Hadron Mass Effects on Kaon production on deuteron Juan Guerrero - PowerPoint PPT Presentation


 Hadron Mass Effects on Kaon production on deuteron Juan Guerrero Hampton University & Jefferson Lab Hadronic Physics with Lepton and Hadron Beams September 6, 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: 3 “valence quarks” p = (u u d) c ¯ c Gluons d u s sea quarks: strange , charm, bottom. u ¯ s 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. 2 juanvg@jlab.org Jefferson Lab, Sep 6 2017

Strange quark PDF one way “Tagging” Kaon in Hard How can we access the s-quark PDF? Scattering reactions h = K For example: Semi inclusive Deep inelastic scattering (SIDIS): e − + p → e − + h + X Kaon contains an s-quark in their l 0 valence structure. Kaon FF: D K q l Detect a Kaon: good proxy for a ¯ s K + strange quark u m K ' 0 . 5 GeV s-PDF BUT: ¯ u Not necessarily negligible at X ¯ p s HERMES and COMPASS s experiments 3 juanvg@jlab.org Jefferson Lab, Sep 6 2017

How to tag s-quarks? Use “integrated Kaon Multiplicities” e xp dQ 2 R 0 . 8 dN K R 0 . 2 dz h Experimentally dx B dQ 2 dz h M K exp = dN e R HERMES, COMPASS: e xp dQ 2 dx B dQ 2 Theoretically LO, neglect masses: R 0 . 8 0 . 2 dz h D h q e 2 P q q ( x B ) q ( z h ) Z M K = dz h D K = s ( x B ) s ( z h ) P q e 2 q q ( x B ) +light quarks Comparing these two expressions Extract the s-quark PDF. 4 juanvg@jlab.org Jefferson Lab, Sep 6 2017

Integrated Kaon Multiplicities: SIDIS on Deuteron HERMES: Claim very different s-quark shape compared to CTEQ6L. ℳ K + + ℳ K − 0.2 Measurements from ATLAS/CMS at COMPASS LHC also show different s-PDF. HERMES Strange PDF may not be what we think! 0.15 But COMPASS: Different x B dependence 0.1 COMPASS overall value higher. 2 1 10 10 − − 1 x Where does this discrepancy come from? Is it real or apparent? 5 juanvg@jlab.org Jefferson Lab, Sep 6 2017

Hadron Mass Effects Usually in pQCD, the masses of the Proton and the Kaon (detected hadron) are neglected. ¯ u K m K ' 0 . 5 GeV s u m p ' 1 GeV p d u Q 2C & Q 2H ' 1 � 10 GeV 2 Maybe masses are not so negligible! 6 juanvg@jlab.org Jefferson Lab, Sep 6 2017

Hadron Mass Effects Let’s consider an example for Pion Mass effects at JLab. Jefferson Lab experiments: Pions at JLab (Exp. # E00-108) Usually low Q 2 . Q 2 ∼ 2 . 5 GeV 2 1/Q 2 corrections have to Accardi et al. be controlled. O(m 2 /Q 2 ) = Hadron Mass Corrections (HMCs) Accardi et al JHEP 0911, 084 (2009) m = M P , m π m π ∼ 0 . 14 GeV 7 juanvg@jlab.org Jefferson Lab, Sep 6 2017

Hadron Mass Effects Back to Kaons: ℳ K + + ℳ K − 0.2 COMPASS HERMES 0.15 0.1 2 1 10 10 1 − − x HERMES & COMPASS: relatively low Q 2 , m 2 K ∼ 12 m 2 π Could the discrepancy be due to m K2 /Q 2 effects? 8 juanvg@jlab.org Jefferson Lab, Sep 6 2017

SIDIS Kinematics Variables DIS invariants M 2 = p 2 Q 2 = − q 2 lepton l 0 l y = p · q detected hadron Q 2 q x B = p · l p h 2 p · q s SIDIS invariants p X Undetected particles m 2 h = p 2 Proton or neutron h z h = p h · p q · p 9 juanvg@jlab.org Jefferson Lab, Sep 6 2017

SIDIS: Massive scaling variables Scaling Variables P 0 Nachtmann: a µ ξ ≡ − q + 2 x B p + = p 1 + 4 x 2 B M 2 /Q 2 1 + a + Q 2 → ∞ a − Bjorken limit: ξ → x B P 3 Fragmentation: a + = a 0 + a 3 √ s 2 ! 1 − 4 x 2 B M 2 m 2 ζ h ≡ p − q − = z h ξ h h 1 + z 2 h Q 4 a − = a 0 − a 3 x B 2 √ 2 Q 2 → ∞ Bjorken limit: ζ h → z h 10 juanvg@jlab.org Jefferson Lab, Sep 6 2017

Collinear momenta (p,q) frame: p and q are collinear and have zero transverse momentum Fragmenting parton collinear to hadron e ! k 0 2 + ( p h ⊥ /z ) 2 , p � k 0 = z , p h ⊥ e h 2 p � z h /z p h Fragmentation into a Approx.: q massive hadron On-shell parton k 0 ≈ e collinear to proton: k 0 2 =? k 0 e H k 2 = 0 Y e k ≈ e e k = ( xp + , 0 , 0 T ) k need to match X partonic & hadronic p kinematics 11 juanvg@jlab.org Jefferson Lab, Sep 6 2017

