Exploring new resonances with direct top flavor changing interactions

This paper investigates three types of new physics resonances that couple to Standard Model quarks through direct top-quark flavor-changing interactions, identifying the relevant SMEFT operators at the electroweak scale and analyzing their phenomenological implications.

The Gist

Imagine the Standard Model of particle physics as a massive, incredibly complex rulebook for a cosmic game. For decades, physicists have been playing by these rules, but they suspect there are hidden "cheat codes" or secret moves that the current rulebook doesn't explain. These secret moves are called New Physics.

This paper is like a detective story where the authors are hunting for a specific type of cheat code: Top Quark Flavor-Changing Neutral Currents (FCNC).

Here is a breakdown of the paper using simple analogies:

1. The Characters: The Top Quark and the "Forbidden" Switch

In the particle world, there are different "flavors" of quarks (like Up, Down, Charm, Strange, Bottom, and Top). Usually, they are very picky about who they talk to.

• The Rule: A Top quark (the heaviest and most famous one) is supposed to stay a Top quark. It rarely, if ever, magically turns into an Up or Charm quark without help. This is like a celebrity who never leaves their mansion.
• The GIM Mechanism: The Standard Model has a built-in "security system" (called the GIM mechanism) that makes these flavor changes incredibly rare.
• The Suspect: The authors are looking for a "New Physics" particle that acts like a magic switch, allowing the Top quark to instantly swap places with a lighter quark (Up or Charm). If we find this, it proves there's a new rulebook being written.

2. The Suspects: Three New "Resonances"

The authors propose three specific types of new heavy particles (resonances) that could act as this magic switch. Think of them as three different types of messengers that run between the Top quark and the lighter quarks:

1. The Singlet Vector Boson ($Z'_R$): Imagine a neutral, invisible courier that can carry a message between a Top and an Up quark. It's like a private phone line.
2. The Octet Vector Boson ($G'_R$): This is similar to the first one, but it's "colorful" (in the physics sense of the strong nuclear force). It's like a courier wearing a bright, high-visibility vest that interacts with the "glue" holding the universe together.
3. The Color Sextet Scalar ($\tilde{S}_R$): This is the most exotic of the bunch. It's a heavy, spinning ball of energy that doesn't just pass a message; it actually violates a conservation law (like "Up-number"). It's the wild card that breaks the rules of the game entirely.

3. The Investigation: How Do We Catch Them?

Since these new particles are too heavy to be created directly in our current particle accelerators (like the Large Hadron Collider, or LHC), we can't see them directly. Instead, we look for their footprints.

The authors use a clever two-step detective method:

• Step A: The UV Match (The Blueprint): They start by imagining these heavy particles exist at a very high energy level. They calculate exactly what kind of "ripples" or "effective operators" these particles would leave behind in the lower-energy world we can observe.
• Step B: The LHC Phenomenology (The Crime Scene): They simulate what happens at the LHC if these ripples exist. They look for three specific types of "crimes":
  1. Single Top Production: A Top quark appearing out of nowhere where it shouldn't be.
  2. Same-Sign Top Pairs: Two Top quarks appearing together with the same "charge" (like two positive charges repelling). In the standard game, this is impossible. If we see this, it's a smoking gun for the exotic scalar particle.
  3. Rare Decays: A Top quark decaying into a Higgs boson or a Z boson and a light quark, which it usually doesn't do.

4. The Clues: Constraints and Patterns

The authors run simulations to see which "suspects" are still in the running based on current data.

• The D-Meson Alibi: They check a separate crime scene involving "D-mesons" (particles made of Charm and Up quarks). If the new particles are too strong, they would have caused too many D-mesons to mix and match in ways we haven't seen. This puts a limit on how strong the "magic switch" can be.
• The Patterns: They test three different scenarios (patterns) of how these particles connect:
  • Pattern 1: Connects Top to Up, and Top to Charm, but not Up to Charm.
  • Pattern 2: Connects Top to Charm, and Up to Charm, but not Top to Up.
  • Pattern 3: Connects Top to Up, and Top to Charm, but the connection between Up and Charm is blocked.

