Hadron mass corrections Hadron mass corrections in SIDIS and DIS in SIDIS and DIS Alberto Accardi Hampton U. and Jefferson Lab FF 2019 Duke U. – Mar 15 th , 2019
Overview Hadron Mass Correctjons in SIDIS – Collinear factorizatjon with non-zero masses – Kaons (and pions) at HERMES vs COMPASS (vs JLab) Testjng HMCs in a spectator model – DIS case, to begin with Fragmentatjon w/o fragments: “Inclusive jet” mass efgects – Dressed vs. perturbatjve quark – Jet mass as χ-simmetry order parameter – Observability: • Non-perturbatjve FF sum rule for Etjlde • g 2 in DIS; e+e– collisions accardi@jlab.org FF 2019 – March 15 th , 2019 2
Hadron mass corrections in SIDIS Guerrero , Accardi, PRD 97 (2018) 114012 Guerrero, Ethier, Accardi, Melnitchouk, Casper, JHEP 1509 (2015) 169 Accardi, Hobbs, Melnitchouk, JHEP 0911 (2009) 084 accardi@jlab.org FF 2019 – March 15 th , 2019 3
Strange quark parton distribution function (PDF) L H C Svenja Pflitsch, C h a r g e d c u r r e n t D I S DIS 2018 A T L A S : n o s u p p r e s s i o n C MS : s u p p r e s s i o n : s u p p r e s s i o n Alekhin et al., N e e d a n o t h e r arXiv:1404.6469 me a s u r e me n t accardi@jlab.org FF 2019 – March 15 th , 2019 4
s-PDF from SIDIS Me a s u r i n g a K a o n i n S e mi i n c l u s i v e D e e p i n e l a s t i c s c a t t e r i n g ( S I D I S ) K a o n s c o n t a i n o n e s - q u a r k i n t h e i r v a l e n c e s t r u c t u r e . D e t e c t a K a o n : g o o d p r o x y f o r a s t r a n g e q u a r k i n p r o t o n accardi@jlab.org FF 2019 – March 15 th , 2019 5
Integrated Kaon Multiplicities: SIDIS on Deuteron H E R ME S : C l a i m v e r y d i ff e r e n t s - q u a r k s h a p e c o mp a r e d t o C T E Q 6 L . → s t r a n g e P D F ma y n o t b e w h a t w e t h i n k ! B u t C O MP A S S : D i ff e r e n t x d e p e n d e n c e B O v e r a l l v a l u e s h i g h e r Wh e r e d o e s t h i s d i ff e r e n c e c o me f r o m? I s i t r e a l o r a p p a r e n t ? accardi@jlab.org FF 2019 – March 15 th , 2019 6
Integrated Kaon Multiplicities: SIDIS on Deuteron H E R ME S : C l a i m v e r y d i ff e r e n t s - q u a r k s h a p e c o mp a r e d t o C T E Q 6 L . → s t r a n g e P D F ma y n o t b e w h a t w e t h i n k ! B u t C O MP A S S r a t i o : ( A l mo s t ) s a me s h a p e O v e r a l l l o w e r → s t i l l d i ff e r e n t f r o m H E R ME S ! Wh e r e d o e s t h i s d i ff e r e n c e c o me f r o m? I s i t r e a l o r a p p a r e n t ? accardi@jlab.org FF 2019 – March 15 th , 2019 7
Because of NLO, Q 2 evolution? NLO calculatjons by Chung-Wen Kao, talk at DIS 2018 H & C s h o u l d b e c l o s e ! MMH T + D S S 1 7 S ma l l Q 2 e v o l u t i o n T h e o r y s h a p e s = / = d a t a N N P D F + D S S 1 7 O t h e r e ff e c t s ? accardi@jlab.org FF 2019 – March 15 th , 2019 8
Because of Hadron Mass Effects? Usually in pQCD, the masses of proton and detected hadron are neglected Ma y b e ma s s e s a r e n o t s o n e g l i g i b l e ! accardi@jlab.org FF 2019 – March 15 th , 2019 9
Massive scaling variables Scaling Variables Nachtmann: Bjorken limit: Fragmentatjon: Bjorken limit: accardi@jlab.org FF 2019 – March 15 th , 2019 10
Collinear factorization with masses Guerrero, Accardi, PRD 2018 (see also Collins, Rogers, Stasto 2007) 1 Expand the correlators c o n t r i b u t e t o H i g h e r - leading terms T w i s t ( H T ) t e r ms 2 Expand the hadronic tensor 3 Approx only the (overall) 4-mom conserv. N o t e : accardi@jlab.org FF 2019 – March 15 th , 2019 11
Approximation: collinear momenta Approximation: collinear momenta (p,q) frame: p and q collinear, 0 tr. mom. Fragmentjng parton collinear to hadron ...but fragments into a massive hadron: Parton collinear to proton … and “on-shell” “Average virtualitjes” How to match partonic and hadronic kinematjcs? accardi@jlab.org FF 2019 – March 15 th , 2019 12
