab = 0.70 xLab = 0.70 x = 0.80 Xx denotes= 0.80 any system of other particles in the 2 2 (mb c Lab (mb c 10 Lab α1c6 (α−(3(0x..6291)± =±0 (0.014).21).74 (3 (0−..04551.±36x0±.08)+00.20).26 x ) (0.98+0.21 p ) (10) 3 3 F F F T xLab = 0.88 xLab = 0.88 4 Particle production for neutrino beams ﬁnal state, p is thec4 proton beam momen- − · · · ·

/dp /dp beam p c8 c7 (0.05 ±± 0.04) - ± σ σ α2 (0.34 0.21) (2.18 0.21)

3 3 B = −c − c θ(p − c±p cos θ)(3) tum in GeV/c, p and3 c5 θ are6 the π 7 beammomentum where the xF dependence is taken from the fit of Barton 10 4.1 Scalingp to targets of different materials c8 (128.6 ± 61.8) - E d E d beam and angle in units of GeV/c and radians, re- et al. at pT =0.3 GeV/c and the pT dependence is fitted α0 (0.69 ± 0.04) (0.72 ± 0.04) spectively, Xd2denotesσ/(Berylliumdpd anyΩ)isexpressedinunitsof system targets of have other been particles used in in most the neutrino beams to Skubic et al. data and normalized in such a way that it what can beα1 accommodated(−0.91 ± 0.21) within (−1.36 ± the0.20) Sanford- 1 final state,derivedp fromis proton the proton beams beam extracted momen- from the Super Pro- reduces to the parameterization of Barton et al. at pT = mb/(GeV/c)/sr and thebeam parameters c1,...,c8 are α (0.34 ± 0.21) (2.18 ± 0.21) tum inton GeV Synchrotron/c, p and θ (SPS)are the at CERN,π± momentum but theWang use of formula, graphite2 where0.3 GeV/c. this ratio is given by g(θ)= obtained from fits to the meson production data. c8 and angleas target in units material of GeV seems/c and promising radians, in re- viewexp[ of− operationc6θ(p − pc)], withIn conclusion,pc ≡ c7pbeam a conservativecos θ. estimate of the uncer- 1 spectively,withd short2σ/(dpd spillsΩ)isexpressedinunitsof in fast extracted proton beams. In partic- tainty in the extrapolation from beryllium to carbon data The parameter c1 is an overall normalization fac- what can be accommodated within the Sanford- mb/(GeVular,/c)/sr the use and of the a graphite parameters targetc1,...,c is foreseen8 are The in the overall design fit of maysits (in be the usedpT asrange a fast of interest approxima- for neutrino beams: up to -1 Wang formula, where this ratio is given by g(θ)= 10 tor, the four parameters c2,c3,c4,c5 describe the 17 600 MeV/c) around 5%, on the top of a measurement obtainedboth from the fits CNGS to the and meson the production NuMI beams data. [1,2].tion Prescriptions of HARP data valid within a factorc8 2–3 of the momentum distribution of the secondary pions in exp[−c6θ(p − pc∼)], with pc ≡ c7pbeam cos θ. to rescale theFig. inclusive 4. Comparison invariant between cross-sections thequoted pro- to di experimentalfferent error errors. of 5–10%, The depending best-fit valueson the secondary of momentum, A. Pion production data parametrizationthe forwardThe direction, parameter andc1 is the anposed overall three parameterization normalization parameters of NA56/SPY fac- for the cross sections on beryllium. The estimate of this TABLEtarget III: Sanford-Wang materials are parameters given in the and following. errors ob-theThe parameters overall fit are may reported be used as in a Table fast approxima- III together -1 tor, the four parameters[6] andc2,c NA203,c4,c [4]5 describe data3 (line)hA the and the systematic uncertainty is based both on data collected by 10 c6,c7,c8 describe theThe corrections invariant+ cross to− the sections pionE mo-d σ for hadron-nucleustion of HARP data valid within a factor 2–3 of the tainedmomentum by fitting distribution the one-pionπ of(π the)datasets.Theerrors inclusive secondary invariant pionsdp3 cross in with sec- their errors.Barton The fit et parameter al. [7] and errors on the are extensive esti- compilation of J. -2 mentum distribution for pion production angles quoted experimental errors.2 The2 best-fit2 values of refer tointeractions the 68.27% ( confidencehAtions in hpC′Xinteractions level) depend for eleven on at 100 the GeVpa- massmated as number by requiringA ∆χ ≡ χ −χ =12.6(10.4), At low energies, it is common to use10 the empir- A SCALINGthe forward2 direction, and the+± three parameters Kuhn on nuclear dependencemin for pA π−X interactions 0 0.2 0.4 0.6 that0 are 0.2 dirametersfferent 0.4of ( from∆ theχ 0.6 target=12 zero..6) nucleusmeasured The for!→ππ via byand [7].production parameterizations Positivenine parameters (negative) of pi-the the parameters type: are reported in Table III together → p (GeV/c) c6,c27,c8 describep (GeV/c)− the corrections to the pion mo- corresponding to[30]. the 68.27% confidence level re- ical data parametrization forT pion production in (∆χ =10.4)T for π . ons are shown in the left (right) panelwith their errors. The fit parameter errors are esti- data on solidmentum targets distribution reported for here pion have production beenα fit- angles proton-nucleus interactions originally developed by ➤ From BMPT: d3σhA1 A d3σhAgion2 mated for eleven by requiring (nine)∆χ variable2 ≡ χ2−χ parameters.2 =12.6(10 Signif-.4), ted simultaneouslythat are di tofferent the empirical fromE zero. Sanford-Wang The= π±1 productionE . (9) min Sanford and Wang [29]. This parametrization has 2 dp3 !0 A " · dp3icantcorresponding correlations to among the 68.27% fit parameters confidence level are found, re- and neutral kaon production is always estimatedformula. from (8) Indataα thehas onχ been solidminimization, clearly targets observed reported the in full hereKS errorand have2 Λ ma- beenproduction fit- by 4.2 Scaling to different centre of mass energies the functional form: + − as showngion for by eleven the (nine) correlation variable matrix parameters. given Signif- in Ta- in the following. trix was used.tedSkubic simultaneouslyParameter et al. [26]. A to suitable theπ empirical representation Sanford-Wangπ of the whole ➤ In accordance2 with the scaling hypothesis,blesicantα IVhas and correlations been V. among fit parameters are found, formula.Scalesset of dataas In ca canpower the beχ (381 obtainedminimization,law.3 of± degree40 with.5) the (307 theα which parameterization: full.6 ± error19 depends.4) ma- on xF, pT found1 to be weakly dependent on the incidentas beam shown mo- by theThe correlation NuMI neutrino matrix beam given atin Ta-FNAL is planned to be de- d2σ(pA → π±X) p To go fromtrix a baseline was used.c nuclear(0.88 targets± 0.07) (typically2 (0.57 ± 0 Be).06) 2 rived from a primary proton beam of 120 GeV/c momen- 4 Particle production= c exp[ forB neutrino]pc2 (1 − beams) , α(xF )mentum. = (02 .74 It0.55 dependsxF +0.26 onx theF ) (0 incident.98+0.21 hadronpT )To (10) typebles showh IVand the and it trend V. of the Sanford-Wang global fit 1 to another nuclear target− A,acorrectionfactor· ± · · ± · tum, resulting in a centre-of-mass energy about two times dpdΩ pbeam To go fromis ac3 smooth a baseline(9 function.16 nuclear0.95) of targetspT (27and. (typically36xF 1of.06) the Be) producedof all HARP hadron. datasets, figure 12 reports the com- 4.1 Scaling to targets of different materials ➤ Atwhere lower the energiesxF dependence HARP isdata taken (Phys.Rev. from the C80 fit of (2009) BartonTo 035208 show the ) trendsmaller of the than Sanford-Wang that available global at NA56/SPY fit and NA20. Be- (2) to anotherIt hasc4 nuclear moreover(1 target.38 been± A0.,acorrectionfactor09) experimentally (1.86 ± 0.04) observed that, in first et al. at pT =0.3 GeV/c andα the pT dependence is fittedparison,of all HARP at 8 GeV/c datasets,sides and its figure general 12 GeV/c, 12 interest, reports between the a test com- of pion the scaling hypothesis of where: has showncorrapproximation, that=(A/A for theBe± it )Sanford-Wang is independent± parameterization(4) of the detected a particle Beryllium targets have been used in most neutrino beams to Skubicc et5 al. data(1. and66 normalized0.12) (2. in23 such0.04) a way that it type, with perhaps the exceptionα of anti-protonsproductionparison, [7]. at data 8 GeV/cone-particle and the and above 12 GeV/c,inclusive parametrization. between invariant pion cross-sections is thus rel- derived from proton beams extracted from the Super Pro- correctionreduces toc6 theof parameterization corr (3 . 62=( ± A/A 0 . 14) Be ) of (3 Barton .where04 ± 0 et. 08) al.(4) at pT = 2 production dataevant and the to assess above parametrization. the range of validity of the proposed pa- c4 was introduced,0.3 GeV/c. withAα parameterization= α + α × x of+α αas× a functionx of xF has been ton Synchrotronp (SPS) at CERN, but the use of graphite c7 (00.05 ± 10.04)F 2 - F For the 8.9 GeV/c MiniBooNE/SciBooNE beam- B = −c − c θ(p − c p cosc8 θ)(3) proposed by Barton et al. on the basis2 of their and pre- rameterization. This has been studied by comparing our as target material3 c5 seems6 promising7 beam in view of operation wasIn introduced, conclusion, with a conservativeα = α0 + α1 estimate× xF + α of2 × thexF uncer-For the 8.9 GeV/c MiniBooNE/SciBooNE beam- p where xF is the Feynmanc x,(128 see.6 ± references+61.8) [10] - - and line and the 12.9parameterisation GeV/c K2K beamline to available twopA ad-data collected at differ- beam wheretaintyx invious theis8 the extrapolation data Feynman at pTπ x,=0 from see.3 berylliumreferences GeV/cπ [7]. to [10] carbon A andpT datadependence of with short spills in fast extracted proton beams.