Matching Hadronic and Partonic Kinematics at LO Hard scattering: 4-momentum conservation at LO respects gauge H LO ( k, k 0 ) ≈ H LO ( e k, e k 0 ) ∝ δ (4) ( q + e k − e G k 0 ) invariance q Bjorken limit: ✓ ◆ e k 0 2 e x = x B k 0 x = ξ 1 + Q 2 H z = z h z = ζ h e k Fragmenting blob: momentum conservation in + direction h + Y + ≥ p + e k 0 + = p + h p h Standard choice: k 0 2 ≥ m 2 = m 2 e k 0 2 = 0 e k 0 e h h z ζ h Y LO Albino et al. Nucl. Phys. B803 (2008) 42-104 12 juanvg@jlab.org Jefferson Lab, Sep 6 2017

Leading Order (LO) Multiplicities at finite Q 2 . With Hadron Masses: Scale dependent Jacobian Finite Q 2 scaling variables e xp. dQ 2 R 0 . 8(0 . 85) J h ( ξ , ζ h , Q 2 ) P q e 2 q q ( ξ h , Q 2 ) D h q ( ζ h , Q 2 ) dz h R 0 . 2 M h ( x B ) = R e xp. dQ 2 P q e 2 q q ( ξ , Q 2 ) 1 + m 2 ⇣ ⌘ h ξ h ≡ ξ ζ h Q 2 Note: Theory integrated over z, Q 2 experimental bins for each x B . ✓ M 2 Q 2 , m 2 ◆ Bjorken limit: h → 0 Q 2 R 0 . 8(0 . 85) e xp. dQ 2 P q e 2 q q ( x B , Q 2 ) D h q ( z h , Q 2 ) dz h R 0 . 2 M h (0) ( x B ) = e xp. dQ 2 P q e 2 q q ( x B , Q 2 ) R Parton model definition 13 juanvg@jlab.org Jefferson Lab, Sep 6 2017

Data over Theory: K + + K - D/T ratio allows to compare experiments at different Q 2 Normalization of Kaon FFs poorly known Massless HMCs COMPASS vs. HERMES: After HMCs: Size discrepancy reduced Slope more flat COMPASS well described (except normalization) Residual tension with HERMES slope 14 juanvg@jlab.org Jefferson Lab, Sep 6 2017

HERMES & COMPASS data: direct comparison Produce approximate “massless” parton model multiplicities “Theoretical correction ratios” Make data directly comparable Largely insensitive to D K normalization HMC ratio HMC = M h (0) R h COMPASS: M h M h (0) exp ≡ M h exp × R h Evolution ratio (HERMES HMC to COMPASS) HERMES: � M h (0) ( x B ) � M h (0) exp ≡ M h exp × R h HMC × R H → C � R H → C COMPASS P.S. = evo evo � M h (0) ( x B ) � � HERMES P.S. 15 juanvg@jlab.org Jefferson Lab, Sep 6 2017

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. 16 juanvg@jlab.org Jefferson Lab, Sep 6 2017

Direct Data Comparison K = K + + K − “Massless data” at same Experimental Data Q 2 Removing HMCs reduce the discrepancy in size. Corrections rather stable with respect to FF choice. 17 juanvg@jlab.org Jefferson Lab, Sep 6 2017

Kaon ratios Ratio reduces experimental systematics. ℳ K + / ℳ K − COMPASS 2.5 HERMES 2 1.5 K + /K − 1 2 1 10 10 1 − − x Size discrepancy persists Slopes are now compatible Except last two HERMES points?. 18 juanvg@jlab.org Jefferson Lab, Sep 6 2017


 Data over Theory: K + /K - D/T ratio allows to compare experiments at different Q 2 Massless HMCs K + /K − K + /K − After HMCs: HERMES overall agreement with COMPASS except last bins? Strange quark in current PDF fits too soft? 19 juanvg@jlab.org Jefferson Lab, Sep 6 2017

Direct Data Comparison “Massless data” at same Experimental Data Q 2 K + /K − K + /K − HERMES & COMPASS fully compatible. large x bins at HERMES still suspicious. 20 juanvg@jlab.org Jefferson Lab, Sep 6 2017

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) e k 0 2 = m 2 Our proposed scheme with with seems able to reconcile h / ζ h HERMES & COMPASS Kaon multiplicities. 21 juanvg@jlab.org Jefferson Lab, Sep 6 2017

Conclusion and outlook. HMCs at LO are captured by new scaling variables ξ h and ζ h K + + K - multiplicities: HERMES vs. COMPASS size discrepancy reduced Difference in slopes still needs to be solved. K + / K - ratio: No slope problem systematics in HERMES K + + K - ? Future developments: Evaluating HMCs for polarized asymmetries. k 0 2 6 = 0 . Prove factorization at NLO with Use the multiplicity data in new fits of FFs with HMC corrected theory 22 juanvg@jlab.org Jefferson Lab, Sep 6 2017

Thank you! 23 juanvg@jlab.org Jefferson Lab, Sep 6 2017

Backup slides 24 juanvg@jlab.org Jefferson Lab, Sep 6 2017

K + + K - Multiplicities Data (dots) vs. Theory (lines) K = K + + K − Kaon FFs poorly known in absolute value Large FFs systematics HMCs are large 25 juanvg@jlab.org Jefferson Lab, Sep 6 2017

Kaon ratios Data (dots) vs. HMC Theory (lines) 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 26 juanvg@jlab.org Jefferson Lab, Sep 6 2017