Recent results from the HARP experiment on the measurements of the
double-differential production cross-section of pions in proton interactions
with beryllium, carbon and tantalum targets are presented. These results are
relevant for a detailed understanding of neutrino flux in accelerator neutrino
experiments MiniBooNE/SciBooNE, for a better prediction of atmospheric neutrino
fluxes as well as for an optimization of a future neutrino factory design.Comment: Presented at the XLIInd Rencontres de Moriond on Electroweak
  Interactions and Unified Theorie

Popov, Boris A.

English

arXiv

Recent results from the HARP experiment on the measurements of the double-differential production cross-section of pions in proton interactions with beryllium, carbon and tantalum targets are presented. These results are relevant for a detailed understanding of neutrino flux in accelerator neutrino experiments MiniBooNE/SciBooNE, for a better prediction of atmospheric neutrino fluxes as well as for an optimization of a future neutrino factory design

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arXiv:0705.3512v1  [hep-ex]  24 May 2007 R ESU LT S FR O M H A R PA N D T H EIR IM P LIC AT IO N S FO R N EU T R IN O P H Y SIC SBO RIS A.PO POVDzhelepov Laboratory ofNuclear Problem s,JINR,Joliot-Curie 6,141980,Dubna(on behalfofthe H A R P C ollaboration)Recent results from the HARP experim ent on the m easurem ents ofthe double-dierentialproduction cross-section ofpionsin proton interactionswith beryllium ,carbon and tantalumtargets are presented. These results are relevant for a detailed understanding ofneutrinoux in accelerator neutrino experim ents M iniBooNE/SciBooNE, for a better prediction ofatm ospheric neutrino uxesaswellasforan optim ization ofa futureneutrino factory design.1 T he H A R P experim entThe HARP experim ent1;2 at the CERN PS was designed to m ake m easurem ents ofhadronyieldsfrom a large range ofnucleartargetsand forincidentparticle m om enta from 1.5 G eV/cto15 G eV/c.Them ain m otivationsarethem easurem entofpion yieldsforaquantitativedesignofthe proton driverofa future neutrino factory,a substantialim provem entin the calculationofthe atm ospheric neutrino  ux and the m easurem ent ofparticle yields as inputfor the  uxcalculation ofacceleratorneutrinoexperim ents,such asK 2K 3;4,M iniBooNE 5 and SciBooNE 6.TheHARP experim entm akesuseofa large-acceptancespectrom eterconsisting ofaforwardand large-angle detection system .A detailed description ofthe experim entalapparatuscan befound in Ref.2. The forward spectrom eter | based on large area drift cham bers7 and adipole m agnet com plem ented by a setofdetectors for particle identi cation (PID):a tim e-of- ightwall8 (TO FW ),a largeCherenkov detector(CHE)and an electrom agneticcalorim eter|coverspolaranglesup to 250 m rad which iswellm atched to theangularrangeofinterestforthem easurem entofhadron production to calculate the propertiesofconventionalneutrino beam s.The large-angle spectrom eter| based on a Tim e Projection Cham ber(TPC)located inside asolenoidalm agnet| hasa large acceptance in the m om entum and angularrange forthepionsrelevant to the production ofthe m uonsin a neutrino factory. Itcovers the large m ajority ofthe pionsaccepted in thefocusing system ofa typicaldesign.Theneutrino beam ofa neutrinofactory originatesfrom thedecay ofm uonswhich are in turn the decay productsofpions.2 R esults obtained w ith the H A R P forw ard spectrom eterThe rstHARP physicspublication9 reported m easurem entsofthe+ production cross-sectionfrom an alum inum targetat12.9 