Laser-assisted production of the light charged Higgs boson from top quark decay in the type-I two Higgs doublet model

This paper investigates the impact of a circularly polarized laser field on top quark decay within the type-I two Higgs doublet model, demonstrating that specific laser parameters can significantly enhance the branching ratio of the $t \rightarrow bH^+$ channel to 0.97, thereby surpassing the standard $t \rightarrow bW^+$ decay and offering a promising strategy for detecting charged Higgs bosons.

The Gist

The Big Idea: Giving Particles a "Head Start" with a Laser

Imagine you are trying to push a heavy boulder (a Top Quark) up a steep hill. Usually, gravity pulls it back down, and it rolls into a specific valley (decaying into a W Boson). This is the "standard" path that nature prefers, and it happens almost 100% of the time.

However, physicists have a theory that there is a second, hidden valley nearby called the Charged Higgs Boson. They want to see the boulder roll into this new valley because finding it would prove that our current understanding of the universe (the Standard Model) is incomplete. The problem? The boulder almost never goes there on its own.

The Solution: The authors of this paper propose using a super-powerful laser as a giant, rhythmic wind to push the boulder. They suggest that if you blast the top quark with a specific type of laser light, you can "nudge" it so hard that it ignores the usual path and rolls into the new, hidden valley instead.

---

The Cast of Characters

1. The Top Quark: The heaviest known elementary particle. It's like a giant, unstable bowling ball that breaks apart almost instantly after being created.
2. The Standard Path ($t \to bW^+$): The "safe" route. The top quark usually breaks into a bottom quark and a W boson. This is the default setting of the universe.
3. The New Path ($t \to bH^+$): The "rare" route. The top quark breaks into a bottom quark and a Charged Higgs Boson. This is the "Holy Grail" of this study. Finding this proves new physics exists.
4. The Laser: Not a sci-fi weapon, but a focused beam of light. In this paper, it's a circularly polarized laser, which means the light waves spin like a corkscrew as they move.

---

How the Laser Works: The "Photon Buffet"

Think of the laser field not as a single push, but as a buffet of tiny energy packets called photons.

• Without the Laser: The top quark has to make a decision on its own. It almost always picks the W Boson path because it's the easiest route.
• With the Laser: The top quark is surrounded by a swarm of photons. It can "eat" (absorb) some of these photons to gain extra energy or "spit out" (emit) some to lose energy.
• The Magic Trick: By absorbing just the right number of these photons, the top quark gains enough "momentum" to overcome the barrier that usually stops it from creating the Charged Higgs.

The authors used a mathematical tool called the Dirac-Volkov formalism. Think of this as a very advanced GPS that calculates exactly how a particle moves when it's surfing on a giant, spinning wave of light.

---

The Results: Turning the Tide

The researchers ran the numbers to see what happens when they crank up the laser power. Here is what they found:

1. Weak Lasers Do Nothing: If the laser is weak (like a flashlight), the top quark ignores it. It still takes the standard path 99% of the time.
2. The Sweet Spot: When they increased the laser intensity to a massive 3.8 × 10¹⁴ Volts per centimeter (an incredibly strong field, though not yet achievable in current labs), something amazing happened.
   • The probability of the top quark choosing the Charged Higgs path jumped to 97%.
   • The probability of the standard path dropped to just 3%.

The Analogy: Imagine a river that usually flows 99% to the left. The scientists found a way to build a dam and redirect the water with a powerful pump (the laser) so that 97% of the water suddenly flows to the right.

Why Does This Matter?

• Solving the "Missing Energy" Mystery: In real particle colliders (like the Large Hadron Collider), detecting new particles is hard because they often disappear into "missing energy." If we can force the top quark to produce Charged Higgs bosons 97% of the time, it becomes much easier to spot them.
• A New Tool for Discovery: This paper suggests that we shouldn't just build bigger colliders; we should also build stronger lasers to attach to them. These lasers could act as a "magnifying glass" or a "spotlight" to reveal particles that are currently hiding in the shadows.

The Catch (Reality Check)

The paper admits that the laser strength required (3.8 × 10¹⁴ V/cm) is currently too strong for our existing laboratories. We don't have lasers that powerful yet.

However, laser technology is advancing incredibly fast. The authors are essentially saying: "We have the math ready. We know exactly what to look for. We just need the laser technology to catch up so we can finally see these new particles."

Summary

This paper is a theoretical blueprint showing that if we can build a sufficiently powerful, spinning laser, we can force the universe's heaviest particle to reveal a secret, hidden cousin (the Charged Higgs). It turns a rare, almost impossible event into a common occurrence, potentially opening the door to a new era of physics.

Technical Summary

1. Problem Statement

The discovery of the Higgs boson at the LHC completed the Standard Model (SM) particle content but left fundamental questions unanswered, such as the nature of dark matter and neutrino masses. The Two-Higgs-Doublet Model (2HDM) is a leading extension of the SM that predicts a charged Higgs boson ($H^\pm$). However, detecting a charged Higgs remains a significant experimental challenge due to background noise and "missing energy" signatures in collider experiments.

Specifically, the decay of the top quark ($t$) into a charged Higgs ($H^+$) and a bottom quark ($b$) is a promising channel for discovery. In the SM, the top quark decays almost exclusively via $t \to bW^+$. In the Type-I 2HDM, the $t \to bH^+$ channel is suppressed under standard conditions. The authors investigate whether an external, intense circularly polarized laser field can modify this decay process, potentially enhancing the $t \to bH^+$ branching ratio to observable levels.

