You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


---
abstract: 'Sea quark contributions to the scalar density and the axial current matrix elements of the nucleon are studied in lattice QCD with two flavours of dynamical Wilson fermions. The results are compared to trends in heavy quark mass expansions, and contrasted with the numbers obtained using dynamical staggered fermions.'
address: 'CTS and SERC, Indian Institute of Science, Bangalore-560012, India'
author:
- Apoorva Patel
title: 'SCALAR AND AXIAL MATRIX ELEMENTS OF THE NUCLEON: SEA QUARK CONTENT'
---

=

In the numerical study of many hadronic properties, a comparison of the full QCD and the quenched approximation results shows that the differences are small (though the bare gauge couplings in the two cases are quite different); small enough that given the various sources of errors it is hard to differentiate between the two sets of numbers. Also the phenomenological quark models, which ignore the sea quarks altogether, do a good job of fitting many of the experimental results. All this suggests a welcome phenomenological simplification of the theory (i.e. the dominant effect of the sea quarks is to generate constituent quarks as valence quarks with renormalised properties), but one would like to understand the dynamical reason behind it.

To find unambiguous signatures of the sea quarks (or failures of the quenched approximation), one has to look for instances where the sea quarks amount to more than mere renormalisation of the gauge coupling. Good places to search are the properties where the quark model is not a good guide. Of particular interest are the quark bilinear matrix elements which naively vanish in the quark model, e.g. the strange quark matrix elements of the proton $\langle p| \bar s \Gamma s |p \rangle$. We concentrate on the scalar ($\Gamma=1$) and the axial vector ($\Gamma=i\gamma_\mu\gamma_5$) bilinears. Both are related to dynamically broken classical symmetries of QCD, and hence have scope for a significant mixing with gluonic sector/sea quarks. Moreover, both correspond to Hermitian operators which are numerically easy to deal with, e.g. using the Hybrid Monte Carlo algorithm. (Complex fermion determinants are difficult to handle as exemplified by the attempts to study QCD at finite chemical potential ($\Gamma = i \gamma_0$) and the $\theta-$dependence of the neutron electric dipole moment ($\Gamma = i \gamma_5$).)

The non-singlet quark bilinear matrix elements of the nucleon, conventionally expressed in terms of $F$ and $D$ couplings, are easily extracted from a direct evaluation of the $3-$point correlators. On the contrary, correlators containing a purely gluonic intermediate state are quite noisy. Experience has shown that instead of a direct evaluation of the $3-$point correlators, it is easier to compute the sea quark matrix elements by making hadrons propagate through a background external field (i.e. creating sea quarks with an extra source term $S_\Gamma = \sum_x h_\Gamma \bar{\psi}(x) \Gamma \psi(x)$ added to the standard fermion action) and then evaluating numerical derivatives with respect to the external field strength $h_\Gamma$. While a singlet scalar density field is obtained just by choosing unequal valence and sea quark masses, configurations with a singlet axial current field have to be created afresh.

Pion-Nucleon Sigma Term {#pion-nucleon-sigma-term .unnumbered}
=======================

The clear and interesting results concern the pion-nucleon sigma term (with $m=m_u=m_d$) : $$\sigpiN = \langle N| m (\bar u u + \bar d d) |N \rangle
        = m (\partial M_N / \partial m) ~,$$ where the quark mass derivatives are to be evaluated at fixed gauge coupling. The most recent analysis [@sigmaexpt] of experimental data (though better data are definitely desirable), gives $\sigpiN \approx 45$ . Within the first order flavour $SU(3)$ breaking parametrisation, the valence quark component is only $\sigpiNv \equiv (3F_S-D_S)
\approx 26$ , leaving ample room for the sea quark component.

We cannot yet directly calculate $\sigpiN$ on the lattice, as it requires extrapolating the matrix element to very small quark masses. Instead we get an indication of the importance of insertions on sea quark loops from the ratio of the full matrix element (valence plus sea) to its valence part.

We generated $16^4$ lattices with two flavours of dynamical Wilson fermions and periodic boundary conditions. These lattices were doubled in the time direction prior to calculation of hadron spectrum and matrix elements. We obtained results [@qcdwftwo] for $\beta \equiv 6g^{-2}
=5.4,5.5,5.6$, with the quark masses in the range $m_s < m_q < 3m_s$. Our results for the ratio of the full matrix element to its valence part are shown in fig.1. We see that the sea contribution is $1-2$ times the valence part. This is in qualitative agreement with the experimental data. The overall magnitude of $m \sigpiNv$ is systematically smaller than the experimental value, however, an effect possibly due to not having explored small enough quark masses.

A similar analysis can be carried out for the staggered fermion results of the Columbia group [@columbia]. Here the numerical derivatives for valence quark matrix elements involve large quark mass intervals, but the consistency between numbers extracted using $(N,\widetilde\Omega)$ and $(\Lambda,\Xi)$ masses provides a check on baryon masses being linear in quark masses over the interval. As table 1 shows, the effect of sea quarks is somewhat smaller in this case compared to Wilson fermions, but nonetheless significant. (Note that the effect is a factor of two smaller for heavy fermions.)

