confronting nucleon strangeness and charm
Friday, November 9, 2018
2018 CTEQ Workshop @ JLab: ‘Parton Distributions as a Bridge from Low to High Energies’
Tim Hobbs, Southern Methodist University and CTEQ and EIC Center@JLab nucleon strange/charm remain very open topics
in spite of extensive effort and significant progess in recent years, ambiguities remain in both the magnitude and properties of the strange & charm components of the nucleon.
● the strangeness magnitude comparatively better constrained,
→ detailed x dependence remains uncertain, despite succession of historical improvements:
increasing sensitivity to flavor asymmetries in the light quark sea ?
● there is much less clarity regarding the nucleon’s charm content → in general, only upper limits to main focus of this talk → very little agreement on the shape of the intrinsic “fitted dists. 2 1. Background charm in perturbative QCD (pQCD)
c(x, Q2 m 2) = ¯c(x, Q2 m 2) = 0 ≤ c ≤ c · F. M. Steffens, W. Melnitchouk and A. W. Thomas, Eur. Phys. J. C 11, 673 (1999) [hep-ph/9903441].
→
intermediateQ 2: 2 � ′ � � F c (x, Q2) = αs(µ ) z dz CPGF(z, Q2, m2) xg x , µ2 · 2, PGF 9π x z c · z highQ 2: · massless DGLAP (i.e., variableflavor-number schemes) 3 1. Background simplest nonperturbative model calculations
→ original models possessed scalar vertices... Brodsky et al. (1980): � � � k2 +m2 −2 · P(p uudc¯c) M 2 5 ⊥i i → ∼ − i=1 xi produces intrinsic PDF,c IC(x) = ¯ICc (x) → Bl¨umlein (2015): � � � 1 2P 1 � � �� τlife = E −E = � k2 +m2 vs. τint = q · i i 5 ⊥i i − 2 x =1 0 M j j i=1 xi comparison constrainsx Q 2 space over which IC is observable → − 4 2. meson-baryon models nonperturbative charm meson-baryon models(MBMs)
we implement a framework which conserves spin/parity · nonperturbative mechanisms are needed to break c(x, Q2 m 2) = ¯c(x, Q2 m 2) = 0! · ≤ c ≤ c We build an EFT which connects IC to properties of the hadronic spectrum: [TJH, J. T. Londergan and W. Melnitchouk, Phys. Rev. D89, 074008 (2014).] � � N = √Z N + dy fMB(y) M(y);B(1 y) | i 2 | i 0 M,B | − i · y=k +/P +:k meson,P nucleon � � �� � � 4.6 − ++ 1 d¯y D* Σ* x _ c − ++ _ c(x) = fBM (¯y)cB * B,M x ¯y ¯y 4.5 D Σ *0 *+ _c D Σ _ c *0 + − ++ D Σ D Σ* 4.4 c _c − ++ _ D Σ 0 *+ _c *0 + D Σ c _ D Λc 4.3 0 + _ D Σ a similar convolution procedure may mass [GeV] c
4.2 0 + D Λ ·be used for¯c(x)... _ c 4.1 J = 0 + 1/2J = 1 + 1/2J = 0 + 3/2J = 1 + 3/2 5 2. meson-baryon models nonperturbative charm charm in the nucleon
tune universal cutoffΛ= Λˆ tofit ISR pp Λ X collider data → c multiplicities· , momentum sum: (charm) n = 2.40% +2.47;P .= x = 1.34% +1.35 h iMB −1.36 c h i IC −0.75
1 2 2 Q = 60 GeV 0.1 c c 2 F 0.01
0.001
0.0001 0.001 0.01 0.1 1 x � � c¯c 2 4x 2 2 F2 (x, Q ) = 9 c(x, Q ) + ¯c(x, Q) evolve to EMC scale,Q 2 = 60 GeV2 → low-x H1/ZEUS data check massless DGLAP evolution 6 3. QCD global analysis systematics of global QCD analysis
extract/constrain quark densities: � � � � 1 dξ x Q2 µ2 F γ (x, Q2) = Cγf , , F ,α (µ2) φ (ξ,µ2 , µ2) qh ξ i ξ µ2 µ S · f/h F f 0 γf Ci : pQCD Wilson coefficients 2 2 ·φf/h(ξ,µF , µ ): universal parton distributions 2 2 2 · (...here, µF = 4mc +Q )
=⇒ exploit properties of QCD to constrain models:
� � 1 dx x f (x, Q2) +f (x, Q2) 1 (mom. conserv.) ·{ q+¯q g }≡ q 0
2 2 2 DGLAP: couples Q evolution off q(x, Q ),f g(x, Q ) · 7 3. QCD global analysis constraints from global fits...