2. Methodology

The study employs a theoretical framework combining the Type-I 2HDM with Strong-Field Quantum Electrodynamics (QED).

• Theoretical Framework:

  • Model: Type-I 2HDM, where all fermions couple to a single Higgs doublet. The interaction vertex for $t-b-H^+$ is defined by coefficients $A$ and $B$ dependent on the top/bottom masses and the ratio of vacuum expectation values ($\tan \beta$).
  • Laser Field: The external field is modeled as a circularly polarized plane wave with four-potential $A^\mu(\phi) = a_1^\mu \cos \phi + a_2^\mu \sin \phi$, where $\phi = k \cdot x$.
  • Formalism: The authors utilize the Dirac-Volkov formalism to describe charged fermions (top and bottom quarks) interacting with the laser field. The wave functions of the quarks are "dressed" by the field, acquiring a quasi-momentum and an effective mass ($m^*$). The charged Higgs boson is treated as an undressed particle in the final state to simplify the calculation and focus on production dynamics.

• Calculations:

  • The S-matrix element is derived by integrating the interaction over space-time, utilizing the expansion of the laser-induced phase factor into a Fourier series of Bessel functions ($J_s(z)$).
  • This expansion accounts for the exchange of $s$ laser photons (where $s > 0$ is absorption and $s < 0$ is emission).
  • The decay width $\Gamma$ is calculated by summing over all possible photon numbers $s$, ensuring energy-momentum conservation including the laser photons ($q_2 + k_H - q_1 - sk = 0$).
  • Branching ratios are computed by comparing the laser-assisted $t \to bH^+$ width against the standard $t \to bW^+$ width.

3. Key Contributions

• Analytical Derivation: The paper provides a comprehensive derivation of the decay width for $t \to bH^+$ in the presence of a circularly polarized laser field within the Type-I 2HDM, explicitly handling the multi-photon exchange processes via Bessel functions.
• Strong-Field Regime Analysis: Unlike previous perturbative studies, this work focuses on the non-perturbative strong-field regime (where the dimensionless intensity parameter $a_0 \gtrsim 1$), demonstrating that the laser field can fundamentally alter decay dynamics rather than just providing small corrections.
• Parameter Sensitivity: The study systematically analyzes the dependence of the decay width and branching ratios on:
  • Laser field strength ($\xi_0$).
  • Laser frequency ($\omega$).
  • Charged Higgs mass ($M_{H^+}$).
  • The model parameter $\tan \beta$.

4. Key Results

The numerical analysis reveals that the laser field can dramatically enhance the $t \to bH^+$ channel under specific conditions:

• Dominance of $t \to bH^+$:

  • At standard field strengths ($< 10^{14}$ V/cm), the $t \to bW^+$ channel remains dominant.
  • However, at a laser field strength of $\xi_0 = 3.8 \times 10^{14}$ V/cm and a frequency of $\hbar\omega = 0.117$ eV (CO$_2$ laser), the branching ratio for $t \to bH^+$ reaches 0.975 (97.5%).
  • In this regime, the $t \to bH^+$ channel becomes the dominant decay mode, surpassing the standard $W^+$ channel.

• Mass and Frequency Dependence:

  • The enhancement is robust for charged Higgs masses in the range 80–150 GeV.
  • Lower laser frequencies (e.g., 0.117 eV) are more effective than higher frequencies (e.g., 1.54 eV) for inducing significant photon exchange and width modification.
  • The effect is most pronounced at high field strengths and low frequencies, consistent with the behavior of Bessel function arguments in the decay amplitude.

• $\tan \beta$ Dependence:

  • The branching ratio is maximized at low values of $\tan \beta$. The study identifies an optimal range of $3 \le \tan \beta \le 18$, with the peak enhancement occurring at $\tan \beta = 3$. This is consistent with Type-I 2HDM Yukawa coupling structures where couplings are inversely proportional to $\tan \beta$.

• Multi-Photon Mechanism:

  • The enhancement is driven by multi-photon processes. As the field strength increases, the argument of the Bessel functions increases, allowing for significant contributions from higher-order photon exchanges, which kinematically opens up the $H^+$ channel.

5. Significance and Implications

• New Detection Strategy: The results suggest that intense electromagnetic fields could serve as a "catalyst" for detecting new physics. By tuning laser parameters, experiments could potentially shift the branching ratios of top quark decays to favor new particles (like the charged Higgs) over standard model backgrounds.
• Experimental Feasibility: While the required field strength ($3.8 \times 10^{14}$ V/cm) exceeds current laboratory capabilities (current limits are $\sim 10^{12}$–$10^{13}$ V/cm), the rapid advancement of high-power laser technology (projected to reach $10^{22}$ W/cm$^2$) suggests this regime may be accessible in the near future.
• Theoretical Validation: The study validates the applicability of the Dirac-Volkov formalism in the strong-field regime for electroweak processes, confirming that non-perturbative effects can drastically alter particle lifetimes and decay channels.
• Future Directions: The authors note that while tree-level calculations show this dramatic effect, one-loop QCD corrections (approx. 6–15%) would shift numerical values but are not expected to qualitatively change the conclusion that strong fields can enhance new physics signals.

In conclusion, this paper proposes a novel mechanism where laser-assisted top quark decays could provide a viable pathway to discover the charged Higgs boson, transforming a suppressed channel into the dominant decay mode under specific strong-field conditions.