The analogous scalar density matrix elements of the $\rho$ and the $\Delta$ show similar factors between the valence and the full value, while the magnitude of the matrix elements is roughly proportional to the number of valence quarks. This suggests a model for constituent quarks in which the bare quarks are dressed strongly, and in a manner independent of the hadron that they are in. Indeed, it can be reasoned [@scanom] that the large sea quark component we see is due to change in the overall scale of the theory; the sea quarks influence the $\beta-$function through vacuum polarisation. The really surprising feature of the lattice results then is (see fig.1) that even relatively heavy sea quarks (corresponding to the pseudoscalar meson mass up to $1-1.2$ GeV) give a contribution comparable to the valence part.

$$\vbox{\tabskip=0pt \offinterlineskip
\halign{\Strut #\ &\Strut #&\vrule #\ &\Strut #\ &\Strut #\ &\Strut #\cr
\ Quark    &$\sigpiN /m$&& \ Quark    &    $\sigpiNv /m$     & $\sigpiNv /m$
\cr
mass range &   ~$(N)$   && mass range
&$(N,\widetilde\Omega)$&$(\Lambda,\Xi)$\cr
\noalign{\hrule}
0.010--0.015 &   ~---    && 0.004--0.010 & 9.0(3.)& 8.5(?)   \cr
0.015--0.020 & 19.2(2.8) && 0.015--0.070 & 8.7(3) & 8.5(1.2) \cr
0.020--0.025 & 11.6(2.3) && 0.020--0.070 & 7.8(2) & 7.8(8)   \cr
             &           && 0.025--0.100 & 7.4(1) & 7.5(3)   \cr
}}$$

Polarisation of Sea Quarks {#polarisation-of-sea-quarks .unnumbered}
==========================

The EMC result on polarised muon-proton scattering is difficult to digest without a sizeable contribution from the sea quarks. Lattice measurement of sea quark and gluon components of the structure function $g_1$ can be attempted in two ways. The simpler approach, possible even within the quenched approximation, is to replace the insertion on sea quark loops by an effective gluon operator [@ffdlatt]. We have adopted the alternative approach of directly determining the axial current coupling to sea quarks in the nucleon [@gonelatt].

In the first trial run, we used two flavours of dynamical Wilson fermions on $8^4$ lattices at $\beta = 5.3$ with $\kappa = 0.165,0.166$. It is necessary to have the field strength $h_A$ of the order of the quark mass to see any signal, and we used $2\kappa h_A = 0.005,0.004$. The pseudoscalar meson masses are about $0.9,0.8$ for these heavy quarks. We only find $2\sigma$ bounds for the sea quark contribution to axial current matrix elements of the nucleon, $|S_A| < 0.05,0.08$ per flavour. These are a factor of $2$ to $4$ below what is required to confirm the EMC result on the lattice. (The lattice one loop and continuum two loop renormalisation constants for the singlet axial current are finite, and can be ignored at the present qualitative level.) This sharply contrasts with the scalar density case, where sea and valence quark components are comparable at similar quark masses. It is entirely possible that $S_A$ moves away from zero at relatively small quark masses only.

Lattice results for non-singlet scalar density and axial current matrix elements have turned out to be reasonable [@nonsinglet]. Heavy quark limits and constituent quark model expectations are easy to evaluate for these matrix elements. Putting everything together: (a) $F_S$, $m S_S$, $F_A$ and $D_A$ are finite in the heavy quark limit and turn out to be smooth functions of the quark mass, while (b) $m D_S$ and $S_A$ vanish in the heavy quark limit as $m^{-2}$ and depart significantly from zero only when the quark mass becomes of the order of $\Lambda_{QCD}$. This suggests that flavour $SU(3)$ breaking effects are probably small in the former case, though likely to be sizeable in the latter case.

ACKNOWLEDGEMENTS {#acknowledgements .unnumbered}
================

I thank LANL and ITP (Santa Barbara) for hospitality during the initial stages of this work, Hong Chen for sending me the detailed results of the Columbia group, and finally the organisers of LAT91 without whose support I would not have been able to attend this conference.

[9]{} J. Gasser, H. Leutwyler and M. Sainio, Phys. Lett. B253 (1991) 252 R. Gupta, C. Baillie, R. Brickner, G. Kilcup, A. Patel and S. Sharpe, Phys. Rev. D44 (1991) 3272 F. Brown et. al., Phys. Rev. Lett. 67 (1991) 1062;\
H. Chen, Ph. D. Thesis, Columbia University (1991) A. Patel, Phys. Lett. B236 (1990) 102 J. Mandula, these proceedings R. Gupta, A. Patel and S. Sharpe, in progress See for instance Ref. 1 and references therein