G eV/c proton m om entum . Thiscorrespondsto the energiesofthe K EK PS and the targetm aterialused by the K 2K experim ent. The resultsobtained inRef.9 were subsequently applied to the  nalneutrino oscillation analysis ofK 2K4,allowinga signi cantreduction ofthe dom inantsystem atic errorassociated with the calculation oftheso-called far-to-near ratio (see9 and 4 for a detailed discussion) and thus an increased K 2Ksensitivity to the oscillation signal.A detailed description ofestablished experim entaltechniques for the data analysis in theHARP forward spectrom eter can be found in Ref.9;10. O ur nextgoalis to contribute to theunderstanding ofthe M iniBooNE and SciBooNE neutrino  uxes. They are both produced bytheBoosterNeutrino Beam atFerm ilab which originatesfrom protonsaccelerated to 8.9 G eV/cby the boosterbefore being collided against a beryllium target. As was the case forthe K 2Kbeam ,a fundam entalinputforthecalculation oftheresulting   ux isthem easurem entofthe+ cross-sectionsfrom a thin 5% nuclearinteraction length (I)beryllium targetat8.9 G eV/cproton m om entum ,which ispresented hereand in the forthcom ing HARP publication11.W ith respectto our rstpublished physicspaper9,a num berofim provem entsto theanal-ysis techniques and detector sim ulation have been m ade. The m ost im portant im provem entsintroduced in thisanalysiscom pared with the onepresented in Ref.9 are: An increaseofthetrack reconstruction e ciency which isnow constantovera m uch largerkinem atic range and a better m om entum resolution com ing from im provem ents in thetracking algorithm ; Better understanding ofthe m om entum scale and resolution ofthe detector, based ondata, which was then used to tune the sim ulation. This results in sm aller system aticerrorsassociated with the unsm earing correctionsdeterm ined from M onte Carlo; New particle identi cation hit selection algorithm s both in the TO FW and in the CHEresulting in m uch reduced background and negligible e ciency losses; Signi cantincreasesin M onteCarloproduction havealsoreduced uncertaintiesfrom M onteCarlo statisticsand allowed studieswhich have reduced certain system atics.Itisim portantto pointoutthatan analysisincorporating theseim provem entsyieldsresultsforthe alum inum data fully consistentwith those published in Ref.9.Theabsolutely norm alized double-di erentialcross-section fortheprocessp+ Be! + + Xcan beexpressed in binsofpion kinem atic variablesin thelaboratory fram e,(p;),asd2+dpd(p;)=AN A t1 p 1N pot N+ (p;); (1)where:d2+dpdisthecross-section in cm 2=(G eV/c)=srad foreach (p;)bin covered in theanalysis.AN A isthereciprocalofthenum berdensity oftargetnucleiforBe(1:2349 1023 percm 3). t is the thickness of the beryllium target along the beam direction. The thickness ism easured to be2.046 cm with a m axim um variation of0.002 cm .  p and   are thebin sizesin m om entum and solid angle,respectively.aap = p m ax   pm in;  = 2(cos( m in)  cos(m ax))Table 1: Totalnum berofeventsin the 8.9 G eV/c beryllium 5% I target and em pty target data sets,and thenum berofprotonson targetascalculated from the prescaled triggercount.D ata Set 8.9 G eV /c B e 5% I 8.9 G eV /c Em pty Targetprotonson target 13,074,880 1,990,400totaleventsprocessed 4,682,911 413,095eventswith accepted beam proton 2,277,657 200,310beam proton eventswith FTP trigger 1,518,683 91,690totalgood tracksin  ducialvolum e 95,897 3,110 Npotisthenum berofprotonson targetaftereventselection cuts. N+(p;) is the yield of positive pions in bins of true m om entum and angle in thelaboratory fram e.Eq.1 can begeneralized