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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

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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 15th, 2019

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FF 2019 – March 15th, 2019 accardi@jlab.org 2

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
  • g2 in DIS; e+e– collisions
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FF 2019 – March 15th, 2019 accardi@jlab.org 3

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

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Strange quark parton distribution function (PDF)

L H C C h a r g e d c u r r e n t D I S

A T L A S : n

  • s

u p p r e s s i

  • n

C MS : s u p p r e s s i

  • n

: s u p p r e s s i

  • n

N e e d a n

  • t

h e r me a s u r e me n t

Alekhin et al., arXiv:1404.6469 Svenja Pflitsch, DIS 2018

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FF 2019 – March 15th, 2019 accardi@jlab.org 5

s-PDF from SIDIS

Me a s u r i n g a K a

  • 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

  • n

s c

  • n

t a i n

  • 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

  • n

: g

  • d

p r

  • x

y f

  • r

a s t r a n g e q u a r k i n p r

  • t
  • n
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FF 2019 – March 15th, 2019 accardi@jlab.org 6

Integrated Kaon Multiplicities: SIDIS on Deuteron Wh e r e d

  • e

s t h i s d i ff e r e n c e c

  • me

f r

  • m?

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

  • mp

a r e d t

  • C

T E Q 6 L . → s t r a n g e P D F ma y n

  • t

b e w h a t w e t h i n k !

I s i t r e a l

  • r

a p p a r e n t ?

B u t C O MP A S S :

D i ff e r e n t x

B

d e p e n d e n c e O v e r a l l v a l u e s h i g h e r

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Integrated Kaon Multiplicities: SIDIS on Deuteron Wh e r e d

  • e

s t h i s d i ff e r e n c e c

  • me

f r

  • m?

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

  • mp

a r e d t

  • C

T E Q 6 L . → s t r a n g e P D F ma y n

  • t

b e w h a t w e t h i n k !

I s i t r e a l

  • r

a p p a r e n t ?

B u t C O MP A S S r a t i

  • :

( A l mo s t ) s a me s h a p e O v e r a l l l

  • w

e r → s t i l l d i ff e r e n t f r

  • m

H E R ME S !

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Because of NLO, Q2 evolution?

MMH T + D S S 1 7 N N P D F + D S S 1 7 H & C s h

  • u

l d b e c l

  • s

e ! S ma l l Q

2

e v

  • l

u t i

  • n

T h e

  • r

y s h a p e s = / = d a t a O t h e r e ff e c t s ? NLO calculatjons by Chung-Wen Kao, talk at DIS 2018

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Because of Hadron Mass Effects?

Ma y b e ma s s e s a r e n

  • t

s

  • n

e g l i g i b l e !

Usually in pQCD, the masses of proton and detected hadron are neglected

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Massive scaling variables

Scaling Variables

Bjorken limit: Nachtmann: Bjorken limit: Fragmentatjon:

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Collinear factorization with masses

1 Expand the correlators

c

  • n

t r i b u t e t

  • H

i g h e r

  • T

w i s t ( H T ) t e r ms

leading terms

3 Approx only the (overall) 4-mom conserv. 2 Expand the hadronic tensor

N

  • t

e :

Guerrero, Accardi, PRD 2018 (see also Collins, Rogers, Stasto 2007)

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Approximation: collinear momenta Approximation: collinear momenta

“Average virtualitjes”

How to match partonic and hadronic kinematjcs?

(p,q) frame: p and q collinear, 0 tr. mom. Fragmentjng parton collinear to hadron ...but fragments into a massive hadron: … and “on-shell” Parton collinear to proton

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Matching Hadronic and Partonic Kinematics at LO Matching Hadronic and Partonic Kinematics at LO

F r a g me n t i n g b l

  • b

: mo me n t u m c

  • n

s e r v a t i

  • n

i n + d i r e c t i

  • n

L O

A l b i n

  • e

t a l . N u c l . P h y s . B 8 3 ( 2 8 ) 4 2

  • 1

4

O r t h

  • d
  • x

c h

  • i

c e : Only in Bjorken limit can one neglect !

H a r d s c a t t e r i n g : 4

  • mo

me n t u m c

  • n

s e r v a t i

  • n

a t L O

(much more detail in Guerrero et al., JHEP 2015)

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Collinear factorization with masses – LO case

4 Let 3 integratjons out of 4 act on correlators, obtain

PDF FF x Hard scatuering coeffjcient

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Leading Order (LO) Multiplicities at finite Q2

Parton model defjnitjon

Massless limit: With Hadron Masses:

Note: Theory integrated over z, Q2 exp. bins for each xB F i n i t e Q

2

s c a l i n g v a r i a b l e s S c a l e d e p e n d e n t J a c

  • b

i a n

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Use suitable “Theoretjcal correctjon ratjos” – Produce approximate “massless” parton model multjplicitjes – Make data directly comparable – Largely insensitjve to FF normalizatjon

HERMES to COMPASS evolutjon HMC correctjon ratjo COMPASS: HERMES:

HERMES & COMPASS data: direct comparison

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Use suitable “Theoretjcal correctjon ratjos” – Produce approximate “massless” parton model multjplicitjes – Make data directly comparable – Largely insensitjve to FF normalizatjon

HERMES & COMPASS data: direct comparison

Multjplicitjes in a massless world: – mass corrected (and evolved) M h –

COMPASS: HERMES:

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Correction ratios

– Hadron mass efgects dominant over evolutjon efgects – COMPASS has smaller HMCs – but non-negligible!

