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QUARK FRAGMENTATION FUNCTIONS from PION and KAON PRODUCTION in DEEP-INELASTIC SCATTERING from COMPASS Nicolas Pierre November 10, 2016 - GDR QCD 2016 CONTENTS

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QUARK FRAGMENTATION FUNCTIONS from PION and KAON PRODUCTION in DEEP-INELASTIC SCATTERING from COMPASS Nicolas Pierre November 10, 2016 - GDR QCD 2016 CONTENTS QUARK FRAGMENTATION FUNCTIONS FROM PION AND KAON PRODUCTION IN DEEP-INELASTIC SCATTERING FROM COMPASS Nicolas Pierre November 10, 2016 - GDR QCD 2016 CONTENTS Extraction of quark fragmentation functions from pion multiplicities Extraction of quark fragmentation functions from kaon multiplicities Radiative corrections Nicolas Pierre - Quark fragmentation functions from pion and kaon production November 10, 2016 - GDR QCD 2016 2 MOTIVATION : STRANGE QUARK POLARIZATION 1 Nucleon spin - Strange quark polarisation is defined by : ∫ Δs(x) + Δs (x)dx = 2ΔS 0 From NLO QCD fits of g1 along with a8 from β decay : 2ΔS = −0.08 ± 0.01± 0.02 (PLB 647(2007) 8-17) K± π ± p,d From NLO QCD fits of longitudinal SIDIS A 1 , A 1 and A 1 : 2ΔS = −0.01± 0.01± 0.01 (PLB 693(2010) 227-235) ΔS form Semi-Inclusive Asymmetries strongly linked to quark fragmentation, especially the strange one, poorly known : K + Ds (z)dz (PRB 75(2007) 114010) ∫ FFs 2ΔS = f (RSF ), RSF = + DK (z)dz ∫ u Nicolas Pierre - Quark fragmentation functions from pion and kaon production November 10, 2016 - GDR QCD 2016 3 MOTIVATION : STRANGE QUARK POLARIZATION (PLB 680(2009) 217) ΔS form Semi-Inclusive Asymmetries strongly linked to quark fragmentation, especially the strange one, poorly known : K + Ds (z)dz (PRB 75(2007) 114010) ∫ FFs 2ΔS = f (RSF ), RSF = + DK (z)dz ∫ u One goal of the analysis : Extract FFs from COMPASS kaon data and then determine RSF Nicolas Pierre - Quark fragmentation functions from pion and kaon production November 10, 2016 - GDR QCD 2016 4 FRAGMENTATION FUNCTIONS Fragmentation functions : Quark fragmentation function into hadron h D q : probability density of finding a hadron h with a certain energy fraction z of the struck quark q at given Q2. Can be measured in several processes, including SIDIS. Are universal quantities, can describe several processes. Nicolas Pierre - Quark fragmentation functions from pion and kaon production November 10, 2016 - GDR QCD 2016 5 HadronHADRON multiplicities MULTIPLICITIES FROM SIDIS from SIDIS What is a SIDIS hadron multiplicity measurement ? 2 Q Q2 What is a SIDISOne can hadron express multiplicity the differential measurement? cross section for hadron x =x 2=M N (El − El′ ) The differentialproduction cross normalised section for to the hadron differential production inclusive DIS 2M N (El − El' ) E normalised crossto the section differential by : inclusive DIS cross section: z = h E (E E )h z 2 3 h 2 2 z = l − l′ h dM2 (x,z,3Q )h d σ (2x,z,Q ) / d2xdQ dz 2 (E2 l − El' ) 2 dM (x, z,Q ) d σ (=x, z,Q2 ) / dx2dQ dz 2 Q = −q = −(p − p ) dz d (x,Q ) / dxdQ l l′ = 2 σ2 2 2 2 dz d σ (x,Q ) / dxdQ Q = −(pl − pl' ) Hadron multiplicitiesThis can also can be beexpressed, expressed in LO pQCDin terms, as a offunction parton of Partondistribution Distribution functions Functions (pdfs (PDFs) and) and Fragmentation Functions (FFs) : fragmentation functions (FFs), in LO pQCD this reads: quark to hadron FFs quark pdfs 2 2 hquark2 to hadron FFs z 2 e q(x,Q )D (z,Q ) dM (x,z,Q ) ∑q q q h 2 2 2 h 2 = 2 2 dM (x, z,Q d)z ∑q eq q(x,Q e)Dqq(x(,zQ,Q) ) ∑q q = 2 2 dz ∑q eq