5. The Verdict: How to Tell Them Apart

The paper concludes with a guide on how to distinguish these three suspects if we actually find a signal at the LHC:

• If you see a "Same-Sign Top" pair (two Tops with the same charge) but NO extra single Tops: You likely found the Exotic Scalar ($\tilde{S}_R$). It's the only one that breaks the rules enough to create this weird pair without making a mess of single Tops.
• If you see a flood of "Single Top" events but NO same-sign pairs: You likely found the Vector Bosons ($Z'_R$ or $G'_R$). These are more "conservative" messengers.
• Distinguishing the two Vector Bosons: It's hard to tell the Singlet ($Z'_R$) from the Octet ($G'_R$) apart because they look very similar. You'd need to count the exact ratio of different collision types (like looking at the angle and speed of the debris) to see the subtle difference in their "color" interactions.

Summary

This paper is a theoretical roadmap. It says: "If we find evidence of Top quarks changing flavors at the LHC, here are the three likely culprits. Here is how they behave, and here is exactly what data we need to look for to figure out which one it is."

It transforms abstract math into a clear strategy for future experiments, helping physicists know exactly what to look for in the mountain of data coming from the world's biggest particle collider.

Technical Summary

1. Problem Statement

Flavor-Changing Neutral Current (FCNC) processes are highly suppressed in the Standard Model (SM) by the Glashow–Iliopoulos–Maiani (GIM) mechanism, making them powerful probes for New Physics (NP). While FCNCs involving light quarks are tightly constrained, the top-quark sector remains less explored.

Current analyses typically follow two paths:

1. Model-Independent: Using the Standard Model Effective Field Theory (SMEFT) to treat operators as arbitrary deformations. This lacks information about the underlying UV physics.
2. Model-Dependent: Starting from specific NP models. This often misses the correlations between different operators.

The Gap: There is a need to bridge these approaches by deriving SMEFT operators from explicit UV-complete models (heavy resonances) to enforce operator correlations that are invisible in generic SMEFT fits. This paper addresses how specific heavy resonances coupling directly to the top quark via flavor-changing interactions manifest at the electroweak scale and the Large Hadron Collider (LHC).

2. Methodology

The authors employ a "bottom-up" approach starting from UV-complete models and matching them to the SMEFT:

• UV Model Construction:

  • They consider heavy spin-0 (scalars) and spin-1 (vectors) bosons.
  • Constraints: The new particles must have well-defined SM gauge quantum numbers, couple directly to the top quark via flavor-changing interactions, have no flavor-conserving couplings to SM quarks, and interact via only one type of vertex.
  • Candidates: A comprehensive list of heavy bosons is generated, including color singlets/octets ($Z'_R, G'_R, Z'_L, G'_L$), weak triplets ($W'_L, \Omega'_L$), and scalars ($H_u, H_d, S_u, S_d, \tilde{S}_R, \tilde{S}_L$).
  • Focus: Due to flavor constraints on bottom quarks, the analysis focuses on three specific resonances coupling to right-handed up-type quarks: the color-singlet vector $Z'_R$, the color-octet vector $G'_R$, and the color-sextet scalar $\tilde{S}_R$.

• Matching and Renormalization Group Evolution (RGE):

  • Matching: Heavy particles are integrated out at the cutoff scale $\Lambda$ using the Covariant Derivative Expansion (CDE) to generate dimension-6 SMEFT operators in the Warsaw basis.
  • RGE: The Wilson coefficients are evolved from $\Lambda$ down to the top-quark mass scale ($m_t$) using Renormalization Group Equations. This accounts for operator mixing, generating operators that contribute to $t \to qZ/h$ decays (e.g., $O_{\phi u}, O_{u\phi}$) even if they were not present at tree level.

• Phenomenological Analysis:

  • Flavor Patterns: The analysis considers three distinct coupling patterns based on which Yukawa-like couplings ($y_{ij}$) are non-zero:
    1. $y_{23} = 0$ (Couples 1st and 3rd generations).
    2. $y_{13} = 0$ (Couples 1st and 2nd generations).
    3. $y_{12} = 0$ (Couples 2nd and 3rd generations).
  • Observables:
    • LHC: Single top production ($tj$), top-pair production ($t\bar{t}$), and same-sign top production ($tt$).
    • Flavor Physics: $D^0-\bar{D}^0$ mixing constraints.
    • Rare Decays: $t \to Zq$ and $t \to hq$.
  • Tools: Calculations performed using MatchingTools, Wilson, and MadGraph5_aMC@NLO (LO).

