QUARK FRAGMENTATION FUNCTIONS FROM AND PRODUCTION IN DEEP-INELASTIC SCATTERING FROM COMPASS Nicolas Pierre November 10, 2016 - GDR QCD 2016 CONTENTS

Extraction of 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 : POLARIZATION

1 - Strange quark polarisation is defined by : ∫ Δs() + 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 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 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 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 , 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 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 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

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 into . + 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 Extraction of quark FF into Pions EXTRACTIONExtractionExtraction OF QUARK of FF of INTOquark quark PIONS FF FF into into Pions Pions Charge and symmetry gives: Assume 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. 8-5 (z1) - dz)z dz ∫ 0.2 αi α βi β DIS 2016 9 2 2 2 0.2 z (1 -i z) dz i Evolution of Q = 1 (GeV/c) 2 to given Q done2 ∫ 2 z (1− z) Evolution from2 Q 0 = 1 (GeV2 /c) to2 Q∫ of data points with DGLAP with Evolution DGLAP equations.from Q 0 = 1 (GeV/c) to Q0.2 of0 .data2 points with DGLAP 2 2 2 Evolution fromNicolas PierreQ - Quark= 1 fragmentation (GeV /c)functions to from Q pion andof kaondata production points with DGLAP 2) Direct extraction in each0 kinematic bin 11 2) Direct extraction in each kinematicNovember bin 10, 2016 - GDR QCD 2016 2) Direct extraction in each kinematic bin DIS 2016 9 DIS 2016 9 DIS 2016 9 arXiv:1604.02695v2 Multiplicities of charged pions and unidentified charged hadrons from deep-inelasticΠ .± . .CERN-EP-2016-095 11 FF FROM COMPASS LO FIT OF M (to be published in PLB)

Q2 = 3 (GeV/c)2 π fav e+e- data COMPASS LO Results from COMPASS LO fit for

zD DSEHS'14 NLO 0.6 HKNS'07 NLO π π LSS'13 NLO D fav and D unf agree with other NLO fits using SIDIS data. 0.4

0.2

0 0.2 0.4 0.6 0.8 z LO fit on COMPASS 2006 data

Q2 = 3 (GeV/c)2 π unf COMPASS LO

zD DSEHS'14 NLO 0.6 HKNS'07 NLO LSS'13 NLO

0.4

0.2

0 0.2 0.4 0.6 0.8 z Nicolas Pierre - Quark fragmentation functions from pion and kaon production 12 2 November2 10, 2016 - GDR QCD 2016 π fav 0.8 Q = 3 (GeV/c) D

/ COMPASS LO DSEHS '14 NLO π unf 0.6 HKNS '07 NLO D LSS '13 NLO

0.4

0.2

0 0.2 0.4 0.6 0.8 z ⇡ ⇡ Figure 9: Favoured (top) and unfavoured (middle) quark-to-pion FFs and the ratio Dunf/Dfav (bottom), as obtained from the COMPASS LO fit, compared to the DSEHS, HKNS and LSS fits at NLO. The bands represent the total uncertainties for the FFs and the total statistical uncertainty for the ratio (see text). (Coloured version online)

An alternative method to extract the FFs from the pion multiplicity data is to solve the system of + two linear equations for M ⇡ and M ⇡ in each (x,y,z) bin for the values of D⇡ ( z , Q2 ) and fav h i h i D⇡ ( z , Q2 ) by using Eqs. (1) and (2). No functional form has to be assumed, and the DGLAP unf h i h i evolution for FFs is not needed. The same PDFs as mentioned above are used. The results from this di- rect extraction of FFs are in good agreement with the results obtained from the LO fit. This is illustrated in Fig. 10 for one (x, y) bin.

6 Summary and conclusions We have presented differential multiplicities of charge-separated pions and unidentified charged hadrons measured in SIDIS of off an isoscalar target. The results are given in 3-dimensional bins of x, y and z and cover the kinematic range Q2 > 1(GeV/c)2,0.004

Q2 = 3 (GeV/c)2 π fav COMPASS LO Results from COMPASS LO fit for

zD DSEHS'14 NLO 0.6 HKNS'07 NLO π π LSS'13 NLO D fav and D unf agree with other NLO fits using SIDIS data. 0.4 Results from direct extraction in 0.2 individual kinematic (x,y,z) bins 12agree with extraction from global The fit COMPASS Collaboration 0 0.2 0.4 0.6 0.8 z LO fit on COMPASS 2006 data Direct extraction for 1 x-y bin

