The oblique parameters in multi-Higgs-doublet models (0802.4353v1)

Abstract: We present general expressions for the oblique parameters S, T, U, V, W, and X in the SU(2)xU(1) electroweak model with an arbitrary number of scalar SU(2) doublets, with hypercharge 1/2, and an arbitrary number of scalar SU(2) singlets.

• The paper introduces generalized expressions for all six electroweak oblique parameters, including S, T, U, V, W, and X.
• It employs mixing matrices to systematically quantify scalar contributions, demonstrating ultraviolet finiteness for all but the T parameter.
• Numerical and graphical analyses elucidate how different scalar configurations refine constraints on physics beyond the Standard Model.

Overview of "The Oblique Parameters in Multi-Higgs-Doublet Models"

The paper "The oblique parameters in multi-Higgs-doublet models" by W. Grimus, L. Lavoura, O.M. Ogreid, and P. Osland addresses the calculation of electroweak oblique parameters in the context of extensions to the Standard Model (SM) involving multiple Higgs doublets and singlets. The paper is focused on the electroweak precision observables that can be affected by new physics through their impact on vacuum polarization phenomena, parameterized by the so-called oblique parameters $S$, $T$, $U$, $V$, $W$, and $X$. These parameters are instrumental in understanding effects that are nearly invisible in processes involving light fermions and are assessed via gauge boson interactions.

Key Contributions

The authors present generalized expressions for the oblique parameters in a theoretical framework extending the SM by considering an arbitrary number of scalar $SU(2)$ doublets with hypercharge ±1/2 and scalar $SU(2)$ singlets. Such models, collectively referred to as multi-Higgs-doublet-and-singlet models (mHDSM), are relevant due to their potential to manifest beyond the Higgs mechanism, offering alternative insights into symmetry breaking and mass generation.

Main Results

The paper provides:

1. Expressions for Oblique Parameters: Unlike the traditional approach where only $S$, $T$, and $U$ are considered important, the authors derive and account for all six parameters $S$, $T$, $U$, $V$, $W$, and $X$.
2. Mathematical Treatment: The oblique parameters are expressed in terms of mixing matrices ${\cal U}$ and ${\cal V}$ which encapsulate the mixing of charged and neutral scalars, respectively. This approach systematically catalogs the contributions of multiple scalar effects across diverse electroweak observables.
3. Ultraviolet Finiteness: All parameters, apart from $T$, are demonstrated to be ultraviolet-finite even before subtracting the SM contributions. $T$, which is inherently divergent, becomes finite only upon appropriate subtraction.
4. Numerical Insights: The paper contains thorough evaluation and graphical representation of key functions involved in their calculation, such as $F(I, J)$, $G(I, J, Q)$, and $H(I, J, Q)$, providing insights into how different scalar configurations affect oblique parameters.

Implications and Future Directions

The findings offer theoretical guidance on how new scalar sectors might influence electroweak precision tests. Practically, the work can help refine constraints on beyond the Standard Model physics based on precision electroweak data, potentially guiding the search for additional Higgs-like particles or interactions at collider experiments like the LHC or future particle accelerators.

From a theoretical perspective, the results enhance the understanding of how additional Higgs sectors can be embedded within the SM framework while ensuring consistency with existing constraints from electroweak precision measurements. The methodology and results provide a foundation for further exploration of more complex scalar models that could yield novel phenomena observable at yet untested energy scales.

Overall, this paper offers valuable insights into the theoretical landscape accommodating extended Higgs sectors and marks a step further in understanding the delicate interplay between new scalar dynamics and precision electroweak physics. The research continues to hold relevance in guiding experimental searches and theoretical investigations as the quest for physics beyond the Standard Model progresses.