to give the inclusive cross-section fora particle oftyped2dpd(p;)=AN A t1 p 1N pot M  1pp000  N0(p0;0); (2)wherereconstructed quantitiesarem arked with aprim eand M   1pp000 istheinverseofam atrixwhich fully describesthem igrationsbetween binsoftrueand reconstructed quantities,nam ely:lab fram em om entum ,p,lab fram e angle,,and particle type,.There is a background associated with beam protons interacting in m aterials other thanthe nucleartarget(partsofthe detector,air,etc.). These events are subtracted by using datacollected withoutthe nucleartarget in place where one hasbeen carefulto norm alize the setsto the sam e num ber ofprotons on target. This procedure is referred to as the ‘em pty targetsubtraction’:N0(p0;0)! [N 0target(p0;0)  N 0em pty(p0;0)]: (3)The event selection is perform ed in the following way: a good event is required to havea single,wellreconstructed and identi ed beam particle im pinging on the nuclear target. Adownstream trigger in the forward trigger plane (FTP) is also required to record the event,necessitating an additionalset ofunbiased, pre-scaled triggers for absolute norm alization ofthe cross-section. These pre-scale triggers(1/64 forthe 8.9 G eV/c Be data set)are subjecttoexactly the sam e selection criteria fora ‘good’beam particle asthe eventtriggersallowing thee ciencies ofthe selection to cancel,thus adding no additionalsystem atic uncertainty to theabsolute norm alization ofthe result.Secondary track selection criteria have been optim ized toensurethequality ofthem om entum reconstruction aswellasaclean tim e-of- ightm easurem entwhile m aintaining high reconstruction and particle identi cation e ciencies.Theresultsoftheeventand track selection in the beryllium thin targetdata setare shown in Table 1.The double-di erentialinelastic cross-section forthe production ofpositive pionsfrom col-lisions of8.9 G eV/c protons with beryllium have been m easured in the kinem atic range from0:75 G eV/c p  6:5 G eV/c and 0:030 rad    0:210 rad,subdivided into 13 m om entumand 6 angular bins. System atic errors have been estim ated. A full(13  6)2 = 6048 elem entcovariance m atrix has been generated to describe the correlation am ong bins. The data arepresented graphically asa function ofm om entum in 30 m rad binsin Fig.1.To characterizetheuncertaintieson thism easurem entweshow thediagonalelem entsofthecovariancem atrix plot-ted on the data pointsin Fig.1. A typicaltotaluncertainty of9.8% on the double-di erentialcross-section valuesand a 4.9% uncertainty on thetotalintegrated cross-section areobtained.01002003000 2 4 6d2 σpi  / (dp dΩ) (mb / (GeV/c sr)) 30-60 mrad01002003000 2 4 660-90 mrad01002003000 2 4 690-120 mrad01002003000 2 4 6120-150 mrad01002003000 2 4 6150-180 mrad01002003000 2 4 6p (GeV/c)180-210 mradFigure1:HARP m easurem entsofthedouble-dierentialproduction cross-section ofpositivepions,d2+=dpd,from 8.9 G eV/c protonson 5% I beryllium targetasa function ofpion m om entum ,p,in binsofpion angle,,in thelaboratory fram e.Theerrorbarsshown includestatisticalerrorsand all(diagonal)system atic errors.Thedotted histogram sshow the Sanford-W ang param etrization thatbesttsthe HARP data.Table 2: Sanford-W ang param eters and errors obtained by tting the dataset. The errors refer to the 68.27%condence levelforseven param eters(2= 8:18).P aram eter c1 c2 c3 c4 = c5 c6 c7 c8V alue (82:2  19:8) (6:47  1:62) (90:6  20:3) (7:44  2:30)  10  2(5:09  0:49) (0:187  0:053) (42:8  13:6)Sanford and W ang12 have developed an em piricalparam etrization fordescribing the pro-duction cross-sections ofm