[30] In partic- for details. AF 9-parameter (11-parameter) fit line and the 12.9ent GeV/c centre-of-mass K2K beamline energies. two ad- [30]sits for (in thedetails.α0pT range A(0 9-parameter. of69 interest± 0.04) for (11-parameter) (0 neutrino.72 ± 0.04) beams: fit hoc up to Sanford-Wang parametrizations, using only ular, the use of a graphite target is foreseen in the design of − + hoc Sanford-Wang0 0 parametrizations, using only X denotes any system of other particleswas in the done over600 24less MeV/c) (25) accurateπ around(π− than)datasets[47],corre- 5%,−± formula+ on the (8)− top in of the± a description measurementthe of relevant the K /K HARPIn datasets, Fig. 4, our have prediction been published for one-particle inclusive in- both the CNGS and the NuMI beams [1,2]. Prescriptions was∼ doneα over1 24 (25)( 0.91π (π0.21))datasets[47],corre- ( 1.36 0.20) the relevant HARP datasets, have been published finalto rescale state, thep inclusivebeam is invariant the proton cross-sections beam momen-sponding to different toerror 1440 ofproduction (1472) 5–10%, dependingexperimental asymmetry on at the points. small/intermediate secondary The momentum,xF variant cross section are compared to data collected with spondingα to2 1440 (1472)(0.34 ± experimental0.21) (2.18 points.± 0.21) The in referencesin references [1] [1] and and [2]. [2]. Given the the poor poor description description tum in GeV/c, p and θ are the π± momentum for the cross sections on beryllium. The estimate of this 11 target materials are given in the following. goodness-of-fitgoodness-of-fit of the Sanford-Wang of the Sanford-Wang parametriza- parametriza- of HARPof HARP pion pion production production data data in in terms terms of theof the orig- orig- d3σhA systematic uncertainty is based both on data collected by andThe angle invariant in units cross of sections GeV/cE and3 for radians, hadron-nucleus re- tion hypothesis for the HARP results can be as- dp tion hypothesisBarton for et al.the [7] HARP and on results the extensive can be compilation as- inal of J.inal Sanford-Wang Sanford-Wang parametrization, parametrization, one one extra extra pa- pa- spectively, d2σ/(dpdΩ)isexpressedinunitsof sessed by considering the best-fit2 χ2 value of interactions (hA h′X) depend on the masssessed number byA whatKuhn considering can on nuclear be accommodated the dependence best-fit for withinχpA value theπ X Sanford- ofinteractionsrameter to better describe the angular dependence mb/(GeV/c)/sr and!→ the parameters c ,...,c are 2 − rameter to better describe the angular dependence of the target nucleus via parameterizations1 of theχ28 type:=13030(8061)for1431(1461)degreesofWangχ[30].min =13030(8061)for1431(1461)degreesof formula, where this ratio is given→ by g(θ)= was introduced in the fit reported in reference [2]. obtained from fits to the meson production data.min freedom for the π− (π+)production,indicatingwas introduced in the fit reported in reference [2]. 3 hA1 α 3 hA2 − + c8 In the global fit presented here, this extra param- d σ A1 d σ freedom forexp[ the−c6θπ(p −(πpc)],)production,indicating with pc ≡ c7pbeam cos θ. E = E . (9) averypoorfitquality.Inparticular,inspectionIn theeter global is not used fit presented for simplicity, here, as it this was extra found thatparam- dp3 !A " · dp3 averypoorfitquality.Inparticular,inspection The parameter c1 is an overall2 normalization fac- of4.2 the Scaling HARP to inclusivedifferent centre pion production of mass energies double- eterit is did not not used improve for simplicity, the fit quality as it in was a significant found that of the HARPThe overall inclusive fit may pion be production used as a fast double- approxima- tor,In accordance the four parameters with the scalingc2,c3,c hypothesis,4,c5 describeα has the been tiondifferential of HARP cross-section, data valid within and resulting a factor Sanford- 2–3 of theit didway. not improve the fit quality in a significant momentum distribution of the secondary pions in The NuMI neutrino beam at FNAL is planned to be de- found to be weakly dependent on the incidentdi beamfferential mo- quotedWang cross-section, parametrization, experimental and errors. points resulting The to a best-fit Sanford- description values of ofway. thementum. forward It depends direction, on the and incident the three hadron parameters typeWangh and parametrization, it therived ratio fromg( aθ)ofthepionmomentumdistribution primary points proton to a beam description of 120 GeV/c of momen-As a final remark, we stress again that due to the thetum, parameters resulting in are a centre-of-mass reported in Table energy III about together two times c6is,c a7 smooth,c8 describe function the of p correctionsT and xF of to the the produced pionthe mo-hadron. ratio gat(θ)ofthepionmomentumdistributionθ =0withrespecttothe̸ θ =0pionmomen-Aspoor a final fit remark, quality our we global stress fit again may be that just due consid- to the It has moreover been experimentally observed that, in first withtumsmaller their distribution than errors. that Theavailable that fit is parameter more at NA56/SPY complicated errors and are thanNA20. esti- Be-ered as a simple way to summarize an extended set mentum distribution for pion productionat anglesθ =0withrespecttothe̸ matedsides its by general requiring interest,∆χθ2 a=0pionmomen-≡ testχ2 of−χ the2 scaling=12. hypothesis6(10.4),poor of fit quality our global fit may be just consid- thatapproximation, are different it is from independent zero. The of theπ± detectedproduction particle min type, with perhaps the exception of anti-protonstum [7]. distributioncorrespondingone-particle that inclusive is to more the invariant 68.27% complicated cross-sections confidence than level is thus re-ered rel- as a simple way to summarize an extended set data on solid targets reported here have been fit- evant to assess the range of validity of the proposed pa- A parameterization of α as a function of xF has been gion for eleven (nine) variable parameters. Signif- tedproposed simultaneously by Barton to et the al. onempirical the basis Sanford-Wang of their and pre- icantrameterization. correlations This among has been fit parameters studied by comparingare found, our formula. In the χ2 minimization, the full error ma- parameterisation to available pA data collected at differ- vious data at pT =0.3 GeV/c [7]. A pT dependence of as shown by the correlation matrix given in Ta- trix was used. ent centre-of-mass energies. less accurate than formula (8) in the description of the K0/K0 blesIn IV Fig. and 4, V. our prediction for one-particle inclusive in- Toproduction go from asymmetry a baseline at nuclear small/intermediate targets (typicallyxF Be) variant cross section are compared to data collected with To show the trend of the Sanford-Wang global fit to another nuclear target A,acorrectionfactor of all HARP datasets, figure 12 reports the comparison, at 8 GeV/c and 12 GeV/c, between pion corr =(A/A )α (4) Be production data and the above parametrization. 2 was introduced, with α = α0 + α1 × xF + α2 × xF For the 8.9 GeV/c MiniBooNE/SciBooNE beam- where xF is the Feynman x, see references [10] and line and the 12.9 GeV/c K2K beamline two ad- [30] for details. A 9-parameter (11-parameter) fit hoc Sanford-Wang parametrizations, using only − + was done over 24 (25) π (π )datasets[47],corre- the relevant HARP datasets, have been published sponding to 1440 (1472) experimental points. The in references [1] and [2]. Given the poor description goodness-of-fit of the Sanford-Wang parametriza- of HARP pion production data in terms of the orig- tion hypothesis for the HARP results can be as- inal Sanford-Wang parametrization, one extra pa- 2 sessed by considering the best-fit χ value of rameter to better describe the angular dependence 2 χmin =13030(8061)for1431(1461)degreesof was introduced in the fit reported in reference [2]. − + freedom for the π (π )production,indicating In the global fit presented here, this extra param- averypoorfitquality.Inparticular,inspection eter is not used for simplicity, as it was found that of the HARP inclusive pion production double- it did not improve the fit quality in a significant differential cross-section, and resulting Sanford- way. Wang parametrization, points to a description of the ratio g(θ)ofthepionmomentumdistribution As a final remark, we stress again that due to the at θ =0withrespecttothe̸ θ =0pionmomen- poor fit quality our global fit may be just consid- tum distribution that is more complicated than ered as a simple way to summarize an extended set ARTICLE IN PRESS 530 M.G. Catanesi et al. / Nuclear Instruments and Methods in Physics Research A 571 (2007) 527–561

