arXiv subjects

Keith S. M. Lee

Publications and source records attributed to Keith S. M. Lee.

17 recordsLinked to original sources

arXiv2019

Quantum Computation of Scattering in Scalar Quantum Field Theories

Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great computational complexity and can generally be performed only when the interaction strength is weak. A full understanding of the foundations and rich consequences of quantum field theory remains an outstanding challenge. We develop a quantum algorithm to compute relativistic scattering amplitudes in massive phi-fourth theory in spacetime of four and fewer dimensions. The algorithm runs in a time that is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. Thus, it offers exponential speedup over existing classical methods at high precision or strong coupling.

hep-th↗

arXiv2018

BQP-completeness of Scattering in Scalar Quantum Field Theory

Recent work has shown that quantum computers can compute scattering probabilities in massive quantum field theories, with a run time that is polynomial in the number of particles, their energy, and the desired precision. Here we study a closely related quantum field-theoretical problem: estimating the vacuum-to-vacuum transition amplitude, in the presence of spacetime-dependent classical sources, for a massive scalar field theory in (1+1) dimensions. We show that this problem is BQP-hard; in other words, its solution enables one to solve any problem that is solvable in polynomial time by a quantum computer. Hence, the vacuum-to-vacuum amplitude cannot be accurately estimated by any efficient classical algorithm, even if the field theory is very weakly coupled, unless BQP=BPP. Furthermore, the corresponding decision problem can be solved by a quantum computer in a time scaling polynomially with the number of bits needed to specify the classical source fields, and this problem is therefore BQP-complete. Our construction can be regarded as an idealized architecture for a universal quantum computer in a laboratory system described by massive phi^4 theory coupled to classical spacetime-dependent sources.

quant-ph↗

arXiv2015

Heavy Color-Octet Particles at the LHC

Many new-physics models, especially those with a color-triplet top-quark partner, contain a heavy color-octet state. The "naturalness" argument for a light Higgs boson requires that the color-octet state be not much heavier than a TeV, and thus it can be pair-produced with large cross sections at high-energy hadron colliders. It may decay preferentially to a top quark plus a top-partner, which subsequently decays to a top quark plus a color-singlet state. This singlet can serve as a WIMP dark-matter candidate. Such decay chains lead to a spectacular signal of four top quarks plus missing energy. We pursue a general categorization of the color-octet states and their decay products according to their spin and gauge quantum numbers. We review the current bounds on the new states at the LHC and study the expected discovery reach at the 8-TeV and 14-TeV runs. We also present the production rates at a future 100-TeV hadron collider, where the cross sections will be many orders of magnitude greater than at the 14-TeV LHC. Furthermore, we explore the extent to which one can determine the color octet's mass, spin, and chiral couplings. Finally, we propose a test to determine whether the fermionic color octet is a Majorana particle.

hep-ph↗

arXiv2014

Quantum Algorithms for Fermionic Quantum Field Theories

Extending previous work on scalar field theories, we develop a quantum algorithm to compute relativistic scattering amplitudes in fermionic field theories, exemplified by the massive Gross-Neveu model, a theory in two spacetime dimensions with quartic interactions. The algorithm introduces new techniques to meet the additional challenges posed by the characteristics of fermionic fields, and its run time is polynomial in the desired precision and the energy. Thus, it constitutes further progress towards an efficient quantum algorithm for simulating the Standard Model of particle physics.

hep-th↗

arXiv2012

New Physics from the Top at the LHC

The top quark may hold the key to new physics associated with the electroweak symmetry-breaking sector, given its large mass and enhanced coupling to the Higgs sector. We systematically categorize generic interactions of a new particle that couples to the top quark and a neutral particle, which is assumed to be heavy and stable, thus serving as a candidate for cold dark matter. The experimental signatures for new physics involving top quarks and its partners at the Large Hadron Collider (LHC) may be distinctive, yet challenging to disentangle. We optimize the search strategy at the LHC for the decay of the new particle to a top quark plus missing energy and propose the study of its properties, such as its spin and couplings. We find that, at 14 TeV with an integrated luminosity of 100 fb^-1, a spin-zero top partner can be observed at the 5-sigma level for a mass of 675 GeV. A spin-zero particle can be differentiated from spin-1/2 and spin-1 particles at the 5-sigma level with a luminosity of 10 fb^-1.

hep-ph↗

arXiv2011

Quantum Algorithms for Quantum Field Theories

Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We develop a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (phi-fourth theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.