P. Jimenez-Delgado, TJH, J. T. Londergan and W. Melnitchouk; PRL 114, no. 8, 082002 (2015).
total H1 FL 300 E605 dimuon E866 pp JLab p E866 pd JLab d 26 sets: SLAC p jets ZEUS 250 E866 rat jets H1 Ndat = 4296 SLAC d jets CDF HERA jets D0 200 E665 BCDMS F2 2 2 NMC BCDMS FL Q 1 GeV 2 0 BCDMS p E140x F2 χ BCDMS d E140x FL ≥ - 150 2 2 2 NMC rat HERA σc χ W 3.5 GeV H1 F2 ≥ 100 = ⇒ 50 ∗∗ HTs, TMCs, smearing... 0
0 0.2 0.4 0.6 0.8 1 �
300 total 250 SLAC rest 200 EMC 2 0
χ 150 - 2
χ 100 50 0 -50 0 0.2 0.4 0.6 0.8 1
EMC alone: x = 0.3 0.4% h i IC − + SLAC/‘REST’:hxi IC = 0.13±0.04%
c¯c 2 ...butF 2 poorlyfit — χ 4.3 per datum! ∼ 9 4. recent developments new/ongoing global analyses
NNPDF3: not anchored to specific parametrizations/models · see: Ball et al. Eur. Phys. J. C76 (2016) no.11, 647 included EMC: x = 0.7 0.3% atQ 1.5 h i·IC ± ∼ GeV drove a very hard c(x) = ¯c(x) → distribution peaked at x 0.5 ∼ AND, required a negative IC · c¯c ·component to describe EMCF 2 !
recent CTEQ-TEA IC analysis, extending CT14 · see: T. J. Hou et al. JHEP02 (2018) 059. pole found x IC � 2%; examinedm c dependence → h i 10 4. recent developments future experimental prospects?
jet hadroproduction: pp (Zc) +X at LHCb → · e.g., Boettcher, Ilten, Williams, PRD93, 074008 (2016). a “direct” measure in the forward region,2<η<5 → ... sensitive toc(x),x 1 for one colliding proton ∼ can discriminate x �0.3% (“valencelike”), 1% (“sealike”) → h i IC prompt atmospheric neutrinos? see: Laha & Brodsky, 1607.08240 (2016). · IceCubeν spectra may constrain IC normalization → + possible impact upon hidden charm pentaquark,P c ? · e.g., Schmidt & Siddikov, PRD93, 094005 (2016).
AFTER@LHC?...fixed-target pp at √s = 115 GeV · Brodsky et al. Adv. High Energy Phys. 2015, 231547 (2015). [Signori] 11 σ terms contribute to nucleon’s mass, BSM cross sections
● the nucleon mass is a matrix ● ALSO: the heavy quark sigma term (esp. element of the QCD energy-terms andDIS-derivequantities,e.g., for charm) is important to WIMP direct momentum tensor, searches :
Hill and Solon, Phys. Rev. Lett. 112, 211602 (2014). Junnarkar, Walker-terms andDIS-derivequantities,e.g.,Loud; PRD 2013.
MANY more lattice determinations of … relatively few for
● in principle, with knowledge of the wave function, there may be a way to 3 correlate σ-terms andDIS-derivequantities,e.g.,terms and DIS-terms andDIS-derivequantities,e.g.,derive quantities, e.g., 12 … need models for both the charm PDF and σcc
light-front wave functions (LFWFs) are one such approach they deliver a frame-independent description of hadronic bound state structure
● the light front represents physics tangent to the light cone:
with them, many matrix elements (GPDs, TMDs) are calculable via the same universal objects:
in fact, have already developed this technology for nucleon strangeness! 1313 TJH, M. Alberg, and G. A. Miller; PRC91, 035205 (2015). DIS and elastic strangeness predict inelastic and elastic observables? requires knowledge of quark-level proton wave function · → eN e ′X eN e ′N ′ → →
� 1 + 2 ′ + xS = dx x[s(x) + ¯s(x)] F1(Q ) P , J P, ∼h ↑| EM | ↑i �0 1 − xS = dx x[s(x) ¯s(x)] 2 ′ + F2(Q ) P , J EM P, 0 − ∼h ↓| | ↑i σµνq J µ =γ µF (Q2) +i ν F (Q2) EM 1 2M 2 14 hadronic light-front wave functions (LFWFs)