q(x,Q ) quark PDFs Nicolas Pierre - Quark fragmentation functions from pion and kaon production November 10, 2016 - GDR QCD 2016 6 DIS 2016 3 COMPASS spectrometer COMPASS SPECTROMETER COMPASS 2006 data ² Designed for fixed-target experiments atFixed CERN target SPS experiment at CERN SPS ² CanCan operateoperate with with muon muon or hadronor hadron beams beams ² This analysis: 160 GeV µ+ beam (2006) This analysis : 160 GeV µ+ beam (2006) SM2 50 m ² Excellent charged π, K, p RICH : excellent charged π, K, p discrimination with the RICH RICH discrimination SAS ²This This analysis analysis: : 1.2 m 1.2 long, m long,SM1 polarizedpolarized 6LID 6isoscalarLiD isoscalar target target (2006) (2006) LAS : Large Angle Spectrometer 6 LID target (low momentum tracks) 160 GeVNicolas µ Pierre - Quark fragmentation functions from pion and kaon production November 10, 2016 - GDR QCD 2016 7 DIS 2016 4 COMPASS KINEMATICS The COMPASS kinematic range : Eµ = 160 GeV/c Q2 > 1 (GeV/c)2 W > 5 GeV/c2 (avoid target fragmentation region) 0.004 < x < 0.4 0.1 < y < 0.7 (avoid momentum resolution deterioration or high radiative effects) 0.2 ≤ z ≤ 0.85 (exclude muon tagged as hadrons, avoid target remnant fragmentation contamination) Hermes kinematic range Nicolas Pierre - Quark fragmentation functions from pion and kaon production November 10, 2016 - GDR QCD 2016 8 MULTIPLICITY ANALYSIS COMPASS Raw Data Event and particle reconstruction Event and particle selection RICH PID Final Multiplicities dM h (x, y,z) N h (x, y,z) / Δz = Detector acceptance dz N DIS (x, y) Kinematic bin smearing Electron contamination * COMPASS Diffractive vector meson correction Monte Carlo Simulation Radiative correction (* Because of poor RICH discrimination btw e-/π, necessary for pion/unidentified hadron multiplicities) Corrections Nicolas Pierre - Quark fragmentation functions from pion and kaon production November 10, 2016 - GDR QCD 2016 9 arXiv:1604.02695v2 8CERN-EP-2016-095 The COMPASS Collaboration PION MULTIPLICITY RESULTS (to be published in PLB) π 3 0.004 < x < 0.01 3 0.01 < x < 0.02 3 0.02 < x < 0.03 3 0.03 < x < 0.04 0.04 < x < 0.06 z M d d 2 π+ 2 2 2 π− 1 1 1 1 0 0 0 0 3 0.06 < x < 0.10 0.10 < x < 0.14 0.14 < x < 0.18 0.18 < x < 0.40 0.2 0.4 0.6 0.8 2 1 0 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 z Systematic studies : Figure 5: PositiveAcceptance (closed) : 5% and negative (open) pion multiplicities versus z for nine xx,bins. y, z The3D-binning bands correspond to the total systematicRICH PID/Efficiency uncertainties. for π± : 0.1% (low y) - 2% (high y) 317 kinematic bins Diffractive VM correction : 12% max (low x, high z) Strong z-dependance h Electron0.004 < x <correction 0.01 :0.01 50% < xconservative < 0.02 sys.0.02 < errorx < 0.03 0.03 < x < 0.04 0.04 < x < 0.06 z 3 3 3 3 M d d Nicolas Pierre - Quark fragmentation functions from pion and kaon production November 10, 2016 - GDR QCD 2016 10 2 h+ 2 2 2 h− 1 1 1 1 0 0 0 0 3 0.06 < x < 0.10 0.10 < x < 0.14 0.14 < x < 0.18 0.18 < x < 0.40 0.2 0.4 0.6 0.8 2 1 0 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 z Figure 6: Same as Fig. 5 for charged unidentified hadrons. product of the strange quark distribution and the fragmentation function of strange quarks into kaons. + The summed ⇡ and ⇡− multiplicities allow us to verify the applicability of the LO pQCD formalism in the COMPASS kinematic domain. For an isoscalar target and taking into account only two independent ⇡ ⇡ + quark FFs Dfav and Dunf (see Section 5), the sum of ⇡ and ⇡− multiplicities