Matching Hadronic and Partonic Kinematics at LO Matching Hadronic and Partonic Kinematics at LO (much more detail in Guerrero et al., JHEP 2015) F r a g me n t i n g b l o b : mo me n t u m c o n s e r v a t i o n i n + d i r e c t i o n O r t h o d o x c h o i c e : L O A l b i n o e t a l . N u c l . P h y s . B 8 0 3 ( 2 0 0 8 ) 4 2 - 1 0 4 H a r d s c a t t e r i n g : 4 - mo me n t u m c o n s e r v a t i o n a t L O Only in Bjorken limit can one neglect ! accardi@jlab.org FF 2019 – March 15 th , 2019 13
Collinear factorization with masses – LO case 4 Let 3 integratjons out of 4 act on correlators, obtain PDF FF Hard scatuering coeffjcient x accardi@jlab.org FF 2019 – March 15 th , 2019 14
Leading Order (LO) Multiplicities at finite Q 2 With Hadron Masses: 2 S c a l e d e p e n d e n t J a c o b i a n F i n i t e Q s c a l i n g v a r i a b l e s Note : Theory integrated over z, Q 2 exp. bins for each x B Massless limit: Parton model defjnitjon accardi@jlab.org FF 2019 – March 15 th , 2019 15
HERMES & COMPASS data: direct comparison – Produce approximate “massless” Use suitable parton model multjplicitjes “Theoretjcal correctjon – Make data directly comparable ratjos” – Largely insensitjve to FF normalizatjon COMPASS: HMC correctjon ratjo HERMES: HERMES to COMPASS evolutjon accardi@jlab.org FF 2019 – March 15 th , 2019 16
HERMES & COMPASS data: direct comparison – Produce approximate “massless” Use suitable parton model multjplicitjes “Theoretjcal correctjon – Make data directly comparable ratjos” – Largely insensitjve to FF normalizatjon Multjplicitjes in a massless world: – mass corrected (and evolved) M h – COMPASS: HERMES: accardi@jlab.org FF 2019 – March 15 th , 2019 17
Correction ratios – Hadron mass efgects dominant over evolutjon efgects – COMPASS has smaller HMCs – but non-negligible! accardi@jlab.org FF 2019 – March 15 th , 2019 18
Direct Data Comparison: K + /K - Experimental Data “Massless data” at same Q 2 – HERMES & COMPASS fully compatjble. – large x downturn at HERMES ?? accardi@jlab.org FF 2019 – March 15 th , 2019 19
Direct Data Comparison: K + + K - Experimental Data “Massless data” at same Q 2 – Afuer HMCs: > almost compatjble in size > negatjve slope, as it should (but hockey stjck at HERMES) – Residual slope difgerence: needs NLO, FF refjt accardi@jlab.org FF 2019 – March 15 th , 2019 20
Pion ratios vs. JLab Experimental Data “Massless data” at same Q 2 Pion ratjos afuer HMCs: – all approximately compatjble – JLab pions slightly prefer COMPASS ...but large stat. uncertaintjes – small difgerences could be solved by: NLO efgects, pion FF refjt with HMCs accardi@jlab.org FF 2019 – March 15 th , 2019 21
Direct Data Comparison: pi + + pi - – Shapes stjll incompatjble – “Hockey stjck” at HERMES: but u, d quarks well known, not like s for Kaons! accardi@jlab.org FF 2019 – March 15 th , 2019 22
Testing the HMC scheme Guerrero, Accardi, in preparation + Accardi, Alcalá, Guerrero, in progress accardi@jlab.org FF 2019 – March 15 th , 2019 23
Factorization with masses in a spectator model Guerrero, AA – in prep. Use spectator model: – Known parameters, analytjcal calculatjons – Full vs. factorized cross sectjon; PDFs: calculated vs. fjtued Start simple: DIS – Then SIA (3-body phase space) – Then SIDIS (cimplex interplay of IS and FS kinematjcs) simulates confjnement accardi@jlab.org FF 2019 – March 15 th , 2019 24
Factorization with masses in a spectator model Gauge invariance: need also quasi-elastjc photon-proton scatuering Moffat et al, PRD 95 (2017) “excited” proton decay Interference DIS Gauge invariant individual contributjons Guerrero, AA – in prep. – Use projectors – Non-negligible interf. contributjon even at small x B accardi@jlab.org FF 2019 – March 15 th , 2019 25
Structure Function: DIS vs. Collinear Factorized DIS structure functjon accardi@jlab.org FF 2019 – March 15 th , 2019 26
“Inclusive jet” mass effects: fragmentation without fragments Accardi, Signori, arXiv:1903.04458 Accardi, Bacchetta, PLB 773 (2017) 632 + work in progress: AA, Signori AA, Bacchetta, Radici, Signori
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