particles in the beam was important, as was the identifica- extracted proton beam from the PS accelerator. It covers tion of secondaries, both at large angles in the TPC, and at the momentum range between 1.5 and 15 GeV=c . Particle small angles in the forward region. Every effort was made identification in the beamline is provided by two gas to re-use existing equipment. However major parts of the Cherenkov detectors (Beam Cherenkov A and B: BCA, experiment, notably the TPC, the Resistive Plate Chambers BCB) and a pair of time-of-flight counters (TOF-A, TOF- (RPC), the Cherenkov counter and the time-of-flight wall B). Four multi-wire proportional chambers (MWPC) (TOFW), had to be designed and constructed specifically measure the position and direction of the beam particles for HARP. The experiment was approved by CERN’s upstream of the target. Several scintillation counters serve Research Board in February 2000 and took data in the to trigger on single incoming beam particles. The beamline years 2001 and 2002. The experimental setup was decom- and its instrumentation are described in Section 3. The missioned at the end of 2002. trigger detectors are described in Section 4. The global layout of the HARP experiment is shown in 2. Overall layout of the experiment Fig. 1. It covers a total length of 13.5 m along the beam direction. The large-angle spectrometer is housed in a The experimental layout consists of four main functional solenoid magnet. It comprises the target and several parts: concentric layers of cylindrical detectors. At the most inner radius the target is surrounded by the Inner Trigger HARP EXPERIMENT(1) The beamline along with the detection and identifica- Cylinder (ITC), six layers of scintillating fibres serving as tion of incoming beam particles; an interaction trigger for large-angle particles. Most of the (2) The trigger detectors; radial space of the solenoid magnet is occupied by the TPC. (3) The large-angle spectrometer housing the target; It provides track, momentum and vertex measurements for ➤ (4) The forward spectrometer. all outgoing charged particles in the angular range from Large-angle fixed target experiment at CERN20 PSto 160 with respect to the beam axis. In addition, it The beamline selects secondary particles with positive or provides particle identification by recording the particle’s negative charge emerging from a primary target in the energy loss in the gas (dE/dx). The particle identification ➤ Took data with p and π± beams from 1.5 to 15 GeV/c on a Calorimeter