integrated over z can be written at LO as + 2S M ⇡ + M ⇡− = D⇡ + D⇡ (D⇡ D⇡ ), (6) fav unf − 5U + 2S fav − unf with M ⇡± = M ⇡± (x,y,z) dz. The combinations of PDFs U = u+u¯ +d+d¯ and S = s+s¯ depend h iy on x and Q2, and D⇡ (Q2)= D⇡ (z,Q2)dz and D⇡ (Q2)= D⇡ (z,Q2)dz are integrated over the R fav fav unf unf measured z range and depend on Q2 only. The pion multiplicity sum is expected to be almost flat in x, R 2 ⇡R ⇡ as the term 2S/(5U + 2S) is small and the Q dependence of Dfav + Dunf is rather weak (of the order of 3%) [7]. ⇡+ ⇡ + Figure 7 (left) shows the result for the sum M + M − of ⇡ and ⇡− multiplicities, integrated over Extraction of quark FF into Pions Extraction of quark FF into Pions EXTRACTIONExtractionExtraction OF QUARK of FF of INTOquark quark PIONS FF FF into into Pions Pions Charge and isospin symmetry gives: Assume strangeness equals unfavoured : π π+ π+ π− π− π π± π± All in all, 12 FFs to extract. But using symmetries and assumptions, reduction to 2 independentDfa vFFs= D :u = D = Dd = D D = D = D ChargeCharge andand isospinisospin symmetry symmetry gives: gives: AssumeAssume strangeness strangeness equals equals unfavoured unfavoured : d : u unf s s ChargeCharge and and Isospin isospin symmetries symmetry gives: StrangenessAssume strangeness = unfavoured equals assumption unfavouredπ π+ π:+ π− π− Dunf = Dd = Du = Du = Dd ππ ππ++ ππ+ + π−π− π−π− π π π± π± π± π± Dffaavv ==DDuπu ==DDπ+ ==DπDd+ d ==DπD− π− D D=π D= D=π±D = πD± D = D d d = D = D u =u D unf unf s s s s π π fav u d d u Dunf = Ds = Ds (4(u + d)+ u + d )D + (u + d + 4(u + d )+ 2(s + s ))D ππ ππ++ ππ+ + π−π− π−π− π+ 2 fav unf D Dπ Dπ+ Dπ+ Dπ− π− M (x,Q , z) = Duunnff == Ddd == Du u == Du u == Dd d Dunf = Dd = Du = Du = Dd 5(u + d + u + d )+ 2(s + s ) π π π π π π π π π− 2 (u + d + 4(u + d ))Dfav + (4(u + d)+ u + d + 2(s + s ))Dunf π+ 2 ((44(u(u+(+4d(d)u+)++udu+)++du)dD+)Dfdav)+D(+u(++ud(+u++d4d+(u+44+(u(du+)++dd2))(+s22+((ss+)+)sDs)u))nD)f D M (x,Q , z) = MM π+ (xM,,QQπ+2,(,zxz),)Q==2, z) = fav fav unuf nf 5(u + d + u + d )+ 2(s + s ) 5(5u(+u5d+(u+d+u+d+u+du+)+d+d)2+)(+s2+2((sss+)+ss)) where π π u, d, u, d, s, s = parton distribution functions(MSTW08) π π π π π− 2 2(u + d(+u +4(du++4d(u))+Ddfa)v)+D(fa4v(+u(+4(du)++du)++du ++d2(+s2+(s +))sD)u)nDf unf are PDFs M π− (xM,Qπ−2,(zx),Q= ,(zu)+= d + 4(u + d ))Dfav + (4(u + d)+ u + d + 2(s + s ))Dunf Two methods of LO extraction M (x,Q , z) = 5(u +5d(u+ ud+ du)+d2)(s +2(ss) s ) + + + + + 1) Fits of experimental multiplicities: αi βi 5(u + d + u + d )+ 2(s + s ) 2 z (1 - z) Functional form: z D i (z, Q0 ) = N i 0.85 u, d, u,u,dd,,su, ,sd,=s ,partons = parton distribution distribution functions(MSTW08) functions(MSTW08) α β Twou, methodsd, u, d, sof, LOs extraction= parton distribution functions(MSTW08) ∫ z i (1 - z) i dz Two methods of LO extraction 0.2 Two Directmethods extraction of LO with extraction above formulas in each kinematic bin (not possible with kaons) 2 2 2 Two methods of LO extraction Evolution from Q 0 = 1 (GeV/c) to Q of data points with DGLAP 1) Fits1) of Fits experimental of experimental multiplicities: multiplicities: α αi β βi 2 i z (1 -i z) 1) FitsFits of to experimental data of multiplicities multiplicities: : 2 z (1 - αz) β Functional Functional form: form:z D (zz, DQ i (z), =Q N 0 ) = N i 0.85αi i βi i i 0 2 2i 0.85 z z(1 -(1 z−) z) 2) Direct extraction in each kinematic bin αi βi Choice Functional of functional form: formz D : (zzD, Q(z,)Q = N ) Nαi β i i i 0 0 =i 0z.85∫i(10z.
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