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Carl R. Schmidt

Publications and source records attributed to Carl R. Schmidt.

At least 19 recordsLinked to original sources
arXiv2011

Constraints on Little Higgs with Fully-Radiative Electroweak Symmetry Breaking

In a recent paper, we introduced a new Little Higgs model, which contains the gauge structure $SU(2)^3\times U(1)$, embedded in an approximate global $SO(5)\times SO(5)$ symmetry. After breaking to the standard model, $SU(2)_L \times U(1)_Y$, this produces two heavy $Z^\prime$ bosons and two heavy $W^{\prime\pm}$ bosons, along with a single Standard Model-like Higgs scalar. The unique feature of the model was that it was possible to obtain electroweak symmetry breaking and a light Higgs mass entirely from perturbative loop contributions to the Higgs effective potential. In this paper we consider the electroweak constraints on this model, including tree and loop contributions to the universal oblique and non-oblique parameters, tree-level corrections to the $ZWW$ vertex, and tree and loop level corrections to $Zb\bar{b}$. The most significant corrections are positive tree-level corrections to $\hat{S}$ and negative fermion-loop corrections to $\hat{T}$, which require that the scale for the global symmetry breaking be $\gtrsim2$ TeV, depending on the top-quark mixing parameter and the extra gauge couplings. In addition, the loop corrections to $Zb\bar{b}$ contain a divergence that must be absorbed into the coefficient of a new operator in the theory. The finite part of this $Zb\bar{b}$ correction, however, is negligible.

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arXiv2010

Radiative Electroweak Symmetry Breaking in a Little Higgs Model

We present a new Little Higgs model, motivated by the deconstruction of a five-dimensional gauge-Higgs model. The approximate global symmetry is $SO(5)_0\times SO(5)_1$, breaking to $SO(5)$, with a gauged subgroup of $[SU(2)_{0L}\times U(1)_{0R}]\times O(4)_1$, breaking to $SU(2)_L \times U(1)_Y$. Radiative corrections produce an additional small vacuum misalignment, breaking the electroweak symmetry down to $U(1)_{EM}$. Novel features of this model are: the only un-eaten pseudo-Goldstone boson in the effective theory is the Higgs boson; the model contains a custodial symmetry, which ensures that $\hat{T}=0$ at tree-level; and the potential for the Higgs boson is generated entirely through one-loop radiative corrections. A small negative mass-squared in the Higgs potential is obtained by a cancellation between the contribution of two heavy partners of the top quark, which is readily achieved over much of the parameter space. We can then obtain both a vacuum expectation value of $v=246$ GeV and a light Higgs boson mass, which is strongly correlated with the masses of the two heavy top quark partners. For a scale of the global symmetry breaking of $f=1$ TeV and using a single cutoff for the fermion loops, the Higgs boson mass satisfies 120 GeV $\lesssim M_H\lesssim150$ GeV over much of the range of parameter space. For $f$ raised to 10 TeV, these values increase by about 40 GeV. Effects at the ultraviolet cutoff scale may also raise the predicted values of the Higgs boson mass, but the model still favors $M_H\lesssim 200$ GeV.

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arXiv2003

Next-to-leading Corrections to the Higgs Boson Transverse Momentum Spectrum in Gluon Fusion

We present a fully analytic calculation of the Higgs boson transverse momentum and rapidity distributions, for nonzero Higgs $p_\perp$, at next-to-leading order in the infinite-top-mass approximation. We separate the cross section into a part that contains the dominant soft, virtual, collinear, and small-$p_\perp$-enhanced contributions, and the remainder, which is organized by the contributions due to different parton helicities. We use this cross section to investigate analytically the small-$p_\perp$ limit and compare with the expectation from the resummation of large logarithms of the type $\ln{m_H/p_\perp}$. We also compute numerically the cross section at moderate $p_\perp$ where a fixed-order calculation is reliable. We find a $K$-factor that varies from $\approx1.6-1.8$, and a reduction in the scale dependence, as compared to leading order. Our analysis suggests that the contribution of current parton distributions to the total uncertainty on this cross section at the LHC is probably less than that due to uncalculated higher orders.

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arXiv2001

Review of BFKL

I describe the underlying physics behind the BFKL resummation and discuss some of the recent ideas and results in this field. On the theoretical side I consider the formalism in the next-to-leading logarithmic (NLL) approximation and the interpretation of the large corrections. On the phenomenological side I discuss several experiments that attempt to observe the BFKL effects in the high energy limit.

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arXiv1999

Status of the BFKL Resummation Program

I discuss the calculation of the next-to-leading logarithmic (NLL) corrections to the BFKL resummation, as well as some of the issues that arise in this formalism at NLL. In particular I consider the large size and apparent instability of the corrections, and I address some of the attempts to understand and tame them.

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arXiv1999

The Infrared Behavior of QCD Cross Sections at Next-to-Next-to-Leading Order

In this talk we examine how one-loop soft and collinear splitting functions occur in the calculation of next-to-next-to-leading order (NNLO) corrections to production rates, and we present the one-loop gluon soft and splitting functions, computed to all orders in the dimensional regularization parameter $ε$. We apply the one-loop gluon soft function to the calculation of the next-to-leading logarithmic corrections to the Lipatov vertex to all orders in $ε$.