esons in proton-nucleus interactions. This param etrization has thefunctionalform :d2(p+ A ! + + X )dpd(p;)= exp[c1  c3pc4pc5beam  c6(p  c7pbeam cosc8 )]pc2(1 ppbeam); (4)where X denotes any system ofother particles in the  nalstate,pbeam is the proton beamm om entum in G eV/c,p and  arethe+ m om entum and anglein unitsofG eV/c and radians,respectively,d2=(dpd ) is expressed in units ofm b/(G eV/c sr),d  2 d(cos),and theparam etersc1;:::;c8 are obtained from  tsto m eson production data.The + production data reported here have been  tted to this em piricalform ula (Eq.4).In the2 m inim ization,thefullerrorm atrix wasused.Thebest- tvaluesoftheSanford-W angparam etersare reported in Table 2,togetherwith theirerrors.The M iniBooNE neutrino beam isproduced from the decay of and K m esonswhich areproduced in collisions of8.9 G eV/c protons from the Ferm ilab Booster on a 71 cm berylliumtarget. The neutrino  ux prediction is generated using a M onte Carlo sim ulation. In thissim ulation the prim ary m eson production rates are taken from a  t ofexisting data with aSanford-W ang em piricalparam etrization in the relevant region. The results presented here,being forprotonsatexactly theboosterbeam energy,arethen a criticaladdition to theseglobal ts. The kinem atic region ofthe m easurem ents presented here contains 80.8% ofthe pionscontributing to theneutrino  ux in the M iniBooNE detector.A sim ilaranalysishasbeen perform ed using the HARP forward spectrom eterforthe m ea-surem entofthe double-di erentialproduction cross-section of in the collision of12 G eV/cp (MeV/c)0 2000 4000 6000 8000) (mb/(GeV/c sr))Ω/(dp dpi σ2 d-210-110110210310-pi  +pi   = 0.03-0.06 radθp (MeV/c)0 2000 4000 6000 8000) (mb/(GeV/c sr))Ω/(dp dpi σ2 d-210-110110210310 = 0.06-0.09 radθp (MeV/c)0 2000 4000 6000 8000) (mb/(GeV/c sr))Ω/(dp dpi σ2 d-210-110110210310 = 0.09-0.12 radθp (MeV/c)0 2000 4000 6000 8000) (mb/(GeV/c sr))Ω/(dp dpi σ2 d-210-110110210310 = 0.12-0.15 radθp (MeV/c)0 2000 4000 6000 8000) (mb/(GeV/c sr))Ω/(dp dpi σ2 d-210-110110210310 = 0.15-0.18 radθp (MeV/c)0 2000 4000 6000 8000) (mb/(GeV/c sr))Ω/(dp dpi σ2 d-210-110110210310 = 0.18-0.21 radθp (MeV/c)0 2000 4000 6000 8000) (mb/(GeV/c sr))Ω/(dp dpi σ2 d-210-110110210310 = 0.21-0.24 radθFigure 2: M easurem entsofthe double-dierentialproduction cross-sections of+(open circles)and  (closedcircles)from 12 G eV/cprotonson 5% I carbon targetasa function ofpion m om entum ,p,in binsofpion angle,,in the laboratory fram e.The errorbarsshown include statisticalerrorsand all(diagonal)system atic errors.protonswith a thin 5% I carbon target.Theresultsareshown in Fig.2.Thesem easurem entsare im portantfora precise calculation ofthe atm ospheric neutrino  ux and fora prediction ofthe developm entofextended airshowers.3 R esults obtained w ith the H A R P large-angle spectrom eterFirstresultson the m easurem entsofthe double-di erentialcross-section forthe production ofcharged pions in proton{tantalum collisions em itted at large angles from the incom ing beamdirection have been obtained recently 13. The pions were produced by proton beam s in am om entum rangefrom 3G eV/cto12G eV/chittingatantalum targetwith athicknessof5% I.Theangularand m om entum rangecovered bytheexperim ent(100M eV/c p < 800M eV/cand0:35 rad   < 2:15 rad)isofparticularim portance forthe design ofa neutrino factory.Trackrecognition,m om entum determ ination and particleidenti cation wereallperform edbased on them easurem entsm ade with the TPC.Resultsforthe double-di erentialcross-sectionsd2=dpdatfourincidentproton beam m om enta (3 G