2 2 π

Q = 3 (GeV/c) D 2 2

π unf 〈 〉

z Q = 5.7 (GeV/c) 0.6 data COMPASS LO π

zD DSEHS'14 NLO zD 0.6 fav HKNS'07 NLO π LSS'13 NLO zDunf 0.4 LO QCD fit 0.4

0.2 0.2

0 0 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 z z Nicolas Pierre - Quark fragmentation functions from pion and kaon production Figure 10: The z dependence of the favoured (closed symbols) and unfavoured (open13 symbols) quark-to-pion 2 November2 10, 2016 - GDR QCD 2016 π fav 0.8 Q = 3 (GeV/c) ⇡ ⇡ fragmentation functions, zDfav and zDunf, extracted directly from pion multiplicities for the bin 0.04

/ COMPASS LO DSEHSand '14 the NLO bin 0.1

π unf 2 2 0.6 HKNSshown '07 NLO at Q = 6(GeV/c) . The bands represent the total uncertainties of the QCD fit (see text). D LSS '13 NLO

The sum of the z-integrated positive and negative unidentified hadron and pion multiplicities shows a 0.4 flat x behavior, as expected in LO pQCD. For unidentified hadrons this sum is in agreement with EMC results taken at comparable kinematics, whereas some inconsistency is observed when comparing to 0.2 HERMES pion data that were taken at different kinematics. The ratio of the z-integrated positive and negative hadron and pion multiplicities as a function of x nicely confirms the previous measurements 0 from HERMES and EMC. 0.2 0.4 0.6 0.8 z The measured charged pion multiplicities were used for a LO extraction of the favoured and unfavoured ⇡ ⇡ Figure 9: Favoured (top) and unfavoured (middle) quark-to-pion FFs andpion the FFs. ratio WhileDunf both/Dfav FFs(bottom), are significantly as obtained different from those obtained in the HKNS fit to only the from the COMPASS LO fit, compared to the DSEHS, HKNS and LSSelectron– fits at NLO. The annihilation bands represent data, they the are totalin good agreement with those obtained in recent NLO fits uncertainties for the FFs and the total statistical uncertainty for the ratiothat (see also text). include (Coloured a preliminary version release online) of the present data.

An alternative method to extract the FFs from the pion multiplicityAcknowledgements data is to solve the system of + two linear equations for M ⇡ and M ⇡ in each (x,y,z) bin for the values of D⇡ ( z , Q2 ) and We gratefully acknowledgefav theh supporti h ofi the CERN management and staff and the skill and effort of D⇡ ( z , Q2 ) by using Eqs. (1) and (2). No functional formthe has technicians to be of assumed, our collaborating and the institutes. DGLAP This work was made possible by the financial support of unf h i h i evolution for FFs is not needed. The same PDFs as mentioned aboveour funding are agencies.used. The Special results thanks from go to this M. di- Hirai and S. Kumano for providing us with the DGLAP rect extraction of FFs are in good agreement with the results obtainedevolution from code the for fragmentation LO fit. This functions. is illustrated in Fig. 10 for one (x, y) bin. References [1] J.C. Collins, D.E. Soper and G.F. Sterman, Nucl. Phys. B 261 (1985) 104. 6 Summary and conclusions [2] BELLE Collaboration, M. Leitgab, et al., Phys. Rev. Lett. 111 (2013) 062002. We have presented differential multiplicities of charge-separated[3] pionsBabar and Collaboration, unidentified J.P. charged Lees, et al., hadrons Phys. Rev. D 88 (2013) 032011. [4] ALEPH Collaboration, R. Barate, et al., Phys. Rep. 294 (1998) 1; measured in SIDIS of muons off an isoscalar target. The results areDEHPI given Collaboration, in 3-dimensional O. Abreu, bins et al., of Eur.x, y Phys. J. C 5 (1998) 585; 2 2 and z and cover the kinematic range Q > 1(GeV/c) ,0.004

Data are averaged over y and integrated over z Data are averaged over y and integrated over z − − 1.2 π h COMPASS COMPASS (Z. Phys. C 52 (1991) 361) (PRD 89 (2014) 097101)