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arXiv1999

Rapidity-Separation Dependence and the Large Next-to-Leading Corrections to the BFKL Equation

Recent concerns about the very large next-to-leading logarithmic (NLL) corrections to the BFKL equation are addressed by the introduction of a physical rapidity-separation parameter $Δ$. At the leading logarithm (LL) this parameter enforces the constraint that successive emitted gluons have a minimum separation in rapidity, $y_{i+1}-y_i>Δ$. The most significant effect is to reduce the BFKL Pomeron intercept from the standard result as $Δ$ is increased from 0 (standard BFKL). At NLL this $Δ$-dependence is compensated by a modification of the BFKL kernel, such that the total dependence on $Δ$ is formally next-to-next-to-leading logarithmic. In this formulation, as long as $Δ\gtrsim2.2$ (for $α_{s}=0.15$): (i) the NLL BFKL pomeron intercept is stable with respect to variations of $Δ$, and (ii) the NLL correction is small compared to the LL result. Implications for the applicability of the BFKL resummation to phenomenology are considered.

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arXiv1999

Virtual Next-to-Leading Corrections to the Lipatov Vertex

We compute the virtual next-to-leading corrections to the Lipatov vertex in the helicity-amplitude formalism. These agree with previous results by Fadin and collaborators, in the conventional dimensional-regularization scheme. We discuss the choice of reggeization scale in order to minimize its impact on the next-to-leading-logarithmic corrections to the BFKL equation.

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arXiv1998

The Infrared Behavior of One-Loop Gluon Amplitudes at Next-to-Next-to-Leading Order

For the case of $n$-jet production at next-to-next-to-leading order in the QCD coupling, in the infrared divergent corners of phase space where particles are collinear or soft, one must evaluate $(n+1)$-parton final-state one-loop amplitudes through $\Ord(\eps^2)$, where $\eps$ is the dimensional regularization parameter. For the case of gluons, we present to all orders in $\eps$ the required universal functions which describe the behavior of one-loop amplitudes in the soft and collinear regions of phase space. An explicit example is discussed for three-parton production in multi-Regge kinematics that has applications to the next-to-leading logarithmic corrections to the BFKL equation.

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arXiv1997

Virtual Next-to-Leading Corrections to the Impact Factors in the High-Energy Limit

We compute the virtual next-to-leading corrections to the impact factors or off-shell coefficient functions in the high-energy limit. When combined with the known real corrections, these results will provide the complete NLO corrections to the impact factors, which are necessary to use the BFKL resummation at NLL for jet production at both lepton-hadron and hadron-hadron colliders.

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arXiv1997

H-->ggg(gqqbar) at Two Loops in the Large-M_t Limit

We present a calculation of the two-loop helicity amplitudes for the processes H-->ggg and H-->gqqbar in the large-M_t limit. In this limit the calculation can be performed in terms of one-loop diagrams containing an effective Hgg operator. These amplitudes are required for the next-to-leading order (NLO) corrections to the Higgs transverse momentum distribution and the next-to-next-to-leading order (NNLO) corrections to the Higgs production cross section via the gluon fusion mechanism.

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arXiv1997

QCD Phenomenology of Charm Production at HERA

We compare different schemes for the treatment of heavy quark production in Deep-Inelastic Scattering (DIS). For fully-integrated quantities such as $F_{2}(x,Q^{2})$, we advocate the use of the General-Massive Variable-Flavor-Number (GM-VFN) scheme; we present some results showing the progress of a Next-to-Leading Order calculation in this scheme. For differential quantities, the Fixed-Flavor-Number (FFN) scheme provides a more appropriate starting point. We present a new calculation of the azimuthal distribution of charm quark production in DIS. All results have been obtained using a Monte Carlo program under development.

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arXiv1996

A Monte Carlo Solution to the BFKL Equation

A simple solution to the BFKL equation is obtained as a series in the number of real gluons emitted with transverse momentum greater than some small cutoff $μ$. This solution reveals physics inside the BFKL ladder which is hidden in the standard inclusive solution, and lends itself to a straightforward Monte Carlo implementation. With this approach one can explore new useful physical observables, which are shown to be independent of the cutoff $μ$. In addition, this approach allows the imposition of kinematic constraints (such as energy conservation) which are important at finite energies. The distribution of $\sum E_\perp$ of particles in a central rapidity bin between two widely-spaced jets is presented as an example.

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arXiv1995

Top Quark Physics at the NLC

A high energy $e^+e^-$ linear collider (NLC) is an excellent tool for studying the properties of the top quark. In this talk I review some of the theory of top quark production and decay in $e^+e^-$ collisions both at threshold and in the continuum. I also report on the results of phenomenological analyses of $t\bar t$ production at the NLC.

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arXiv1995

Top Quark Production and Decay at Next-to-leading Order in $e^+e^-$ Annihilation

We study the effects of QCD corrections to the process $e^+e^-\rightarrow t\bar t+X\rightarrow b\ell^+ν\bar b\ell^-\bar ν+X$ above threshold. We show how to treat consistently to ${\cal O}(α_s)$ the gluon radiation in both the production and the decay of the top quarks, while maintaining all angular correlations in the event. At this order there is an ambiguity in the event reconstruction whenever a real gluon occurs in the final state. We study the effects of this ambiguity on the top mass and helicity angle distributions. For a top mass of 175 GeV and collider energy of 400 GeV the gluon radiation is emitted predominantly in the decay of the top quarks.

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arXiv1994

BFKL versus O(α_s^3) Corrections to Large-rapidity Dijet Production

We examine dijet production at large rapidity intervals at Tevatron energies by comparing an exact ${\cal O}(α_s^3)$ calculation with the BFKL approximation, which resums the leading powers of the rapidity interval $y$ to all orders in $α_s$. We analyze the dependence of the exact ${\cal O}(α_s^3)$ calculation on the jet cone-size as a function of $y$, and use this cross section to define an ``effective rapidity'' $\hat y$ which reduces the error that the large-$y$ approximation induces on the kinematics. Using $\hat y$ in the BFKL resummation, we reexamine jet production at large transverse momenta and the transverse momentum decorrelation of the tagging jets. We find less dramatic, but still significant, effects than found previously using the large-$y$ approximation.

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