quant-ph↗

arXiv2010

Trispectrum versus Bispectrum in Single-Field Inflation

In the standard slow-roll inflationary cosmology, quantum fluctuations in a single field, the inflaton, generate approximately Gaussian primordial density perturbations. At present, the bispectrum and trispectrum of the density perturbations have not been observed and the probability distribution for these perturbations is consistent with Gaussianity. However, Planck satellite data will bring a new level of precision to bear on this issue, and it is possible that evidence for non-Gaussian effects in the primordial distribution will be discovered. One possibility is that a trispectrum will be observed without evidence for a non-zero bispectrum. It is not difficult for this to occur in inflationary models where quantum fluctuations in a field other than the inflaton contribute to the density perturbations. A natural question to ask is whether such an observation would rule out the standard scenarios. We explore this issue and find that it is possible to construct single-field models in which inflaton-generated primordial density perturbations have an observable trispectrum, but a bispectrum that is too small to be observed by the Planck satellite. However, an awkward fine tuning seems to be unavoidable.

hep-ph↗

arXiv2009

Nonperturbative m_X cut effects in B -> Xs l+ l- observables

Recently, it was shown that in inclusive B -> Xs l+ l- decay, an angular decomposition provides three independent (q^2 dependent) observables. A strategy was formulated to extract all measurable Wilson coefficients in B -> Xs l+ l- from a few simple integrals of these observables in the low q^2 region. The experimental measurements in the low q^2 region require a cut on the hadronic invariant mass, which introduces a dependence on nonperturbative b quark distribution functions. The associated hadronic uncertainties could potentially limit the sensitivity of these decays to new physics. We compute the nonperturbative corrections to all three observables at leading and subleading order in the power expansion in Λ_QCD/m_b. We find that the subleading power corrections give sizeable corrections, of order -5% to -10% depending on the observable and the precise value of the hadronic mass cut. They cause a shift of order -0.05 GeV^2 to -0.1 GeV^2 in the zero of the forward-backward asymmetry.

hep-ph↗

arXiv2008

Subleading Shape-Function Effects and the Extraction of |V_ub|

We derive a class of formulae relating moments of B -> Xu l nu to B -> Xs gamma in the shape function region, where m_X^2 ~ m_b Lambda_QCD. We also derive an analogous class of formulae involving the decay B -> Xs l+ l-. These results incorporate Lambda_QCD/m_b power corrections, but are independent of leading and subleading hadronic shape functions. Consequently, they enable one to determine |V_ub|/|V_tb V_ts*| to subleading order in a model-independent way.

hep-ph↗

arXiv2007

Extracting short distance information from b -> s l+ l- effectively

We point out that in inclusive B -> Xs l+ l- decay an angular decomposition provides a third (q^2 dependent) observable sensitive to a different combination of Wilson coefficients than the rate and the forward-backward asymmetry. Since a precise measurement of q^2 dependence requires large data sets, it is important to consider the data integrated over regions of q^2. We develop a strategy to extract all measurable Wilson coefficients in B -> Xs l+ l- from a few simple integrated rates in the low q^2 region. A similar decomposition in B -> K* l+ l-, together with the B -> K* γrate, also provides a determination of the Wilson coefficients, without reliance on form factor models and without having to measure the zero of the forward-backward asymmetry.

hep-ph↗

arXiv2006

Universality and m_X cut effects in B -> Xs l+ l-

The most precise comparison between theory and experiment for the B -> Xs l+ l- rate is in the low q^2 region, but the hadronic uncertainties associated with an experimentally required cut on m_X potentially spoil the search for new physics in these decays. We show that a 10-30% reduction of dΓ(B -> Xs l+ l-) / dq^2 due to the m_X cut can be accurately computed using the B -> X_s gamma shape function. The effect is universal for all short distance contributions in the limit m_X^2 << m_B^2, and this universality is spoiled neither by realistic values of the m_X cut nor by alpha_s corrections. Both the differential decay rate and forward-backward asymmetry with an m_X cut are computed.

hep-ph↗

arXiv2006

Shape-Function Effects and Split Matching in B-> Xs l+ l-

We derive the triply differential spectrum for the inclusive rare decay B -> Xs l+ l- in the shape function region, in which Xs is jet-like with $mX^2 \lesssim mb Λ_QCD$. Experimental cuts make this a relevant region. The perturbative and non-perturbative parts of the matrix elements can be defined with the Soft-Collinear Effective Theory, which is used to incorporate alphas corrections consistently. We show that, with a suitable power counting for the dilepton invariant mass, the same universal jet and shape functions appear as in B-> Xs gamma and B-> Xu l nu decays. Parts of the usual alphas(m_b) corrections go into the jet function at a lower scale, and parts go into the non-perturbative shape function. For B -> Xs l+ l-, the perturbative series in alphas are of a different character above and below mu=mb. We introduce a ``split matching'' method that allows the series in these regions to be treated independently.