EMC ℳ HERMES

ℳ 0.9

+ + + + π h 1 charged hadrons 0.8 charged pions ℳ ℳ

0.7 0.8 Multiplicities of charged pions and unidentified charged hadrons0.6 from deep-inelastic . . . 9

arXiv:1604.02695v2 0.6 0.5 CERN-EP-2016-095 10−2 10−1 1 10−2 (to be published in PLB) 10−1 1 z fromMULTIPLICITY 0.2 to 0.85 and averaged SUM over y between 0.1 andx 0.7, as a function of x. The expected weak x x dependence is indeed observed in the data. In the same figure, the results of HERMES [8] integrated over Results on charged hadrons are in good agreement with those of EMC (similar kinematic range) z from 0.2 to 0.8 are shown using the so-called x representation. The HERMES multiplicities are larger ResultsThe multiplicity on charged sum pions has a are very in simplegood agreement expression with at LO LO : predictions: Dπ = Dπ+ = Dπ+ = Dπ− and show a different dependence on x. Note however that the HERMES data were measuredfav at au lower d d π π 2(s(x) s (x))(D D ) π− energy andπ+ correspondπ− π to differentπ kinematics. In+ order to comparefav − unf the COMPASS resultssmall= also x-dependentD with M +M = Dfav + Dunf − u the EMC ones [9], the sum of unidentified-charged-hadron5(u(x)+ d(x)+ u(x)+ d ( multiplicitiesx))+ 2(s(x)+ iss shown(x)) in Fig. 7 (right).terms The Dπ = Dπ+ = Dπ+ = Dπ− results from COMPASS and EMC, which correspond to comparable kinematics, are foundunf in excellentd u u π− π± π± agreement. very small x-dependent term Data are here averaged over y and integrated over z = Dd = Ds = Ds

− − 1.2 π howeverCOMPASS there is a disagreement with HERMESh (lowerCOMPASS energy)

ℳ HERMES EMC

0.9 ℳ + + DIS 2016 11

+ Charged pions Charged hadrons + π h 0.8 1 ℳ ℳ

0.7 0.8 0.6

0.5 0.6 10−2 10−1 1 10−2 10−1 1 x x

+ FigurePion 7: Left: : Flat Sum shape of M as⇡ expectedand M ⇡ fromversus LOx. predictions. The COMPASS data (closed circles) are compared to HERMES + results (open Disagreement circles); Right: Sumwith of HERMESM h and (howeverM h versus taken atx .lower The COMPASSenergy). data (closed circles) are compared to EMCHadron results : (openResults circles). on charged The systematic hadrons uncertainties in good agreement are shown as with bands EMC at theresults bottom. (similar kinematic range). Nicolas Pierre - Quark fragmentation functions from pion and kaon production 14 November 10, 2016 - GDR QCD 2016 + Another quantity of interest is the x dependence of the ratio M ⇡ /M ⇡ , where most experimental systematic effects cancel. The results are shown in Fig. 8 (left) as a function of x. They are in reasonable agreement with the HERMES values in the measured range. The values obtained from the JLab E00-108 experiment [24] for z>0.3 at higher x and lower W values are also shown for completeness. In Figure 8 + (right), the ratio M h /M h calculated for unidentified hadron multiplicities is shown for COMPASS and EMC data. These results are in excellent agreement.

− COMPASS COMPASS − π HERMES h EMC JLab E00-108 ℳ ℳ / 1.6 / + +

π h 2 ℳ ℳ 1.4

1.5 1.2

1 1 10−2 10−1 1 10−2 10−1 1 x x

+ Figure 8: Left: Ratio M ⇡ /M ⇡ versus x from COMPASS (closed points), HERMES (open circles) and JLab + (open squares). Right: Ratio M h /M h versus x for COMPASS (closed circles) and EMC (open circles) results. The systematic uncertainties are shown as bands at the bottom.

5 Extraction of quark-to-pion fragmentation functions The present data on pions cover a wide kinematic range in x and z and represent an important input for the extraction of quark-to-pion FFs in future NLO pQCD analyses of the world data. We present here Multiplicities of charged kaons from deep-inelastic muon scattering off an isoscalar target 7

0.004 < x < 0.01 0.01 < x < 0.02 0.02 < x < 0.03 0.03 < x < 0.04 0.04 < x < 0.06 α α = 0.20 + − α = 0.15