variety of targets Muon identifier

Drift chamber ➤ Forward spectrometer could measure particles up to 250 mrad.

Forward RPC ➤ Could also make high FTP angle measurements up to 1050 mrad using TOF wall TPC in solenoid Cherenkov Spectrometer magnet y

Solemoid magnet x z Taget+ITC+TPC+RPC

Beam chambers 12 Nucl. Instr. Meth. A 571(2007) 527 Trigger+Halo counters 1 m

Fig. 1. Overall mechanical layout of the HARP detector. The different sub-detectors are shown. The target is inserted inside the TPC. The convention used for the coordinate system is drawn in the ﬁgure. KEY THIN TARGET DATA BELOW 18 GEV/C

Data Experiment Hadron Published 8.9 GeV/c p + HARP π+ Eur. Phys J C 52 (2007) 29 thin Be 6.4, 12.3, and 17.5 GeV/c p BNL E910 π± Phys. Rev. C 77 (2008) 015209 + thin Be 12.9 GeV/c p Nucl. Phys. B 732 HARP π+ + thin Al (2006) 1 12 GeV/c p HARP π± Astr. Phys. 29 (2008) 257 and π± + C

➤ Additional HARP data on heavy targets, and at high angles ➤ Errors for 8.9 GeV/c data were ~9.8% on shape, 5% on normalization

➤ MiniBooNE ﬂux predictions, hadrons give ~10% on νμ ﬂux Phys Rev D 79 072002 (2009)

➤ MicroBooNE and SBL will build on 10 years of experience with Booster beam 13 NA61/SHINE EXPERIMENT

➤ SPS Heavy Ion and Neutrino Experiment: Fixed target experiment using CERN SPS ➤ Primary 400 GeV/c p beam, Secondary beams ~26 to 160 GeV/c

Top View

PSD

JINST 9 (2014) P06005 ➤ Comprises several large acceptance TPCs, Two inside magnets 14 THIN TARGET DATA AROUND 31 GEV/C

Data Experiment Hadron Published 19.2 GeV/c p on Allaby et al p,pbar, π±, K± Tech. Rep. 70-12 (CERN, 1970) p,Be, Al, Cu, Pb 24 GeV/c p on ±, ± Eichten et al p,pbar, π K Nucl. Phys. B44, 333 (1972) Be, Al, Cu, Pb 31 GeV/c p + ± NA61/SHINE π Phys. Rev. C84 (2011) 034604 thin C target 31 GeV/c p + NA61/SHINE K+ Phys. Rev. C85 (2012) 035210 thin C target