3. Key Contributions

• Operator Correlations: The paper explicitly derives the correlations between four-fermion operators (induced at tree level) and dipole-like operators (induced via RGE mixing) for specific heavy resonances. This allows for a more constrained phenomenological analysis than generic SMEFT fits.
• Distinct Signatures for Different Resonances:
  • $Z'_R$ and $G'_R$ (Fermion-number conserving): These generate tree-level same-sign top ($tt$) production and contribute significantly to $D^0-\bar{D}^0$ mixing if $y_{12} \neq 0$.
  • $\tilde{S}_R$ (Fermion-number violating): As a color sextet scalar, it does not generate tree-level same-sign top production (due to "up-number" conservation in the UV). Its contribution to $D^0-\bar{D}^0$ mixing is loop-suppressed ($O(\Lambda^{-4})$), making it much less constrained by flavor physics.
• Flavor Pattern Discrimination: The authors demonstrate that the ratio of cross-sections and the initial state parton distributions (valence $u$-quark vs. sea $c$-quark) allow for the discrimination between the $y_{13}=0$ and $y_{23}=0$ patterns.

4. Results

• Constraints from $D^0-\bar{D}^0$ Mixing:
  • For $Z'_R$ and $G'_R$, the coupling $y_{12}/\Lambda^2$ is severely constrained by $D^0-\bar{D}^0$ mixing ($C_{12}/\Lambda^2 \lesssim 1.3 \times 10^{-7} \text{ TeV}^{-2}$).
  • For $\tilde{S}_R$, the constraint is much weaker due to loop suppression, allowing for larger parameter space.
• LHC Sensitivity:
  • Single Top ($tj$): Highly sensitive to the $y_{23}=0$ and $y_{13}=0$ patterns. The $Z'_R$ and $G'_R$ are more constrained by single top data than $t\bar{t}$ data.
  • Same-Sign Top ($tt$): This is the most powerful channel for $Z'_R$ and $G'_R$ (especially when $y_{12}=0$). The current upper limit ($\sigma(tt) < 1.6$ fb) provides the strongest constraint on these vectors.
  • $\tilde{S}_R$ Behavior: Since it does not produce same-sign tops at tree level, its primary signature is excess in single top production without a corresponding same-sign top excess.
• Discrimination Power:
  • $Z'_R$ vs. $G'_R$: Difficult to distinguish solely by cross-sections due to similar Lorentz structures. The ratio $\delta\sigma(tt)/\delta\sigma(tj)$ is required to probe the color structure (singlet vs. octet).
  • Flavor Patterns:
    • If $y_{12} \neq 0$, $D^0-\bar{D}^0$ mixing strongly constrains the model.
    • If $y_{12} = 0$, the model is less constrained by flavor physics but can be tested via the specific kinematic distributions (rapidity) of single top events, which differ between $u$-quark and $c$-quark initiated processes.

5. Significance

This work provides a crucial bridge between UV model building and low-energy effective field theory. By enforcing correlations derived from specific heavy resonances, the authors show that:

1. Flavor Physics is a powerful filter: $D^0-\bar{D}^0$ mixing can effectively rule out specific coupling patterns ($y_{12} \neq 0$) for vector bosons.
2. Collider Signatures are Diagnostic: The presence or absence of same-sign top events can distinguish between fermion-number conserving vectors ($Z'_R, G'_R$) and fermion-number violating scalars ($\tilde{S}_R$).
3. Future Prospects: The paper outlines a strategy for the LHC (and future top factories) to not only discover new resonances but to identify their spin, color representation, and the specific flavor structure of their couplings, moving beyond generic SMEFT limits.

In summary, the paper argues that a combined analysis of LHC top physics and flavor observables is essential to distinguish between different classes of New Physics models that induce top FCNCs.