K 0.6 0.6 0.6 0.6 α = 0.10 z M

d α = 0.05 d 0.4 α = 0 0.4 0.4 0.4

0.2 0.2 0.2 0.2

0 0 0 0

0.06 < x < 0.10 0.10 < x < 0.14 0.14 < x < 0.18 0.18 < x < 0.40 0.20.2 0.4 0.6 0.6 0.8 0.8

0.6

0.50 < y < 0.70

0.4 0.30 < y < 0.50

0.20 < y < 0.30 0.2 0.15 < y < 0.20 0.10 < y < 0.15

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 arXiv:1608.06760v1z CERN-EP-2016-206 KAON MULTIPLICITYFigure 5:RESULTSSame as Fig. 4 but for negative kaons.(submitted to PLB)

K 0.004 < x < 0.01 0.01 < x < 0.02 0.02 < x < 0.03 0.03 < x < 0.04 0.04 < x < 0.06 z M d d 0.4 0.4 0.4 0.4 K+ − 0.2 K0.2 0.2 0.2

0 0 0 0

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 0.4

0.2

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 : FigureAcceptance 6: Positive (closed) : 5% and negative (open) kaon multiplicities vs z for the nine x ranges.x, y, Thez 3D-binning bands correspond to the totalRICH systematic PID/Efficiency uncertainties. for K± : 0.2% (low y) - 15% (high y, high z) 317 kinematic bins Diffractive VM correction : < 6% max (low x, mid z) Strong z-dependance quark-to-kaon FF. For the COMPASS kinematics, the applicability of the LO pQCD formalism to pion Nicolas Pierre - Quark fragmentation functions from pion and kaon production multiplicities was already demonstrated [13]. For an isoscalar target and assuming isospin and charge 15 + November 10, 2016 - GDR QCD 2016 symmetry, the sum of K and K multiplicities can be written in LO in a very simple way [24] . For multiplicities integrated over z, M K± = MK± (x,y,z) dz, the equation reads: h iy R K K + UD + SD M K + M K = U S , (6) 5U + 2S with U = u + u¯ + d + d¯, and S = s + s¯. The z-integrated FFs, DK(Q2)= DK(z,Q2)dz, depend on Q2 R Leading order extraction of fragmentationChargeEXTRACTION and isospin OF symmetry QUARK gives:FF INTO functions KKAONSK± K+ K− into kaons D fav = Dfav = Du = Du All in all, 12 FFs to extract. But using similar symmetriesK and assumptionsK± K,+ reductionK+ to 3 independentK− K− FFs : K± K± Dunf = Dunf = Du = Ds = Du = Ds = Dd = Dd K K± K+ K− Dstr = Dstr = Ds = Ds ForFor an an isoscalar isoscalar target, target, in LO :in LO: 2sD + 4(u + d)D + (u + d + 5(u + d )+ 2s)D M K+ (x, z,Q2 ) = str fav unf 5(u + d + u + d )+ 2(s + s ) 2sD + 4(u + d )D + (5(u + d)+ u + d + 2s )D M K− (x, z,Q2 ) = str fav unf 5(u + d + u + d )+ 2(s + s ) u, d, u, d, s, s = parton distribution functions(MSTW08) Only possibility to extract the quark FFs into kaons is to fit the multiplicities. Fits of experimental multiplicities: These Functional precise data form: will z constituteD (z, Q an2 ) important = N zα iinput(1 - for z) globalβi (1 NLO(1 QCD - z fits)δi ) i 0 i +γi K i = fav and to extract the quark fragmentation functions, in particular D str. 2 αi βi zDi (z, Q0 ) = Niz (1 - z) i = str,unf, glu 2 2 Evolution from Q 0 to Q of data points with DGLAP

DIS 2016 21 Nicolas Pierre - Quark fragmentation functions from pion and kaon production November 10, 2016 - GDR QCD 2016 16 8 The COMPASS Collaboration − 0.004 < < 0.01 0.01 < < 0.02 0.02 < < 0.03 0.03 < < 0.04 0.04 < < 0.06

K x x x x x z M

d 3 3 3 3 3 d / + K z M d d 2 2 2 2 2

1 1 1 1 1

15 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

10

5

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 7: Ratio of multiplicities (dMK /dz)/(dMK /dz) vs z for the nine x ranges. The bands correspond to the total systematic uncertainties.