S. J. Brodsky, D. S. Hwang, B. Q. Ma and I. Schmidt; Nucl. Phys. B 593, 311 (2001). � � � � �n 2 �n · λ + dxid k⊥i 3 P ⊥ ΨP (P , ) = 3 16π δ 1 xi | i √xi(16π ) − � n� i=1 i=1 �n (2) λ + δ k⊥ ψ (xi,k ⊥ ,λ i) n;k , xiP⊥ +k ⊥ ,λ i × i n i | i i i i=1
q n = 2 P u u d q
� � 2 λ + 1 �dxd k⊥ λ ΨP (P ,P ⊥) = ψqλ (x,k ⊥) | i 16π3 x(1 x) q q=s,¯s − + q; xP , xP⊥ +k ⊥ × | i λ 3D helicity WFψ (x,k ⊥); light-front fraction:x=k +/P + → qλq 15 electromagnetic form factors the quarkq contribution from any5-quark state is then:
· � 2 � q 2 dxd k⊥ ∗λ=+1 ′ λ=+1 F (Q ) =e q ψ (x,k ⊥)ψ (x,k ⊥) 1 16π3 qλq qλq λ � q 2 � q 2 2M dxd k⊥ ∗λ=−1 ′ λ=+1 F (Q ) =e q ψ (x,k ⊥)ψ (x,k ⊥) 2 [q1 + iq2] 16π3 qλq qλq λq
for strangeness,q s; total strange:s+¯s → · F s¯s(Q2) =F s (Q2) +F ¯s (Q2) = 1,2 1,2 1,2 ⇒ Q2 Sachs form : Gs¯s(Q2) =F s¯s(Q2) F s¯s(Q2) E 1 − 4M 2 2 s¯s 2 s¯s 2 s¯s 2 GM (Q ) =F 1 (Q ) +F 2 (Q ) � � s¯s� s¯s 2 D dGE 2 2 µs =G M (Q = 0) ρs = � whereτ=Q 4M dτ τ=0 16 strangeness wave functions require a proton quark + scalar tetraquark LFWF: → k I. C. Clo¨etand G. A. Miller; Phys. Rev. C 86, 015208 (2012). · p λ λs 2 λ ψλs (k, p) = ¯us (k) φ(M0 ) uN (p)
2 φ(M0 ): scalar function quark-spectator interaction 2 → 2 (M0 = quark-tetraquark invariant mass !) � � λ=+1 1 ms e.g., ψ (x,k ⊥) = +M φs sλs=+1 √1 x x − � � � √Ns 2 2 k ⊥ q ⊥ gaussian :φ s = 2 exp M0 (x, , ) 2Λs Λs − � � � 2 s 2 esNs dxdk⊥ 2 2 1 2 2 F1 (Q ) = 2 4 2 k⊥ + (ms + xM) (1 x) Q 16π Λs x (1 x) − 4 − − 2 2 ′2 s 2 exp( ss/Λs)s s = (M0 +M 0 )/2 sim. forF 2 (Q )! × −
17 s¯sdistribution functions s quark distribution x-unintegratedF s(Q2 = 0) form factor ≡ 1 · (up toe s!): � 2 � d k⊥ ∗λ=+1 λ=+1 s(x) = ψ (x,k ⊥)ψ (x,k ⊥) 16π3 sλs sλs λs λ=+1 again inserting helicity wave functionsψ (x,k ⊥) qλq → ′ (Q2 = 0 = k ⊥ =k ⊥): ⇒ � 2 � � Ns dk⊥ 2 2 2 s(x) = k⊥ + (ms + xM) exp( ss/Λ ) 16π2Λ4 x2(1 x) − s s − � � 1 2 2 2 1 2 2 ss = k⊥ + (1 x)m s + xmS + (1 x) Q x(1 x) − p 4 − −
total of eight model parameters! → (Ns,Λ s,m s, andm Sp ... AND anti-strange) 18 limits from DIS measurements DIS measurements have placed limits on the PDF-level total ·strange momentum xS+ and asymmetry xS− CTEQ6.5S: − 0.018 xS + 0.040 0.001 xS 0.005 ≤ ≤ − ≤ ≤ SCAN the available parameter space subject to the DIS limits; D SEARCH· for extremal values of µs,ρ s
0.3 0.2 (a) (b) 0.25 0.1 0.2
0.15 0 s(x) 0.1 s(x) -0.1 s(x) - s(x) 0.05 x [s - s](x)
0 -0.2 0 0.2 0.4 x 0.6 0.8 1 0 0.2 0.4 x 0.6 0.8 1 19 constraints on elastic form factors
0.2 0.3 LFWF E (a) LFWF (b) 0.15 G0 0.2 M PVA4 0.1 0.1 ) ) 2 2 (Q (Q s s
0.05 s 0 s E M G G 0 -0.1
-0.05 -0.2
-0.1 -0.3 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 2 2 Q Q
0.15 G0, 2005 DIS-driven limits to elastic PVA4 HAPPEX-III 0.1 HAPPEX-I, -II s
FFs are significantly more s · M stringent than current 0.05 + η G s s E
experimental precision G 0
-0.05 2 2 η(Q ) 0.94Q 0 0.2 0.4 0.6 0.8 1 2 ∼ → Q 20 models may also enlighten PDF parametrization dependence
see talks by C.-P. Yuan; E. Nocera
● results of fits with different parametric forms preliminary! * for symmetric * strangeness * motivated by models, e.g., on the QCD light front *
● fitted parameters in this instance are identified with quantities like constituent quark masses
21 we build a model for the charm wave funcn… 1st the PDF
● use a scalar spectator picture; details in helicity wave funcns :
TJH, Alberg and Miller, Phys. Rev. D96 (2017) no.7, 074023.