31 GeV/c p + 0 ΝΑ61/SΗΙΝΕ Ks , Λ Phys.Rev. C89 (2014) 025205 thin C target

31 GeV/c p + ± ± 0 NA61/SHINE π , K ,Ks , Λ,p Eur.Phys.J. C76 (2016) 84 thin C target

➤ Errors on π+ production ~4-5% for 20-140 mrad; K+ errors <~10% for p<12 GeV

15 THICK TARGET DATA AT 31 GEV/C

Data Experiment Hadron Published

31 GeV/c p + Nucl.Instrum.Meth. A701 (2013) T2K replica NA61/SHINE π+ target 99-114

31 GeV/c p + π± Eur.Phys.J. C76 (2016) no.11, T2K replica NA61/SHINE 2 target 617

νµ at SK (p250ka) ➤ 6 10 Diﬀerential yieldsAll Pions in (p,θ,ztarget) Z6 Kaons Kaons0 Z1 Z2 Z3 Z4 Z5 5 Muons ➤10 In upstream slices and high-angleFig. 2: A sketchdownstream of the longitudinal binningslices of the errors T2K replica POT/50 MeV) target. The aluminum ﬂange at the upstream edge is used in NA61/ 21 104 SHINE to hold and align the target. /10

2 generally dominated by extrapolation of track back to target

3 νµ energy spectrum at SK 10 ×106 ➤ In middle slices, dominated by 1.2pion loss and feed-down Flux (/cm

2 POT)

10 21 corrections from the decays of strange1 particles and /10 2 10 interactions outside of the target0.8 0.6 16 1 z 1 0 2 4 6 8 10 z 2 Eν [GeV] 0.4 z 3 z 4 Flux (/50 MeV/cm z 5 νe at SK (p250ka) 0.2 z 6 104 All Pions 0 Kaons Kaons0 0 0.5 1 1.5 2 2.5 3 Muons EN [GeV]

POT/50 MeV) 103 Fig. 3: Stacked histograms showing the contribution of each of the 21 6 longitudinal target bins (see Fig. 2) to the muon neutrino ﬂux at /10 2 SK.

102 GEANT3 [20] simulation using GCALOR [21] as hadronic model Flux (/cm for re-interactions in the detector. During the MC simulation, information on particle production 10 and decay is stored, so the full history of neutrinos crossing either the near or far detector is available. This allows to study different components of the neutrino beam and the origin of the neutrino 1 0 2 4 6 8 10 species. As shown in Fig. 1, the nµ flux around the beam peak Eν [GeV] energy at the SK far detector arises mainly from pion decays, while it is mainly due to kaons at higher energies. This motivates the Fig. 1: Contribution of different parent particles to the total neu- extraction of charged pion yields at the surface of the target, which trino flux at SK for nµ (top) and ne (bottom), computed with the is the subject of this paper. T2K beam Monte-Carlo simulation program [11] for the positive It is important to note that not only the pion angular and mo- focussing at 250 kA horn current (’p250ka’ configuration). mentum spectra are of interest, but also the longitudinal position where they exit the target. By dividing the 90 cm long graphite rod into 5 bins of 18 cm length each and considering the downstream By choosing the polarity of the horn currents, it is possible to cre- face of the target as an additional sixth bin, as shown in Fig. 2, it ate either an enhanced neutrino beam or an enhanced antineutrino is possible to study the contribution of each of these bins to the beam. In this article we concentrate on the case of the enhanced total neutrino flux. Figure 3 presents these different contributions neutrino beam but the results of this paper can also be used for the as predicted at SK. prediction of the flux in the enhanced anti-neutrino configuration. A detailed description of the beam and its properties can be found in Ref. [11]. 2.2 Requirements on the T2K neutrino flux prediction The neutrino beam predictions are based on a detailed Monte- The T2K experiment pursues three main physics goals [2] with Carlo simulation. The input parameters are given by the values de- an off-axis (essentially narrow band) neutrino or antineutrino beam scribing the ellipsoid representing the primary proton beam impact peaked around the so-called atmospheric oscillation maximum (en- points on the target upstream face as measured by the beam posi- ergy range from 0.2 to 1.2 GeV). These are: tion detectors placed along the proton beam line. The FLUKA2011 [17–19] model is used to simulate the interactions of beam pro- (i) the muon neutrino disappearance, tons with the long graphite target. The propagation of the par- (ii) the electron neutrino appearance (n n ), µ ! e ticles emerging from the surface of the target is modeled by a (iii) neutrino cross section measurements. + NA61 LONG TARGET ERRORS LOW ANGLE PI 11

0<θ<20 Z 1 0<θ<20 Z 2 0<θ<20 Z 3 0<θ<20 Z 4 0<θ<20 Z 5 0<θ<20 Z 6 0.15 0.15 0.15 0.15 0.15 0.15

0.1 0.1 0.1 0.1 0.1 0.1

0.05 0.05 0.05 0.05 0.05 0.05 relative uncertainties

0 10 20 10 20 10 20 10 20 10 20 10 20 20<θ<40 Z 1 20<θ<40 Z 2 20<θ<40 Z 3 20<θ<40 Z 4 20<θ<40 Z 5 20<θ<40 Z 6 0.15 0.15 0.15 0.15 0.15 0.15

0.1 0.1 0.1 0.1 0.1 0.1

0.05 0.05 0.05 0.05 0.05 0.05 relative uncertainties

0 10 20 10 20 10 20 10 20 10 20 10 20 40<<60 Z 1 40<<60 Z 2 40<<60 Z 3 40<<60 Z 4 40<<60 Z 5 40<<60 Z 6 0.15 θ 0.15 θ 0.15 θ 0.15 θ 0.15 θ 0.15 θ