K K K K+ K+ K+ K+ only. The symbols DU and DS denote the combinations of FFs DU = 4Du +4Du¯ +Dd +Dd¯ and K K+ K+ DS = 2Ds + 2Ds¯ . At high values of x, the strange content of the nucleon can be neglected, and in + K Kaona good approximation multiplicity the sum of K and K multiplicities sum is related to DU /5. This value is expected to have a rather weak Q2 dependence when integrated over z, so that it can be used at smaller values of + K K K x to determine the SDS value. The result for M + M is presented in Fig. 8 as a function of x at For the isoscalar target, when expressed2 at LO the sum has a simple form: + − the measured values of Q . The data are integrated over z in the range 0.20 to 0.85 and averaged over y dNK +K (u + d + u + d )(4DK +6DK )+ 2(s + s )(DK +arXiv:1608.06760v1DK ) QDK + SDK in the range 0.1 tofa 0.7.v Onlyunf those eight sxtr binsCERN-EP-2016-206un whichf haveQ a sufficientS z coverage are shown. A weak DIS = = dN x dependence5( isu + observed.d + u + d ) Figure+ 2(s + 8s also) shows(submitted the HERMES to PLB)5Q + 2S results [11] that were taken at 27.6 GeV KAONRecall, MULTIPLICITY u, d, u, dKaon, s, sbeam= parton energy. SUM distribution Theymultiplicity lie well functions below the COMPASS points sum and exhibit a different x behaviour. and charge and isospin symmetry gives: + K K K K K± K+ KFrom− the COMPASS result on M + MData areat highaveragedx (x =over0.25) y and we integrated extract D over z0 .65 0.70. This ForForD anthe= isoscalar Disoscalar= D target,= target,D at whenLO : expressed at LO the sum has a simple form: U fav fav u u COMPASS2 2006 data2 preliminaryK ⇡ + − differs from the earlierK DSSK fit result atKQ =K3(GeV/c)K , DU =K 0.43 0.04 [6], which was mainly K K± K +K K+ K+ K− K− K± K± ± dN (u + d + u + d )(4Dfav +6Dunf )+ 2(s + s )(DHERMESstr + Dunf )(PRDQ 89D (2014)Q + S097101)DS D unf = Dunf = Du = Dsbased= D onu = HERMESDs = Dd results.= Dd Towards0.2 low x, COMPASS data show a flat behaviour, unlike the rise that is = (z) ) dz = DIS − COMPASS lepto/jetset K Kd± N K+ Ksuggested− by5(u the+ d HERMES+ u + d )+ data2(s K and+ s ) the DSS FF parametrisation5Q + 2S [6]. Dstr = Dstr = D = Ds Recall, u, d, u, ds , s, s = parton distribution functions At high x, S~0 then − 0.2 K

andAt charge high x, and the Sisospin term can symmetry be neglected: gives: (z) + M + + − 0.15COMPASS ℳ K KK±+K K+ K − K K K Data are averaged over y and integrated over z D =dND = D (=4Dfav +6Dunf ) DQ fav fav u u + HERMESCOMPASS 2006 data preliminary ≈ = +

DIS ( M

K dNK± K+ K+5 K− 5K− K± K K± K HERMES (PRD 89 (2014) 097101) D un f = Dunf = Du = Ds = Du = Ds = Dd = Dd 0.2 (z) ) dz

This analysis: D ≈ 0.7 ℳ

Q − K 0.15 COMPASS lepto/jetset K FromK± COMPASSK+ Kfit− : D Q ~ 0.7K K 0.1 Dstr = Dstr = D = DsK DSS: D ≈ 0.43 ± 0.04 From DSSs fit : D Q ~ 0.43 ±Q 0.04 Again, as with the LO fits results the COMPASS At high x, the S term can be neglected: (z) + M 2 1 + − − Points+ −to larger non-strange FFs 0.15 10 10 kaonK + Kresults pointK to largerK non-strangeK FFs than K in x dN (4Dfav +6Dunf ) DQ the DSS parametrisation≈ than DSS = 0.1 dNDIS 5 5 ( M K This analysis: DQ ≈ 0.7 −2 −1 K K K 10 0.1 10 1 At low x, D str > D DSS:fav then D ≈ 0.43 ± 0.04 x Q DIS 2016 14 + K 2 K K D Q has weak Q dependanceFigure 8: Sum in ofourz-integrated range, one multiplicities, would expectM + Ma . COMPASS data (full points) are compared to HER- Again, as with the LO fits results the COMPASS 2ΔS = f (RSF ), MES data [11] (open points). The bands show−2 the total systematic uncertainties.−1 kaonrise inresults the kaon point multiplicity to larger non-strange sum at low FFs x, whichthan in is not10 the case. 10 K + x the DSS parametrisation Ds (z)dz Points to smaller RSF than DSS R ∫ SF = K + Du (z)dz Nicolas Pierre - Quark fragmentation functions from pion and kaon production ∫ 17 November 10, 2016 - GDR QCD 2016 DIS 2016 14 Corrections to data: Corrections to data: RADIATIVE CORRECTIONS Corrections to data: emission of an additional real ,radiative vertex correction, diffractive emission of an additional real and vacuum polarization photon,radiative vertex correction, diffractive emission of an additional real and vacuum polarization vector photon,radiative vertex correction, diffractive 2 vector