use a power-terms andDIS-derivequantities,e.g.,law (γ=3) covariant vertex function,
invariant mass
6 covariant k2 22 then, a covariant formalism gives the sigma term:
● IF the LFWFs can be constrained with information from the DIS
sector, we may evaluate σcc
…we determine probability distribution functions (p.d.f.s) for this quantity
● this formalism is required because the LFWFs contain noncovariant parts:
it remains to determine the (free) parameters of the light-front model,
23 ● we constrain the model with hypothetical pseudo-data (taken from the `confining’ MBM) of a given
(input data normalizations are inspired by the just-terms andDIS-derivequantities,e.g.,described global analysis)
[ upper limit tolerated by the full fit/dataset ]
[ central value preferred by EMC data alone ]
● rather than traditional χ2 minimization, the model space is instead explored using Bayesian methods 24 model simulations with markov chain monte carlo (MCMC)
● specifically, use a Delayed-terms andDIS-derivequantities,e.g.,Rejection Adaptive Metropolis (DRAM) algorithm Haario et al., Stat. Comput. (2006) 16: 339–354.
5 6 construct a Markov chain consisting of nsim ≈ 10 – 10 simulations, sampling the joint posterior distribution
: input data
: parameters
BROAD gaussian priors
likelihood function
● asymptotically, the MCMC chain fully explores the joint posterior distribution ✔ from this, we extract probability distribution functions (p.d.f.s) for the model parameters and derived quantities, including ¾cc . 25
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1 =
γ p.d.f.s 26 the charm TMD is consistent with deeply internal quarks
prob. dist. func.
(see talk by F. Yuan…)
knowledge of the wave function may help with building a give-and-take between efforts to describe collinear PDFs and TMDs for detailed tomography 27 are directly correlated.
prob. dist. func.
● we find better concordance cf. existing lattice determinations, for somewhat larger IC magnitudes; also, close correlation with the DIS sector –
(χQCD)1 (MILC)2
1Gong et al., Phys. Rev. D88, 014503 (2013). (AR)3 2Freeman and Toussaint, Phys. Rev. D88, 054503 (2013).
3 Abdel-terms andDIS-derivequantities,e.g.,Rehim et al., Phys. Rev. Lett. 116, 252001 (2016). 28 an intrinsic charm component with a small normalization is would likely need very substantial precision to unambiguously disentagle… NLO DGLAP … but an EIC would be well-adapted to try. EIC Whitepaper, Eur. Phys. J. A (2016) 52: 268
LHeC, EIC sensitivity to charm PDF
● e.g., for a ‘generic’ (slightly higher energy) EIC scenario,
C e ● LH EIC can access the crucial nonpert. region of the charm distribution!
IC E PDFSense: see talk tomorrow by Bo-Ting Wang.
B.T. Wang et al., arXiv:1803.02777 [hep-ph]: accepted, Phys. Rev. D 29 closing observations
● understanding the nucleon’s non-terms andDIS-derivequantities,e.g.,valence structure remains an important challenge for the field
→ can construct interpolating models that can help unravel the flavor structure of the proton wave function and unify, inter alia, – for strangeness, form factors and structure function (GPDs)
– for charm, σ-terms andDIS-derivequantities,e.g.,terms and IC PDFs:
– in general, the collinear PDFs and transverse momentum dists.
→to exploit these connection, more experimental information is required, but diverse channels are/will be available (e.g., at EIC)
– exploring these connections will be inseparable from the task of mapping the nucleon’s internal tomography
thanks! 30