Hadron Mass Effects on Kaon Multiplicities: HERMES vs. COMPASS Juan Guerrero Hampton University & Jefferson Lab QCD evolution 2017 May 26, 2017 Based on: J. G., J. Ethier, A. Accardi, S. Casper,W. Melnitchouk, JHEP 1509 (2015) 169 J.G & Alberto Accardi, work in progress
What can we see inside a proton? Partons: s u s c u d c 3 valence quarks p = (u u d) Gluons sea quarks: strange, charm, bottom. Parton (momentum) Distributions Function (PDFs): Well determined for the valence quarks and gluons. Interested in the s-quark. Not the case for the sea quarks. juanvg@jlab.org QCD evolution 2017, May 26 2017 2
Strange quark PDF one way How can we access the s-quark PDF? Tagging Kaon in Hard Scattering reactions For example: Semi inclusive Deep inelastic scattering (SIDIS): e + p! e + h + X h = K l l 0 s s ū s u X K + Kaon contains an s-quark in their valence structure. Detect a Kaon: good proxy for a strange quark p juanvg@jlab.org QCD evolution 2017, May 26 2017 3
Integrated Kaon Multiplicities Experimentally HERMES (COMPASS): M K exp = Rexp R dq2 0.8(0.85) dn K 0.2 dx B dq 2 dz h dz h Rexp dq2 dn e dx B dq 2 Parton model Multiplicities (fixed Q 2 ) : M K (x B,Q 2 )= Pq e2 q q(x B ) R 0.8(0.85) 0.2 D h q (z h )dz h P q e2 q q(x B ) Z s(x B ) D K s (z h )dz h Comparing these two expressions Extract the s-quark PDF. juanvg@jlab.org QCD evolution 2017, May 26 2017 4
Integrated Kaon Multiplicities: SIDIS on Deuteron HERMES: Claim very different s-quark shape compared to CTEQ6L. Measurements from ATLAS/CMS at LHC also show different s-pdf. Strange PDF may not be what we think! But COMPASS: Different x B dependence M K + + M K 0.2 0.15 0.1 COMPASS HERMES COMPASS overall value higher. 2 1 1 x Where does this discrepancy come from? juanvg@jlab.org QCD evolution 2017, May 26 2017 5
Hadron Mass Effects Usually in pqcd, the masses of the Proton and the Kaon (detected hadron) are neglected. s ū K m K ' 0.5 GeV p u u d m p ' 1 GeV Q 2 C & Q 2 H ' 1 GeV 2 Maybe the masses are not so negligible juanvg@jlab.org QCD evolution 2017, May 26 2017 6
Hadron Mass Effects Let s consider an example for Pion Mass effects at JLab. Jefferson Lab experiments: Usually low Q 2. Q 2 2.5 GeV 2 Pions at JLab. 1/Q 2 corrections have to be controlled. Accardi et al. O(m 2 /Q 2 ) = Hadron Mass Corrections (HMCs) m = M P,m Accardi et al JHEP 0911, 084 (2009) m 0.14 GeV juanvg@jlab.org QCD evolution 2017, May 26 2017 7
Hadron Mass Effects Back to Kaons: M K + + M K 0.2 0.15 COMPASS HERMES 0.1 2 1 1 x HERMES & COMPASS: relatively low Q 2, m 2 K 12m 2 Could the discrepancy be due to m 2 /Q 2 effects? juanvg@jlab.org QCD evolution 2017, May 26 2017 8
SIDIS Kinematics Variables DIS invariants l q l 0 lepton detected hadron p h M 2 = p 2 Q 2 = q 2 y = p q p l x B = Q2 2p q s p Proton or neutron X Undetected particles SIDIS invariants m 2 h = p 2 h z h = p h p p q juanvg@jlab.org QCD evolution 2017, May 26 2017 9
SIDIS: Massive scaling variables P 0 a µ Nachtmann: Scaling Variables a a + q+ p + = Bjorken limit: 2x B 1+ p 1+4x 2 B M 2 /Q 2 Q 2!1! x B P 3 a + = a 0 + a 3 p 2 a = a 0 a 3 p 2 Fragmentation: h p h q = z h 2 x B 1+ s 1 4x 2 B M 2 m 2 h z 2 h Q4! Bjorken limit: Q 2!1 h! z h juanvg@jlab.org QCD evolution 2017, May 26 2017