Radiative correctionsand (RC) vacuum polarization d σ1γ / dxdy 2 correctionmeson factor to the hadron yields determined η(x, y) = 2 = Emission of a real photon, vertex correction and d σ 1γvector/ dxdy d σ measured / dxdy using LEPTO(SIDIS) correctionmeson factorand HEPGEN(Diffractive) to the hadron yields determined η(x, y) = 2 vacuum polarization. 2 d σ meas ured / dxdy Monte Carlo,using with LEPTO(SIDIS) each sample andnormalized HEPGEN(Diffractive) using d σ1γ / dxdy η(x, y) = correctionmeson factor to thethe hadron respective yieldsMonte luminosities determined Carlo, with each sample normalized using 2 correction factors for both the numerator (Nh) d σ measured / dxdy using LEPTO(SIDIS) and HEPGEN(Diffractive) correction factors for both the numerator (N ) the respective luminositiesh and denominator (NDIS) of the multiplicity: h h N (x, y, z) COMPASS uses RADGEN. Monte Carlo, with each sample normalized usingHEP GEN h and denominator (NDIS) of the multiplicity: f 0 (x, y, z) = h Nh (x, y, z) OK for inclusive DIS, but not for SIDIS. Does not include the z dependence. the respective luminositiesρ ,Φ h HEPGEN correction factors for both the numerator (Nh) f 0 N(xL,EPyT,Oz()x=, y, zh )+ NHEPGEN (x, hy, z) NDIS correction: Dubna scheme (TERAD) ρ ,Φ h NLEPTO (x, y, z)+ NHEPGEN (x, y, z) and denominator (NDIS) of the multiplicity:N correction: Dubna scheme (TERAD)similar correction for the diffractive events in the Nh correction: “TERADDIS − el tail −h qel tail” NHEPGEN (x, y, z) f 0 (x, y, z) = similar correction for the diffractive events in the Nh correction: “TERADρ ,Φ − el tail − qelh tail”DIS sample h Total RC applied to theN multiplicity correction: goes Dubna from 5% scheme at low x - (TERAD) high y to <1% at high x - low y. NLEPTO (x, y, z)+ NDISHEP sampleGEN (x, y , z) DIS The total radiative correction applied to the similar correction for the diffractive events in the Nh correction: “TERAD − el tail −The qel tail”total radiative correction appliedoverall to the correction is <10% in most bins multiplicity ranges from ~5%DIS at lowsample x - high multiplicity ranges from ~5% at low xexcept: - high overall correction is <10% in most bins y, down to <1% at high x - low y. except: The total radiative correction appliedy, down to to the <1% at high x - low y. kaons: low x, mid z where it can reach ~25% overall correction is <10% in mostkaons bins: low x, mid z where it can reach ~25% multiplicity ranges from ~5% at low x - high pions: low x, high z where it can reach ~55% y, down to <1% at high x - low y. except: pions: low x, high z where it can reach ~55% Nicolas Pierre - Quark fragmentation functions from pion and kaon production kaons: low x, mid z where it can reach ~25% November 10, 2016 - GDR QCD 2016 18 DIS 2016 7 pions: low x, high z where it can reach ~55% DIS 2016 7

DIS 2016 7 IMPROVING THE RESULTS

NU-nu_true {Y>0.8&&Y<0.9&&Q2>1&&Q2<2&&irad>0}2 Energy of radiated photon (0.8

800 Naïve thinking : in theory, more soft than hard photons. 600

400 But : MC simulation + RADGEN do Ongoing analysis not describe well data : too much 200 hard photon. 0 −20 0 20 40 60 80 100 120 140 160 NU-nu_trueGeV

Can we use another MC generator for radiative events and see if it reproduces the results of RADGEN ?