hep-ph↗

arXiv2005

Factorization for Power Corrections to B->Xs gamma and B-> Xu e nu

We derive factorization theorems for Lambda_QCD/mb power corrections to inclusive B-decays in the endpoint region, where mX^2 ~mb Lambda_QCD. In B-> Xu e nu our results are for the full triply differential rate. A complete enumeration of Lambda_QCD/mb corrections is given. We point out the presence of new Lambda_QCD/mb-suppressed shape functions, which arise at tree level with a $4 pi$-enhanced coefficient, and show that these previously neglected terms induce an additional large uncertainty for current inclusive methods of measuring |Vub| that depend on the endpoint region of phase space.

hep-ph↗

arXiv2002

An Index Theorem for Domain Walls in Supersymmetric Gauge Theories

The supersymmetric abelian Higgs model with N scalar fields admits multiple domain wall solutions. We perform a Callias-type index calculation to determine the number of zero modes of this soliton. We confirm that the most general domain wall has 2(N-1) zero modes, which can be interpreted as the positions and phases of (N-1) constituent domain walls. This implies the existence of moduli for a D-string interpolating between N D5-branes in IIB string theory.

hep-th↗

arXiv2000

Further studies on relic neutrino asymmetry generation II: a rigorous treatment of repopulation in the adiabatic limit

We derive an approximate relic neutrino asymmetry evolution equation that systematically incorporates repopulation processes from the full quantum kinetic equations (QKEs). It is shown that in the collision dominant epoch, the said equation reduces precisely to the expression obtained previously from the static/adiabatic approximation. The present treatment thus provides a rigorous justification for the seemingly incongruous assumptions of a negligible repopulation function and instantaneous repopulation sometimes employed in earlier works.

hep-ph↗

arXiv1998

Path generating transforms

We study combinatorial aspects of q-weighted, length-L Forrester-Baxter paths, P^{p, p'}_{a, b, c}(L), where p, p', a, b, c \in Z_{+}, 0 < p < p', 0 < a, b, c < p', c = b \pm 1, L+a-b \equiv 0 (mod 2), and p and p' are co-prime. We obtain a bijection between P^{p, p'}_{a, b, c}(L) and partitions with certain prescribed hook differences. Thereby, we obtain a new description of the q-weights of P^{p, p'}_{a, b, c}(L). Using the new weights, and defining s_0 and r_0 to be the smallest non-negative integers for which |p s_0 - p' r_0|=1, we restrict the discussion to P^{p, p'}_{s_0} \equiv P^{p, p'}_{s_0,s_0,s_0+1}(L), and introduce two combinatorial transforms: 1. A Bailey-type transform B: P^{p, p'}_{s_0}(L) -> P^{p, p'+p}_{s_0 + r_0}(L'), L \leq L', 2. A duality-type transform D: P^{p, p'}_{s_0}(L) -> P^{p'-p, p'}_{s_0}(L). We study the action of B and D, as q-polynomial transforms on the P^{p, p'}_{s_0}(L) generating functions, χ^{p, p'}_{s_0}(L). In the limit L -> \infinity, χ^{p, p'}_{s_0}(L) reduces to the Virasoro characters, χ^{p, p'}_{r_0, s_0}, of minimal conformal field theories M^{p, p'}, or equivalently, to the one-point functions of regime-III Forrester-Baxter models. As an application of the B and D transforms, we re-derive the constant-sign expressions for χ^{p, p'}_{r_0, s_0}, first derived by Berkovich and McCoy.

math.QA↗

arXiv1997

A Burge tree of Virasoro-type polynomial identities

Using a summation formula due to Burge, and a combinatorial identity between partition pairs, we obtain an infinite tree of q-polynomial identities for the Virasoro characters χ^{p, p'}_{r, s}, dependent on two finite size parameters M and N, in the cases where: (i) p and p' are coprime integers that satisfy 0 < p < p'. (ii) If the pair (p', p) has a continued fraction (c_1, c_2, ... , c_{t-1}, c_t+2), where t >= 1, then the pair (s, r) has a continued fraction (c_1, c_2, ... , c_{u-1}, d), where 1 =< u =< t, and 1 =< d =< c_{u}. The limit M -> infinity, for fixed N, and the limit N -> infinity, for fixed M, lead to two independent boson-fermion-type q-polynomial identities: in one case, the bosonic side has a conventional dependence on the parameters that characterise the corresponding character. In the other, that dependence is not conventional. In each case, the fermionic side can also be cast in either of two different forms. Taking the remaining finite size parameter to infinity in either of the above identities, so that M -> infinity and N -> infinity, leads to the same q-series identity for the corresponding character.

q-alg↗