0.1 0.1 0.1 0.1 0.1 0.1 PID Feed-down rec.eff 0.05 0.05 0.05 0.05 0.05 0.05 tof.eff π loss back extrap

relative uncertainties Total 0 0 0 0 0 0 0 10 20 10 20 10 20 10 20 10 20 10 20 p [GeV/c] p [GeV/c] p [GeV/c] p [GeV/c] p [GeV/c] p [GeV/c]

60<θ<80 Z 1 60<θ<80 Z 2 60<θ<80 Z 3 60<θ<80 Z 4 60<θ<80 Z 5 60<θ<80 Z 6 0.15➤ Backward0.15 extrapolation0.15 dominates0.15 at small angles0.15 and upstream0.15 bins 0.1 0.1 0.1 0.1 0.1 0.1 17

0.05 0.05 0.05 0.05 0.05 0.05 relative uncertainties

02468 2468 2468 2468 2468 2468 80<θ<100 Z 1 80<θ<100 Z 2 80<θ<100 Z 3 80<θ<100 Z 4 80<θ<100 Z 5 80<θ<100 Z 6 0.15 0.15 0.15 0.15 0.15 0.15

0.1 0.1 0.1 0.1 0.1 0.1

0.05 0.05 0.05 0.05 0.05 0.05 relative uncertainties

02468 2468 2468 2468 2468 2468 100<<140 Z 1 100<<140 Z 2 100<<140 Z 3 100<<140 Z 4 100<<140 Z 5 100<<140 Z 6 0.15 θ 0.15 θ 0.15 θ 0.15 θ 0.15 θ 0.15 θ

0.1 0.1 0.1 0.1 0.1 0.1 PID Feed-down rec.eff 0.05 0.05 0.05 0.05 0.05 0.05 tof.eff π loss back extrap

relative uncertainties Total 0 0 0 0 0 0 02468 2468 2468 2468 2468 2468 p [GeV/c] p [GeV/c] p [GeV/c] p [GeV/c] p [GeV/c] p [GeV/c]

Fig. 14: Components of the systematic uncertainties for positively charged pion spectra, in the polar angle range from 0 to 140 mrad, and for the six longitudinal bins as a function of momentum.

7 Towards T2K flux predictions each produced neutrino. Recording these parameters allows, once the full neutrino beam simulation is completed, to come back to 7.1 Monte-Carlo re-weighting with replica target pion spectra each pion exiting the surface of the target and being a parent of neutrinos. The neutrinos are then assigned a weight which is de- The implementation of the T2K replica target results within the pendent on the (p,q,z) parameters of the pions at the surface of T2K neutrino flux prediction can essentially follow the one for the the target and computed as thin target re-weighting procedure [11]. The major modification w(p,q,z)=Nmeas (p,q,z)/Nsim (p,q,z), (3) to be introduced is to save the relevant parameters of the particles NA61 T2K meas exiting the surface of the target in the simulation process. This spe- where NNA61 are the hadron yields at the surface of the target mea- sim cific information is added to the already existing history chain for sured by NA61/SHINE and NT2K are the yields of emitted particles IMPROVEMENTS TO LONG TARGET MEASUREMENTS

➤ Updated long target results later this summer, including ➤ Increased data statistics ➤ K± and p yields ➤ Expected to reduce T2K ﬂux uncertainties to 5% level ➤ Future analysis of data taken with higher magnetic ﬁeld, which can improve acceptance for forward particles like protons

18 NA61/SHINE DATA FROM 60-120 GEV/C

➤ New eﬀort in NA61 to collect data at energies and on targets of interest for Fermilab program, including NuMI and LBNF beamlines ➤ Analysis in progress of the following datasets collected in NA61/ Shine in Fall 2016

Data Type triggers p + C @ 120 GeV/c 4.3 M p + Be @ 120 GeV/c 2.2 M p + C @ 60 GeV/c 2.9 M p + Al @ 60 GeV/c 3.2 M p + Be @ 60 GeV/c 2.1M π+ + C @ 60GeV/c 4.2 M π+ + Be @ 60 GeV/c 2.6 M 19 NA61/SHINE UPGRADES

➤ Upgrades to NA61/SHINE electronics underway ➤ 3 new TPCs added to improve forward coverage

Top View

ToF-F

FTPC1 FTPC2/3 PSD

20 FUTURE NA61/SHINE PLANS

➤ Plan to collect more neutrino-relevant data over next 2 years possibly including the following ➤ 120 GeV p+C and p+Be with new FTPCs ➤ 90 GeV p+C ➤ 60 GeV π+ + Al ➤ 30 GeV π+ + C ➤ 60 GeV π- + C ➤ NuMI ME replica target

21 MIPP EXPERIMENT

➤ Fermilab E907: Main Injector Particle Production 2

➤ p, π,K beams 5 GeV/c-120 GeV/c on thin LH2,C, Be, Bi, U

targets and NuMI LE replica targetRICH! Detector ToF! Detector

Ckov! Detector

EM & Hadronic! 25 m Calorimeters TPC ((x,y) −(x,y) )/sum intxDensitynon Proﬁle−intx of the NuMI Target Wire! 2 1 aluminum water cooling

y (cm) pipe holes • Three upstream beam Chambers wire chambers give 0.2 carbon mm resolution of the Rosie! 1 0.5 incident beam track position at the front face of Magnet graphite! the target. ! Target slabs ! 0 0 • Center of circle represents measured mean position Beam! of reconstructed incident JGG! beam particles in selected ChambersCkov events! Magnet −1 −0.5 ! • Width of circle represents aluminum! measured 1mm2 beam tube width ! air! −−22 −10 122 2−1 x (cm) FIG. 1. Schematic view of the MIPP spectrometer. Jonathan'Paley,'ANL'HEP'Division 9 on-target in approximately 120 bins of longitudinal and The high multiplicities present in this data set compli- transverse momentum. The statistical and systematic cate the use of the Cherenkov and ToF detectors, and uncertainties in most bins are between 5 and 10%. this analysis relies on measurements from the TPC and RICH detectors. Measurements from the ToF detector are used to estimate backgrounds. II. THE MIPP SPECTROMETER