Nicolas Pierre - Quark fragmentation functions from pion and kaon production November 10, 2016 - GDR QCD 2016 19 DJANGOH / RADGEN COMPARISON

Energy of radiated photon (0.80.8&&Y<0.9&&Q2>1&&Q2<2&&irad>0} Eγ E htemp γ 1400 Entries 20003 Entries 14895 Mean 120 7000 Mean 39.41 RMS 34.79

# Events Std Dev 46.5 1200

#Events 6000 #Events

1000 5000 DJANGOH RADGEN

800 4000

600 3000

400 2000 Ongoing analysis 1000 Ongoing analysis 200

0 0 −20 0 20 40 60 80 100 120 140 160 −20 0 20 40 60 80 100 120 140 160 E (GeV) NU-nu_true γ GeV GeV

First observation : DJANGOH produces more soft photons than hard photons

Nicolas Pierre - Quark fragmentation functions from pion and kaon production November 10, 2016 - GDR QCD 2016 20 DJANGOH / RADGEN COMPARISON

20 18,6% DJANGOH 16,3% RADGEN 15

Proportion of 10 8,6% inelastic events in

% of events of % range [20,140] GeV over total number of 5 Ongoing analysis 3,6% DIS events. 1,3% 1% 1,5% 0,6% 0,9% 0,4% 0,5% 0,7% 0 20-40 40-60 60-80 80-100 100-140 Total

DJANGOH produces less hard photons than RADGEN

Nicolas Pierre - Quark fragmentation functions from pion and kaon production November 10, 2016 - GDR QCD 2016 21 SUMMARY AND PROSPECTS

Summary High precision data on charged pion, kaon and hadron multiplicities measured from COMPASS data taken with an isoscalar 6LiD target and a 160 GeV µ+ beam. Good agreement with EMC results and a discrepancy with respect to HERMES results. π π Pion : D fav and D unf extracted from LO fits to COMPASS multiplicities in good agreement with NLO fits of world data.

K Kaon : present results point to potentially larger D fav than previously thought. Very large set of precise data will constrain FF into kaons. The result is much awaited for the nucleon spin puzzle. Prospects

RC results from DJANGOH may have an impact on kaon multiplicities.

Ongoing work on 2016 COMPASS data taken with a lH2 target and a 160 GeV µ+/µ- beam.

Nicolas Pierre - Quark fragmentation functions from pion and kaon production November 10, 2016 - GDR QCD 2016 22 BACKUP THE DJANGOH GENERATOR

Event generator for neutral/charged current ep interactions at HERA by H. Spiesberger.

Simulates DIS using LEPTO including both QED and QCD radiative effect.

Includes single photon emission from /quark line, self energy corrections and complete set of one-loop weak corrections.

Includes also the background from e p → e p γ.

Capable of obtaining hadronic final state via the use of JETSET.

Modified to work for μp interactions.

Nicolas Pierre - Quark fragmentation functions from pion and kaon production November 10, 2016 - GDR QCD 2016 Corrections to data: ACCEPTANCE AND SMEARING

Correction for theacceptance limited geometrical acceptance, and reconstruction smearing and detectors Correctioninefficiencies for the aslimited well asgeometrical resolutions acceptance,and contamination reconstruction in the and reconstructed detector inefficiencies as well sample. as resolutions and electron contamination in the reconstructed sample

reconstructed multiplicity kinematic bin determine using reconstructed multiplicities kinematicreconstructed bin values determined using reconstructed values

h DIS Mrec Nrec (x', y', z') / Nrec (x', y') A(x, y, z) = = h DIS ~70% Mgen Ngen (x'', y'', z'') / Ngen (x'', y'')

generated multiplicities kinematic bin determine using generated multiplicity kinematicgenerated bin values determined using generated values MC technical features : MC technicalEvents features: are generated with the LEPTO generator ² Events JETSETare generated package withfor parton the LEPTO harmonization generator with compass(LUND model) high pT tuning FLUKA used to simulate secondary interactions in the target ² JETSET package for parton hadronisation with COMPASS high pT tuning ² FLUKA Spectrometerused to simulate simulated secondary using GEANT3 interactions in the target ² Spectrometer simulated using GEANT3