eV/c,5 G eV/c,8 G eV/cand 12 G eV/c)areshownin Fig.3.Sim ilaranalysesare being perform ed forthe Be,C,Cu,Sn and Pb targetsusing the sam edetector,which willallow a study ofA-dependenceofthepion yieldswith a reduced system aticuncertainty to beperform ed.4 C onclusionsM easurem entsofthedouble-di erentialproduction cross-section ofpositivepionsin thecollisionof8.9 G eV/cprotonswith aberyllium targethavebeen presented.Thedata havebeen reportedin binsofpion m om entum and anglein thekinem aticrangefrom 0:75 G eV/c p  6:5 G eV/cand 0:030 rad    0:210 rad. A system atic error analysis has been perform ed yielding anaveragepoint-to-pointerrorof9.8% (statistical+ system atic)and an overallnorm alization errorof2% .Thedatahavebeen  tted totheem piricalparam eterization ofSanford and W angand theresulting param etersprovided. These production data have directrelevance forthe predictionofa   ux forM iniBooNE and SciBooNE experim ents.Prelim inary resultsforthe m easurem entofthe double-di erentialproduction cross-sectionof in thecollision of12 G eV/c protonswith a carbon targethave been presented.Figure 3: D ouble-dierentialcross-sections for +(left) and  (right) production in p{Ta interactions as afunction ofm om entum displayed in dierentangular bins(shown in m rad in the panels). The results are givenfor allincident beam m om enta (lled triangles: 3 G eV/c;open triangles: 5 G eV/c;lled rectangles: 8 G eV/c;open circles:12 G eV/c).The errorbarstake into accountthe correlationsofthe system atic uncertainties.Firstresultson the production ofpionsatlarge angleswith respectto the beam directionforprotonsof3 G eV/c,5 G eV/c,8 G eV/c and 12 G eV/c im pinging on a thin tantalum targethave been described. These data can be used to m ake predictions for the  uxes ofpions toenable an optim ized design ofa futureneutrino factory.A cknow ledgm entsItisa pleasureto thank theorganizersforthe nancialsupportwhich allowed m eto participatein theconference and to presenttheseresultson behalfofthe HARP Collaboration.R eferences1. M .G .Catanesietal. [HARP Collaboration],\Proposalto study hadron production fortheneutrino factory and forthe atm ospheric neutrino  ux",CERN-SPSC/99-35 (1999).2. M .G .Catanesietal.[HARP Collaboration],Nucl.Instrum . M ethodsA 571,527 (2007).3. M .H.Ahn etal.[K 2K Collaboration],Phys.Rev.Lett.90,041801 (2003).4. M .H.Ahn etal.[K 2K Collaboration],Phys.Rev.D 74,072003 (2006).5. A.A.Aguilar-Arevalo etal.[TheM iniBooNE Collaboration],arXiv:0704.1500 [hep-ex].E.Church etal.[BooNE Collaboration],FERM ILAB-PRO PO SAL-0898,(1997).6. A.A.Aguilar-Arevalo etal. [SciBooNE Collaboration],\Bringing the SciBardetectortotheBoosterneutrino beam ",FERM ILAB-PRO PO SAL-0954,(2006),[hep-ex/0601022].7. M .Anfreville etal.,Nucl.Instrum . M ethodsA 481,339 (2002).8. M .Baldo-Ceolin etal.,Nucl.Instrum .M ethodsA 532,548 (2004).9. M .G .Catanesietal.[HARP Collaboration],Nucl.Phys.B 732,1 (2006).10. M .G .Catanesietal.[HARP Collaboration],Nucl.Instrum .M ethodsA 572,899 (2007).11. M .G .Catanesietal.[HARP Collaboration],\M easurem entoftheproductioncross-sectionofpositive pionsin thecollision of8.9 G eV/c protonson beryllium ",[hep-ex/0702024].12. J.R.Sanfordand C.L.W ang,"Em piricalform ulasforparticleproduction in p-Becollisionsbetween 10 and 35 BeV/c",BNL,AG S internalreport,(1967)(unpublished).13. M .G .Catanesietal.[HARP Collaboration],\M easurem entoftheproduction ofchargedpionsby protonson a tantalum target",(in preparation).

Results from HARP and their implications for neutrino physics

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