For the MIPP experiment, an open geometry 25 m long III. TARGET AND INCIDENT BEAM spectrometer was assembled with two dipole magnets for momentum determination, a 1.5 m long time-projection The NuMI target used in this measurement was a spare chamber [4] (TPC) located just downstream of the in- target that was eventually used by the NuMI complex teraction region, and 3 drift chambers (DCs) and 2 mul- after the MIPP data run. The target was designed for tiwire proportional chambers (MWPCs) located further operation in the low-energy configuration of the NuMI downstream for particle tracking. The TPC sits inside beamline and consists of a 90-cm long, 3-cm diameter alu- the most upstream dipole magnet, and targets are placed minum vacuum can encompassing 47 2-cm thick graphite just upstream of the TPC. Three wire chambers [8] (BCs) slabs, adding up to two nuclear interaction lengths of ma- positioned across 36 meters upstream of the target are terial. The downstream end of the tube was positioned used to track incident beam particles. A schematic of 8 cm away from the upstream end of the TPC active the spectrometer is shown in Fig. 1. volume. The electric field used to drift ionization electrons pro- The incident beam was 120 GeV/c protons, slow- duced in the MIPP TPC is aligned the MIPP was de- extracted directly from the MI. A pinhole collimator was signed to provide particle identification (PID) with 2 3 used to reduce the incident MI proton beam flux by 8 separation across the momentum range of a few hundred orders of magnitude, such that the rate of incident beam MeV/c to greater than 80 GeV/c using dE/dx informa- pileup in the target over the 16 µs required to read out tion from the TPC (0.2–1.2 GeV/c), a plastich scintillator-i the TPC was reduced to a few percent. based time-of-flight (ToF) detector (0.5–2.5 GeV/c), a In order to ensure that the incident beam was centered segmented gas Cherenkov detector [5] (2–20 GeV/c) and on the face of the target, a NuMI trigger detector con- a gas ring imaging Cherenkov [6] (RICH) detector (4–80 sisting of three thin (L < 0.5%) overlapping pieces of GeV/c). Electromagnetic and hadronic calorimeters are plastic scintillator was mounted on the upstream face of used to measure forward-going neutrons and photons [7]. the NuMI target. The light from each of the scintillator DATA AT 120 GEV/C

Data Experiment Hadron Published 58, 84, 120 GeV/c p + MIPP n Phys.Rev. D83 (2011) 012002 various thin targets

120 GeV/c p + NuMI 12 MIPP π± Phys.Rev. D90 (2014) 032001 replica target

10 10 )/(GeV/c)/POT )/(GeV/c)/POT - + 1 1 π π N( N(

10-1 10-1 + π- 10-2 π 10-2

-3 -3 10 0.00 - 0.10 GeV/c 10 0.00 - 0.10 GeV/c

0.10 - 0.20 GeV/c, N x 3.00 0.10 - 0.20 GeV/c, N x 3.00

0.20 - 0.30 GeV/c, N x 10.00 0.20 - 0.30 GeV/c, N x 10.00

-4 -4 10 0.30 - 0.40 GeV/c, N x 30.00 10 0.30 - 0.40 GeV/c, N x 30.00

0.40 - 0.50 GeV/c, N x 100.00 0.40 - 0.50 GeV/c, N x 100.00

0.50 - 2.00 GeV/c, N x 300.00 0.50 - 2.00 GeV/c, N x 300.00 10-5 10-5 1 10 1 10 p (GeV/c) p (GeV/c) 23 z z

+ (a)⇡ yields. (b)⇡ yields.

) + π

( 6

Data 0.50 - 2.00 GeV/c, R+5.0 )/N - π ( 5 Data

= N 0.40 - 0.50 GeV/c, R+4.0 Data R 4

0.30 - 0.40 GeV/c, R+3.0

0.20 - 0.30 GeV/c, R+2.0

0.10 - 0.20 GeV/c, R+1.0

0.00 - 0.10 GeV/c

0 1 10 p (GeV/c) z

+ (c)⇡/⇡ ratios.

FIG. 13. Pion yields (top) and ratios (bottom) as a function of pz in bins of pT. Di↵erent colors and markers represent bins of pT, and the yields are scaled and the ratios o↵set such that the points in di↵erent pT bins do not overlap. All eciency corrections have been applied, and both statistical and systematic error bars are plotted. KEY THIN TARGET DATA AT 158 GEV/C

Data Experiment Hadron Published 158 GeV/c p +C NA49 π± Eur.Phys.J. C49 (2007) 897

158 GeV/c p +C NA49 p, pbar, n, d, t Eur.Phys.J. C73 (2013) 2364

3 3

)] 10 10 3

/c a) b) 2 pC → π+ X pC → π- X

p = 0.05 p = 0.05 T T f [mb/(GeV 0.1 0.1 0.2 0.2 2 2 10 0.3 10 0.3 0.4 0.4 0.5 0.5 ➤ For π± errors typically at the 10 10 several % level

1 1

10-1 10-1

0.6 0.6 0.7 0.7 0.8 0.8 10-2 0.9 10-2 0.9 1.0 1.0 1.2 1.2 1.4 1.4 1.6 1.6 1.8 1.8

10-3 10-3 0 0.2 0.4 0.6 0 0.2 0.4 0.6 24

xF xF

+ − Figure 18: Invariant cross section as a function of xF at ﬁxed pT for a) π and b) π produced in p+C collisions at 158 GeV/c

18 LONG TARGET DATA FOR DUNE?

➤ DUNE is likely to have a graphite or Be target. ➤ Current optimized design favors a 2 m long target. ➤ Extrapolation to determine where the particle exited the target could be a big issue ➤ Some ideas: (See also A. Blondel’s talk on Friday) ➤ Place target (partially) inside ﬁrst TPC? ➤ Additional tracking detectors around target?