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“Massless data” at same Q2 Experimental Data

Direct Data Comparison: K+/K-

– HERMES & COMPASS fully compatjble. – large x downturn at HERMES ??

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Experimental Data “Massless data” at same Q2

Direct Data Comparison: K+ + K-

– Afuer HMCs: > almost compatjble in size > negatjve slope, as it should (but hockey stjck at HERMES) – Residual slope difgerence: needs NLO, FF refjt

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Pion ratios vs. JLab

Experimental Data “Massless data” at same Q2 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

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Direct Data Comparison: pi+ + pi-

– Shapes stjll incompatjble – “Hockey stjck” at HERMES: but u, d quarks well known, not like s for Kaons!

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Testing the HMC scheme

Guerrero, Accardi, in preparation + Accardi, Alcalá, Guerrero, in progress

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Factorization with masses in a spectator model

 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 Guerrero, AA – in prep.

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Factorization with masses in a spectator model

 Gauge invariance: need also quasi-elastjc photon-proton scatuering  Gauge invariant individual contributjons – Use projectors – Non-negligible

  • interf. contributjon

even at small xB

DIS “excited” proton decay Interference

Moffat et al, PRD 95 (2017) Guerrero, AA – in prep.

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Structure Function: DIS vs. Collinear

 Factorized DIS structure functjon

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“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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Inclusive jet correlator

 Quark are not asymptotjc states – Hadronizatjon products pass the cut – Defjne a gauge invariant quark-to-jet amplitude squared  Integrate out the large momentum component:

Inclusive q → X “jet” correlator TMD Inclusive jet correlator

AA, Signori, 1903.04458

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TMD jet correlator in full glory

 Expand in Dirac structures, take traces, use spectral representatjon: where, in light-cone gauge,  ρ1,3 are Khallen-Lehman spectral functjons: → strength of quark-to-multjhadron coupling

AA, Signori, 1903.04458 + work in preparation

Jet’s “virtuality” Jet “mass” ~ dressed quark mass ~ O(100 MeV) Jet’s “transverse size”

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TMD jet correlator in full glory

 Expand in Dirac structures, take traces, use spectral representatjon: “Perturbatjvely”, or neglectjng quark-gluon-quark correlatjons:

On-shell quark Current quark mass ~ O(1 MeV) << Mjet

AA, Signori, 1903.04458 + work in preparation

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Novel FF sum rules: Mjet is observable!

 General jet correlator sum rule:  For TMDs, integrate out k+, take suitable traces Quark-quark sum rules

Collins-Soper

Quark-gluon-quark sum rules

AA, Signori 1903.04458

Non-zero in χ limit:

  • rder parameter for DχSB
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Inclusive DIS with jet correlators

AA, Bacchetta, PLB 773 (‘17) 632

Jet correlators: → non-asymptotjc quark states / dressed quarks

NEW!

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proton

g2 structure function revisited

 Integratjng SIDIS, and using EOM, Lorentz Invariance Relatjons: Consequences: – h1 accessible in inclusive DIS ↔ Potentjally large signal – Burkardt-Cottjngham sum rule broken – ETL: novel way to measure tensor charge

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Measuring the jet correlator

Accardi, Bacchetta, Signori, Radici, in progress

 Jet mass Mjet can be measured in polarized e+ + e– : – Needs LT asymmetry in semi-inclusive Lambda productjon – Similarly a LU asymmetry in unpolarized dihadron productjon

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Where can we measure jet correlators?

 Can we get a (polarized) e+ e- collider at JLab / BNL? – At JLab12 ? EIC + positron beam ?  Are existjng facilitjes enough?  What else?

BEPC super KEKB ILC JLab/BNL E beam [GeV] 1.9 4 (e--) 7 (e--) 250 ? √s [GeV] 3 – 5 10 500 ? polarizatjon ? maybe 80% e-- 60% e+ YES!

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A new “universal” fits

 Chiral-odd collinear sector across processes:

(Di)e+e– DIS (Di)SIDIS

polarized unpolarized

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Conclusions

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Conclusions

 Hadron mass correctjons possible in collinear factorizatjon – Accounts for phase space available for hadronisatjon

  • with non-zero “virtuality” for fragmentjng quark:

– But needs to go beyond the usual “parton model approximatjon” – Proposed scheme phenomenologically successful!  HMCs non negligible – Kaon ratjos at H & C largely reconciled – Pion correctjons large only at Jlab; systematjc shape difgerence at H, C – Need to account for HMCs in fjts  “Inclusive” fragmentatjon and jet correlator: – Novel FF sum rules – New phenomenology

  • χSB from SIDIS, tensor charge in DIS, SIA !!
  • ...and more possible, the door is open...
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Extras

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Phase space limitations

Guerrero et al., JHEP 09 (2015) 169

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Current vs. target fragmentation regions

Guerrero et al., JHEP 09 (2015) 169

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Current vs. target fragmentation regions

 Baryon in in target vs. current region:

Guerrero, Accardi, PRD 97 (2018) 114012

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C h u n g

  • We

n K a

  • ,

t a l k a t D I S 2 1 8

NLO vs. LO: – ~20% higher (cancels in ratjos) – slight change of shape

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(Refitted) DSS2017 vs. HERMES

Borsa, Sassot, PRD96 (2017) Kao, Yang, Chang, arXiv:1807.06524 (DIS 2018)

DSS2017

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Evolutjon ratjo:

(HERMES to COMPASS)

HMC ratjo:

HERMES & COMPASS data: direct comparison