DIS 2016 24 RICH PID RICHANDRICH UNFOLDING PIDPID andand unfoldingunfolding

RICH PID and unfolding COMPASSCOMPASS 20062006 data data ²² Particle ParticleParticle identification identificationidentification uses uses uses likelihoods likelihoods likelihoods basedbased onon thebased number on the and number distribution and of distribution detected of the number and distribution of detected COMPASS 2006 data photons in RICH associated to a charged ² detectedParticlephotons identification in photons RICH associated inuses RICH likelihoods associatedto a charged based to on a particlechargedtheparticle number particle and distribution of detected Purityphotons of in the RICH pion associated and kaon to a samplecharged ²² Purity dependsparticlePurity of of the the on pion pionthe and probabilityand kaon kaon sample sample of correct dependsdepends onon thethe probabilities, probabilities, P, P, of of correct correct identification identification andand ²misidentification, identificationPuritymisidentification, of the pion and anddetermined determined misidentification, kaon sample through through depends analysisanalysis on ofdeterminedtheof known known probabilities, decay decay through channels P,channels of correct analysis in in identificationdata data of known and decaymisidentification, chainel in determined data through analysis ²² The ofThe known pion pion and decayand kaon kaon channels yields yields in are aredata corrected corrected usingusing ) The pion and kaon yields are corrected ) - - π π

theseusingthese probabilities probabilitiesthe probabilities by by unfolding: unfolding: by unfolding : 11 → ² The pion and kaon yields are corrected using →

) - - - π these probabilitiesRICHRICH by unfolding: probabilities probabilities 1 0.80.8 P(h P(h COMPASS 2006 data → COMPASS 2006 data

I I PP(π(π±±ππ±)± ) PP(π(π±±KK±±) ) PP((ππ±±pp±±)) TT - π- → π- preliminary π π RICH probabilities ππ 0.8 0.6 - - preliminary P(h 0.6 K → π K- → π- COMPASS 2006 data ± ± ± ± ± ± - p- - → π- I P(π±± π ±)± P(π ±±K ) ± ± P(π ±p± ) ±± T π → πp → π preliminary I Iπ = = PP(K(Kππ) ) PP(K(KKK) ) PP((KKpp )) π TT 0.6 - - K K KK 0.40.4K → π p- - I = P(K±π±) P(K±K±) P(K±p±) T → π IK P(p±±π± ±) P(p±±K±±) P(p±±p±±) K T 0.4 Ip p P(p π ) P(p K ) P(p p ) Tpp 0.20.2 ± ± ± ± ± ± Ip P(p π ) P(p K ) P(p p ) Tp 0.2 0 Identified “True” 0 Identified “True” 0 15 20 25 25 30 30 35 35 40 40 pp (GeV/c) (GeV/c) Identified “True” 15 20 25 30 35 40hh p (GeV/c) h DIS 2016 2222 DIS 2016 22 MULTIPLICITY FITSMultiplicity fits

α 0.004 < x < 0.01 0.01 < x < 0.02 0.02 < x < 0.03 0.03 < x < 0.04 0.04 < x < 0.06 α = 1.00 +

− 3 3 3 3 π α = 0.75 −

z α = 0.50 π d

dM α = 0.25 2 2 2 2 α = 0

1 1 1 1

0 0 0 0

0.06 < x < 0.10 0.10 < x < 0.14 0.14 < x < 0.18 0.18 < x < 0.40 0.20.2 0.4 0.6 0.6 0.8 0.8 3

2 0.50 < y < 0.70 0.30 < y < 0.50 0.20 < y < 0.30 1 0.15 < y < 0.20 0.10 < y < 0.15 curves: COMPASS 0 LO fit 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

DIS 2016 19 MULTIPLICITY FITSMultiplicity fits

α 0.004 < x < 0.01 0.01 < x < 0.02 0.02 < x < 0.03 0.03 < x < 0.04 0.04 < x < 0.06 α = 1.00 +

+ 3 3 3 3 π α = 0.75 +

z α = 0.50 π d

dM α = 0.25 2 2 2 2 α = 0

1 1 1 1

0 0 0 0

0.06 < x < 0.10 0.10 < x < 0.14 0.14 < x < 0.18 0.18 < x < 0.40 0.20.2 0.4 0.6 0.6 0.8 0.8 3

2 0.50 < y < 0.70 0.30 < y < 0.50 0.20 < y < 0.30 1 0.15 < y < 0.20 0.10 < y < 0.15 curves: COMPASS 0 LO fit 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 zzz

DIS 2016 20