25 ATMOSPHERIC NEUTRINO FLUXES G. D. BARR, S. ROBBINS, T. K. GAISSER, AND T. STANEVPhys PHYSICAL Rev D REVIEW74 094009 D 74, 094009 (2006) (2006) aprotonandthetargetisalightnucleussuchasberyllium, SPY carbon or aluminum, which can be extrapolated to nitrogen high latt. Atherton et al.

and oxygen, which are the targets in the atmospheric GeV/c

low latt.

➤ π cascade. Flux errors ~15% in FNAL When a shower develops, the initial cosmic ray under- p Serpukhov goes several interactionsmost in which important the initial energy region is split Allaby et al. among the branchesfor of the underground shower. Tracing backwards Eichten et al. through the shower from the neutrino, through the ances- Abbott et al. tors to the original cosmicneutrinos ray, one can define the branch along which any particular neutrino was produced. At Cho et al. ➤ some point along theAdditional branch, there is 12 a meson GeV ( HARP, K or K0) which decays. The neutrino may be produced directly in this decaydata or via aon muon. N2 Itand is the O distribution2 since of energy, position onthen the globe Astr. and Phys. direction 30 (2008) of these 1 mesons which govern the neutrino fluxes. This meson will be referred to➤ as ‘‘theMore decay data meson’’. below 20 GeV To simplify, we have limited the study of hadron pro- HARP duction uncertaintieswould to the interaction help in which the first meson in the branch has been produced (i.e. its parent was a baryon). We now discuss two aspects which have been neglected in the uncertainties due to this simplification. 26 (1) It is possible in the branch that the first meson to be pprimary GeV/c produced interacts and produces a subsequent string of FIG. 1 (color online). Summary of measurements of single hadrons before we reach the decay meson. This depends particle production yields as a function of primary energy and on the local atmospheric density and because of time secondary energy. The bands for each experiment represent the dilation effects, is important only for higher energy mesons range of primary and secondary particle energies where mea- (above 200 GeV for pions and 600 GeV for kaons). The surements exist for at least one value of pT. The boxes on the secondaries of such interactions will be lower in energy, a plot show the contribution of the phase space to the generation of contained underground neutrino events as computed by the region populated by a large number of directly produced simulation. The outer (red) and inner (black) boxes indicate decay mesons from lower energy cosmic rays, so the addi- the extremes of geomagnetic field effects for high and low tional uncertainty because of such interactions is small. geomagnetic latitude, respectively. (2) The branch may contain a chain of interactions in which the initial cosmic ray baryon is converted into lower accelerator beams where magnetic fields are used to focus energy baryons before the decay meson is produced. This specific regions of pT to form the beam). Measurements could happen both by near-elastic scatters or in higher over the whole pT range are important to determine the multiplicity interactions. Some of these daughter baryons integral. are neutrons and very few hadron production measure- Most of the experiments report yields for both signs of ments concerning either the production of neutrons or charged pions and charged kaons. We discuss the uncer- interactions with neutron projectiles are available. tainties on charged pion yields first and then kaon yields. Therefore all aspects of neutrons in cosmic ray showers The uncertainties assigned are summarized in Fig. 2. There is a series of measurements with primary energies around are obtained from isospin arguments from proton measure- 20 GeV [37–39] with consistent measurements spread over ments. The uncertainty associated with this simplification as much as 80% of the p phase space [36], allowing the (2) requires separate study. T Figure 1 shows a map of the E ;E phase space which i s is important for the production of neutrinos with energies E i (GeV) Pions Kaons appropriate to produce contained events in underground <8 10% 30% 40% detectors and indicates the locations of hadron production 8−15 30% 10% 30% 40% experiments. 15−30 30 10 5% 10% 30 20 10% 30−500 30 15% 40 30% Engel, et al. [36] summarize the extent to which these >500 3015%+Energy dep. 40 30%+Energy dep. measurements cover the third dimension of phase space, 1 00.5x LAB 1 0 0.5 x LAB transverse momentum pT. It is most important in atmospheric neutrino interactions to understand the FIG. 2. Uncertainties assigned to the production rate of pT-integrated yields. Yields at specific values of pT are charged pions (left) and charged kaons (right) as a function of less important since all pT values are collected with the xlab. The uncertainties are shown for various ranges of incident same probability in underground detectors (in contrast to particle energy Ei for interactions of protons on light nuclei.

094009-4 SUMMARY OF DATA SO FAR

➤ Lots of progress over the past 5 years in understanding hadron production uncertainties and their impact on neutrino ﬂux uncertainties ➤ Increasingly measurements are available with uncertainties at the few % level ➤ More measurements that can have a major impact on the T2K and NuMI/LBNF ﬂuxes expected over the next few years

27 FUTURE NEEDS AND IMPROVEMENTS

➤ While there is a lot of thin target data (and some of it has uncertainties of a few %), most of this data is focussed on interactions of primary protons ➤ Often large uncertainties on hadron production to reinteractions of hadrons elsewhere in target or beam ➤ Need more data with π+, π-, and K beams ➤ Long target measurements ideally include all of the reinteractions in the target, so these are always desirable when possible ➤ Not a lot of low energy data. More Pion interaction data below 30 GeV could benefit T2K/HyperK, and data around 9 GeV could benefit the short-baseline program at Fermilab and the predictions for atmospheric neutrino fluxes