Collinear momenta (p,q) frame: p and q are collinear and have zero transverse momentum Fragmenting parton collinear to hadron e k 0 = e k 02 +(p h? /z) 2 2p h /z, p h z, p h? z! On-shell parton collinear to proton: e k 2 =0 q H k 0 e k 0 p h Y Fragmentation into a massive hadron e k 02 =? e k =(xp +, 0, 0 T ) p k e k X need to match partonic & hadronic kinematics juanvg@jlab.org QCD evolution 2017, May 26 2017 11
Matching Hadronic and Partonic Kinematics at LO Hard scattering: 4-momentum conservation at LO e k q H e k 0 x = 1+ e k 02 z = h Q 2 Bjorken limit: x = x B z = z h Fragmenting blob: momentum conservation in + direction e k 0 p h Y e k 0+ = p + h + Y + e k 02 p + h m 2 h z = m2 h LO h Standard choice: e k 02 =0 Albino et al. Nucl. Phys. B803 (2008) 42-4 juanvg@jlab.org QCD evolution 2017, May 26 2017 12
Leading Order (LO) Multiplicities at finite Q 2. With Hadron Masses: Scale dependent Jacobian Finite Q 2 scaling variables Rexp. R M h (x B )= dq2 0.8(0.85) J 0.2 h (, h,q 2 ) P q e2 q q( h,q 2 ) Dq h ( h,q 2 )dz h R P exp. dq2 q e2 q q(,q 2 ) h 1+ m2 h h Q Note: Theory integrated over z, Q 2 experimental bins for each x 2 B. Bjorken limit: M h(0) (x B )= M 2 Q 2, m2 h Q 2! 0 Rexp. dq2 P q e2 q q(x B,Q 2 ) R 0.8(0.85) 0.2 D h q (z h,q 2 )dz h R exp. dq2 P q e2 q q(x B,Q 2 ) Parton model definition juanvg@jlab.org QCD evolution 2017, May 26 2017 13
K + + K - Multiplicities Data (dots) vs. Theory (lines) K = K + + K Kaon FFs poorly known in absolute value Large FFs systematics HMCs are large juanvg@jlab.org QCD evolution 2017, May 26 2017 14
Data over Theory: K + + K - D/T ratio allows to compare experiments at different Q 2 Massless HMCs COMPASS vs. HERMES: After HMCs: Size discrepancy reduced Slope changes COMPASS well described (for overall size) Residual tension with HERMES slopes juanvg@jlab.org QCD evolution 2017, May 26 2017 15
Comparing HERMES vs. COMPASS data Theoretical correction ratios HMC ratio Evolution ratio (HERMES to COMPASS) R H!C evo = R h HMC = M h(0) M h(0) (x B ) M h(0) (x B ) M h COMPASS P.S. HERMES P.S. Make data comparable Produce approximate massless parton model multiplicities COMPASS: M h(0) exp HERMES: M h(0) exp M h exp R h HMC M h exp R h HMC R H!C evo juanvg@jlab.org QCD evolution 2017, May 26 2017 16
Correction ratios Theoretical correction ratios R HERMES HMC R COMPASS HMC R H!C evo Hadron mass effects dominant over evolution effects At COMPASS smaller HMCs than at HERMES. juanvg@jlab.org QCD evolution 2017, May 26 2017 17
Kaons at HERMES vs. COMPASS Experimental Data K = K + + K Massless data at same Q 2 Removing HMCs reduce the discrepancy in size. Corrections rather stable with respect to FF choice. juanvg@jlab.org QCD evolution 2017, May 26 2017 18
Kaon ratios Ratio reduces experimental systematics. M K + /M K 2.5 2 COMPASS HERMES 1.5 K + /K 1 2 1 x 1 Size discrepancy persists Slopes are now compatible Except the last two HERMES points. juanvg@jlab.org QCD evolution 2017, May 26 2017 19
Kaon ratios Data (dots) vs. HMC Theory (lines) K + /K COMPASS: theory dependence similar to experimental values HERMES: less steep than theory and at large-x Some PDF systematics, due very likely to s PDF (slopes) need to refit the s quark PDF juanvg@jlab.org QCD evolution 2017, May 26 2017 20
Data over Theory: K + /K - D/T ratio allows to compare experiments at different Q 2 Massless HMCs K + /K K + /K Ratios show less discrepancy HMCs much smaller for ratios (partial cancellation) Slopes with HMCs compatible Strange quark in current PDF fits too soft? juanvg@jlab.org QCD evolution 2017, May 26 2017 21
Kaon ratios at HERMES vs. COMPASS Experimental Data Massless data at same Q 2 K + /K K + /K Size and slope fully compatible. large x bins at HERMES still suspicious. juanvg@jlab.org QCD evolution 2017, May 26 2017 22
Coming back to the s-pdf Can we extract s-quark from SIDIS Kaon multiplicities? Yes, but: Make sure you control the FFs or fit at the same time with PDFs (e.g. Ethier, Sato, Melnitchouk. arxiv:1705.05889) Include mass corrections Non negligible even at small-x (because Q 2 is small) Our proposed scheme with with e k 02 = m 2 h / h seems able to reconcile HERMES & COMPASS Kaon multiplicities. juanvg@jlab.org QCD evolution 2017, May 26 2017 23
Conclusion and outlook. HMCs at LO are captured by new scaling variables ξ h and ζ h HMCs reduce the discrepancy in size between HERMES and COMPASS data for integrated Kaon Multiplicities Difference in slopes stills needs to be resolved for K + + K - No slope problem for ratio K + / K - systematics in HERMES K + + K -? Future developments: Include nuclear corrections (large x B behavior?) Prove factorization at NLO with k 02 6=0. Use the multiplicity data in new fits of FFs with HMC corrected theory juanvg@jlab.org QCD evolution 2017, May 26 2017 24
Thank you! juanvg@jlab.org QCD evolution 2017, May 26 2017 25
Backup slides juanvg@jlab.org QCD evolution 2017, May 26 2017 26
Pions at HERMES vs. COMPASS HMC ratios: HERMES (blue line), COMPASS (red line) Evolution ratio (green line) Systematic theoretical uncertainties: (FFs, PDFs) HMCs much smaller than for Kaons. Comparable to evolution effects. juanvg@jlab.org QCD evolution 2017, May 26 2017 27
Pions at HERMES vs. COMPASS Experimental Data Parton level multiplicities Slopes still incompatible also for pions. Hockey stick shape as for Kaons, likely due to nuclear effects. juanvg@jlab.org QCD evolution 2017, May 26 2017 28
Pions ratio + / juanvg@jlab.org QCD evolution 2017, May 26 2017 29
Fragmentation Functions Systematics Large variations of the multiplicities with the choice of FFs, why? Parton model: M K (x B,Q 2 )= Q(x B, Q 2 ) R D K Q (z,q2 )dz + S(x B, Q 2 ) R D K S (z,q2 )dz 5Q(x B, Q 2 )+2S(x B, Q 2 ) Q(x) u(x)+ū(x)+d(x)+ d(x) D K Q (z) 4D K u (z)+d K d (z) S(x) s(x)+ s(x) D K S (z) 2D K s (z) 30
Fragmentation Functions Systematics Large variations of the multiplicities with the choice of FFs, why? Parton model: M K (x B,Q 2 )= Q(x B, Q 2 ) R D K Q (z,q2 )dz + S(x B, Q 2 ) R D K S (z,q2 )dz 5Q(x B, Q 2 )+2S(x B, Q 2 ) Q(x) u(x)+ū(x)+d(x)+ d(x) D K Q (z) 4D K u (z)+d K d (z) S(x) s(x)+ s(x) D K S (z) 2D K s (z) u, d, s FFs 2 z D(z,Q ) http://lapth.cnrs.fr/generators 1 + - u K /K DSS LO + - u K /K HKNS LO 2 2 Q = 5 GeV 2 z D(z,Q ) http://lapth.cnrs.fr/generators 1 + - d K /K DSS LO + - d K /K HKNS LO 2 2 Q = 5 GeV 2 z D(z,Q ) http://lapth.cnrs.fr/generators 1 + - s K /K DSS LO + - s K /K HKNS LO 2 2 Q = 5 GeV -1-1 -1-2 -2-2 -3-4 K = K + + K 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 z -3-4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 z -3-4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 z <z h > 0.38 Large uncertainty with the choice of FFs because D HKNS Q Q>S >D DSS Q 31